Technology and Finance: Drivers of a Profit Margin Explosion

In this piece, I’m going to show that the profit margin expansion seen in the U.S. corporate sector over the last two decades has been driven largely by gains in the financial and technology sectors.  I’m then going to examine arguments for and against the sustainability of this shift.

Profit Margin Contributions By Sector

The following chart shows the aggregate net profit margin of publically-traded U.S. equities with market capitalizations greater than $200MM from January 1964 to October 2014.  Recessionary periods are shaded in gray.


The next chart separates out the contribution to the aggregate profit margin by sector. For each sector, the colored area represents the individual earnings of the sector divided by the total revenues (sales) of all sectors.  Note that the sum, the black line, is just the aggregate profit margin shown in the previous chart.


Notice the rising contribution from the financial sector (light purple) and the technology sector (olive green), and the falling contribution from the other sectors in aggregate:



In January of 1964, financial and technology sector earnings contributed 0.49% to the aggregate profit margin, which was 6.60% at the time.  Today, they contribute almost seven times that amount, 3.42%, to an aggregate profit margin of 8.09%.

Changes in  Sectoral Revenue Contributions

A better way to think about what has happened here is to think in terms of sectoral revenue contributions: revenues of individual sector as a percentage of the total revenue of all sectors.  The following chart shows the evolving revenue contributions of each sector, from January of 1964 to October of 2014.


As the chart illustrates, the revenue contribution of the combined financial and technology sectors–the amount of total revenues that are revenues from those sectors–has increased substantially over time.  In January of 1964, the revenue contribution was 5.41%.  Today, it is 23.83%–almost a quarter of the total.



This change in revenue contribution matters because technology and financial sector revenues tend to be earned at higher profit margins than the revenues of other sectors: historically, 7.74% for technology and finance, versus 5.19% for the rest.  And so if the revenue contribution from the financial and technology sectors has increased, then we should expect the “normal” profit margin of the aggregate corporate sector–if there is such a thing–to have increased as well.  The targeted “mean” in a “mean reversion” will have shifted upward, rendering the ensuing picture less bearish.

(Note: the revenue contribution of healthcare, shown in brown, has also increased substantially over time.  But, to the surprise of many, current healthcare profit margins, at 6.2%, are below their own historical average, and only slightly above the historical average of the aggregate corporate sector.  They are not appreciable contributors to current profit margin elevation).

It turns out that we can correct for this shift, creating an “adjusted” profit margin that accounts for the effects of changing sectoral revenue contributions.  What we need to do is take the average historical revenue contribution of each sector, and compute what the aggregate profit margin would have been, at each point in time, if each contribution had been equal to its individual historical average.

The following table shows the historical average revenue contributions of each of the 10 GICS sectors:


So, historically, energy revenues have represented 12.78% of total revenues, materials revenues have averaged 7.80%, health care revenues have averaged 5.46%, and so on. What we want to know is, what would the profit margin of the aggregate corporate sector have been at each point in history if the revenue contribution of each individual sector had been equal to its average?  This “adjusted” profit margin will filter out changes that have been driven solely by shifts in sector size and contribution, and will thus provide a more accurate picture of the aggregate profit margin to use when making historical comparisons.

At this point, Bulls are probably hoping that I pull out a chart showing that when profit margins are properly adjusted in this way, that they end up not being historically elevated. Sorry, not quite.  As the chart below shows, the adjustment doesn’t make much of a difference.


The unadjusted profit margin (blue) is 45% above its historical average, versus 35% for the adjusted profit margin (green).  Relative to the respective averages, the adjusted profit margin is only about 10% “less elevated” than the unadjusted profit margin.  This difference is worth something, no question–but it’s not enough to eliminate profit margin concerns outright.

The reason that the adjustment doesn’t make the kind of difference that we might otherwise expect is that the profit margins of the financial and technology sectors have themselves expanded dramatically in recent years.  The truth is that profit margin increases within the financial and technology sectors, rather than increases in their contribution to total revenue, have been the primary drivers of the aggregate profit margin increase.

The following chart shows the profit margins of the combined finance and technology sectors (red) alongside the profit margins of the combined other sectors (blue):


As you can see, profit margins in finance and technology have exploded.  Combined, they are running at almost twice their historical averages–86% above, to be precise.  The profit margins of the combined other sectors are hardly elevated at all–only around 18% above their historical averages.

The following charts show the profit margins of the finance and technology sectors individually:



Notice that a large chunk of the move is recent–a phenomenon unique to this specific cycle–especially in the technology sector.

Explaining the Rise

It goes without saying that finance and technology, which together represent over 42% of current U.S. corporate earnings, are two sectors that we should keep a close eye on going forward.  Changes within them have driven the profit margin expansion of the last several years, which itself has driven the bull market, having made possible a “goldilocks” scenario in which earnings have been able to grow robustly despite slow top-line growth and almost non-existent inflation.  The slow top-line growth and almost non-existent inflation has pushed the Fed into an aggressively easy monetary stance that has served as fuel for persistent P/E multiple expansion, with more and more investors ditching the misery of zero-yield cash and bonds to join the market advance.

The finding that the profit margin expansion has been driven largely by changes inside the finance and technology sectors sheds doubt on other stories that have been offered as explanations.  Weaker labor unions, increased access to cheap foreign workers, a rise in earnings taken in from abroad, lower corporate taxes, more effective corporate tax avoidance schemes, and so on–these explanations fail to make sense of the fact that profit margins haven’t increased nearly as much in sectors outside of finance and technology. Whatever the correct explanation for the current state of profit margins ends up being, it needs to be one that applies with some preference to finance and technology, which is where the most dramatic shift has taken place.

What, then, is the explanation for the rise?  Why have profit margins in finance and technology increased so dramatically over the last several years?  Will the increase hold up?

A Bullish Angle

On the finance front, bulls can make a compelling argument that the financial sector’s contribution to the profit margin increase is likely to be sustained.  The increase in the financial sector share of total revenues has been driven by higher debt levels across the economy–that change will almost certainly prove to be secular.  At the same time, the increase in profit margins within the financial sector has arguably been driven by the drop in short-term interest rates (funding costs for financial institutions), which is a change that is also likely to be secular.  Note that the last time that financial profit margins were at their current levels was in the early 1960s, when short-term interest rates were low.  The Fed tightening cycle that lasted from the late 1960s through the 1980s seems to have been what pulled them down, as they fell much more precipitously during that period than the profit margins of any other sector.  They only began to regain their prior levels in the mid-to-late 1990s, as the Fed shifted to an easier monetary stance.

On the technology front, bulls can make a similarly compelling argument that the revolutionary technology of the information economy, which has only been fully fleshed out in the last decade, has been the game-changer, having created an increasingly “winner takes all” environment in which it has become more and more difficult for potential new entrants to credibly compete with the first-mover.  If they are right, then profit margin mean reversion–in the technology sector and in any other sectors that manage to piggy back on the dynamic–would seem to be less likely.

A Bearish Angle

Of course, bears can offer compelling counter-arguments to this optimism.  On the finance front, they can point to the fate of the yield curve–which, assuming the Fed follows through on its normalization plans, does not look good.

When the Fed cuts rates for the first time, the long end of the curve usually stays put. People continue to expect an eventual return to normalcy, and price the long end accordingly.  The result ends up being a steep curve that boosts financial sector profit margins.  But when the Fed cuts rates and keeps them cut, for a period that seems to drag on forever, because the economy never seems to get hooked into the kind of genuine inflationary expansion that would justify a tightening cycle, the market eventually figures things out. Investors realize that long-term rates need to be lower, and pulls the long-end down accordingly, at the expense of financial sector profitability.

Eventually, the Fed will raise the short-end–if not simply out of a desire to restore some normalcy to monetary policy.  When that time comes, the long end will again be slow to respond–this time slow in the opposite direction, slow to rise, given the anchoring and inertia of market participants who, by then, will have grown accustomed to the idea of secularly low interest rates.  The result will be a yield curve that gets flatter and flatter with each hike, and a financial sector whose profit margins get squeezed.  That seems to be exactly where we are currently headed, and it is not bullish.

In the most recent earnings data from banks, we’ve seen a consistently weak trend: flat YOY revenue growth and negative YOY EPS growth, brought on by increased competition, particularly among smaller banks, increased regulatory expenses, and reduced profitability due to a flattening yield curve.  Loan growth, which would otherwise represent the bright spot, is not making up for the reduced profitability.

On the technology front, bears can make a similarly compelling argument.  “Tech” is the most cutthroat and competitive of all sectors.  Historically, it has produced subpar returns for investors (ranked number 6 out of 10 sectors), likely due to the way in which disruption and competition have worked to break down dominant positions within it. When we look at the seemingly impenetrable empires of the $AAPLs and $GOOGs and $MSFTs and $FBs of the world, it can be tempting to think that the truly massive levels of profitability they currently enjoy will be forever secure–but this kind of thinking is not supported by history.

There’s a particularly interesting and relevant analogy that bears can raise in this context, one that involves a different sector: commodities.  The historical evidence on the real return potential of spot commodities is overwhelming: there is no real return potential, spot commodities do not offer real returns.  For proof, consider the following 130 year chart from Dylan Grice.  Notice the black line languishing stupidly at the bottom:


But then again, over the last decade, we saw a massive boom in commodity prices around the world.  As always happens, compelling stories emerged to explain why the boom had occurred and why it would almost certainly hold up–insatiable demand growth from China, India, and other emerging markets, an increasingly constrained supply that fails to grow, even in response to large price increases, and so on.  If you had told people in 2007 or 2008, or in 2010 or 2011, that these were just stories, and that there would eventually be a painful reversion to the mean just a few years later, very few people would have taken you seriously.  Nobody in the commodity complex at the time was seriously entertaining the possibility.

But now here we sit, in a healthy economic expansion, with oil trading below $45 (!!), the same inflation-adjusted price that it traded at 30 years ago, near the lows of the last oil downturn.  A 30 year period of zero real returns for this and other spot commodities has once again vindicated the apparent lesson of history: that spot commodities do not produce real returns.  Now, to be clear, I don’t expect profit margin bearishness to receive the same degree of vindication–but some caution and humility are certainly in order, given the possibility.

Special thanks to Patrick O’Shaughnessy (twitter: @millennialinvest) of O’Shaugnessy Asset Management for his help on this piece.

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Intrinsic Value: Interest Rates, Inflation, and the Forgotten Concept of the Time Value of Money

In the previous piece, I offered a definition of the investment concept of “intrinsic value.” Intrinsic value is the value that the owner of a security realizes from holding the security, rather than selling it.

To determine the intrinsic value of a given security, we can apply a simple test.  We posit that the security that cannot ever be sold, but must be held until maturity.  We then ask ourselves: what is the maximum price that we would be willing to pay, or alternatively, the maximum amount of cash that we would be willing to exchange, to own the security?  That amount of cash must equal the intrinsic value of the security, the value that accrues to us simply from owning it, otherwise the exchange would not make rational sense.

In this piece, I’m going to explore the set of fundamental considerations that would impact a rational agent’s assessment of the intrinsic value of different types of securities.  The analysis will seek to clarify “the way things ought to be” in financial markets–the way they would be if everyone invested rationally, based solely on the intrinsic value contained in the investment opportunities presented.

To be clear, “the way things ought to be” in financial markets is not the way things actually are, particularly with respect to long-dated assets, assets whose maturities are too far out in the future to “wait for.”  Market participants that trade and invest in long-dated assets do so based not on estimations of “intrinsic value”, but rather on estimations of how the prices of those assets will evolve over the short-term to medium-term, a few months to several years, which is the limit of human look-forward capacity, and the time horizon on which investor performance is measured.  Investors are not able, personally or professionally, to seriously consider longer time horizons, on the order of decades or even centuries, even though that is often how long it takes for the “intrinsic value” of long-dated assets to play out.

Investors worry about the “fundamentals” of long-dated assets not for their own sake, but because the fundamentals influence the prices, through non-fundamental perceptual and behavioral channels.  The fundamentals serve as subjective inputs into the minds of investors, factoring into the rule-based calculations that drive actions and outcomes in the market: “X is happeningit probably means Y.  From a portfolio standpoint, the right move is probably for us to do Z.”

Cash, Bonds, Stocks, Other

Investors are confronted with a range of different types of assets in which to hold their wealth.  We can simplify this range into four categories: Cash, Bonds, Stocks, and Other. To determine the “intrinsic value” of assets in each category, we need to express them in terms of cash, which is the basis for measurement.

Cash is just cash, money, whatever must be accepted by law to repay debts, public and private.  The prices of all assets are expressed in terms of it, therefore the intrinsic value of one unit of it is one.  Bonds are a finite collection of more-or-less guaranteed cash payments, usually consisting of small cash payments for a time (coupons), followed by a large cash payment at the end (return of principal).  Equities are an infinite collection of non-guaranteed cash payments (dividends, or rental payments on the use of capital, land, housing, and so on).  The “other” category consists of unproductive assets, assets that do not generate a cash flow–think, gold bars.  These assets have very little intrinsic value, and are almost always purchased with the intent of eventually offloading the investment onto someone else.

The dividends that shares of equity pay out to their owners tend to grow at a rate that exceeds the rate of inflation.  The reason is twofold:

  • First, the dividends are backed by corporate earnings, and are paid out as a percentage thereof.  On a unit basis, corporate earnings equal price minus cost.  Inflation–a change in the price index–acts to increase both of these entries equally, therefore it acts to increase their differenceearningsequally as well.
  • Second, not all of the earnings are paid out as dividends.  Some of the earnings are used up in the purchase of growth.  The amount of growth purchased adds additional earnings, and therefore additional dividends, to the numbers of the future.

Now, to be clear, funding costs–for example, dilution–can cause per-share earnings to not keep up with inflation, particularly when the corporate sector is inefficient in its use of the proceeds.  In the present context, we will assume that corporations fund their growth internally, without increasing share count (an assumption that has proven valid in recent experience), rendering the issue of dilution moot.

Leaving the “other” category aside, we are left with two types of assets whose intrinsic value we want to measure: bonds and shares of equity.  So we return to the critical question: how much of each type of asset would we be willing to exchange for cash, if we could not ever go back on the exchange?

A bond is just a future stream of small cash payments (coupons), followed by a final payment (repayment of principal).  How much cash, held in hand right now, would we be willing to trade for that future stream?  The answer, for us, is the intrinsic value of the bond.

A share of equity is a future stream of small, growing, inflation-linked cash payments, without a maturity date. How much cash, held in hand right now, would we be willing to trade for that future stream?  The answer, for us, is the intrinsic value of the share of equity.

The Time Value of Money

Money now obviously is not the same as money later.  Money now is better, for a myriad of reasons, not the least of which is that it can be used now, at the option of its owner. Money later, in contrast, cannot be used until it is received.

The difference between money now and money later is the “time value of money.”  Looking at the current state of bond prices in the developed world, we might think that money has no time value to current investors.  After all, long-term bonds in the developed world trade at prices with implied yields approaching zero.  An investor who lends his money to a government in the developed world for five, ten, twenty, even thirty years, gets essentially nothing in return–nothing except the original money that was lent out, for a net nothing.

But to conclude that money has no time value to current investors would be a huge mistake.  The reason that current investors are willing to lend their money to governments at zero rates of interest for prolonged periods of time is that they know they can easily get out of the loans by selling the associated securities back into the market.  For all intents and purposes, in a liquid market, where investors are confident that they will be able to sell their investments at or near cost, the “time value of money” loses relevance.  The assets become the functional equivalents of “money now”, given that they can be converted into “money now” at the push of a button.  In purchasing the asset, the investors don’t have to “part” with their money, therefore they don’t have to put a price on the cost, to them, of “parting” with it.  If they did, the price dynamics observed in developed world bond markets would be very different from what they are.

Take any institutional fund that is currently eager to lend its money to the Swiss or Japanese governments for decades at near-zero interest rates, and tell that fund that it will have to hold the associated debt security until maturity–that it will not, under any circumstances whatsoever, be allowed to get the money back by selling the security to other investors (or engaging in any “tricks” that might simulate a sale, such as posting the security as collateral for a loan, or selling short a similar security).  You would quickly see the time value of money come back into play, in a dramatic way.  To be sure, it is not zero.  Not even close.

When word gets out that a financial institution is in trouble and is facing a liquidity crisis, its customers rush to redeem their money.  The main fear that drives their behavior isn’t the prospect that the money will be lost forever–the investors know they will almost surely get it back, after everything has been cleaned up, years later.  Their most pressing worry is actually the prospect that the money will get stuck inside of a black hole in the interim–a confused, entangled “what belongs where?” scenario, a court battle involving complicated and drawn-out litigation–and that the customers therefore won’t be able to access the money for months, years, maybe decades.  Ouch.  Again, we see the importance of the “time of value of money”–when it is actually at stake.  In a stable, liquid market with a confident bid, it is not at stake, and so it doesn’t factor in.  But things can easily and quickly happen to put it at stake, which is why long-term assets–assets with maturities on the orders of many years, decades or centuries, that cannot realistically be “waited out”–are prone to violent bouts of volatility, when confidence in the presence of future bids near the current price is lost.

The Exercise

Cash held in the banking system carries essentially all of the benefits of cash held in hand, with a number of additional perks and conveniences.  For this reason, individuals usually choose to hold their cash in banks, in the form of deposits.  The banks normally pay interest on the deposits, which they fund through the income they generate on their loans. Without getting into the details, central banks in modern financial systems have the ability to adjust the rate of interest that banks, in the presence of market forces, have to pay on their deposits.  Expectations with respect to the future path of this rate of interest have a substantial effect on the “intrinsic value” of all other assets, because all other assets must compete with it.

To illustrate, let’s do the exercise.  You have $100,000 in wealth, and three modalities in which to store it:

(1) Cash: You can hold the wealth as a cash deposit in an insured bank, and earn interest on it.  While in the bank, you will be able to spend it on consumption.  Depending on the nature of your deposit, you may have to wait a few weeks to spend it, maybe a month or two, but you can afford to wait that long.  To keep things fair, let’s suppose that if you choose this option, you can only spend the money on consumption–you cannot go and invest it in the other options later.  You will have to make the “investment” decision now, and you will have to stick with it for good, at least as far as that money, the $100,000, is concerned.

The interest rate that you will be paid will be determined by the central bank, chosen so as to bring the rate of inflation–and any other macroeconomic target that the central bank might have–onto target.  In periods where there are strong inflationary pressures, the rate will be increased, so as to incentivize you and others to hold your cash rather than spend or invest, and to disincentivize others from borrowing it to spend or invest.  The same is true in reverse: in periods where inflationary pressures are weak or negative, the rate will be reduced, so as to disincentivize you and others from holding your cash, get you to spend or invest it instead, and to incentivize others to borrow it to spend and invest.

(2) Bond: You can buy (miniature) 10 year treasury bonds.  Each bond pays guaranteed fixed interest payments of $60 per year, followed by a large principal repayment, $1,000, in 10 years. Importantly, you cannot sell one of these miniature bonds after you have bought it.  You must hold it to maturity.  The money that is figuratively “contained” inside it will be locked up, unable to be used by you in any way, until then.

(3) Equity: You can buy diversified shares of equity, say, the 500 companies of the S&P 500.  The share pays $40 per year in dividends, the dividends grow anywhere from 1% to 4% per year, plus inflation, with a sharp recessionary drop every several years that is eventually fully recovered.  Crucially, the shares have no maturity.  You will never get the original principal back–what you will get back is an ever-growing stream of dividends, which over the very long-haul, will exceed what you put in by many orders of magnitude.

We have not yet stated the per-share price of the bond and the equity.  The goal here is for you to seriously think about the options, as if they were presented to you right now, and identify the maximum price that you would be willing to pay for each share, the maximum amount of cash that you would be willing to permanently exchange for them–which, for you, is the “intrinsic value.”

As a rational agent, what do you need to know in order to determine the “intrinsic value” of each type of security?  For starters, you need to know, or estimate, the concrete specifics of the payout stream. How much is the bond going to pay?  How much is the cash going to pay?  How much is the equity going to pay?

For the bond, you already know the entirety of the future stream–$60 per year, plus $1,000 in ten years. The stream carries no uncertainty in its payouts.  But knowing that alone is not enough.  You also need to know the nominal interest rate that cash in the bank will pay you over the next ten years.  It will not make rational sense for you to pay a price for the bond that implies a return that is any lower than that, any lower than what you can get in cash, because cash also affords you the precious ability to have the money and use it, which the bond does not afford  you.  Therefore the bond needs to be priced to pay you more.

Now, we know that the central bank is going to set the cash interest rate so as to control inflation.  So the true variable that matters here is the future neutral nominal interest rate, the nominal rate of interest that the central bank will have to set going forward, given the structural dynamics of the economy, in order to keep inflation and any other target that it might have–employment, foreign exchange control, financial stability–on target.

In truth, of course, you’re going to demand even more than the expected neutral nominal rate, you’re going to demand a premium to compensate you for the time value of money, the cost of losing the ability to use your money.  How much you demand will be determined by the amount of value that money in hand has for you in comparison with money promised in the future.

How different, for you, is “money now” from “money later”?  The answer will obviously depend on the myriad of complex psychological and economic factors that define your unique personal situation. How much do you value the comfort and security of having access to your money, the ability to use it if you should want to use it, or need to use it?  How much more valuable is that kind of money to you, in comparison with money that will be locked away for a long period of time, inaccessible to you?  How many things are there in the economy for you to buy right now that might tangibly increase your happiness, or the happiness of those you care about?  How old are you, and to what extent is the money needed to fund your desired consumption expenses?  If the money is needed, will the coupon or dividend payments that will accrue on it if it is permanently locked away in a bond or an equity be large enough to fund those expenses?  If so, then you may be fine with seeing it locked away, given that you can get by on the infinite payouts that will accrue.  What are your expectations with respect to inflation?  Inflation eats away at the future purchasing power of money.  High inflation therefore widens the difference between “money now” and “money later”, given that it makes “money later” into “less money.”  All of these variables, and a number of others, will factor into your estimation of the “time value” that money has for you.

To summarize the bond case, then, we’ve identified two variables that matter to the intrinsic value of a long-term treasury bond: (1) the expected neutral nominal interest rate on cash over the life of the bond, which sets the minimum floor for what you can rationally accept from the bond, given that you have the alternative of holding cash, and (2) the time value of money, which you ultimately have to specify for yourself, given the unique psychological and financial details that characterize your individual situation.

For the equity case, the evaluation is more complex.  We need to estimate the future growth of the dividends, and by extension, the future growth of the earnings out of which they will be paid (and which will pay for their future growth).  In the scenario, we set a range of 1% to 4% after inflation, but that’s a huge range–any information that pushes the number in either direction is going to be very important.

We can separate the growth of dividends into two components: real per-share growth, and inflation.  The first component is determined primarily by the health and dynamism of the underlying economy, and by the efficiency and capital allocation skill of the aggregate corporate sector. The second component is driven by culture, demographics, supply constraints and policy.

The two factors that were relevant to the intrinsic value of the bond–the expected neutral nominal interest rate and the time value of money–are just as important to the intrinsic value of the equity.  As with the return produced by holding the bond, the return produced by holding the equity competes directly with the alternative of holding cash in the bank and collecting the future neutral nominal interest rate.  Similarly, holding the equity instead of the cash entails loss of a large amount of money that would otherwise be accessible.

What we end up with, then, are four variables that determine the “intrinsic value” of the equity: (1) the expected neutral nominal interest rate, (2) the time value of money, (3) the expected future rate of real per-share growth, and (4) the expected future rate of inflation.

Now, here comes a critical move.  We can combine (4) and (1) into a single variable, the expected neutral real interest rate.  Going forward, what real interest rate, after inflation, will the central bank have to set in order to maintain inflation, and any other targeted macroeconomic variable, on target?  That rate is critical, because it expresses the difference between (a) inflation, a crucial component of the nominal growth that the equity payouts will exhibit, and (b) the nominal interest rate that the cash holdings will earn.

The Fed Model

The Fed Model is a popular a method of measuring equity valuations.  The model assesses valuation by comparing the earnings yield on equities to the long-term government bond yield. When equity earnings yields are substantially higher than the long-term government bond yield, equities are said to be cheap.  When equity earnings yields are not appreciably higher than the long-term government bond yield, equities are said to be expensive, or at least neutrally priced.

In practice, the Fed Model has caused a number of analysts to push back on the growing consensus that the US stock market is expensive, while Emerging Market stock markets are cheap.  These analysts acknowledge that earnings yields in the US are lower than in the Emerging Markets (or alternatively, that P/E ratios in the US are higher than in the Emerging Markets), but they point out that we cannot talk about yields and P/E ratios in a vacuum.  We have to compare them to the available alternatives, the attractiveness of which are captured by prevailing interest rates.

But this way of thinking is partially wrong.  It ignores the fact that interest rates are typically set at low or high levels in response to low or high levels of another variable that matters greatly to equity returns–inflation.  Why has the US  central bank set the interest rate at a low level? Because the US does not have enough inflation. Why has the Brazilian central bank set the interest rate at a high level? Because Brazil has too much inflation. The low inflation in the US contributes to an environment of low nominal earnings and dividend growth, and therefore low nominal total returns, all else equal (and note that all else is not equal, in this case).  The high inflation in Brazil (or Argentina or Zimbabwe) contributes to an environment of high nominal earnings and dividend growth, and therefore high nominal returns, all else equal.  The Fed Model fails to capture and factor in the impact of this crucial difference.

If we’re going to connect P/E ratios to interest rates, as the Fed Model tries to do, the interest rates that we should use are real interest rates, interest rates that take out expected future inflation, which is a significant component of nominal equity returns. When we do this, we see that a number of emerging markets with high interest rates and high P/E ratios, such as India, deserve to have high P/E ratios, because their real interest rates are very low, if not outright negative (making cash and bonds that much less attractive in comparison with inflation-linked equities).  Similarly, a number of countries with low interest rates, such as Japan under pre-Abenomics deflation, deserve to have low P/E ratios, because their real interest rates are high (making cash and bonds that much more attractive relative to inflation-linked equities).

Foreign Equity Investing

This dynamic extends quite elegantly to the realm of foreign equity investing. To use the example of Brazil, Brazilian equities currently sell at very low P/E multiples–at last check, around 8-9 times, with correspondingly high dividend yields and substantial room for P/E multiple expansion over the long-term.  For this reason, many US investors, frustrated with the lack of attractive options at home, have explored the country as a potential investment opportunity.

Suppose that you are a US investor that wants to capture the return potential of the Brazilian equity market.  But you want to capture that return in dollar terms–the terms of your own currency.  If the Brazilian market goes up 200% over the next 10 years, you want the value of your Brazilian investment, in your own currency, the Dollar, to achieve that same return.  The only way that you can make this happen is by hedging the currency.  You would go simultaneously long the Brazilian stock market, and short the Brazilian currency, the Real.  Then, your return in dollars would exactly mimic the local currency return of the Brazilian stock market.

But there’s a problem. The cost of shorting the Brazilian currency is the Brazilian interest rate; you will have to pay that interest rate to whomever you borrow the currency from in your short.  Right now, the rate is quite high, north of 10%.  That 10% will represent a significant drag on your returns.  For this very reason, it’s impossible for you to create a dollar-denominated investment that will exactly track with the Brazilian stock market. The best you can hope to do is create an investment that tracks with the Brazilian stock market minus 10% per year.

Not all is lost, of course.  Your investment might still produce an attractive return, even in the presence of the high carry.  The interest rate in Brazil is high, 10%, but that’s because inflation in Brazil is very high–well north of 6%.  The 6% inflation is going to add to the nominal growth in Brazilian earnings and dividends.  When combined with the high dividend yield, and the significant multiple expansion that is likely to occur as sentiment improves, the return that the investment might be able to make up for the 10% carrying cost.

What we need to do in a valuation analysis is combine these two numbers–the inflation and the interest rate–since they offset each other in terms of their effects on the return. The inflation adds to the return, and the interest rate–which is the carrying cost–subtracts from it.  The combination of the two,  of course, just is the real interest rate, which, you will recall, is what we found to also be a critically important variable in the determination of the intrinsic value of domestic equities.

The real interest rate in Brazil is 10% minus 6% which equals 4%–on the high side globally. For this reason, Brazil probably should have a lower P/E multiple than the developed world, where zero or negative real interest rates have become the policy norm.

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What Is Intrinsic Value, And Who Decides It?

James Osborne of Bason Asset Management recently published an excellent critique of the investment concept of “Intrinsic Value.”  I urge readers to take a minute and go check it out.  In this piece, I’m going to try to tackle a question that James poses.

That question: what is intrinsic value, and who decides it?

No Selling Allowed 

Here’s my answer.  The “intrinsic value” of a security is the maximum price that an investor would be willing to pay to own the security if she could not ever sell it.

Three points:

(1) All I am doing here is defining the term.  You can define the term in another way if you wish, but then you will be talking about something else.  When I use the term “Intrinsic Value”, I am talking about the maximum price that an investor would be willing to pay to own a security if she had to hold it until “maturity”, i.e., for the entirety of its natural life as a security, which, for an equity security, means forever.

(2) According to the definition, the “intrinsic value” of a security is different for different individuals.  That’s to be expected.  Value, like beauty, is a judgement made by the individual–it exists only in the mind of the individual, the eye of the beholder.

(3) The definition fits with the literal meaning of the word intrinsic–”inherent, innate, inborn, inside the thing itself.”  The value that an asset has, inside itself, cannot be a function of the quantity of other useful things that other people happen to be willing to exchange it for in a market.  Rather, the value must remain present even when no trading is allowed.

Intrinsic Value: A Thought Experiment

So let me now ask you a question.  Suppose that I have a security to sell you.  The security works as follows.  It pays out $10 in dividends per year.  The dividends grow at a real (inflation-adjusted) rate that ranges anywhere from 3% to 5% per year.  Of course, over the short-term, the dividends can grow at different rates–sometimes they can even grow at negative rates, i.e, fall.  But, crucially, over the very long-term, they always recover. They always regain their 3% to 5% long-term growth trendline.

Now, to avoid uncertainty, let’s assume that the aforementioned features of the security are guaranteed by the full faith and credit of the U.S. government.  So there is essentially zero risk that the security will not behave  in the way that I just described.  The question: what is the maximum price that you would be willing to pay, in cash, to own the security, if you could not ever sell it?  Alternatively, what, for you, is the “intrinsic value” of the security?

Take a moment and consider the question as if the proposition were really there for you to take. What is the maximum price that you would be willing to pay? I’m not going to mention any number as a starting offer, because I don’t want to influence your answer.

I’ve posed this question to a number of individuals, both inside and outside the financial industry.  Almost everyone answers with a price that is less than $250.  Note that at a price of $250, the security would offer a 4% yield, fully protected from inflation, with 3% to 5% real per annum growth added on top.  Not bad.  That valuation is seen as minimally necessary to compensate the investor for the cost of forever parting with his principal.

The S&P 500: A Growing Stream of Dividends

If you’re particularly clever, you’ve probably noticed that the security that I’ve described here is basically the S&P 500 stock index divided by four.  The S&P 500 presently pays an annual dividend of around $40 per year.  Not all of the earnings of the companies in the S&P 500 are paid out to shareholders as dividends–some are spent (read: “used up”) on capital expenditures and asset acquisitions.  That is precisely why the dividends are able to grow over time at a rate that exceeds the rate of inflation, i.e., the rate at which the prices of all things in the economy, including the prices of the goods and services that corporations sell, changes.

The reason that I divided the S&P 500′s dividend by four is to prevent the current price, 2070, from creating a false anchor in the mind that influences the “intrinsic value” intuitively ascribed to it.  So take your earlier price, the maximum price that you would pay for the $10 per year security, and multiply that price by four.  That’s your final price, the intrinsic value that you ascribe to the S&P 500.  I ascribe around 800.  You might ascribe 1000.  Or maybe 600.  Certainly not the present price of 2070–unless you’re crazy.

If you doubt the logic here, ask yourself: what is the S&P 500, intrinsically, apart from all of this baseball-card-trading that we engage in when we play in markets? That’s the question that you will have to confront if you decide to make a genuine, non-redeemable investment in the security, that is, buy the security without having the ability to sell it.  The answer: to you, it is just a growing stream of dividends, nothing more.

Now, how reliable is the assumption that the dividends will grow over the long-term at a rate that exceeds the rate of inflation?  Pretty reliable.  The historical reliability of the assumption is demonstrated in many centuries of actual data, not only in the US, but in other capitalist economies. That reliability is supported by the inherent diversification of the index–we’re talking about many different companies from many different industries, rather than a single company that might one day go bust.  But even if we view the dividend stream as not growing reliably over the long-term, or posit a larger uncertainty around the growth than the previous 3% to 5% range allowed, that will only pull the “intrinsic value” lower–and the lowness relative to the current market price is precisely what I’m trying to emphasize.


As you can see in the chart, the historical real rate of growth of per-share dividends for the S&P 500 has been significantly less than the stipulated 3% to 5%.  It’s actually been closer to 1.4%. But there’s an important factor at work.  Most of the S&P’s history was dominated by periods in which only a small portion of earnings were consumed on the purchase of future growth.  Most of the earnings were delivered directly to shareholders in the form of dividends.  Corporate managers have since evolved a preference for earnings reinvestment, and so the current dividend stream tends to grow faster, though it is smaller than it could be, or would have been in the past.

Now, to create a full analogy with the “intrinsic” (i.e., can’t-sell) S&P 500, let’s add a final caveat to the security.  You, as the owner, get to determine the payout ratio.  We can think of the payout ratio as a dial that you can adjust, any time, at will.  You can opt for less dividends now, and more dividend growth, or for less dividend growth, and more dividends now.  If you want, you can even choose to have all of the annual earnings that back the security–in the case of the S&P 500, around $110–paid out to you in dividends. The cost of doing this, of course, is that the earnings and dividends will stop growing.  They will grow at a real rate of 0%.

You might think that the S&P’s current price of 2070 is a reasonable price for a growthless security that pays out $110 a year.  But check that thought.  Suppose you had $100,000 in cash sitting around, earning nothing.  Suppose further that there is nothing else on earth that you can invest it in but the “intrinsic” (i.e., can’t-sell) S&P 500, priced at 2070.  Would you really be willing to part with all of that money, permanently, in exchange for a perpetual payment of only 5.3%, $5,300 per year?  Not very many people would be.  Some people wouldn’t even be willing to accept 10%$10,000 per  year, or even 20%, $20,000 per year.

Even if never used, the simple ability to get your money out of the security and back into your pocket is worth a ton.  That ability represents the difference between your being willing to pay 2070 for the security, on the trust and confidence that you will only be one mouse click–one sell order–away from getting your money back, and being willing to pay only 600, on the stipulation that you will be stuck holding the security until maturity, i.e., for the rest of its life, which means the rest of your life.

Now, to be clear, I’m not saying that it’s irrational for you to be willing to pay 2070 for the security.  I’m saying that, built into your willingness to own it at that price, is a (largely justified, at least for now) expectation that you will be able to sell it, on demand, to someone else at a price near that price–hopefully, at a price higher.  That expectation makes the security dramatically more attractive to own than it would be if it were just what it is intrinsically–a simple stream of growing dividends that had to be held as such.

The Dividend Discount Model

In 1956, Myron Gordon and Eli Shapiro developed the dividend discount model of equity valuation.  On this model, the intrinsic value of an equity security is the sum total of all of the security’s future payouts, from time now until time infinity, discounted back to the present.  Gordon and Shapiro showed mathematically that when discounted at a required rate of return r, an infinite stream of dividends with a starting annual dividend level of d and an annual growth rate is worth a present price p, roughly equal to,

(1) p = d / (r – g)

Rearranging to solve for r, we get,

(2) r = d / p + g

which neatly says that the rate of return that an equity security produces for its owner equals the dividend yield (d / p) plus the dividend growth (g).  Note that if we want, we can make the dividend yield equal the earnings (e) yield, but then g will go to zero, so we will end up with,

(3)  r = e / p

which simply states that the rate of return that an equity security produces for an investor equals the earnings yield, provided that all of the earnings are paid out in present dividends.

Now, the dividend discount model is just a way of formalizing the intrinsic valuation process. The ambiguity and subjectivity in that process remains–the model simply places the ambiguity and subjectivity inside the convenient term r, the discount rate, which is the rate of return that investors demand in order to exchange cash now for cash later.  You can make the intrinsic value of a security be anything you want, any number from 0 to infinity, depending on the discount rate that you choose to impose.  And why must you choose to impose any one discount rate over any other?  As an investor, it’s your call.

To illustrate the power of the discount rate, let’s do the actual exercise for the S&P 500. The index pays a dividend of $40 per year, and the dividend grows at a real rate of 3% per year.  Pick your discount rate, and make sure that it’s a real discount rate, adjusted for inflation).  If you pick a 7% discount rate, then the S&P 500 is intrinsically worth  $40 / (.07 – .03) = 1000.  If you pick a 5% discount rate, then the S&P is intrinsically worth $40 / (.05 – .03) = 2000.  The difference in rate is only 2%–but the difference in price is 100%.

Ask yourself: what makes a 7% discount rate any more “privileged” than a 5% discount rate?  To cover the “losses” associated with converting a present cash sum into an infinite stream of future cash payments, why must an investor demand 7% rather than %5?  Or 5% rather than 3%?  Note that all of these rates are above the loss-adjusted rates that can presently be earned in other asset classes.  Indeed, the risk-free dollar benchmark is priced (in dollars) to deliver an inflation-adjusted rate close to zero, even on very long time horizons.

Robert Shiller and Equity Volatility

In the 1981 masterpiece that earned him a Nobel Prize, Robert Shiller posed the question: “Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?” He empirically demonstrated that the answer was yes, and concluded that markets cannot be described as “efficient.”  Notably, he used a definition of the term “efficient” that his efficient market hypothesis (EMH) opponents, chiefly Eugene Fama, would never accept. But that is a topic for a different piece.

Shiller blamed the large discrepancy between realized price fluctuations and realized dividend fluctuations on the irrational psychological and emotional forces that drive investor behaviors.  His underlying point–that behavior drive the market–is obviously true, but I think there is a more elegant, less demeaning way to frame it.

The intrinsic value of a security–the price that investors would be willing to pay to own it on the stipulation that they would have to hold it indefinitely–is dramatically different from the price that investors are willing to pay knowing that they can easily sell it to others (without incurring a large loss.)  That difference is the value of liquidity.

When liquidity is present, backed by trust and confidence in the stability of the market, investors tend to view their equity holdings as if those holdings were identical to cash in the bank.  They don’t price in the lost liquidity associated with making a genuine, non-redeemable investment in something, an irreversible conversion of present cash into long streams of small future cash payments.  Nor should they price in that lost liquidity–it’s not lost.

If lost liquidity were a reality that had to priced into stock market investments, equities would trade at valuations that are significantly lower than the valuations at which they currently trade. Instead of being willing to pay 2070, and probably higher in the coming months, for the $40 per year, 3% to 5% real growth security that the the S&P 500 represents, investors would demand a far more attractive price–probably a price below 1000.  For some investors, a price as  low as 200 might not even be enough.

Suppose you have $1,000,0000.  I ask you how much money you have, in your name. You will answer $1,000,000–whether that money is invested in an S&P 500 index fund, or whether it’s sitting in the bank.  If it’s in the index fund, it’s not money–but, for you, it might as well be, because you have access to a simple, on-demand means of exchanging it for money, a stable, reliable market in which you can exchange it.  Because of that access, you are able to derive all of the psychological and consumptive benefits of having the money, even though it is not actually in your possession.

But now let me put you in a situation where you might not be able to get that $1,000,000 out of the S&P 500 for a very long time, maybe for the rest of your life, because the markets are crashing and are going to stay crashed.  If I tell you “Don’t worry, the dividends that underlie the true value of your investment will be unaffected by the crash”, will that be much consolation to you?  Will it relieve you of the sense of loss?  Obviously not.

As an investor, you lose your money not when the prices of your investments fall, but when you exchange money for them in the first place.  When you initially buy in–that is when the money is no longer yours.  Crashes force you to view the condition of no longer having access to the money as a genuine loss, a genuine sacrifice, because it removes the people who are otherwise there to give the money back to you.

Now, to the main point of this piece.  Equity prices are volatile–much more volatile than the earnings-backed dividend payments that render them intrinsically valuable, i.e., valuable in themselves–because the trust and confidence that forms the basis for liquidity in the market can be fickle and unreliable.  The market can pull its liquidity in a heartbeat, and sometimes does pull it. When the liquidity is pulled–when investors conclude that they aren’t going to be able to sell at the prices they paid, at least not for a long time–their desire to be invested falls dramatically, as it should, given that they did not enter into their investments on the stipulation that they they would be permanently stuck inside them.

We can think of market prices as hovering between two poles: (1) the “intrinsic value” price, the maximum price that investors would be willing to pay to own a cash flow stream if there were no liquidity, no ability to sell the investment, ever, and (2) the “bubble” price, the maximum price that investors would be willing to pay own a cash flow stream, however paltry, if they were certain they would be able to get out of the investment without losing money, and hopefully be able to get out of it making money, realizing a return simply from the trading process.  These poles are separated by many thousands of points, many hundreds of percent.  The market swings between them based on factors that seem to have little to do with the long-term earnings and dividend prospects of companies because the factors influence the tender trust and confidence that investors have in the market’s future stability and trajectory, a trust and confidence that ultimately separates the two poles from each other.

Interestingly, on this way of thinking, the main reason why bond prices are less volatile than equity prices is not that the coupon payments of bonds are more reliable than the dividend payouts of well-diversified equity indices.  Rather, the reason is that bonds have a maturity date, a date where you can get your money out of the investment even if no one is willing to buy it from you.  That difference makes all the difference in the world.

If you buy a brand new 10 year treasury bond, and its price plunges in a panic, the worst that will happen to you is that you will be stuck holding the security for 10 years.  At 10 years, you will be made whole on your investment, regardless of what the market decides to do with the price.  Having to wait 10 years is certainly not as costly as having to wait forever, as one would have to do with an equity security that no one wants to buy.

Importantly, as the maturity date–the “finish line”–of a bond gets closer, it becomes easier to find others willing to risk a loss of liquidity in the security, given that that the “finish line” represents their “finish line” as well.  The security becomes easier to buy and just hold to maturity, which essentially ensures that there will be liquidity–a price reasonably to close to fair value–driven by confident investors that are willing to buy regardless of whether they think there will be yet others willing to buy from them.

For equities, however, there is no maturity, no “finish line.”  There is no amount of time that you can wait inside the investment in order to be guaranteed of being made whole on it.  Being made whole on it requires other people to want to buy it from you–without their interest, which depends crucially on their trust and confidence in the reciprocal process, their sense that others will be willing to buy from them at some point, you cannot be made whole on the investment, at least not in any finite amount of time.

Now, to be clear, if you hold an equity security for a long enough period of time, you can get your initial investment back in dividends.  But that’s not the issue.  You are not in the investment to get your initial money back, a return of your initial capital.  You are in the investment to get an appropriate return on your capital–you cannot get such a return in any finite amount of time without other people to sell to.

To use an example, if  you hold an equity security with a growing 2% yield, you will get your money back after 30 years or so.  But you will not get the return on your money that holding a security for 30 years demands.  In contrast, if you hold a 30 year government bond for the same amount of time, the entirety of its term, you will get such a return, which is why the two types of securities–bonds and equities–are fundamentally incomparable as instruments.

Valuation: Why It Matters

As investors in the real world, we do not invest in securities on the assumption that we are going to hold them forever, and therefore realize their “intrinsic value.”  Rather, we invest in them with the specific expectation of being able to sell them to other people at higher prices than we paid, thereby realizing a return.  We expect this return to be realized in a reasonable amount of time–months, years, maybe decades–certainly not any longer. A dividend stream can help pad our returns over those horizons, but the prices at which we sell the securities ultimately determine them.

We should worry about valuation, then, not because it determines the dividend return that we will receive on our investments, but rather because valuation is a factor that influences the perceived attractiveness of the security to other potential buyers of the security, those to whom we will sell, who we should view as our customers.  It is their perception of an equity security’s valuation–not our opinion of the reality–that will determine the price that they will be willing to pay for it.

That’s why it can be misguided for investors to focus on valuation metrics that no one uses. The value of an attractive valuation is that the valuation will be attractive to other potential buyers of the security–not that it is attractive to us, using our own pet methods.

Now, to be fair, let me add some nuance to the point.  Attractive valuations can either be obvious–readily seen by all–or they can be hidden.  When they are obvious to all, manifest in the classic “P/E” heuristic that investors use to quickly assess valuation, there will usually be some other factor–some set of fears–that is causing investors to not want to buy, despite the low P/E.  If we know that those fears are misguided and will eventually subside, then we can buy now, at the low P/E, and sell later, at what will by then be a more normal P/E.

Alternatively, the value may be hidden by the present P/E ratio.  It is then that unconventional metrics–metrics such as price-to-book, price-to-sales, enterprise value to EBITDA, Shiller CAPE, and so on–can be useful.  Such metrics can point to situations where the P/E is high, but high because of an abnormally low present E, rather than an abnormally high P.  Knowing that the E will eventually rise in a way that the market is not presently expecting, we can buy a cheap security that the market does not yet know is cheap, and then sell it when the value becomes evident to all, at which point the price will already have been pushed up.  Note that we can do the same in reverse, using unconventional metrics to stay away from expensive securities that appear cheap, appearing cheap because their Es have been artificially inflated by unsustainable trends–fads, bubbles, and so on.

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Dilution, Index Evolution, and the Shiller CAPE: Anatomy of a Post-Crisis Value Trap

In the first century, the historian Plutarch introduced a famous philosophical paradox.  The paradox goes like this.  A ship–”The Ship of Theseus”–was returning home to Athens from Crete.  As it sailed, the wooden planks that made up its structure gradually decayed.  The sailors kept the ship afloat by replacing the decaying planks, one by one, using fresh wood that they were carrying onboard.  Eventually, the sailors replaced all of the wooden planks that made up the the ship’s original structure, so that the new form of the ship had no material in common with the old form.  The question followed: was the ship the same ship through the change? If so, what made it the same ship, rather than a new ship, a different ship?

“For they took away the old planks as they decayed, putting in new and stronger timber in their places.  The ship became a standing example among the philosophers of the logical question of things that grow: with one side holding that the ship remained the same, and the other contending that it was not the same.” – Plutarch, Theseus, 75 A.C.E.

Approximately 1500 years later, the philosopher Thomas Hobbes took the paradox further.  He asked us to imagine the following.  All of the old, decayed wood of the original Ship of Theseus is gathered up from scrap and used to build a new ship.  There are then two ships: one ship that is spatially continuous with the original Ship of Theseus, whose material has been fully changed out, piece by piece, and another ship made from the scrap material of the original Ship of Theseus.  Which of these ships is the true Ship of Theseus? 

The “Ship of Theseus” problem frequently arises in the world of music fandom.  Consider, for example, the 1970s soft rock group, the Little River Band, which produced famous hits such as “Reminiscing” and “Lonesome Loser“.  To this day, the Little River Band remains together.  But there are no current members of the band that were in the band when it was originally formed.  All of the founding members, those who sang the hits as we are used to hearing them, have been swapped out.  A “Ship of Theseus” question thus arises: is the band that currently goes on tour as “The Little River Band” the true Little River Band, or is it the equivalent of a cover band, singing the same songs, while only pretending to be the original? To add the Hobbesian twist, what if the original members of the Little River Band were to come together to form a new band, a cover band of the Little River Band.  Would this new cover band be the true Little River Band, since it contains the founding members?  Or would it be a mere replica, since it is not continuous with the original?

You’re probably asking yourself what relevance this paradox has to finance, or to anything. But now here’s a question for you. Suppose that we have an index of stocks that represents the equity market of a given country, an index that we use, without further questioning, to draw conclusions about important topics such as the country’s valuation and expected future performance. What would happen if, like planks on the Ship of Theseus, or members of the Little River Band, most or all of the individual companies in the index were to be removed, replaced with new companies?  Would the index remain the same index? Or would it become a different index?

The question of “sameness” and “difference” is inherently metaphysical, and therefore has no answer.  But there is a more practical question that we as investors have to be concerned with.  That question is this.  Given radical changes in the constituents of an index, is it appropriate to use the index’s historical metrics–its historical earnings, growth rates, valuations, profit margins, returns on equity, and so on–to draw conclusions about what the index’s future performance is likely to be?

Ireland: The Perfect International Value Play?

Looking out over the long-term, it’s going to be very difficult for US investors to receive the “normal” 10% nominal annual equity returns that they have received historically.  Literally everything will have to go right.  Profit margins and returns on equity will have to stay elevated, contrary to the tendency of mean-reversion.  Multiples will also have to stay elevated, which means that interest rates will have to stay low.  But low interest rates are a consequence of weak economic growth and weak inflation.  How are companies going to consistently produce strong earnings per share (EPS) growth–the kind that would be needed to underpin 10% total returns for shareholders over the long-term–in an environment of weak economic growth and weak inflation?

Up to now in the current recovery, and really over the last 10 years, profit margin expansion and share buybacks have been the primary drivers of EPS growth for U.S. equities.  They are the reasons that strong EPS growth has been possible amid the persistent softness in economic growth and inflation (softness that has depressed the corporate top-line, but that has also provoked zero interest rates and an elevated P/E multiple).  Can profit margin expansion and share buybacks continue to be robust drivers of EPS growth, indefinitely, even as shares become more and more expensive for corporations to buy back, and as the income imbalances between capital and labor, the rich and everyone else, get closer and closer to the limits of economic and societal stability?  There are good reasons to think not.

Because long-term equity returns in the U.S. are likely to be sub-par, many investors have turned to foreign equity markets for better opportunities.  Where is the value in the equity world right now?  According to the Shiller CAPE, a popular technique for measuring value across economic cycles, the value is in Europe, specifically, the distressed countries of the Eurozone.

In my view, out of all of the countries of the Eurozone, the most interesting from an investment perspective is Ireland.  As a country, it has all of the features needed for strong long-term equity performance, features that many of its cousins in the Eurozone lack: a productive, highly-skilled, flexible labor force, capital-friendly, pro-business government policies, and a young, growing population in a demographic sweet spot.  To complete the investment case, Irish stocks are apparently very cheap, with the Irish index sporting a Shiller CAPE under 10.

It would seem, then, that Ireland is set up to produce spectacular returns.  But there’s a problem.  If you look closely at the actual names that make up the Irish index, you will be hard-pressed to find significant value.  The following table shows the constituents of the ISEQ 20, Ireland’s benchmark, sorted by market cap weighting as of March 2014:


Most of these companies enjoy above-average valuations.  That’s to be expected, as the companies are high-quality.  Glanbia?  Kerry Group?  Smurfit Kappa? Aryzta?  These are growing, thriving businesses.  They deserve to be priced as such.

There are two potential cases of deep value in the index: The Bank of Ireland and the building material producer CRH.  But these companies together only make up 29% of the index capitalization.  The majority of the index–71%–is composed of companies that are not deep value.  How can an index represent deep value when 71% of its constituents are not deep value?  How can an index trade at a CAPE below 10 when 71% of its constituent companies sport CAPEs significantly higher than that number?  Where exactly is the low CAPEness coming from?

Enter the Ship of Theseus paradox.  It turns out that many of the companies presently in the ISEQ 20 are new entrants, having replaced the financial roadkill that died off in Ireland’s massive housing bubble and subsequent banking crisis–roadkill that includes Anglo-Irish Bank, Allied Irish Banks, and so on.  That roadkill is gone, forever, having either been nationalized or diluted into oblivion.  But, crucially, the earnings that it generated during the bubble, from 2004 to 2008, is still part of the ISEQ’s earnings per share during those periods, and is therefore getting credited in the CAPE calculation for the index.

The following table shows constituents of the ISEQ 20 as of March 2014 alongside the constituents as of January 2007.


As you can see, there has been substantial turnover in the index.  The current ISEQ 20 has one major commercial bank, The Bank of Ireland, which represents ~9% of the index’s total capitalization and 0% of the index’s current earnings.  The ISEQ 20 of 2007, however, had three major commercial banks, which together made up ~40% of the index’s total capitalization and an even greater share of its earnings at the time.

The Shiller CAPE is a tool for detecting hidden value.  During cyclical weakness, a company’s classic trailing-twelve month (ttm) P/E ratio will be abnormally elevated by temporarily depressed earnings, and will therefore give an inaccurate picture of the company’s future earnings potential.  To get around this problem, we use the Shiller CAPE, which compares the company’s price to the average earnings that the company generated over the previous 10 years.  The 10 year average of earnings gives a more complete picture of the earnings that the company can be expected to produce in the future, when conditions return to normal.

At the index level, the same logic applies.  We compare the price of the index with the average of the index’s earnings over the previous 10 years, to get an accurate picture of the earnings that the index can be expected to produce when conditions return to normal.  In this case, however, there’s a really big problem.  The index has undergone a radical makeover.  It’s not the same index anymore.

Conceptually, it doesn’t make sense to expect a normalization in Ireland’s economic condition to catapult the ISEQ’s earnings back to the levels seen from 2004 to 2008, when the ticking time bomb of a highly-leveraged banking system was the engine of profit growth. Of the three banks that made up the majority of the index’s earnings at the time, two are no longer in the index, and the other is an unrecognizable version of its former self, having undergone a massively dilutive recapitalization.

The Shiller CAPE: The Dilution Distortion

It turns out that there is an even more significant illusion being produced here.  To illustrate the illusion, I’m going to present calculations of the Shiller CAPEs of individual companies in the Irish index.  Note that the data, the majority of which is taken from GuruFocus, may contain minor errors, specifically related to the capitalization and share count of the companies, given how complex the changes have been since the crisis. Regardless, the calculations are adequate to illustrate the underlying process at play.

Consider the Bank of Ireland, whose CAPE calculation is shown in the table below:


Notice the column “Shares (MM).”  As you can see, there’s been a huge explosion in the shares outstanding of the Bank of Ireland, obviously related to the massively dilutive recapitalization that the bank was forced to undergo in conjunction with the financial crisis.

Let’s think about how this dilution might impact the CAPE.  In an extreme dilution, a company’s share price will fall by orders of magnitude–appropriately.  In the case above, the price fell from over 900 to 15.  In the CAPE calculation, the appropriately-collapsed price will be compared with the company’s past earnings per share, earnings that were earned when the share count was orders of magnitude smaller than it currently is.  The dilution-depressed current price per share will thus get measured against an artificially inflated past earnings per share, a number that in no way reflects the company’s future earnings potential. Users of the metric will therefore walk away with a completely false picture of the company’s valuation.

It turns out that there is an additional illusion associated with the dilution.  One would expect the crisis that caused the dilution to have produced a period of negative earnings that will get averaged into the Shiller CAPE, negating at least a portion of the artificial earnings excess of the boom.  To be sure, in the case of the Bank of Ireland, those negative earnings did come through.  Crucially, however, they were “registered” during the same reporting period as the dilution.  The losses were therefore diluted over an artificially large number of shares, producing a relatively small per share loss (relative to the large per share gains that were enjoyed during the boom).

To make the point more clear, let’s get specific.  To arrive at a per-share basis, the $1B to $2.5B that the Bank of Ireland earned each year in the pre-crisis period is being divided by the pre-dilution number of shares, approximately 24 MM.  But then, after the crisis, the subsequent $4B loss is being divided by the post-dilution share count, a number ranging from 100 MM to 750MM.  The result is what you see above.  The Bank of Ireland appears to have earned $50 to $100 dollars per share per year during the boom times, and to then have lost only around $20 per share during the entirety of the bust.  When you average these per-share numbers together to compute the average earnings, you get a deceptively high average, and therefore a deceptively low Shiller CAPE.

Now, to eliminate this distortion, what I’ve done in the table is calculate the CAPE on an absolute basis in addition to on a per-share basis.  Instead of comparing the price per share to the average real earnings per share over the last 10 years, the “Absolute CAPE” compares the current market capitalization to the average real net income over the past 10 years, with both numbers unadjusted for share count.  On this absolute basis, the CAPE for the Bank of Ireland rises from a ridiculously cheap 0.40 to a seemingly expensive 20.62.

The same distortion emerges to an even greater degree in the case of Allied Irish Banks, whose CAPE calculation is shown in the table below:


Uncorrected for the dilutive distortion, Allied Irish shows a CAPE of 1.99.  But the absolute CAPE is actually steeply negative, indicating that, on an absolute basis, the bank lost more money in the crisis than it earned during the boom.  Is that surprising? It shouldn’t be–over the long-term, bubble-bust finance is not a good business.  You eventually get completely wiped out.

There are similar distortions associated with the way in which troubled company’s tend to exit the index.  Troubled companies often get delisted and removed from an index before all of their losses have been taken, allowing the index to escape from the losses scot-free, even though the corresponding gains were registered without hindrance.  Worse yet, with some types of indices, even when the troubled company does remain in the index to register its losses, the publishers of the index don’t count the losses in the index earnings, because the losses represent one-time, non-recurring events.

I would have included a CAPE analysis of Anglo-Irish Bank, but they represent a prime example of an exit distortion, having been nationalized in 2009.  From 2004 to 2008, they earned a profit typical of the other banks, on the order of around $1B per year.  But then, in 2010, well after they had been nationalized and removed from the ISEQ, they took a cool $15B impairment loss, a loss that, if registered in the index, would have more than wiped out any profit that they contributed during the boom.  How convenient.  The ISEQ is able to count Anglo-Irish’s highly artificial profits earned during the boom, but then when the bust comes along, and it’s time for Anglo-Irish to drop its turd, the bank is already long gone from the index.  Its turd gets dropped in a black hole, leaving the ISEQ’s earnings unaffected.

Now, let’s look at the CAPEs of some of the larger non-financial companies in the ISEQ. First, CRH:


As the table shows, there’s clearly some value in CRH.   But it’s nothing to write home about. Notice that the company enjoyed the same dilutive effect that the banks enjoyed, albeit to a much smaller degree.  The absolute CAPE is 3 points higher than the per share CAPE, owing to the fact that the share count has increased by almost 50% over the period.

CRH is easily the cheapest non-financial stock in the Irish stock market, and yet it’s CAPE isn’t even below 12.  We should therefore be extremely suspicious when we see the Irish stock market as a whole register a CAPE below 10.  Trivially, a country cannot have a CAPE lower than the CAPE of its cheapest current constituent.  If it does, then something has necessarily gone wrong in the analysis.

Here is the CAPE for Ryanair, Ireland’s premier airline, which makes up about 9% of the ISEQ:


Ryanair sports a CAPE of 36.45–hardly a case of deep value.  Notice that its per share CAPE is actually higher than its absolute CAPE.  The reason is that it’s been shrinking its shares, rather than growing them.

Here is the CAPE for Kerry Group, a food producer in the ISEQ:


Again, a very high CAPE, on par with the CAPE levels that you might see in a growing U.S. company.  The per share CAPE is roughly the same as the absolute CAPE because there’s little change in the share count.

U.S. Banks: Similar CAPE distortions?  

The U.S. banking sector is often cited as the cheapest sector of the U.S. equity market.  It may be the cheapest sector–I’m not going to argue that point.  But the CAPE should not be what leads us to this conclusion.  The CAPE is not a conceptually valid way of measuring value in a post-crisis environment where share counts have appreciably changed.

The same distortion that we saw in the CAPEs of the Bank of Ireland and Allied Irish is present in the CAPEs of America’s junky financial analogues.  Consider, for example, the CAPE of Bank of America ($BAC), calculated below:


As you can see, $BAC suffered significant dilution in the crisis aftermath, simultaneous with its post-crisis writedowns, creating a distortion in its per share CAPE.  The per share CAPE comes in at 8.14, when the absolute CAPE is 19.29.

The following table shows the CAPE calculation for another junky financial, Citigroup ($C):


Again, the same distortion is present, to an even greater degree, given the greater dilution. The per share CAPE is 4.77, whereas the Absolute CAPE is 18.25.

Energy Companies: A More Benign Distortion

It turns out that the Shiller CAPE also creates distortions in the valuation of energy companies.  The reason is that energy companies generate earnings off of a depreciating asset base.  The appropriate way to value them is not to look at their past earnings, generated on assets that are now used up, but to conduct a discounted cash flow analysis of the future earnings that they will generate on their current asset base, as that base depletes away.

Consider, as an example, the case of Total, the integrated French oil company.  The following table shows Total’s Shiller CAPE:


As you can see, Total trades at a very attractive CAPE relative to the market.  It also trades at an attractive ttm P/E ratio–and always has.  The reason that it trades at an attractive CAPE and ttm P/E ratio is that its past earnings are not directly relevant to its current value.  What is relative to its current value is the ratio of its price to the discounted sum of its future earnings, earnings that will be generated as its finite oil reserves are drilled out of the ground and sold.  How plentiful are those reserves?  What is their quality?  How expensive will drilling them out of the ground be?  From a valuation perspective, these are the questions that matter.

The intrinsic value of an asset is the discounted sum of its future cash flows.  If you have a company with recurring cash flows generated off of a surviveable asset base, then it makes sense to use trailing metrics like the CAPE, the ttm P/E ratio, and the ttm dividend yield to approximate the value.  But if you have an energy company with an asset base that depletes every time product is pumped out and sold, an asset base that is difficult and costly to replace through new discovery, then these metrics will not provide an accurate picture of the value.

Discounted at 10%, the net present value of Total’s proven oil and gas reserves is $47B. The company trades at a market capitalization of $139B, with an enterprise value, including net debt, that is even higher.  On those numbers, Total is hardly a case of deep value. To the contrary, it appears to be overvalued–by at least 200%.  Before we jump to that conclusion, however, let’s consider a few points:

  • 10% may be too large of a discount rate to apply to the assets in the present interest rate environment.  Of course, lowering the discount rate won’t fully alleviate the apparent overvaluation.  Even at a 0% discount rate, the net present value of Total’s oil and gas assets is only $105B (and that’s before the recent oil price drop).
  • Total is an integrated company, and generates profit from refining and marketing in addition to production.  The profits associated with its refining and marketing arms have to be included in the valuation analysis, just as its net debt has to be included.
  • Proven reserves are often only a conservative estimate of the quantity of oil and gas that an energy company has access to and will be able to produce and sell over time. Given that the company trades at a 50% premium to its undiscounted proven oil and gas reserves, the market probably expects Total’s unproven reserves to be significant, possibly even larger and more valuable than its proven reserves.

The point, however, is that an analysis of the cash flow that will be generated out of Total’s current oil and gas assets, and not an analysis of the cash flow that it generated last decade, off of assets that have long since been converted into carbon dioxide, is what will determine the price that oil and gas investors will be willing to pay to own the company, and the price that they should be willing to pay.  That’s why Total trades at depressed P/E and CAPE multiples.  P/E and CAPE multiples simply are not relevant considerations in the oil and gas valuation process.

Reasons to Be Skeptical of European Value

If you examine the indices of the country’s in Europe that are allegedly offering investors deep value, you will notice that these indices are heavily allocated to financials and to energy as sectors.  In cases such as Ireland where the indices are not heavily allocated to the financial and energy sectors, there’s little deep value to be found.

The following table shows the CAPEs of important European countries, borrowed from Star Capital’s fantastic interactive website, alongside the country allocations to the financial and energy sectors in the respective MSCI indices.


As we see, the countries have low CAPEs, but they also have lopsided allocations to the financial and energy sectors.  In fact, there’s an apparent pattern: the higher the allocation to the financial and energy sectors–especially the financial sector–the lower the CAPE.

The heavy exposure to the financial sector substantially increases the risks of distortion, particularly given the credit bubble and subsequent crisis that Europe experienced. Greece, with a whopping 56% allocation to financials, and an unrecognizably low CAPE of 3.5, is particularly suspect in that respect. Where is its ultra-low CAPE coming from?  My guess: not from healthy business selling at attractive prices, but from crashed-out zombie banks that are distorting the index.

Of all of the regions in the world, Europe offers what is clearly the worst fundamental backdrop for investment.  The continent is overregulated, with inflexible labor laws and a generally business-unfriendly political climate, at least in certain countries.  The continent’s household, corporate, and financial sectors are heavily-indebted.  The population is in clear demographic decline.  The different countries that make up the continent have different cultural and competitive dynamics, yet are all trapped in a single currency union.  The exchange rates between the countries are therefore unable to naturally adjust so as to bring payment balances into line.

As if these structural headwinds weren’t enough, the monetary authority in Europe is a joke.  It has no ability to do anything to stimulate the European economy except talk.  The northern bloc won’t allow it to do anything more.  How long have we been attending to these meetings, listening to Mario Draghi tell us about the things that he might one day do?  At every meeting, the date of eventual action is pushed off to the next meeting, or beyond.  Nothing ever happens.

Markets love monetary policy, but in truth, monetary policy has little to offer in a situation like this, where households and corporations are deleveraging, and where the population and the workforce are shrinking.  In addition to supply-side labor reforms, what Europe needs is aggressive fiscal policy.  Fiscal policy has the ability to directly and reliably increase aggregate demand.  If aggregate demand is strong, real investment will start making economic sense (it doesn’t make economic sense right now).  Real investment will therefore increase, creating new sources of employment and income, fueling further increases in aggregate demand, incentivizing additional real investment, and so on, in a virtuous cycle.  For such a cycle to reliably take hold in a world that faces the kinds of headwinds that Europe faces, there needs to be an aggressive commitment on the part of policymakers to take whatever fiscal actions are necessary to keep aggregate demand strong–to intentionally and unapologetically run the economy hot, even if this means dropping freshly printed euros from a helicopter in the sky.

On that front, Europe could not possibly be worse off.  The weaker countries that need aggressive fiscal stimulus have no ability to borrow in their own currencies.  To conduct fiscal expansion, they have to get the permission of a separate country, Germany, a country with an obsessive fear of inflation and government debt, that does not have to share in any of their pains.

We can celebrate the fact that Mario Draghi said something, and that markets around the world rallied, but we should not let superficial price action blind us to the fact that the project of the Eurozone is an unsustainable mess.  The union is going to have to eventually dissolve, or at least undergo a substantial makeover.  Such a change is sure to bring turmoil to European financial markets, whether it comes next year, 5 years from now, or 20 years from now.  European investors deserve to be appropriately compensated for the risk.

Are they being appropriately compensated?  It’s not clear.  From a Shiller CAPE standpoint, it looks like they are being compensated, but that’s likely to be a result of the high financial and energy sector exposures that European indices contain.

Interestingly, U.S. investors can find the “deep value” that allegedly exists in Europe right here at home, in their own backyards.  All they have to do is go to the sectors that dominate European indices–financials and energy.  If they want a low CAPE, they can buy low-quality U.S. banks that were forced to recapitalize in the credit crisis–$BAC and $C, for example–or large cap integrated oil companies that trade on the productivity of their underlying oil and gas assets, rather than on P/E ratios–$CVX and $XOM, for example. These companies sport Shiller CAPEs that are just as low as the deep value companies of Europe.  There’s hardly a difference, for example, between the Shiller CAPE of a $BAC and that of a Banco Santander ($SAN), or the Shiller CAPE of a $CVX and that of an Eni Spa ($E).  The numbers are essentially the same.

Solutions to the Problem

As a metric, the Shiller CAPE is still useful.  It just needs to be employed with caution in countries that are coming out of large credit booms and busts, particularly those that have heavy exposure to financials, or that have had heavy exposure to financials in the past.  I’m therefore going to conclude the piece with some proposals for how investors might be able to avoid, or at least work around, the CAPE distortions that these countries give rise to.

One way would be to get under the hood of the indices themselves–examining how they’ve changed over time, how much dilution has taken place, what specific crisis-related losses have and haven’t been counted in the earnings numbers, and so on–adding whatever adjustments may needed to allow for an accurate valuation analysis to take place.  Unfortunately, this would be a difficult task.  The data is hard to find, and would take a very long time to piece together.

Another approach would be to use indices that intentionally exclude financials, and possibly energy companies as well. Unfortunately, none of the major index publishers produce ex-financial or ex-energy indices–for Europe or for any country.  Investors would have to build them directly, which would again be very complicated and time-consuming.

A more practical approach would be to evaluate the countries using ttm valuation measures, as a sort of “second check” on the Shiller CAPE metric.  The ttm P/E ratio is often criticized for only providing a picture of the last twelve months.  But that’s actually an advantage in this context, as it eliminates “The Ship of Theseus” problem. When you look at the ttm P/E ratio for an index, you can be sure that the “E” that you are looking at in the denominator is associated with the same companies as the “P” that you are looking at in the numerator. As we saw in the case of Ireland, you cannot always be sure of this fact when you use the Shiller CAPE on an index.

One good valuation metric to use, backed up by significant academic research, is the ttm enterprise value to ebitda (EV/EBITDA) ratio.  The advantage of ttm EV/EBITDA is that it includes net debt, which should be part of any valuation analysis, and also that it eliminates many of the non-recurring non-cash charges that tend to distort earnings, particularly around recessions.  The disadvantage, of course, is that it doesn’t count depreciation, and therefore it causes companies that have high depreciation costs, such as energy companies, to look artificially cheap.

If strictly non-cyclical measures are preferred, two additional ttm metrics that can be used to “second check” the Shiller CAPE are the ttm price to sales (P/S) ratio and the ttm price to book (P/B) ratio.  Like the P/E and EV/EBITDA ratios, these metrics only look at the prior year, and therefore avoid the “Ship of Theseus” problem.  At the same time, they solve the problem of cyclicality, given that sales and book values do not significantly fluctuate across the business cycle.

The problem with P/S and P/B ratios is that they tend to be different for countries that have different sectoral compositions.  Naturally, countries with higher allocations to high margin and high ROE sectors will tend to exhibit higher P/S and P/B ratios than those dominated by low margin and low ROE sectors.  We don’t necessarily want to penalize them for that in the analysis.  Additionally, for the P/B ratio, not all countries writedown their assets using the same standards.  European companies, for example, did not take the “goodwill” writedowns that U.S. companies took during the crisis.  For that reason, their P/B ratios tend to be lower, as explained in this analysis from KPMG.

A clean way around this problem would be to normalize the P/S and P/B ratios of different country indices to reflect the different sectoral compositions that those country indices exhibit and to reflect an application of the same writedown accounting standards.  Then, an apples-to-apples comparison between countries would become possible. Unfortunately, such a project would be too difficult and too time-consuming to put into motion.

When we check Ireland’s CAPE against its ttm P/S and P/B ratios, we quickly notice that our prior suspicions were correct: Ireland is not a case of deep value.  The country trades at a P/B ratio of 2.3 and a P/S ratio of 1.4, both of which register as expensive in comparison with the rest of the globe.  To be clear, Ireland may still be an attractive long-term investment opportunity–it probably is, given its many strengths–but the reason has nothing to do with its apparent status as deep value.

Fortunately, when we check the CAPE of the more-distressed PIIGS countries–Portugal, Italy, Greece, and Spain–against their respective P/S and P/B ratios, the countries continue to register as cheap.  It’s probably true, then, that the countries represent deep value–specifically, deep value concentrated in the financial sector, and to a lesser extent, the energy sector.  With respect to Greece, however, the P/B and P/S ratios, at 1.0 and 0.5 respectively, are not as cheap as would be expected given the 3.5 CAPE, which is almost half that of the closest competitor. Something is likely wrong with that number.

A final solution would be to not discriminate at all on the basis of country borders. If we’re looking for international value, let’s look for international value, in whatever country it happens to be located.  By looking strictly at individual companies, we can eliminate the need for indices altogether, bypassing the “Ship of Theseus” problems they create.

On that theme, there are a number of well-run international ETFs that take valuation factors with solid historical track records and apply them in foreign markets to locate attractive individual company opportunities.  Examples include (1) Cambria’s $FYLD, an international version of the successful $SYLD, which invests in companies that have a high shareholder yield, (2) Invesco’s $IPKW, an international version of the successful $PKW, which invests in companies that are buying back significant quantities of their own shares, and (3) Valueshares’ $IVAL, a not-yet-launched international version of the recently launched $QVAL, which invests in companies that exhibit attractive ttm EV/EBITDA ratios and that pass various quality screens.

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Not Everyone Sucks at Investing

Judging from the financial headlines, we live in a world where everyone sucks at investing.

Hedge funds?  Consistent underperformers: this year, last year, the year before that, the year before that, the year before that.  Every year, it seems.  Just google “hedge funds” and “underperform”, to see the flurry of giddy articles that pop up.


Individual Investors?  Again, consistent underperformers.  They get excited at the tops, they panic at the bottoms, they do everything exactly backwards to the maximum extent possible.  The published numbers here are quite ugly: according to Dalbar’s 2013 QAIB publication, the average individual equity fund investor has earned a pathetic 3.69% annualized return over the last 30 years, versus the S&P’s 11.11% (note: the QAIB report may contain distortions).

How is such consistent underperformance possible?  The answer, we are told, is behavioral. Investors, of both the professional and the layman stripe, tend to herd.  They prefer to do what everyone else is doing.  And so they end up buying when assets are in high demand, at the worst possible prices, and selling when assets are out of favor, again at the worst possible prices.

There’s an obvious problem with this narrative, which you’ve probably already noticed. For every party in a trade, there is a counterparty–for every buyer, a seller, for every seller, a buyer.  There must, then, be an outperforming counterparty to the underperforming average investor, and the undeperforming average hedge fund, and the underperforming average day trader, and the undeperforming average endowment, and whoever else underperforms on average.  Someone had to be smartly selling to those groups in 2000 and 2007, for example, when they were frantically trying to get in, and smartly buying from them in 2003 and 2009, when they were desperately trying to get out.  Who–what group–is that someone?  And why doesn’t the financial media ever celebrate its achievements?

I’m glad to be able to tell you that I am a member of that group.  Over the last 15 years, I have compounded my own capital at a 35.9% annual rate, profiting handsomely from the ill-timed and ill-advised decisions of “average” individual investors, mutual fund managers, and hedge fund managers alike.  And don’t be fooled; it’s not just me.  A lot of us do quite well, thankfully.

Of course, everything I just said is a bald-faced lie.  So don’t worry.  I’m not better at life than you.  But how did it make you feel to read about someone else’s spectacular performance?  Probably not very good.  That’s why the media prefers the “everyone sucks” headline.  It makes for fun, satisfying, ego-pleasing reading.

The truth is this.  Investors in aggregate are the market.  Before frictions (fees, transaction costs, etc.), they cannot underperform.  Nor can they outperform.  For they would be underperforming and outperforming themselves, and that is obviously impossible.  Now, if we arbitrarily divide the market into different categories of participants–individual investors, hedge funds, pension funds, corporations, and so on–then it would be possible for some categories to consistently underperform others (note that this would create tension for the efficient market hypothesis–pure negative alpha is, in fact, a type of alpha). But, necessarily, the other categories would be outperforming.

What category of investor, then, is consistently outperforming the market, against the consistent underperformance of hedge funds, individual investors, and other losers?  You will be hard pressed to find an answer.  An obvious candidate would be the corporate sector, which has, in recent years, taken large amounts of equity out of the market through share buybacks and acquisitions, effectively forcing the rest of the market to be net sellers.  The problem with citing corporations as the clever counterparties, however, is that corporate managers exhibit the same herding tendencies as the rest of the market.  According to Z.1 data, they too prefer to buy high and sell low, having bought heavily around the 2000 and 2007 peaks, and having sold at the 2003 and 2009 troughs.


Part of the problem here is that we arbitrarily treat the S&P 500 as “the market”, the benchmark for evaluating performance.  But the S&P 500 is not a reasonable benchmark to use, since investors in aggregate do not allocate the entirety of their portfolios to U.S. equities.  Indeed, investors in aggregate cannot allocate the entirety of their portfolios to U.S. equities–if they tried, prices would go to infinity.  The strategy of devoting an entire portfolio to U.S. equities, which may look brilliant right now given the recent performance, would necessarily become a bad idea (if it isn’t already a bad idea).

The appropriate benchmark for performance evaluation is the global asset market, which includes all global assets: stocks from all countries, bonds from all countries, real estate in all countries, and, importantly, cash from all countries (commercial paper, government bills, bank deposits, and so on).  Over the long-term, some groups will surely outperform this market.  If the efficient market hypothesis is true, we should expect it to be those groups that choose to accept the most risk in the choice of what they own.  If the efficient market hypothesis is not true, then we should expect it to also include those groups that possess skill, that manage to own the right assets at the right prices at the right times.

Similarly, some groups will surely underperform the global asset market, because those groups choose to take on less risk than the global asset portfolio contains (making it possible for other groups to take on more risk), because those groups lack skill (making it possible for other groups to demonstrate skill), or because those groups stupidly accept unnecessary frictions–management fees uncompensated by skill, overtrading with high commission costs across large bid-ask spreads, and so on (making it possible for financial middlemen to earn a living).  But the point is, with performance properly measured, it’s not possible for everyone to consistently underperform.  Not everyone sucks at investing.

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Valuation from All Angles: S&P 500, Russell 2000, and the 10 GICS Sectors

(Much thanks to the must follow @ElliotTurn for valuable help and feedback in the development of these charts and tables)

In this piece, I’m going to present a series of charts and tables that seek to efficiently convey the state of U.S. equity valuations from all available vantage points–that is, “from all angles.”  Note that a convenient slideshow aggregating the tables and charts together is presented at the bottom.

S&P 500:

The following “ttm” chart shows trailing-twelve month (ttm) values and ratios from 1996 to 2014 (click on the chart to enlarge):


(Legend: The squares show the following metrics (1 to 20, left to right, top to bottom): (1) real price returns and real total returns (with dividends reinvested at market prices), (2) trailing-twelve month (ttm) dividend yields, (3) ttm price to earnings (P/E) ratios and fwd P/E ratios based on analyst estimates, (4) ttm enterprise value to earnings before interest, taxes, depreciation and amortization (EV/EBITDA) ratios, (5) ttm price to ebitda (P/EBITDA) ratios, (6) real ttm sales and book value growth, (7) real ttm dividend growth, (8) real ttm EPS growth, (9) real ttm EBITDA growth, (10) annualized inflation rates for the prior 6 years and long-term government bond yields, (11) ttm price to sales (P/S) ratios, (12) ttm dividend margins (ttm dividends as a % of sales), (13) ttm EPS margins (ttm EPS as a % of sales), (14) ttm EBITDA margins (ttm EBITDA as a a % of sales), (15) interest, taxes, depreciation and amortization (ITDA) as a % of EBITDA (which gives a picture of how much the earnings are being reduced by those expenses at any given time–very important), (16) price to book (P/B) ratios, (17) ttm dividend payout ratios (ttm dividends divided by ttm EPS), (18) ttm EPS return on equity (ROE) (ttm EPS divided by book value), (19) ttm EBITDA ROE (ttm EBITDA divided by book value), (20) real net debt (debt minus cash and liquid assets, i.e., the difference between enterprise value and price).  The dotted black line in each chart shows the metric’s average for the period.)

The following “Shiller” chart shows different types of Shillerized valuations from 1996 to 2014:


(Legend: The squares show the following metrics (1 to 15, left to right, top to bottom): (1) shiller P/E ratio (real price divided by the of average real ttm EPS seen over the prior 6 years (10 leads to too much information loss), (2) price to peak earnings (P/PkEPS) ratio (real price divided by the highest ttm real EPS earnings reading seen over the prior 6 years), (3) Shiller EV/EBITDA (using 6 years), (4) enterprise value to peak EBITDA (EV/PkEBITDA) ratio (using 6 years), (5) Shiller price to EBITDA ratio (using 6 years), (6) real shiller EPS (average of real ttm EPS over the prior 6 years), real peak EPS (highest ttm EPS seen over the prior 6 years), (7) real Shiller EBITDA (average of real ttm EBITDA over the prior 6 years), (8) real peak EBITDA (highest ttm EBITDA seen over the prior 6 years), (9) real ttm Sales and real ttm Book value, (10) – (14) margins and ROEs for all Shiller and peak metrics (Shiller EPS / sales, Shiller EPS / book value, Peak EPS / sales, Peak EPS/ book value, Shiller EBITDA / sales, Shiller EBITDA / book value, peak EBITDA / sales, peak EBITDA / book value, (15) asset turnover, i.e., sales / book value.)

The following table presents data from the above charts in numeric form.


(Legend: The upper left quadrant shows valuation metrics as of the close on 11/13/14 and the average for the period (along with the delta between the present value and the average). The upper right quadrant decomposes the returns into dividends, growth in fundamentals, and changes in valuation for three different fundamental bases: price to sales, Shiller P/E, and Shiller P/EBITDA.  Note that the “true ROE” of the corporate sector is the return that it would produce in a given period if valuation were held constant during that period.  Thus the true ROE equals the dividend return plus the return due to growth in the given fundamental (which will necessarily equal the growth in the price if the valuation relative to that fundamental stays constant).  The lower left quadrant shows margins and ROE as of the close on 11/13/14 and relative to the average for the period.  The lower right quadrant shows valuation metrics relative to the long-term government bond yield.)

I will now present the same charts and tables for the the Russell 2000 and the 10 GICS sectors–Consumer Discretionary, Consumer Staples, Energy, Financials, Healthcare, Industrials, Materials, Technology, in that order–in slideshows.

Slideshow: TTM Charts

Here are all of the “ttm” charts (ttm valuation ratios, growth, margins, ROEs, inflation, government bond yields, etc.) in a slideshow (going from upper left to lowe right: SPX, R2K, Discretionary, Staples, Energy, Financials, Healthcare, Industrials, Materials, Technology).  Click on any image to start the slideshow there:

Slideshow: Shiller Charts

Here are all of the “Shiller” charts (Shillerized data) in a slideshow (going from upper left to lowe right: SPX, R2K, Discretionary, Staples, Energy, Financials, Healthcare, Industrials, Materials, Technology).  Click any image to start the slideshow there:

Slideshow: Tables

Here are all of the tables (going from upper left to lowe right: SPX, R2K, Discretionary, Staples, Energy, Financials, Healthcare, Industrials, Materials, Technology).  Click on any image to start the slideshow there:

In a subsequent piece, I will present the same charts and tables for 17 different countries.  I will also present tables that rank the sectors and countries by the different valuation and growth factors.

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How Often Does the Stock Market Correct?

‘Tis the season for corrections, and so we ask, how often do they occur historically?  To answer the question, we need to precisely define the the term “correction.”  If the stock market falls 20% in a straight line, most of us would interpret the move to be a single 20% correction.  But suppose that the stock market falls 10% in a straight line, then stabilizes or bounces, then falls another 10%. Would that be one correction, or two?  We need to specify.

Here, we will arbitrarily define “correction” as follows.  The market is in a correction of X% on a given day if it closes on that day at a level that is more than X% off of its closing 52 week high.  The question we will then ask is, how often is the market in a correction of X%–3%, 5%, 7%, 10%, 15%, 20% and so on?

To answer the question, we will use a total return index (daily, built from CRSP data back to January 3rd, 1928), rather than a simple price index.  The reason we will use a total return index is that in the past, companies paid out a much greater share of their earnings as dividends than they do in the present.  But dividends, when paid out, represent step reductions in corporate net worth, and therefore entail step reductions in price. Dividends thus make it more likely that the market will hit an X% correction target on price, all else equal.  By using a total return index rather than a price index, we eliminate this distortion.

We will analyze two different periods: a full period, from January 3rd, 1928 to August 28th, 2014 and a post-war period, from January 2nd, 1945 to August 28th, 2014.



7pctcorrxn 10pctcorrxn







Note that the term “correction”, as we’ve defined it, isn’t very helpful in depicting the larger moves, because those moves tend to happen over periods that exceed 52 weeks.  In cases where the moves do exceed periods of 52 weeks, they often don’t get captured in the definition, because the previous 52 week high moves lower as the market moves lower, preventing the market from separating from it (falling relative to it) by the X% number.

The following charts seek to provide a more useful depiction of the larger moves.  They show all of those times where a buy and hold investor was down, on a total return basis, by more than X% from any prior all-time high.








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The State of Investment Around the World

In this piece, I’m going to share a few charts on the state of investment around the world. The data is taken from FRED, and shows the percentage change in trailing twelve month real gross fixed capital formation from 1Q 2000 levels.

US, Europe, Japan, 1Q 2000 to 2Q 2014:


Notice the recent downtick in Japan.  Is the downtick a short-term effect of the consumption tax increase, or a sign that the “Abenomics” boom is already petering out?

Germany, Italy, France, Eurozone, 1Q 2000 to 2Q 2014:


Notice the investment strength that Germany has seen since the crisis.  This strength stands in stark contrast to the investment decline seen in the other countries. Interestingly, the situation is a mirror image of the situation of the prior decade, wherein German investment remained subdued while investment in the other countries experienced a boom.

The subdued investment in Germany, coupled to the unproductive investment boom experienced by the rest of the Eurozone, created wage, price and competitiveness differentials between the countries that now stand at the heart of the Eurozone problem. German goods and services are simply too cheap relative to the goods and services of the rest of the Eurozone for the countries to remain in a currency union that precludes exchange rate adjustment.

The boom in employment that Germany, due to its significant competitive advantages, is experiencing as it attracts consumption and investment flows from the rest of the Eurozone is the system’s attempt to rebalance in the only way that it can.  The problem is that the rebalancing is extremely painful for the rest of the Eurozone countries, which are experiencing the opposite of what Germany is experiencing–depressed investment, high unemployment, and a tendency towards deflation.

The only politically viable mechanism for the system to restore balance is for Germany to “boom” more, to take on more inflation relative to the other countries, which will raise the relative prices of goods and services in Germany, and create conditions where consumption and investment flows begin to naturally move back in the other direction, towards the rest of the continent.  If Mario Draghi’s monetary experiments will have any hope of saving the Eurozone, the hope will rest on that mechanism: stimulating the German economy and raising German inflation in a way that helps restore relative price competitiveness in the other countries.

Spain and Greece, 1Q 2000 to 2Q 2014:


These countries had enormous residential investment booms in the last decade, five times as large as the Eurozone in aggregate.  The booms did not lead to appreciable increases in Spanish or Greek productivity, though they increased wages and prices, which is why Spain and Greece now have a competitive deficit relative to Germany–a deficit that cannot adjust via the exchange rate, because the countries are in a single currency union.

United States, United Kingdom, 1Q 2000 and 2Q 2014:


These economies tend to track each other, despite the distance between them. The UK is doing reasonably well right now, much more like the US than the rest of Europe.

United States, Brazil, India, 1Q 2000 to 2Q 2014:


From an investment perspective, the emerging market boom of the last decade was much larger than the US housing boom.  The challenge for the emerging markets going forward will be to digest the large credit expansion associated with that boom, some of which was surely unproductive.  Both countries have significant inflation problems, completely different from the problems faced by the developed world.

United States, Brazil, India, 2Q 2011 to 2Q 2014:


Since 2011, investment in the US has actually been stronger than in India and Brazil. At present, Brazil is showing clear signs of being in recession.

Some thoughts:

In terms of balanced growth, the US is the strongest economy in the world right now. On a net basis, fiscal and monetary policy in the US are not as accomodative as they should be. But they’re close enough.  The combination of tight fiscal policy and extremely loose monetary policy is where the problem lies–it’s a suboptimal combination, given the circumstances.

Europe desperately needs a large, deficit-financed fiscal stimulus program to shore up the savings-investment gap in its private sector.  Germany needs to lead the way on that front, aggressively stimulating its own economy so as to produce higher domestic inflation. Higher inflation in Germany will make the rest of the Eurozone more competitive and will provoke a sustainable reversal of consumption and investment flows back towards the rest of the continent.  Monetary stimulus may help some at the margin, but with long-term interest rates already at record lows, with banks and households eager to deleverage, and with asset prices already elevated, particularly in the residential sector, it’s unlikely to get the job done.

Japan is at a crossroads.  The consumption tax hikes were unnecessary and ill-advised. Japanese policy makers continue to show a lack of understanding of government debt. They don’t understand what the actual risks are.

To be clear, the risk that large government debt poses in Japan, and in any depressed economy, is not the risk of a bond market “revolt.”  Governments fund themselves at the short-end of the curve, a part of the curve that they themselves fully control, through their central banks.  A “revolt” is therefore impossible.  To the contrary, the risk of large government debt is that someday, well out into the future, the economy will be in a genuine boom again.  In such an environment, higher interest rates will be necessary to contain inflation.  The government will then have to choose between leaving rates low or zero–a choice that could spur intolerably high inflation, asset bubbles, stagnant real economic activity given the lack of price stability, capital flight, unwanted currency depreciation, a currency crisis, or all of the above–or raising rates and dramatically increasing the interest cost on the debt, given the high degree of leverage.  But if the interest cost on the debt rises substantially, the government will have to engage in aggressive austerity.  Such austerity is socially divisive and economically destabilizing. And so neither choice is attractive.

But there’s no reason for Japan to forego recovery altogether, forever, simply because the government debt will be large when it is finally achieved.  Japanese policymakers need to focus on getting to the destination first–a durable, self-sustaining expansion.  Once they get there, then they can worry about implementing measures to deal with the large debt, as the heavily-indebted US and UK governments successfully did in the aftermath of World War II.  If Japan has to enact substantial tax hikes and spending cuts at some point in the future, when the economy is overheating, then fine.  The worst that will happen is that the country will end up back in a recession, which is effectively what it is trying to get out of right now.  And if the country ends up experiencing a few years, or a decade, of double-digit inflation, because the tax hikes and spending cuts are too little, too late, then fine. Worse things have happened.  The inflation will eat away at the debt in real terms and pull the system towards a stable equilibrium.

Brazil and India have classic inflation problems.  To deal with these problems, they need to institute supply-side reforms alongside tighter monetary policy, so as to ensure that capital goes to its most efficient destinations.  Brazil needs to focus more on supply-side reforms, as its monetary policy is already reasonably tight.

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Free Banking on a Bitcoin Standard–The State Prepares its Death Blow


In a previous piece, we examined the inner workings of a gold-based fractional-reserve free banking system–the monetary system that was roughly used in the United States for much of the 19th century and before.  The system works as follows.  Customers deposit gold–which is the system’s actual money, legal tender–at private banks, and receive paper banknotes in exchange for it. Customers can redeem the banknotes for the gold at any time.

In such a system, the market eventually comes to accept the banknotes of credible banks as payment in lieu of payment in gold.  The banknotes become “good as gold”, operationally equivalent to the base money that “backs” them.

Importantly, banks take advantage of the fact that, on a net basis, very few banknotes actually get redeemed for gold.  This convenient fact allows them to issue a quantity of banknotes that exceeds the quantity of customer gold that they have on hand to meet redemptions.  They issue the excess banknotes as loans to borrowers in exchange for interest.  In this way, they expand the functional money supply, and make it possible for the economy to grow in a non-deflationary manner, despite being on a hard monetary standard.

A fractional-reserve free banking system with gold as the base represents a coveted Libertarian ideal because it requires no government involvement, other than the simple enforcement of contracts.  There are no complicated and cumbersome regulatory rules to follow, no externally-imposed reserve requirements or capital adequacy ratios, no interest rate manipulations on behalf of economic, corporate, and political interests, and so on.  All that the system contains are individuals, banks, and naturally-occurring gold (legal tender, base money), with the individuals and banks free to use fractional-reserve lending to “multiply” the gold into whatever quantity of circulating paper money they wish.  Consistent with the Libertarian ideal, if they screw up, they pay the consequences.  There is no lender of last resort to come in and clean up the mess, only private entities entering into contractual agreements with each other and doing the due diligence necessary to ensure that those agreements work out.

In the modern era, it is inconceivable that any serious legislative body would choose to put an economy on a fractional-reserve free banking system.  Such systems are highly unstable, prone to bank runs and severe liquidity crises, particularly during periods of heightened risk-aversion.  That’s precisely why central banking was invented–because free-banking doesn’t work.

However, it is conveivable that the private sector, working on its own, could one day put the economy on a fractional-reserve free banking system.  The most likely way for it to accomplish this feat would be through the use of a cryptocurrency such as Bitcoin. In what follows, I’m going to explain why fractional-reserve free Bitcoin banking is a necessary condition for Bitcoin to become a dominant form of money, and how the government will easily stop its emergence and proliferation.

Economic expansion in a capitalist system is built on the following process.  Individuals borrow money and invest it.  The borrowing for investment does three things.  First, it adds capital to the economy and increases the economy’s real output capacity.  Second, it expands the operational money supply.  Third, it creates new streams of monetary income.  The new streams of monetary income are used to consume the new streams of real output that the investment has made possible.  The spending of the new income streams by those who receive them creates income for those that made the investments.  That income is used to finance the borrowing, with some left over as profit to justify the investment.  The economy is thus able to “grow”–engage in a larger total value of final transactions at constant-prices–without needing to increase its turnover of money, because it has more money in it, money that was created through the process of borrowing and investing.  The relevant economic aggregates–real output capacity, money supply, income–all grow together, proportionately, in a balanced, virtuous cycle.

Crucially, for Bitcoin to evolve into a dominant form money, it needs to be the dominant form of money in each stage of this process.  If workers are going to get paid in Bitcoins, the investment that creates their jobs will need to be financed in Bitcoins.  If consumers are going to go shopping with Bitcoins, the associated Bitcoin revenues that their shopping creates will need to be distributed as wages and dividends in Bitcoins, or reinvested as Bitcoins.  And so on and so forth.  Trivially, we can’t just pick one part of this process and say “that’s going to be the part that uses Bitcoin.”  If Bitcoin is going to reliably displace conventional money, the whole package will need to use it.

To be clear, it’s possible that Bitcoins could become popular for use as a form of payment intermediation–in the way, that, say, a gift card is used.  You put money on a gift card, give it to someone as a gift, and they spend it.  When they spend it, the merchant that receives it converts it out of literal “plastic” form and back into money, by electronically zeroing it out and taking final claim of the money that was used to buy it.  In a similar way, even though the corporate recipients of spending have no reason to want Bitcoins–they don’t owe debts to bondholders in Bitcoins, salaries to workers in Bitcoins, dividends to shareholders in Bitcoins, or taxes to the government in Bitcoins–it is conceivable that they might still accept Bitcoins, given that there is a market to convert Bitcoins into what they do want: actual money.

But with a gift card, the intermediation is conducted for a clear reason–to eliminate the coldness and impersonality associated with giving cash as a gift, even though cash is always the most economically efficient gift to give.  With respect to Bitcoin, what would be the purpose of the intermediation?  Why, other than for techy shits and giggles (“Hey, look guys, I just bought a pizza with Bitcoins, isn’t that cool!”), or to hide illicit activity, would anyone bother to hassle with it?  Just use conventional money–in this case, dollars.  The fees associated with using dollars are imperceptible, hardly a reason to waste time with an intermediary, especially an intermediary that is extremely volatile and speculative in nature.  And it’s not even clear that those who use Bitcoin for intermediation will manage to escape fees.

When we talk about the proliferation of Bitcoin as a replacement for conventional money, we’re talking about something much bigger than a situation where certain people switch into and out of it for purchasing convenience.  In such an environment, the underlying dollars are still the ultimate monetary “end”–the cryptocurrency acts merely as a way of temporarily “packaging” that end for preferred transport.  Instead, we’re talking about a situation where the Bitcoin becomes the actual money, the medium through which incomes are earned and spent.

Fundamentally, such an outcome requires a mechanism through which Bitcoins can be borrowed.  If Bitcoins can be borrowed, then it will be possible for the virtuous process of borrowing and investing to grow the supply of Bitcoins at a pace commensurate with the demand to use them in commerce, and commensurate with the growth in the supply of everything else that grows in an expanding economy.  But if Bitcoins cannot be borrowed, then their supply will only be able to grow at the pace of computer mining output–a pace that, by design, is very slow (and that has to be slow, in order to prevent the currency from being excessively produced and depreciating in value), and that, unlike conventional money, has no logical or causal connection to the growth that occurs in any other economic aggregate.

If, as output and incomes grow, the supply of Bitcoins is unable to efficiently increase to sustain the increased volume of commerce conducted, then the exchange value of Bitcoin will always be appreciating relative to real things.  The continual appreciation will bring with it extreme bi-directional volatility as individuals come to expect continual appreciation, and attempt to speculate on it in pursuit of an investment return. Consequently, “money illusion”, the conflation of money in the mind of the user with the things that it can buy, will not be able to form.  Without “money illusion”, no one is going to be inclined to measure the commercial world in Bitcoin terms, and therefore nobody is going to be comfortable storing wealth in the currency.

Granted, individuals will be comfortable speculating in Bitcoin, trying to aggresssively grow and expand wealth by investing in it, but not storing wealth in it, which is a different activity entirely.  The result will be a volatile, stressful-to-hold instrument that functions more like an internet stock–say, $FB or $TWTR, except without the earnings prospects–than like cash in the bank or under a mattress, which is how money is supposed to behave.  Internet stocks can certainly rise on reflexive hype, but without the prospect of eventual income (something that Bitcoins don’t offer), they don’t stay risen.

Ironically, the extreme bi-directional price volatility will give Bitcoins the opposite characteristic of gift cards and other temporary stores, which is why they won’t even be survivable as forms of payment intermediation.  Who wants to buy a gift card, or receive payment with a gift card, that randomly increases or decreases in value by huge amounts every minute, every hour, every day?  Again, it’s conceivable that someone might want to purchase such a thing for shits and giggles–as a fun gamble of sorts–but not for serious commercial purposes.

It’s important to recognize that the vast majority of people that are buying Bitcoins are not doing so because Bitcoins removes hardships associated with conventional money. In everyday life, the people that are buying Bitcoins still use their dollar bills, their credit cards, their online bill pay, and everything else, with no real gripe or complaint.  The reason they are buying Bitcoins is to speculate.   They want to get in on a futuristic technology that they think has the potential to massively “disrupt” the financial world, creating wealth for those that invest ahead of the pack.  That is the only thing that’s “in” the current sky-high price–that expectation, held in the minds of a large number of people.  The current price is not evidence that Bitcoin has successfully solved any economic or financial problem that actually needs to be solved–expense, intermediation, value storage, whatever.  Conventional money is working just fine.

Now, to return to free banking, the natural way for Bitcoin to latch onto an expansionary mechanism that would allow it to become a dominant economic currency, and to thereby displace conventional money, would be if a free banking system based on Bitcoins, similar to what existed in the U.S. in the 19th century, were to evolve.  On such a model, banks would “hold” Bitcoins for their customers, and issue electronic deposits redeemable for Bitcoins in exchange.  Because depository Bitcoin inflows would roughly match or exceed depository Bitcoin outflows for the system as a whole, it would be possible for the banks to issue more Bitcoin deposits than exist in actual Bitcoins on reserve.  The excess deposits would then be available for use in lending, which would increase the operational Bitcoin supply in a way that would allow for credit transactions–the lifeblood of economic growth–to shift to Bitcoin in lieu of conventional money, and for price stability and an associated money illusion in the Bitcoin space to emerge.

On such a system, investors and entrepreneurs would be able to take out Bitcoin loans to build homes, buildings, factories, technologies, and so forth.  The workers that build those entities would receive the Bitcoins as new income, and spend them.  The new spending would produce Bitcoin revenues, which would turn into recurring Bitcoin interest payments to the Bitcoin lenders, recurring Bitcoin wages to the workers, recurring Bitcoin dividends for the investors and entrepreneurs, and so on.  At that point, Bitcoin will have “arrived.”

If people were so inclined, one can envision this setup producing a situation where conventional government currencies become obsolete–where no one wants to use them anymore, or has a need to.  If that happens, the Fed’s central planning, and the central planning of other central banks, will have been fully bypassed–defeated once and for all. Central banks will no longer be able to force bailouts, excessive inflation, negative real interest rates, financial repression, and so on down the throats of unwilling market participants.  The system will be a true Libertarian utopia, based on limited government, private enterprise, and personal responsibility.

Fortunately (in my view), and unfortunately (in the view of Bitcoin aficionados), legislators and policymakers can easily prevent this outcome from happening.  All they have to do is put in place a regulation that imposes a 100% reserve requirement on entities that “bank” in Bitcoins, i.e., that hold Bitcoins for customers.  Then, expansion of the Bitcoin supply through lending will be impossible, and the currency will forever remain a constrained, volatile, illiquid, wholely speculative venture, something inappropriate and improperly fitted for serious, non-speculative, non-shits-and-giggles, non-scandalous economic activity.  Those that are seeking to borrow and invest–to take the first steps in the virtuous process of economic and monetary growth–will have no reason to want to mess around with the cryptocurrency.

Which brings us to the “death blow.”  It appears that legislators and policymakers are already a few steps ahead.  The New York State Department of Financial Services, for example, recently issued a set of proposed virtual currency regulations.  Among them:



That line right there, if accepted into regulation, would be enough to conclusively destroy any hope of a Bitcoin monetary takeover.  It effectively sets a 100% reserve requirement for Bitcoin banks, making it imposible for the supply of Bitcoin to expand in the ways that would be necessary for the cryptocurrency to displace conventional money.

The significance of this vulnerability should not be understated or underestimated.  It’s very easy for the government to stop the proliferation of Bitcoin, and ultimately send the cryptocurrency to the graveyard of investment fads.  The government doesn’t have to resort to draconian, unpalatable, freedom-killing measures that would try to stop consenting adults from innocently trading Bitcoins amongst each other. All the government has to do is impose a full-reserve banking requirement on any institution that purports to engage in Bitcoin banking.  Far from wading into controversy, it can impose such a requirement under the seemingly noble and politically palatable auspice of “protecting” Bitcoin users from risky bank behavior, even though the requirement will have the intended side effect of eventually extincting the cryptocurrency, or at least of squashing its hopes for greatness.

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Supply and Demand: Untangling the Market’s Greatest Mystery

hwagnerOver the last ten years, the “collectibles” market has produced a fantastic return for investors.  According to the Knight Frank Luxury Investment Index, classic cars are up 550%, coins and stamps are up 350%, and fine wine and art are up 300%, with coveted items inside these spaces up by even greater amounts.

Why have collectibles performed so well, so much better than income earning assets like stocks and bonds?  Here’s a simple answer.  Over the last ten years, the supply of collectibles–especially those that are special in some way–has stayed constant.  In the same period, the demand for collectibles–driven by the quantity of idle financial superwealth available to chase after them–has exploded. When supply stays constant, and demand explodes, price goes up–sometimes, by crazy amounts.

For collectibles, “supply” is a crucial factor in determining price.  Often, the reason that a collectible becomes a collectible is that an anomaly makes it unusually rare, as was the case with the T206 Honus Wagner baseball card, shown above.  The card was designed and issued by the American Tobacco Company–one of the original 12 members of the Dow–as part of the T206 series for the 1909 season.  But Wagner refused to allow production of the card to proceed.  Some say that he refused because he was a non-smoker and did not want to participate in advertising the bad habit of smoking to children. Others say that he was simply greedy, and wanted to receive more money for the use of his image. Regardless, fewer than 200 issues of the card were manufactured, with even fewer released to the public, in comparison with hundreds of thousands of issuances of other cards in the series.  This anomaly turned an otherwise unremarkable card into a precious collectible that has continued to appreciate in value to this day.  The card most recently traded for $2,800,000, more than 100 times its price 30 years ago, even as baseball and baseball card collecting have waned in popularity.

A Similar Effect in Financial Assets?

Since 2009, the Federal Reserve and foreign central banks have purchased an enormous quantity of long-term U.S. Treasury bonds.  At the same time, the quantity of idle liquidity in the financial system available to chase after these bonds has greatly increased, with central banks issuing new cash for each bond they purchase, and also offering to loan new cash to banks at near zero interest on request.  Might this fact help explain why U.S. Treasuries–and bonds in general–have become so expensive, with yields so unexplainably low relative to the strengthening U.S. growth and inflation outlook? (h/t Anti Petajisto)


Similarly, over the last 30 years, the U.S. corporate sector has been aggressively reducing its outstanding shares, taking them off the market through buybacks and acquisitions. A continually growing supply of money and credit has thus been left to chase after a continually narrowing supply of equity.  Might this fact help explain why stocks have become so expensive relative to the past, so relentlessly inclined to grind higher, no matter the news?


In this piece, I’m not going to try to answer these questions.  Rather, I’m going to present a framework for answering them.  The purpose of the framework will be to help the reader answer them, or at least think about them more clearly.

Supply and Demand: Introducing A Simple Housing Model

We often think about the pricing of financial assets in terms of theoretical constructs–”fair value”, “risk premium”, “discounted cash flow”, “net present value”, and so on.  But the actual pricing of assets in financial markets is driven by forces that are much more basic: the forces of supply and demand.  At a given market price, what amount of an asset–how many shares or units–will people try to buy? What amount of the asset–how many shares or units–will people try to sell?  If we know the answer to these questions, then we know everything there is to know about where the price is headed.

To sharpen this insight, let’s consider a simple, closed housing market consisting of some enormously large number of individuals–say, 10 billion, enough to make the market reliably liquid. Each individual in this market can either live in a home, or in an apartment.  The rules for living in homes and apartments are as follows:

(1) To live in a home, you must own it.

(2) If you own a home, you must live in it.

(3) Only one person can live in a home at a time.

(4) A person can only own one home at a time.

(5) New homes cannot be built, because there is no new land to support building.

(6) Whoever does not live in a home must live in an apartment.

(Note: We introduce these constraints into the model not because they are realistic, but because they make it easier to extend the model to financial assets, which we will do later.)

Now, let’s suppose that the homes are perfectly identical to each other in all respects. Furthermore, let’s suppose that each of the homes has already been purchased, and already has an individual living inside it. Finally, let’s suppose that there is a sufficient supply of apartment space available for the total number of people that are not in homes to live in, and that the rent is stable and cheap.  But the apartments aren’t very nice.  The homes, in contrast, are quite nice–beautiful, spacious, comfortable. Unfortunately, there are only 1 billion homes in existence, enough for 10% of the individuals in the economy to live in.  The other 9 billion individuals in the economy, 90%, will have to accept living in apartments, whether they want to or not.

At any given moment, some number of people in homes that want to collect cash and downgrade into apartments are going to try to sell.  Conversely, some number of people in apartments that want to spend the money to upgrade are going to try to buy.  The way the market executes transactions between those that want to buy and those want to sell is as follows.  At the beginning of every second, a computer, remotely accessible to all members of the economy, displays a price.  Those that want to buy homes at the displayed price send buy orders into the computer.  Those that want to sell homes at the displayed price send sell orders into the computer.  Note that these orders is are orders to transact at the displayed price.  It’s not possible to submit orders to transact at other prices.  At the end of the second, the computer takes the buy orders and sell orders and randomly matches them together, organizing transactions between the parties.


Now, here’s how the price changes.  If the number of buy orders submitted in a given second equals the number of sell orders, or if there are no orders, then the price that the computer will display for transaction in the next second will be the same as in the previous second.  If the number of buy orders submitted in a given second is greater than the number of sell orders, such that not all buy orders get executed, then the computer will increase the price displayed for transaction in the next second by some calculated amount, an amount that will depend on how many more buy orders there were than sell orders.  If the number of buy orders submitted in a given second is less than the number of sell orders, then the same process happens in the opposite direction.


The purpose of this model is to provide a useful approximation of the price dynamics of actual markets.  The key difference between the model and a real market is that the model constrains buyers and sellers such that they can only offer to buy or sell at the displayed price, with the displayed price changing externally based on whether an excess of buyers or sellers emerges.  The reason we insert this constraint is to make the market’s path to equilibrium easy to conceptually follow–the path to equilibrium proceeds in a step by step manner, with the market trying out each price, and moving higher or lower based on which flow is greater at that price: buying flow or selling flow.  But the constraint doesn’t change the eventual outcome.  The price dynamics and the final equilibrium price end up being similar to what they would be in a real market where investors can accelerate the market’s path to equilibrium by freely shifting bids and asks.

Unpacking the Model: The Price Equation

The question we want to ask is, at what price–or general price range–will our housing market eventually settle at?  And if prices are never going to settle in a range, if they are going to continually change by significant, unpredictable amounts, what factors will set the direction and magnitude of the specific changes?

To answer this question, we begin by observing that the displayed price will change until a condition emerges in which the average number of buy orders inserted per unit time at the displayed price equals–or roughly equals–the average number of sell orders inserted per unit time at the displayed price.  Can you see why?  By the rules of the computer, if they are not equal, the price will change, with the magnitude of the change determine by the degree of unequalness.  So,

(1) Buy_Orders(Price) = Sell_Orders(Price)

“Price” is in parentheses here to indicate that the average number of buy orders that arrive in the market per unit time and the average number of sell orders that arrive in the market per unit time are functions of the price.  When the price changes, the average number of buy orders and sell orders changes, reflecting the fact that buyers and sellers are sensitive to the price they pay.  They care about it–a lot.

Now, we can separate Buy_Orders(Price), the average number of buy orders that occurs at a given price in a given period of time, into a supply term and a probability term.

Let Supply_Buyers be the supply term.  This term represents the number of potential buyers, which equals the number of individuals living in apartments–per our assumptions, 9 billion.

Let Probability_Buy(Price) be the probability term.  This term represents the average probability or likelihood that a generic potential buyer–any unspecified individual living in an apartment–will submit a buy order into the market in a given unit of time at the given price.

Combining the supply and probability terms, we get,

(2) Buy_Orders(Price) = Supply_Buyers * Probability_Buy(Price)

What (2) is saying is that the average number of buy orders that occurs per unit time at a given price equals the supply of potential buyers times the probability that a generic potential buyer will submit a buy order per unit time, given the price.  Makes sense?

Now, we can separate Sell_Orders(Price) in the same way, into a supply term and a probability term.  Let Supply_Homes be the supply term–per our assumptions, 1 billion.  Let Probability_Sell(Price) be the probability term, with both terms defined analogously to the above.  Combining the supply and probability terms, we get,

(3) Sell_Orders(Price) = Supply_Homes * Probability_Sell(Price)

(3) is saying the same thing as (2), except for sellers rather than buyers.  Combining (1), (2), and (3), we get a simple and elegant equation for price:

(4) Supply_Buyers * Probability_Buy(Price) = Supply_Sellers * Probability_Sell(Price)

The left side of the equation is the flow of attempted buying.  The right side of the equation is the flow of attempted selling.  The price that brings the two sides of the equation into balance is the equilibrium price, the price that the market will continually move towards. The market may not hit the price exactly, or be able to remain perfectly stable on it, but if the buyers are appropriately price sensitive, it will get very close, hovering and oscillating in a tight range.

The Buy-Sell Probability Function

Now, we know how many potential buyers–how many apartment dwellers–the market has: 9 billion.  We also know how many potential sellers–how many homes and homeowners–the market has: 1 billion.  9 billion is nine times 1 billion.  It would seem, then, that the market will face a permanent imbalance–too many buyers, too few sellers. But we’ve forgotten about the price.  As the price of a home rises, the portion of the 9 billion potential buyers that will be willing to pay to switch to a home will fall.  These individuals do not have infinite pocket books, nor do they have infinite supplies of credit from which to borrow.  Importantly, paying a high price for a home means that they will have to cut back on other expenditures–the degree to which they will have to cut back will rise as the price rises, making them less likely to want to buy at higher prices.

Similarly, as the price rises, the portion of the 1 billion homeowners that will be eager to sell and downsize into apartments will rise.  In selling their homes, they will be able to use the money to purchase other wanted things–the higher the price at which they sell, the more they will be able to purchase.

This dynamic is what the buy-sell probability functions, Probability_Buy(Price) and Probability_Sell(Price), are trying to model.  Crucially, they change with the price, increasing or decreasing to reflect the increasingly or decreasingly attractive proposition that buying and selling becomes as the price changes.  By changing with price, the terms make it possible for the two sides of the equation, the flow of attempted buying and selling, to come into balance.

Now, what do these functions look like, mathematically?  The answer will depend on a myriad of factors, to include the lifestyle preferences, financial circumstances, learned norms, past experiences, and behavioral propensities of the buyers and sellers.  There is some price range in which they will consider buying a home to be worthwhile and economically justifiable–this range will depend not only on their lifestyle preferences and financial circumstances, but also, crucially, on (1) the prices they are anchored to, i.e., that they are used to seeing, i.e., that they’ve been trained to think of as normal, reasonable, versus unfair or abusive, and (2) on what their prevailing levels of confidence, courage, risk appetite, impulsiveness, and so on happen to be.  Buying a home is a big deal.

For buyers, let’s suppose that this price range begins at $0 and ends at $500,000.  At $0, the average probability that a generic potential buyer–any individual living in an apartment–will submit a buy order in a given one year time frame is 100%, meaning that every individual in an apartment will submit one buy order, on average, per year, if that price is being offered (to change the number from per year to per second, just divide by the number of seconds in a year).  As the price rises from $0 to $500,000, the average probability falls to 0%, meaning that no one in the population will submit a buy order at $500,000, ever.

In “y = mx + b” form, we have,

(5) Probability_Buy(Price) = 100% – Price * (100%/$500,000)

The function is graphed below in green:


Notice that the function is negatively-sloping.  It moves downward from left to right.

For sellers, let’s suppose that the price range begins at $1,000,000 and ends at $400,000. At $1,000,000, the average probability that a generic potential seller–any individual living in a home–will submit a sell order in a given one year time frame is 100%.  As the price falls to $400,000, the average probability falls to 0%.

In “y = mx + b” form,

(6) Probability_Sell(Price) = Price * (100%/$600,000) – 66.6667%

The function is shown below in red:


Notice that the function is positively-sloping.  It moves upward from left to right.

Knowing these buy-sell probability functions, and knowing the number of individuals in apartments and the number of individuals in homes (the supplies that the probabilities will be acting on, 9 billion and 1 billion, respectively), we can plug equation (5) and equation (6) into equation (4) to calculate the equilibrium price.  In this case, the price calculates out to roughly $491,525 for a home.  The average probability of buying per individual per unit time will be low enough, and the average probability of selling per individual per unit time high enough, to render the average flow of attempted buying equal to the average flow of attempted selling, as required, even as the supply of potential buyers remains 9 times the supply of potential sellers.

Notably, the turnover, the volume of buying and selling, is going to be very low, because the buy-sell probability functions overlap at very low probabilities.  The buyers and the sellers are having to be stretched right up to the edge of their price limits in order to transact, with the buyers having to pay what they consider to be a very high price to transact, and the sellers having to accept what they consider to be a very low price to transact.

Now, keeping these buy-sell functions the same, let’s massively shrink the supply of potential buyers, to see what happens to the equilibrium price.  Suppose that instead of having 9 billion individuals in the economy living in apartments, suppose that we only have 1 million individuals living in apartments–1 million potential buyers of homes, none of whom are willing to pay more than $500,000.  As before, we’ll assume that there are 1 billion homes that can potentially be sold. What will happen to the price?  The answer: it will fall from roughly $491,525 to roughly $400,119.

Notice that the price won’t fall by very much–it will fall by only roughly $90,000–even though we’re dramatically shrinking the supply of potential buyers, by a factor of 9,000. The reason that the price isn’t going to fall by very much is that the sellers are sticky–they don’t budge.  Per their buy-sell probability functions, they simply aren’t willing to sell properties at prices below $400,000, and so if there aren’t very many people to bid at prices above $400,000, because the supply of buyers has been dramatically shrunk, then the volume will simply fall off.  In the former case, with the supply of potential buyers at 9 billion, 155 million homes get sold, on average, in a one year period.  In the latter case, with the supply of potential buyers at only 1 million, 200,000 homes get sold, on average, in a one year period.

Behavioral Factors: Anchoring and Disposition Effect

Recall that for buyers, the buy-sell probability function slopes negatively–i.e., falls downward–with price.  For sellers, the function slopes positively–i.e., rises upward–with price.  The reason the function slopes negatively for buyers is that price is a cost, a sacrifice, to them.  The lower or higher the price, the higher or lower that cost, that sacrifice.  Additionally, there is a limit to the cost the buyer can pay–he only has so much money, so much access to credit. The reason the function slopes positively for sellers is that price is a benefit, a gain, to them.  The lower or higher the price, the lower or higher that benefit, that gain.  Additionally, there is a limit to the price that the seller can accept without pain, particularly if he has debts to pay against the assets that he is trying to sell.

In addition to these fundamental considerations, there are also behavioral forces that make the functions negatively-sloping and positively-sloping for buyers and sellers respectively.  Of these forces, the two most important are anchoring and disposition effect.

Over time, buyers and sellers become anchored to the price ranges that they are used to seeing.  As the price move out of these ranges, they become more averse, more likely to interpret the price as an unusually good deal that should be immediately taken advantage of or as an unfair rip-off that should be refused and avoided.

Anchoring is often seen as something bad, a “mental error” of sorts, but it is actually a crucially important feature of human psychology.  Without it, price stability in markets would be virtually impossible.  Imagine if every individual entering a market had to use “theory” to determine what an “appropriate” price for a good or service was.  Every individual would then end up with a totally different conception of “appropriateness”, a conception that would shift wildly with each new tenuous calculation.  Prices would end up all over the place.  Worse yet, individuals would not be able to quickly and efficiently transact.  Enormous time resources would have to be spent in each individual transaction, enough time to do all the necessary calculations.  This time would be spent for nothing, completely wasted, as the calculation results would not be stable or repeatable.  From an evolutionary perspective, the organism would be placed at a significant disadvantage.

In practice, individuals need a quick, efficient, consistent heuristic to determine what is an “appropriate” price and what is not.  Anchoring provides that heuristic.  Individuals naturally consider the price ranges that they are accustomed to seeing and transacting at as “appropriate,” and they instinctively measure attractiveness and unattractiveness against those ranges.  When prices depart from the ranges, they feel the change and alter their behaviors accordingly–either to exploit bargains or to avoid rip-offs.

Disposition effect is also important to price stability.  Individuals tend to resist selling for prices that are less than the prices for which they bought, and tend to be averse to paying higher prices than the prices could have paid in the recent past.  This tendency causes price to be sticky, discinlined to move away from where they have been, as we should want them to be if we want markets to hold together, and not become chaotic.

Housing markets represent an instance where these two phenomena–anchoring and disposition effect–are particularly powerful, especially for sellers.  The phenomena is part of what makes housing such a stable asset class relative to other asset classes.


Homeowners absolutely do not like to sell their homes for prices that are lower than the prices that they paid, or that are lower than the prices that they are accustomed to thinking their homes are worth.  If a situation emerges in which buyers are unwilling to buy at the prices that homeowners paid, or the prices that homeowners are anchored to, the homeowners will try to find a way to avoid selling.  They will choose to stay in the home, even if they would prefer to move elsewhere.  If they need to move–for example, to take a new job–they will simply rent the home out; anything to avoid selling the home, taking a loss, and giving an unfair bargain to someone else.  Consequently, market conditions in which housing supply greatly exceeds housing demand tend to clear not through a fall in price, but through a drying up of volume, as we saw in the example above.

This effect was on fully display in the last recession.  Existing home sales topped out in 2005, but prices didn’t actually start falling in earnest until the recession hit in late 2007 and early 2008.  Prior to the recession, the homes were held tightly in the hands of homeowners.  As long as they could afford to stay in their homes, they weren’t going to sell at a loss.  But when the recession hit, they started losing their jobs, and therefore their ability to make their mortgage payments.  The result was a spike in foreclosures that put the homes into the hands of banks, mechanistic sellers that were not anchored to a price range and that were not averse to selling at prices that would have represented losses for the prior owners.  The homes were thus dumped onto the market at bargain values to whoever was willing to buy them.


When Is Supply Important to Price? 

Returning to the previous example, what would be the market outcome if buyers and sellers were completely insensitive to price, such that their buy-sell probability functions did not slope with price?  Put differently, what would be the market outcome if the average probability that a potential buyer or seller would buy or sell in a given unit of time–a given year–stayed constant under all scenarios–always equal to, say, 10%, regardless of the price?

The answer is that supply imbalances would cause enormous fluctuations in price.  Theoretically, any excess in the number of potential buyers over the number of potential sellers would permanently push the price upward, all the way to infinity, and any excess in the number of potential sellers relative to the number of potential buyers would permanently pull the price downward, all the way to zero.

In concrete terms, if there are 1,001 eager buyers that submit buy orders per unit time, and 1,000 eager sellers that submit sell orders, and if the buyers are completely indifferent to price, then there will always be one buyer left out of the mix.  Because that buyer is indifferent to price, he will not hesitate to raise his bid, so as to ensure that he isn’t left out of a transaction.  But whoever he displaces in the bidding will also be indifferent to price, and therefore will not hesitate to do the same, raise the bid again–and so on.  Participants will continue to raise their bids ad infinitum, continually fighting to avoid being the unlucky person that gets left out.

The only way for the process to end is for 1 of the buyers in the group to conclude, “OK, enough, the price is just too high, I’m not interested.”  That is price sensitivity.  Without it, a stable equilibrium amid a disparate supply of potential buyers and sellers cannot be achieved.

We now have the ability to answer an important question at the heart of this piece: when is “supply” most important to price, most impactful?  The answer is, when price sensitivity is low.  If the probability of buying doesn’t fall quickly in response to an increase in price, and if the probability of selling doesn’t fall quickly in response to a decrease in price, then even a small change in the supply of potential buyers or sellers will be able to create a large change in the price outcome.  In contrast, if the price sensitivity is high, if the probability of buying falls quickly in response to price increases, and the probability of selling falls quickly in response to price reductions, then the price will be able to remain steady, even in the presence of large supply excursions.  Intuitively, the reason the price will be able to remain steady is that the potential buyers and sellers will be holding their grounds–they won’t be budging off of their desired price ranges simply to make transactions happen.

Low price sensitivity is part of the reason why small speculative stocks with ambiguous but potentially exciting futures–low-float stocks with large potentials that are difficult to confidently value and that exhibit significant price reflexivity–tend to be highly volatile.  If there is a net excess or shortage of eager buyers in these stocks relative to eager sellers, the price will end up changing.  But the change will not correct the excess or shortage. Therefore the change will not stop.  It will keep going, and going, and going, and going.

To use a relevant recent example, if there is a shortage in the supply of $LOCO shares being offered in an IPO relative to the amount of $LOCO that investors want to allocate into, then the price is going to increase.  For the market in $LOCO to remain stable, this price increase will need to depress the demand, reduce the amount of $LOCO that investors want to allocate into.  If the price increase fails to depress the demand, or worse, if it does the opposite, if it increasess the demand–for example, by drawing additional attention to the name and increasing investor optimism about the company, given the rising price–then the price is going to get pushed higher and higher and higher.

At some point, something will have to reverse the process, as the price can’t go to infinity. In the case of $LOCO, more and more people might start to ask themselves, have things gone to far?  Is this stock a bubble that is about to burst?  An excess of sellers over buyers will then emerge, and the same process will unfold in the other direction.  When the price falls, the fall will not sufficiently clear the excess demand to sell, and may even increase it, by fueling anxiety, skepticism and fear on the part of the remaining holders.  And so the price will keep falling, and falling, and falling.

Now, if we shift from $LOCO IPO to a market where price sensitivity is strong, this dynamic doesn’t take hold.  To illustrate, suppose that the treasury were to issue a massive, gargantuan quantity of three month t-bills.  The same instability would not emerge.  The reason is that there is a strong inverse relationship between the price of three month t-bills and the demand to own them, a relationship held in place by the possibility of direct arbitrage in the banking system.  Recall that a three month t-bill offers a return that is fully-determined and free of credit risk.  It also carries no interest rate risk beyond a period of three months (the money will have been returned by then).  Thus, as long as the Fed holds overnight interest rates steady over the next three months, as the current Fed has effectively promised to do, banks will be able to borrow funds and purchase three month t-bills, capturing any excess return above the overnight rate that the bills happens to be offering, without taking on any risk.  And so any fall in the price of a three month treasury bill, and any rise in the yield, will represent free money to banks.  That free money will attract massive buying interest, more than enough to quench whatever increased selling flow might arise out of a large increase in the outstanding supply. Ultimately, when it comes to short-term treasuries, supply doesn’t matter much to price.

Extending the Model to Financial Assets: Equity and Credit

To extend the housing model to financial assets, we begin by noting that units of financial “wealth”–that is, units of the market value of portfolios, in this case measured in dollars–are analogous to “individuals” in the housing model.  Just as individuals could either live in homes or apartments–and had to choose one or the other–units of financial “wealth” can either be held in the form of equity (stocks), credit (bonds), or money (cash).  Just as every home had to have an owner and every apartment a tenant living inside it, every outstanding unit of equity, credit, and money in existence has to have a holder, has to be a part of someone’s portfolio, with a portion of the wealth contained in that portfolio stored inside it.

Now, to make the model fully analogous, we need to reduce the degrees of freedom from three (stocks, bonds, cash) to two (stocks, cash). So we’re going to treat bonds and cash as the same thing, referring to both simply as “cash.”  Then, investors will have to choose to hold financial “wealth” either in the form of “stocks”, or in the form of “cash”, just as “individuals” had to choose to live either in “homes”, or in “apartments.”

Let’s assume, then, that our stock market consists of some amount of cash–some number of individual dollars–and some amount of stock, some number of shares with a total dollar value determined by the price.  Let’s also assume that the same computer is there to take buy and sell orders–orders to exchange cash for stock or stock for cash respectively. The computer processes orders and moves the price towards equilibrium in the same way as before, by displaying a price–an exchange rate between stock and cash–then taking orders, then raising or lowering the price in the next moment based on where the excess lies.

The derivation of the price equation ends up being the same as in the housing model, and gives the following result.

(7) Supply_Cash * Probability_Buy(Price) = Supply_Stock(Price) * Probability_Sell(Price)

Here, Supply_Cash is the total dollar amount of cash in the system. Probability_Buy(Price) is the average probability, per dollar unit of cash in the system, per unit of time, that the unit of cash will be sent into the market to be exchanged for stock at the given price.  Supply_Stock is the the total market value of stock in existence. Probability_Sell(Price) is the average probability, per dollar unit of value of stock in the system, that the unit will be sent into the market to be exchanged for cash at the given price.

Now, where this model differs from the previous model is that Supply_Stock, the total market value of stock in existence, which is the total amount of stock available for investors to allocate their wealth into, is a function of Price.  It equals the number of number of shares times the price per share.

(8) Supply_Stock(Price) = Number_Shares * Price

Unlike in the housing model, the supply of stock in the stock market expands or contracts as the price rises and falls.  This ability to expand and contract helps to quell excesses that emerge in the amount of buying and selling that is attempted.  If investors, in aggregate, want to allocate a larger portion of their wealth into stocks than is available in the current supply, the price of stocks will obviously rise.  But the rising price will cause the supply of stocks–the shares times the price–to also rise, helping, at least in a small way, to relieve the pressure.  The same is true in the other direction.

Combing (7) and (8), we end up with a final form for the equation,

(9) Supply_Cash * Probability_Buy(Price) = Number_Shares * Price * Probability_Sell(Price)

Note that we’re using this equation to model stock prices, but we could just as easily use the equation to model the price of any asset, provided that simplifying assumptions are made.

A more accurate form of the equation would include a set of terms to model the possibility of margin buying and short selling.  These terms are shown in green,

(10) Supply_Cash * Probability_Buy(Price) + Supply_Borrowable_Cash * Probability_Borrow_To_Buy(Price)Number_Shares * Price * Probability_Sell(Price) + Number_Borrowable_Shares * Price * Probability_Borrow_To_Sell(Price)

But the introduction of these terms makes the equation unnecessarily complicated.  The extra terms are not needed to illustrate the underlying concepts, which is all that we’re trying to do.

A Growing Cash Supply Chases A Narrowing Stock Supply: What Happens?

It is commonly believed that the stock market–the aggregate universe of common stocks–rises over time because earnings rise over time.  Investors are sensitive to value. They estimate the future earnings of stocks, and decide on a fair multiple to pay for those earnings. When the stock market is priced below that multiple, they buy.  When the stock market is priced above that multiple, they sell.  In this way, they keep the price of the stock market in a range–a range that rises with earnings over time.

In a set of pieces from last year (#1, #2), I proposed a competing explanation.  On this explanation, the stock market rises over time because we operate in an inflationary financial system, a system in which the quantity of money and credit are always growing. Given its aversion to dilution, the corporate sector does not issue enough new shares to keep up with this growth.  Consequently, a rising quantity of money and credit is left to chase after a limited quantity of shares, pushing the prices of shares up through a supply effect.  Conveniently, as prices rise, the supply of stock rises, bringing the supply back into par with the supply of money and credit.

The truth, of course, is that both of these factors play a role in driving the stock market higher.  Which factor dominates depends on the degree of price sensitivity–or, in this case, the degree of value sensitivity–of the buyers and sellers.  In a world where buyers and sellers are highly sensitive to the price-earnings ratio, the supply effect will not exert a signficant effect on prices. Prices will track with earnings and earnings alone.  In a world where buyers and sellers are not highly sensitive to the price-earnings ratio, or to other price-based measurements of value, the supply effect will become more significant and more powerful.

We can illustrate this phenomenon by running the model computationally, with random offsets and deviations inserted to help simulate what happens in a real market.  Assume, that there are 1,000,000 shares of stock in the market, and $2B dollars of cash.  Assume, further, that each share of stock earns $100 per year in profit.  Finally, assume that the buy-sell probability functions for buyers and sellers are symmetric cumulative distribution functions (CDF) of Gaussian distributions with very small standard deviations.  These functions take not only price as input, but also earnings.  They compute the PE ratio at a given price and output a probability of buying or selling based on it.

The functions look like this:


We’ve centered the functions around a PE ratio of 15, which we’ll assume is the “normal” PE, the PE that market participants are trained and accustomed to view as “fair.”  Per the above construction of the function, at a PE 15, there is a 50% chance per day that a given dollar in the system will be submitted to the market by a buyer to purchase stock, and a 50% chance per day that a given dollar’s worth of stock in the system will be submitted to the market by a seller to purchase cash (what selling is, inversely).  As the PE rises above 15, the buying probability falls sharply, and the selling probability rises sharpy.  As the PE falls below 15, the buying probability rises sharply, and the selling probability falls sharply. Evidently, the buyers and sellers are extremely price and valuation sensitive.  15 plus or minus a point or two is the range of PE they are willing to tolerate; whenever that range is breached in the unattractive direction, they quickly step away.

Now, if we wanted to make the function more accurate and realistic, we would make it a function not only of price and earnings, but also of interest rates, demographics, growth outlook, culture, past experience, and so on–all of the “variables” that conceivably influence the valuations at which valuation-sensitive buyers and sellers are likely to buy and sell.  We’re ignoring these factors to keep the problem simple.

In the first instance, let’s assume that the supply of cash stays constant and the earnings stay constant.  Starting with a price of 2,000 for the index, holding the number of shares constant, and iterating through to an equilibrium, we get a chart that shows the trajectory of price over time, from now, the year 2014, to the year 2028.


The result is as expected.  If the buyers are highly value sensitive, and if the earnings aren’t growing, then the price should settle tightly on the price range that corresponds to a “normal” PE ratio–in this case, a range around 1500, 15 times earnings, which is what we see.

Now, let’s run the simulation on the assumption that the supply of cash stays constant and the earnings grow at 10% per year.


The result is again as expected.  The index price, the blue line, initially falls from 2000 to 1500 to get from a PE ratio of 20 to the normal PE ratio of 15.  It then proceeds to grow by 10% per year, commensurately with the earnings.  The cash supply stays constant, but this doesn’t appreciably hold back the price growth, because the buyers are value sensitive. They are going to push the price up to ensure that the PE ratio stays around 15, no matter the supply.

If you look closely, you will notice that the green line, the PE ratio, drifts slightly below 15 as time passes.  This drift is driven by the stunted supply effect.  The quantity of cash is not growing, which holds back the price growth by a miniscule amount relative to what it would be on the assumption of a perfectly constant 15 PE ratio.  The supply effect in the scenario is tiny, but it’s not exactly zero.

Now, let’s run the simulation on the assumption that the supply of cash rises at 10%, but the earnings stay constant.


The result is again as expected.  The index price stays constant, on par with the earnings, which are not growing.  The cash supply explodes, but this doesn’t exert an appreciable effect on the price, because the buyers are extremely value sensitive.

If you again look closely, you will notice that the green line, the PE ratio, drifts slightly above 15 as time passes.  This drift is again driven by the stunted supply effect.  The quantity of cash is growing rapidly, and this pushes up the price growth by a miniscule amount relative to what it would be on the assumption of a perfectly constant 15 PE ratio.

Now, let’s introduce a buy-sell probability function that is minimally sensitive to valuation, and see how the system responds to supply changes.  Instead of using CDFs of Gaussian distributions with very small standard deviations, we will now use CDFs of Gaussian distributions with very large standard deviations.  In the actual simulations, we will also insert larger random deviations and offsets to help further model the price insensitivity.


Evidently, under these new functions, the buying and selling probabilities remain essentially stuck around 50%, regardless of the PE ratio.  The functions are only minimally negatively-sloping and positively-sloping.  What this means qualitatively is that buyers and sellers don’t care much about the PE ratio, or any other factor related to price.  Price is not a critical consideration in their investment decision-making process.  They will accept whatever price they can get in order to take on or avoid the desired or unwanted exposure.

Now, let’s run the simulation on the assumption that the cash supply grows at 10%, while the earnings stay constant.


Here, the outcome changes significantly.  The index price, shown in blue, separates from the earnings, and instead tracks with the growing cash supply, shown in red.  Instead of holding at 15, the PE ratio, shown in green, steadily expands, from 20 in 2014 to roughly 65 in 2028.  All of the market’s “growth” ends up being the result of multiple expansion driven by the growth in the cash supply–growth in the amount of cash “chasing” the limited amount of shares.  Now, there is still some valuation sensitivity, which is why the index price fails to fully keep up with the rising cash supply.  The valuation sensitivity acts as a slight headwind.

Now, let’s run the simulation on the assumption that the earnings grow at 10%, but the cash supply shrinks by 10%.


Once again, the price tracks with the contracting supply of cash, not with the growing earnings.  Consequently, the PE ratio falls dramatically–from 20 down to 1.25.

Supply Manipulations in a Live Experiment

Everything that we’ve presented so far is theoretical.  We don’t have a buy-sell probability function for real buyers and sellers that we could use to determine the prices that their behaviors will produce in a market with a growing supply of cash and fluctuating earnings. Even if we could come up with such a function, it would not be useful for making actual price predictions, as it would contain far too many fuzzy and hard-to-measure variables, and would always be changing in unpredictable ways.

At the same time, the modeling that we’re doing here is useful in that it allows us to think more clearly about the way that supply factors interact with buying and selling probability factors to determine price.  When confronted with questions about the impact of supply factors in specific market circumstances, the best approach to evaluating these questions is to explore the kinds of buying and selling probabilities that those circumstances will lend themselves to–that is, the kind of buy-sell probability functions the circumstances will tend to produce.

If the circumstances will tend to produce significant price and value sensitivity–that is, sharply negatively-sloping buying probabilities and sharply positively-sloping selling probabilities, as a function of price–then supply will not turn out to be a very important or powerful factor in determining price.  As supply differences lead to price changes, the number of people that want to buy and sell at the given price will quickly adjust, arresting the price changes and stabilizing the price.

But if the circumstances will tend to lend themselves to price and valuation insensitivity–that is, flatly-sloping buying and selling probabilities, or worse, reflexive buying and selling probabilities, buying probabilities that rise with rising prices, and selling probabilities that rise with falling prices–then supply as a factor will prove to be very important and very powerful.  As supply differences emerge and cause price changes, the number of people that want to buy and sell at the given price will not adjust as needed, causing the price to continue to move, the momentum to continue to carry.

With this in mind, let’s qualitatively examine a famous genre of experiments that economists have performed to test the impact of supply on price.  In these experiments, a large closed group of market participants are endowed with a portfolio of cash or stock, and are then left to trade the cash and stock with each other.


The shares of stock pay out a set quantity of dividends on a scheduled periodicity throughout the scenario, or at the end, and then they expire worthless.  Each dividend payment equals some constant value, plus a small offset that is randomly computed in each payment period.

At any time, it’s easy to calculate what the intrinsic value of a share is.  It’s the sum of the expected future dividend payments up to maturity, which is just the number of dividend payments that are still left to be paid, times the value of each payment.  The offset to the payments is random, it acts in both directions, therefore it effectively drops out of the analysis.  Granted, the offsets insert an “uncertainty” into the value of the shares, the undesirability of which investors might choose to discount.  But the uncertainty is small, and the participants aren’t that sophisticated.

Before the experiment begins, the experimenters teach the participants how to calculate the intrinsic value of a share.  The experimenters then open the market, and allow the participants to trade the assets with each other (through a computer).  Crucially, whatever amount of money the participants end up with at the end of the experiment, they get to keep.  So there is a financial incentive to trade and invest intelligently, not be stupid.

The experiment has been run over and over again by independent experimenters, incorporating a number of different individual “tweaks.”  It’s been run on large groups, small groups, financially-trained individuals, non-financially-trained individuals, over short time periods, long time periods, with margin-buying, without margin-buying, with short-selling, without short-selling, and so on.

The experiments consistently produce results that defy fundamentals, results in which prices deviate sharply from fair value, when in theory they shouldn’t.  Shown below is a particularly egregious example of the deviation, taken from an experiment run on 304 economic students at Indiana University consisting of a 15 round trading period that lasted 8 weeks:


As you can see, the price deviates sharply from intrinsic value.  In the early phases, the buyers lack courage to step up and buy, so the price opens below fair value.  As the price rises, the buyers gain confidence, and more and more try to jump on board.  This process doesn’t stop when the limits of fair value are reached; it keeps going.  Buyers throw caution to the wind, and push the market into a bubble.  The bubble then bursts.  As the maturity nears, the price gravitates back towards intrinsic value.

If we think about the experiment, it’s understandable that this outcome would occur, at least in certain circumstances. “As long as the music is playing, you have to get up and dance.” Right?  Valuation is important only to the extent that it impacts price on the time horizons that investors are focused on.  In the beginning of the experiment, the investors are not thinking about what will happen at the end of the experiment, which is many months away.  They are thinking about what price they will be able to sell the security for in the near term.  They want to make money in the near-term, do what the other successful people in the game seem to be doing.  As they watch the price travel upward, above fair value, they start to doubt whether valuation is something that they should be focusing on. They conclude that valuation doesn’t “work”, that it’s a red herring, that focusing on it isn’t the way you’re supposed to play the game.  So they set it aside, and focus on trying to profit from the continued momentum instead.  In this way, they contribute to the growing excesses, and help create the eventual bubble.

As the security gets closer to its maturity, more and more participants start worrying about valuation.  It can’t be ignored forever, after all, for the bill’s eventually going to come due. And so as the experiment draws to a close, the price falls back to fair value.

Now, the question that we want to ask is, if we change the aggregate supply of cash in this experiment relative to the supply of shares, what will happen?  Of course, we already know the answer.  The valuation excesses will grow, multiply, inflate.  The buyers, after all, have demonstrated that they are not value sensitive–if they were, they wouldn’t let the price leave the fair value range.  As the price rises in response to the supply imbalances, the buyers aren’t going to pull back, and the sellers aren’t going to come forward–therefore, the imbalances aren’t going get relieved.  The price will keep rising until something happens to shift the psychology.

Interestingly, one practical finding from the experiment is that the most effective way to arrest the excess is to reduce the supply of cash relative to the supply of shares. When you reduce the supply of cash, the bubbles have a much more difficult time forming and gaining traction.  Sometimes, they don’t form at all.  Central Banks of the world, take note!

Now, some have objected to the results of the experiments, arguing that the participants often don’t understand how the maturity process works–that they often don’t recognize, until late in the game, that the security is going to expire worthless.  Put differently, the participants wrongly envision the dividends as investment returns on a perpetual security, rather than as returns of capital on a decaying security.  For our purposes, this potential flaw in the experiment doesn’t really matter, for even if the value of the security is misunderstood, that alone shouldn’t cause supply changes to appreciably impact prices. Supply should only appreciably impact prices if investors are not paying attention to value. Evidently, they aren’t.

A potentially more robust version of the experiment is one where there are no interim dividends, but only a single final payment, a single return of capital, paid to whoever owns the shares at the end.  In this version of the experiment, it’s painfully obvious what the security is worth, there is no room for confusion.  The security is worth the expected value of the final payment.

Professor Gunduz Caginalp of the University of Pittsburgh ran the experiment under this configuration, allowing groups of participants to trade cash and shares that pay an expected value of $3.60 at maturity (the actual value has a 25% chance of being $2.60, a 25% chance of being $4.60, and a 50% of being $3.60).  In one version, he kept the supply of cash roughly equal to the supply of shares, in another version, he roughly doubled the supply of cash.  He then ran each version of the experiment multiple times on different groups of participants to see whether the different versions of the experiment produced different prices.  The following chart shows the average price evolution for each version:


As you can see, the version in which the supply of cash is twice the supply of shares (blue line) produces prices that are persistently higher than the version in which the supply of cash equals the supply of shares.  This is especially true in the early trading rounds of the experiment–as the experiment draws to an end, valuation sensitivity increases, and the average prices of the two versions converge.

Interestingly, in the later rounds, the market in the high cash scenario seems to have an easier time moving the price to fair value than in the low cash scenario.  In the low cash scenario, a meaningful discount to fair value remains right up until the last few rounds, a discount that defies fundamental justification (why should the price be roughly $2.75 in round 12 when there is a 75% change of the price being substantially higher, and essentially a 0% chance of the price being lower, at maturity?).  This peculiarity illustrates the previous point that even when valuation is the dominant consideration for market participants, even when the market in aggregate is trying to move the price to fair value, supply still matters–it can nudge the market in the right or wrong direction.

It turns out that the only consistently reliable way to prevent an outcome in which individuals push prices in the experiment out of the range of fair value is to run the experiment on the same subjects multiple times–then, the investors learn their lessons. They start paying attention to valuation.

Evidently, the perceived connection between valuation and investment returns–the connection that leads investors to care about value, and to use it in their investment processes–is learned through experience, at least partially.  To reliably respect valuation, investors often need to go through the experience of not respecting it, buying too high, and then getting burned.  They need to lose money.  Then, valuation will become important, something to worry about.  Either that, or investors need to go through the experience of buying at attractive prices and doing well, making money, being rewarded.  In response to the supportive feedback, investors will grow hungry for more value, more rewards.

As with all rules that investors end up following, when it comes to the rule “though shalt respect value”, the reinforcement of punishment and reward, in actual lived or observed experience, cements the rule in the mind, and conditions investors to obey it.

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