The Fed Model And The Money Illusion

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Larry Swedroe


  • The Fed Model has been used by many investors to judge whether stocks are under or overvalued.
  • However, understanding how valuations are impacted by changes in real and nominal interest rates exposes the flaws in using that metric.
  • The Fed Model should not have any predictive value, and the evidence from research shows this to be the case.

There are well-dressed foolish ideas just as there are well-dressed fools. – Nicolas Chamfort

Magic, or conjuring, is the art of entertaining an audience by performing illusions that baffle and amaze, often by giving the impression that something impossible has been achieved, as if the performer had supernatural powers. Practitioners of this art are called magicians, conjurors or illusionists. Specifically, optical illusions are tricks that fool your eyes. Most magic tricks that fall into the category of optical illusions work by fooling both the brain and the eyes together at the same time.

Fortunately, most optical illusions don’t cost the participants anything, except perhaps some embarrassment at being fooled. However, basing investment strategies on illusions can lead investors to make all kinds of mistakes.

There are many illusions in the world of investing. The process known as data mining – torturing the data until it confesses – creates many of them. Unfortunately, identifying patterns that worked in the past doesn’t necessarily provide you with any useful information about stock price movements in the future. As Andrew Lo, a finance professor at MIT, points out:

“Given enough time, enough attempts, and enough imagination, almost any pattern can be teased out of any data set.”1

The stock and bond markets are filled with wrongheaded data mining. David Leinweber, of First Quadrant Corp., famously illustrated this point with what he called “stupid data miner tricks.” Leinweber sifted through a United Nations CD-ROM and discovered the single best predictor of the S&P 500 Index had been butter production in Bangladesh.2 His example is a perfect illustration that the mere existence of a correlation doesn’t necessarily give it predictive value. Some logical reason for the correlation to exist is required for it to have credibility. For example, there is a strong and logical correlation between the level of economic activity and the level of interest rates. As economic activity increases, the demand for money, and, therefore, its price (interest rates), also increases.

An illusion with great potential for creating investment mistakes is known as the “money illusion.” The reason it has such potential for creating mistakes is it relates to one of the most popular indicators used by investors to determine if the market is under- or overvalued, what is known as The Fed Model.

The Fed Model

In 1997, in his monetary policy report to Congress, Federal Reserve Chairman Alan Greenspan indicated that changes in the ratio of prices in the S&P 500 to consensus estimates of earnings over the coming 12 months have often been inversely related to changes in long-term Treasury yields.3 Following this report, Edward Yardeni, at the time a market strategist for Morgan Grenfell, speculated that the Federal Reserve was using a model to determine if the market was fairly valued – how attractive stocks were priced relative to bonds. The model, despite no acknowledgment of its use by the Fed, became known as the Fed Model.

Using the “logic” that bonds and stocks are competing instruments, the model uses the yield on the 10-year Treasury bond to calculate “fair value,” comparing that rate to the E/P ratio (the inverse of the popular price-to-earnings, or P/E, ratio). For example, if the yield on the 10-year Treasury were 4 percent, fair value would be an E/P of 4 percent, or a P/E of 25. If the P/E is greater (lower) than 25, the market is considered overvalued (undervalued). If the same bond were yielding 5 percent, fair value would be a P/E of 20. The logic is that higher interest rates create more competition for stocks, and this should be reflected in valuations. Thus, lower interest rates justify higher valuations, and vice versa.

For a long time after Yardeni coined the phrase, it seemed almost impossible to watch CNBC for more than a few days without hearing about the market relative to “fair value.” The Fed Model as a valuation tool had become “conventional wisdom.” However, conventional wisdom is often wrong. There are two major problems with the Fed Model. The first relates to how the model is used by many investors. Yardeni speculated that the Federal Reserve used the model to compare the valuation of stocks relative to bonds as competing instruments. The model says nothing about absolute expected returns. Thus, stocks, using the Fed Model, might be priced under fair value relative to bonds, and they can have either high or low expected returns. The expected return of stocks is not determined by their relative value to bonds. Instead, the expected real return is determined by the current dividend yield plus the expected real growth in dividends. To get the estimated nominal return, we would add estimated inflation. This is a critical point that seems to be lost on many investors. The result is that investors who believe low interest rates justify a high valuation for stocks without the high valuation impacting expected returns are likely to be disappointed (and perhaps, not have enough funds with which to live comfortably in retirement). The reality is when P/Es are high, expected returns are low and vice versa, regardless of the level of interest rates.

The second problem with the Fed Model, leading to a false conclusion, is it fails to consider that inflation impacts corporate earnings differently than it does the return on fixed income instruments. Over the long term, the nominal growth rate of corporate earnings has been in line with the nominal growth rate of the economy. Similarly, the real growth rate of corporate earnings has been in line with the real growth of the economy.4Thus, in the long term, the real growth rate of earnings is not impacted by inflation. On the other hand, the yield to maturity on a 10-year bond is a nominal return – to get the real return you must subtract inflation. The error of comparing a number that isn’t impacted by inflation to one that is leads to what is called the “money illusion.” Let’s see why it’s an illusion.

We begin by assuming the real yield on a 10-year TIPS (treasury inflation-protected security) is 2 percent. If the expected long-term rate of inflation were 3 percent, a 10-year Treasury bond would be expected to yield 5 percent (the 2 percent real yield on TIPS plus the 3 percent expected rate of inflation). According to the Fed Model, that would mean a fair value for stocks at a P/E of 20 (E/P of 5 percent). Let’s now change our assumption to a long-term expected rate of inflation of 2 percent. This would cause the yield on the 10-year bond to fall from 5 to 4 percent, causing the fair value P/E to rise to 25. However, this makes no sense. Inflation doesn’t impact the real rate of return demanded by equity investors. Therefore, it shouldn’t impact valuations. In addition, as stated above, over the long term, there is a very strong relationship between nominal earnings growth and inflation. In this case, a long-term expected inflation rate of 2 percent, instead of 3 percent, would be expected to lower the growth of nominal earnings by 1 percent, but have no impact on real earnings growth (the only kind that matters). Because the real return on bonds is impacted by inflation, while real earnings growth is not, the Fed Model compares a number that is impacted by inflation with a number that isn’t (resulting in the money illusion).

Let’s also consider what would happen if the real interest rate component of bond prices fell. The real rate is reflective of the economic demand for funds. Thus, it’s reflective of the rate of growth of the real economy. If the real rate falls due to a slower rate of economic growth, interest rates would fall, reflecting the reduced demand for funds. Using the same example from above, if the real rate on TIPS fell from 2 percent to 1 percent, that would have the same impact on nominal rates as a 1 percent fall in expected inflation, and, thus, the same impact on the fair value P/E ratio – causing fair value to rise. However, this too does not make sense. A slower rate of real economic growth means a slower rate of real growth in corporate earnings. Thus, while the competition from lower interest rates is reduced, so will be future earnings.

Since corporate earnings grown in line with nominal GNP growth, a 1 percent lower long-term rate of growth in GNP would lead to a 1 percent lower expected growth in corporate earnings. The “benefit” of falling interest rates would be offset by the equivalent fall in future expected earnings. The reverse would be true if a stronger economy caused a rise in real interest rates. The negative effect of a higher rate of interest would be offset by a faster expected growth in earnings. The bottom line is there is no reason to believe stock valuations should change if the real return demanded by investors has not changed.

Clifford S. Asness studied the period 1881-2001. He concluded the Fed Model had no predictive power in terms of absolute stock returns – the conventional wisdom is wrong. (As we discussed, however, this is not the purpose for which Yardeni thought the Fed Model was used. Given the purpose for which the model was designed, it would have been more appropriate for Asness to study the relative performance of stocks vs. bonds given the “signal” – under/overvalued – the model was giving.) Asness also concluded that, over 10-year horizons, the E/P ratio does have strong forecasting powers. Thus, the lower the P/E ratio, the higher the expected returns to stocks, regardless of the level of interest rates, and vice versa.5

There is one other point to consider. A stronger economy, leading to higher real interest rates, should also be expected to lead to a rise in corporate earnings. A stronger economy reduces the risks of equity investing. In turn, that could lead investors to accept a lower risk premium. Thus, it is possible that higher interest rates, if caused by a stronger economy and not higher inflation, could actually justify higher valuations for stocks. The Fed Model, however, would suggest that higher interest rates mean stocks are less attractive. The reverse would be true if a weaker economy led to lower real interest rates.

Before coming to the moral of this tale, it’s worth noting that, when the COIVD-19 crisis drove the yield on 10-year Treasuries to under 1 percent, I have heard not a single reference to Fed Model. That’s because a yield below 1 percent would create a fair value P/E of more than 100! Which, of course, would not make any sense. In other words, the sharp fall in interest rates exposed the “wizard behind the curtain.” However, my guess is that if and when interest rates return to more historical levels, the Fed Model will be resurrected by the financial media. After all, they need something to try and keep your attention.

The Moral of the Tale

While gaining knowledge of how a magical illusion works has the negative effect of ruining the illusion, understanding the “magic” of financial illusions is beneficial because it should help you avoid mistakes. In the case of the money illusion, understanding how the illusion is created will prevent you from believing an environment of low (high) interest rates allows for either high (low) valuations or for high (low) future stock returns. Instead, if the current level of prices is high (a high P/E ratio), that should lead you to conclude that future returns to equities are likely to be lower than has historically been the case, and vice versa. Note that this doesn’t mean investors should either avoid equities because they are “highly valued” or increase their allocations because they have low valuations.

Hopefully, you are now convinced that the Fed Model should not be used to determine if the market is at fair value and that a much better predictor of future real returns is the E/P ratio.

1. Kiplinger’s Personal Finance, February 1997.

2. Wall Street Journal, April 5, 1996.

3. Humphrey-Hawkins Report, Section 2: Economic and Financial Developments in 1997 Alan Greenspan, July 22, 1997.

4. William Bernstein, “The Efficient Frontier,” (Summer 2002).

5. Clifford S. Asness, “Fight the Fed Model: The Relationship Between Stock Market Yields, Bond Market Yields, and Future Returns,” (December 2002).

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Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions.