The Fed Model of Stock Market Investing

In the last post, we examined how liquidity–the ability to trade an asset, rather than hold it to maturity–radically changes the dynamics of investment.  When there is no liquidity, the return of an investment can only come from one place: the underlying cash flow.  That cash flow is all that matters.  There is no rising market price to use as confirmation of a successful investment, “Great job buying that dip. You nailed it!”, just as there is no falling market price to fear and fret over, “Geez, how low do you think it will go?”  There is just the investment.  The investor has already psychologically parted with his money, said his goodbyes, and is now patiently collecting the income that the investment is producing and delivering, with a focus on the very long-term.

When liquidity is introduced, the dynamics change completely.  The investor no longer approaches the investment as a genuine parting with his money–a long-term goodbye.  He views his money as still there, at a fingertip’s reach, contained within the market price.  For this reason, he takes the market price extremely seriously.  When he buys a stock that plunges in price, he conceptualizes the plunge as a real loss–and feels real regret and frustration.  When he buys a stock that rises in market price, he conceptualizes the rise as a a real profit–and rejoices internally.  In addition to serving as the arbiter of his performance, the market price impacts his anchoring, his assessment of the fundamentals, and his future expectations–these in turn affect the prices that he is willing to pay, which in turn affect future market prices.  The process is recursive and reflexive–with a tendency to exhibit momentum and to generate price equilibria in highly path-dependent manners.

The Performance of the Fed Model

A number of investment approaches wrongly attempt to evaluate liquid investments in the stock market in the same way that an illiquid investment in real business would be evaluated–based strictly on the underlying cash flow.  A classic example is the popular “Fed Model”, coined by analyst Ed Yardeni, and recently touted by Hedge Fund Manager David Tepper and researchers from the New York Fed.  For those that aren’t familiar, the “Fed Model” argues that the attractiveness of the stock market as an investment should be measured by comparing its earnings yield (trailing twelve month earnings divided by price) to the yield on long-term bonds.  On this model, the stock market at 20 times earnings (5% earnings yield) is “expensive” if the 10 year treasury bond is yielding 6%, and “cheap” if the 10 year treasury bond is yielding 1.5%.

What do the terms “cheap” and “expensive” mean, precisely?  Granted, if we define the terms to mean “has a higher yield than long-term bonds” and “has a lower yield than long-term bonds” respectively, then, tautologically, the Fed Model is the arbiter of cheapness and expensiveness.  But if that is all that “cheap” and “expensive” mean, then there is no immediate reason to care about whether the stock market is cheap or expensive.  The terms “cheap” and “expensive” are only worth caring about if they can be linked to future returns, on some time scale.  What we need, then, is a market-based definition.  Is the stock market, given its current price, likely to produce high future returns, or low future returns?  If high future returns, then it is cheap. If low future returns, then it is expensive. With the terms appropriately defined in this way, the Fed Model ceases to be the arbiter of anything.

With respect to future returns, the Fed Model does not appear to have any independent predictive power.  The following chart plots future 2 year annualized total returns (y-axis) versus the “equity risk premium” or ERP (the difference between the market’s earnings yield and the 10 year treasury yield, x-axis) from April 1933, the month that FDR ended the gold standard, to present:


The coefficient of determination is roughly 0.  You could splatter paint on a page and get the same chart.  There are a number of instances where low future equity returns followed high ERPs, and a number of instances where high future equity returns followed low (or negative) ERPs.  Let’s extend the horizon out to 10 years.  


The coefficient of determination increases to 0.10.  Still not attractive.  Granted, when the ERP approaches double-digit extremes (and it is nowhere near such extremes right now), it seems to correctly signal that high future equity returns are coming.  But at those extremes, the earnings yield itself (inverse of the P/E ratio) produces the same signal, without any reference at all to the bond yield.  Here is the simple earnings yield versus subsequent 10 year returns back to April 1933:


The coefficient of determination increases to 0.48, far more attractive.  Demonstrably, then, all that the comparison to bond yields is doing is taking an otherwise meaningful signal–the earnings yield–and distorting it, screwing it up.  The comparison is making markets that were generationally cheap–for example, the market of the early 1980s–look historically expensive (indeed, as expensive as the market of the late 1990s), and markets that were expensive–for example, the market of late 1936 and early 1937–look cheap.  

It makes perfect intuitive sense that the bond yield would represent a distraction in the analysis of long-term future equity returns.  To the extent that long-term future equity returns are driven strictly by the underlying cash flows of the equities themselves, in the approximation of an illiquid investment, we should expect the equities themselves–the cash flows that they produce–to be the drivers of the return, regardless of how those cash flows stack up to the cash flows produced by other investments: bonds, real estate, collectibles, whatever.

The fundamental problem with the Fed Model is this.  It is simply incorrect to assess the cheapness or expensiveness of one asset class by blindly comparing it to another.  Such an approach dismisses the very real possibility that both asset classes are cheap or expensive at the same time–that they will both produce strong or weak future returns.  History clearly demonstrates that such an outcome is possible.  In the spring of 1937, stocks and bonds were both expensive, they both produced unattractive future returns.  In the summer of 1982, stocks and bonds were both cheap, they both produced excellent future returns.

A Charitable Interpretation

But maybe the Fed Model isn’t saying that stocks should be considered cheap or expensive based on how their yields compare with bond yields.  Maybe the model is simply telling us which asset class offers a higher return, and therefore which asset class an investor seeking to maximize return should choose, if she is forced to choose.  In 1937, an investor should choose stocks.  In 1982, an investor should choose bonds.  

But if this is the model’s contribution, then it isn’t of much value.  With the exception of the ends of recessions and bubbles, stock earnings yields are almost always higher than bond yields.  You don’t want a model that will have you out of the market at the end of recessions–those are the most attractive times to invest.  And though the Fed Model can spot bubbles, so can a plain vanilla P/E approach–where the bond yield is thrown out of the calculation.  What value, then, does the model add?   

Surprisingly enough, if an investor reliving the 1933-present period demands any kind of premium at all between earning yields and bond yields as a condition for investing in equities, he will underperform “buy and hold” on an absolute basis.  The following chart illustrates the total return performance of various Fed Model approaches back to April 1933.  Each line shows a Fed Model that uses a different cutoff risk premium (where you own the stock market if the difference between its earnings yield and the 10 year bond exceeds that premium, and you own 10 year treasury bonds otherwise).  The decision whether to switch is made at the end of each month.  To simplify the calculations, and also to capture the full upside of the 1981-present bond bull market, it is assumed that when 10 year bonds are owned, they are rolled over each month into new issues at no tax or transaction cost, with the capital gain or loss pocketed:


To make the points of relative performance more clear, let me introduce a different type of chart.  This chart plots the ratio of the performance of each strategy (numerator) to the performance of buy and hold (denominator), over time.  When a line is rising, the associated strategy is accumulating outperformance relative to buy and hold.  When a line is falling, the associated strategy is accumulating underperformance relative to buy and hold.  When a line is straight, the associated strategy is tracking buy and hold (usually because it is invested in stocks):


All premia except a 0% premium generate a lower return than buy and hold.  The 0% premium generates a higher return by about 17% (total, not annualized).  This excess return is good, but in the real world, would not be enough to make up for transaction costs, switching (slippage) frictions, and tax hits, which we have not modeled.  The strategy spends essentially all of the time before the early 1970s invested in stocks, and then proceeds into bonds at various points during the 1970s inflation, where it generates the bulk of its excess return.  The strategy avoids the downside of the tech bubble, but there is no net gain, because it also avoids the upside.

Note that during the 1970s, cash invested at the Fed Funds rate outperformed both stocks and bonds.  From Jan 1972 to Jan 1982, $1 in cash became $2.44, versus $2.31 for the Fed Model, $1.64 for Buy and Hold, and $1.28 for the rolled-over 10 year.  Surprisingly, then, the only period in which the Fed Model reliably outperforms the return of Buy and Hold is a period in which cash is king–certainly not the kind of period that most analysts have in mind when they tout the model.

The Fed Model’s Mistake

The Fed Model makes an appeal for a certain a type of investment consistency.  If investors are willing to pay a lot for the cash flow that one type of asset–e.g., the aggregate bond market–offers, they should be willing to pay a lot for the cash flow that another type of asset–e.g., the aggregate stock market–offers.

As discussed in the previous post, if we lived in a world without liquidity or trading, where all investments had to be true investments, held to maturity, with all returns generated directly from the underlying cash flows–the earnings, coupons, and interest payments, rather than the appreciation of price–then this appeal might make sense.  If you are willing to pay 33 times earnings for a 30 year treasury bond, why wouldn’t you also be willing to pay 33 times earnings for a well-diversified index of blue-chip stocks?  With the stocks, you would accrue the same initial yield, plus decades of eventual growth in yield.  The only real uncertainty, over the 30 year period, would be the upside: how much would the earnings grow?  Over 30 years, probably a lot.  Maybe we would have a recession in a few years, and the earnings would fall by 20%.  Big deal.  Even if we assume no earnings growth between now and then, the yield would fall from 3% to 2.4%, before coming back to 3%.  The difference is 0.6%–the equivalent of a paltry one-time transaction fee, certainly not a reason to forego 30 years of growth in yield.

But the truth is this.  In a world without trading, where each investment had to stand on its own merits, investors wouldn’t want to be involved with either option!  They wouldn’t want to buy the aggregate stock market at 33 P/E, nor would they want to buy a 30 year treasury bond at 33 times coupon.  They would hold cash instead, because the financial and psychological value of decades worth of liquidity for them would far outweigh the paltry 3% annual return that they might receive.  Maybe 8% or 10% would be worth it, but certainly not 3%.

Bonds and stocks are fundamentally different types of investments.  Bonds have a lower duration, and a defined maturity date, when the principal must be returned.  Stocks have no such date–to earn a decent profit over the time horizon of an adult human life, you must find someone to sell them to.  Bonds pay out all of their cash flows to the investor.  Stocks only pay a fraction–with the amount ultimately at the mercy of management, a group of strangers that can do whatever they want with the money.  Bonds are a guaranteed cash flow, a repayment contract that can be recovered in court and that moves investors to the front of the line in bankruptcy.  Stocks, in contrast, are risky ventures that have no repayment contract to back them, and that almost always go to zero in the event of business failure.  Finally, in the case of treasury and mortgage bonds, these bonds can be legally bought–suppressed in yield and supported in price–by the Federal Reserve as a stimulus measure, a measure that the current Federal Reserve is very much inclined to use.

Within a secondary market, these differences have caused each type of  investment to behave differently, with different financial and economic correlations, different trading properties and conventions, and a different audience.  In an environment where the market determines the outcome, the differences make all the difference in the world.  4% on a 10 year treasury feels reasonable to most bond investors, they will comfortably buy at that yield–at least in the current environment, where they know that short-term rates will be kept low for a long-time.  But to stock investors, the same 4% yield, which implies a 25 P/E–an S&P 500 price of 2,500–categorically does not feel reasonable, regardless of where short-term or long-term rates are.  Now, one can argue that it is irrational for investors to fear owning a market at 25 times P/E, if the bond yield is low enough to compensate.  But “rational” doesn’t matter.  All that ever matters is what investors feel, because what they feel determines what they do, and what they do determines the market’s outcome.  If you poll investors, they will make it very clear: outside of a recession, where profits are artificially depressed, 25 times earnings for the S&P 500 does not feel like a reasonable price.

Legitimate Ways to Use the Equity Risk Premium

If the equity risk premium has value as a market signal–and there may be cases in which it does–the reason is not that “consistency” dictates that an investor should choose higher yielding assets over lower yielding assets.  In a secondary equity market, on realistic time horizons, returns don’t come from yields, they come from capital appreciation.  So the point is a non-starter.

Maybe a high equity risk premium reflects excessive fear in the market–fear that is depressing equity prices, and that will create significant price gains when it normalizes.  Maybe a high equity risk premium reflects an aggressively expansionary Fed that, through its pro-growth stance, will eventually rekindle risk appetite, and push investors back into the stock market.  Or maybe, in a reflexive sense, “high equity risk premium” plus “stocks are the only place left to get a return” plus “yield chase” are memes that will implant themselves into investors’ minds and create the expectation of rising prices, which will cause investors to buy, which will push prices higher, which will validate the prior expectation of rising prices, which will increase confidence in this way of thinking, which will lead to even more buying, and so on, in a positive feedback loop.  (But be careful, because when the Fed hints that they might “taper”, everyone will freak the f— out and rush to the other end of the ship).

In each of these uses, the equity risk premium is being linked to price–and therefore the appeal has validity.  But a simple appeal to investor consistency in the purchase of yield does not.  The yield alone, especially the small part that investors actually collect–the dividend–will take years or decades to accrue in meaningful amounts, and can be lost in a single day of trading.  Whatever they may say, that yield is not what equity investors–or even many bond investors–are ultimately after.

Note that when a large equity risk premium is appealed to in this way, as a condition that sets the stage for higher future prices, the details associated with the premium become important.  Why is it large?  Is it large because the earnings yield is high?  Or is it large because the bond yield is low?  And if the bond yield is low, why is it low?  The fact that a 10% earnings yield and a 6% bond yield are correlated with fantastic future equity returns is not, in and of itself, a reason for investors to expect similarly fantastic equity returns from a 6% earnings yield and a 2% bond yield, especially if both the 6% earnings yield and the 2% bond yield were engineered through a policy intervention that will eventually end.

Put differently, any noteworthy return that an investor generates from buying a market with a 4% equity risk premium will not come from the premium itself, the “spread”, but from the future willingness of others to pay higher prices than they are willing to pay now.  For this reason, the underlying factors that are driving the premium, and the way that those factors are “setting the market up” for bullish future changes in investor behavior, are critically important to the calculation.    

Buying the Nikkei at 9,600 in September 2010

In September of 2010, the Nikkei 225 traded at roughly 9600, a P/E of 16.4.  The S&P 500 traded at roughly 1125, a P/E of 16.0.  The P/Es for all countries at the time are shown below, courtesy of FT:

japan sep 2010 yld

The 10 year JGB yield was around 1%, and the 10 year US treasury yield was around 4%.  So the Japanese stock market had an equity risk premium of 5%, and the US stock market had an equity risk premium of 2%.

What was the investment outcome two years later, in September 2012?  The S&P was up 31%, and the Nikkei was down 6%.  All while Japanese investors were (supposedly) collecting an (invisible) 5% spread, versus an (invisible) 2% spread for US investors.  Did the (invisible) spread matter?  Not in the slightest.  Yields of 2%, 5%, or 6% collected over a year don’t matter when they aren’t actually collected, and when the price can change by twice that amount in a period of a few days or weeks.

Now, fast forward to May 2013.  Voila, the Nikkei is up 51%.  Have the Fed Model and the Equity Risk Premium been vindicated?  Hardly. What drove the abrupt increase in returns was not Japan’s high ERP (due mostly to a low bond yield), but “Abenomics”, which turned horrid investor sentiment into budding optimism, a contagious desire to be invested for the coming “recovery.”  That’s all it took.  On the time scale that most investors care about, changes in sentiment, outlook, expectation, and the effect on price, are what drive returns–not small yields or spreads that take years to collect in meaningful amounts.

Buying the S&P at 1400 in December 2012

If you joined David Tepper last December and bought the S&P 500 because it was “cheap” relative to its earnings, or relative to what bonds can offer, you’ve made about 17% on your investment so far, including dividends.  Congratulations.  But you haven’t made that 17% directly from the earnings themselves, or from their spread relative to bond yields.  All that the earnings themselves amount to–assuming they were paid directly to you, which of course they weren’t–is about $40-$50, 3%.  The added 14%–almost 5 times as much–came from the changing sentiment of others, who will now pay you 1630 for each share, instead of 1400.

What has driven this changing sentiment?  The answer: steadily improving U.S. economic conditions, especially in the housing market, a sense of a return to normalcy after the resolution of the “fiscal cliff” and the stabilization of the European debt crisis, both of which suggest an end to the “era of crisis” and a return to a more normal era of steady progress, an investor-friendly Fed that continues to promise to support the economy and the market with zero interest rates for an extended period of time, corporate earnings that are managing to hold up despite feared headwinds, and finally, the market’s best friend: QE.  The Fed is perceived to be endlessly “flooding” the market with liquidity–newly “printed” money that, allegedly, has to go somewhere–thereby lifting the prices of every asset that is considered to be worth owning.  It doesn’t matter whether this dramatized description reflects the actual mechanics of the low-yield asset swap that takes place in QE–all that matters is whether investors think it does.  And many do.

These trends and conditions have not lifted the markets directly.  They’ve lifted the markets indirectly–by functioning as “inputs” into the minds of investors.  They’ve caused investors to focus more on the long-term gain of equities, and less on the short-term risk, which seems to be dwindling.  As a general rule, whenever investors are thinking optimistically about the long-term–personally, financially, or economically–they tend to want to be invested in equities, the asset class that has historically offered the highest long-term returns.  They exhibit this tendency regardless of where P/E ratios, or ERPs, or whatever other metric you prefer, happen to be.  If they see the future as sufficiently promising and exciting, as in the fall of 1999, they will buy equity markets all the way up to 40 times earnings to be “in”, even with bond yields at 6%.  And if they see the future as sufficiently scary, as in the spring of 2009, they will sell equity markets all the way down to below 10 times earnings to be “out”, even with bond yields at 2%.  Compare this 400% swing in price to the 7.5% difference in earnings yield that it represents–a yield that would take a full year, 365 days, to collect–and you will see what really drives returns.

Rest assured, if the improving trends and conditions that have materialized in the US and global economy had not emerged, you would not have your 17% return right now, even though you bought at a “cheap” price.  And if the trends and conditions had emerged at a more expensive price–if, in December, the market had been treading water for months at 1630, rather than 1400–the bottom line would have likely been the same.  Instead of moving up to 1630 from 1400, the market would have moved up to 1860 from 1630, or to some other attractive number.  Investors in the 1630 to 1860 move would be just as happy as you are now–completely unaware of the fact that they bought the market at a P/E a couple points higher, or an ERP a point lower, than you did–and those left out, just as frustrated to not have bought the market, regardless of what some manufactured metric says.  Moves in a secondary market are constrained not by absolute levels, but by the levels that participants are psychologically anchored to.  The outcome is path dependent; where you start matters.

Arguably the biggest “input” of all is the steadily rising price itself.  It creates a positive feedback loop in the minds of investors that confirms the “rightness” of the decision to invest and strengthens the optimistic expectation of what future investments will produce.  It validates the narratives that investors have been using to rationalize why they should be in the market, why it is heading higher–in this way, it increases their confidence and willingness to take future risks.  On the other end of the spectrum, the price action creates a negative feedback look in the minds of those that are not invested.  It confirms the “wrongness” of their decision to be cautious, to wait, and creates fears of perpetually missed future gains–a train that will permanently leave the station–if they stay on the sidelines.  Eventually, the pain of being the only person on the block that is not participating in the collective prosperity becomes too much to bear, and they jump back in.

When things are good, and the market is in an uptrend, most people–even those near or in retirement–want to be involved.  They want to be invested in the high-return asset class, participating in the gains that “everyone else” is enjoying.  But per the “Hold Rule”, not everyone can be invested in the high-return asset class–someone has to hold the other stuff.  It certainly doesn’t help, in the present situation, that the other stuff is yielding zero, and will continue to yield zero for many years.  But even when the other stuff is not yielding zero, these types of uptrends still happen–sometimes, more aggressively than they are happening now.

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