There is much discussion today about whether equities are overvalued. Stock market observers who believe this to be the case often cite the very high level of the Shiller Cyclically Adjusted Price-to-Earnings (CAPE) 10 ratio. As I write this, the Shiller CAPE 10 stands at roughly 24.7, way above its historical average. Among those using this argument are Jeremy Grantham and John Hussman.

On the other side are market observers, such as Jeremy Siegel, who make the case that adjustments need to be made to the Shiller CAPE 10, due to changes in accounting rules (FAS 142) and historically lower dividend payouts, for it to be an accurate metric for market value. With those adjustments made, the Shiller CAPE 10 is about at its average since 1960.

There are still others who believe that stocks aren’t highly valued, let alone overvalued, by using what has become known as the Fed Model. They compare the earnings yield (E/P) to the yield on the 10-year Treasury to determine fair value.

With the 10-year Treasury yielding about 2.25%, the earnings yield (even using the Shiller CAPE 10, which gives us an E/P of about 4%), and current earnings (which gives us an E/P of more than 5% using trailing 12-month figures), make stocks look attractive. Unfortunately, there’s a real problem with the Fed Model.

The belief that nominal interest rates should matter to stock valuations is based on the idea that bonds are competing instruments for stocks. But those using metrics that compare bond yields to price-to-earnings (P/E) ratios to determine “fair value” are making an error. By thinking of things in isolation, they fail to see the whole picture. In this case, the belief is based on what is called the “money illusion.” The money illusion has great potential for causing investors to make mistakes, because one of the most popular indicators used to determine if the market is under- or overvalued is the Fed Model.

In 1997, in his monetary policy report to Congress, then Federal Reserve Chairman Alan Greenspan indicated that changes in the ratio of prices in the S&P 500 to consensus estimates of earnings during the coming 12 months have often been inversely related to changes in long-term Treasury yields. Following this report, Edward Yardeni speculated the Fed was using a model to determine if the market was fairly valued (how attractively stocks were priced relative to bonds). The model, despite no acknowledgement from the Fed, became known as the Fed Model.

Since Yardeni first coined the phrase, the Fed Model as a valuation tool has become “conventional wisdom.” Unfortunately, much of what serves as conventional investment wisdom is wrong. There are two major problems with the Fed Model. The first is that the expected return of stocks isn’t determined by their relative value to bonds. The expected real return is governed by the current dividend yield plus the expected real growth in dividends. To get the estimated nominal return, you add estimated inflation.

This is a critical point that seems to be lost on many investors. The end result is that those who believe low interest rates justify a high valuation for stocks, without that high valuation ever impacting expected returns, are likely to be disappointed. When P/E ratios are high, expected returns are low, and vice versa, regardless of the level of interest rates.

The second problem with the Fed Model is that it fails to consider that inflation impacts corporate earnings differently than 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. Thus, 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 us to the money illusion. Let’s see why.

To keep our example simple we’ll assume that there’s no risk premium in the yield on nominal bonds for unexpected inflation and there’s no liquidity premium in the yield on TIPS (Treasury Inflation-Protected Securities). Let’s also assume the real yield on 10-year TIPS is 2% (wouldn’t that be nice), and the expected long-term rate of inflation is 3%. Thus, the 10-year Treasury bond yield would be 5% and the fair value for stocks would be at a P/E of 20. Now, lower the 3% assumption for inflation to 2%. This would result in yields on the 10-year Treasury bond falling from 5% to 4%, causing the fair value P/E to rise to 25. But, since inflation does not impact the real rate of return demanded by equity investors, it shouldn’t impact valuations. In addition, as stated above, over the long term there is a strong relationship between nominal earnings growth and inflation. In this case, a long-term expected inflation rate of 2%, instead of 3%, would be expected to lower the growth of nominal earnings by 1%, 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 measures a number that is impacted by inflation against a number that isn’t, causing the money illusion.

Now let’s 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 also 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 our earlier example, if the real rate on TIPS fell from 2% to 1%, it would have the same impact on nominal rates as a 1% drop in expected inflation, and thus have the same impact on the fair value P/E ratio — causing fair value to rise.

This too, however, doesn’t make sense. A slower rate of real economic growth means a slower rate of real growth in corporate earnings. Thus, while competition from lower interest rates is reduced, future earnings will be as well.

Because corporate earnings have grown in line with nominal GNP growth, a 1% lower long-term growth rate in GNP would lead to 1% lower expected growth in corporate earnings. So 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 hasn’t changed.

When AQR Capital’s Clifford Asness studied the period from 1881 through 2001, he concluded that the Fed Model had no predictive power in terms of absolute stock returns. In other words, the conventional wisdom was wrong. 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.

There’s one final point to consider. A stronger economy, leading to higher real interest rates, should be expected to lead to a rise in corporate earnings. The stronger economy reduces the risks of equity investing. In turn, that could lead investors to accept a lower risk premium.

Thus, it’s 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 indicate that stocks are less attractive. And the reverse would be true if a weaker economy led to lower real interest rates.

Even smart people make mistakes, usually out of ignorance. You, however, now have the tools to see through the money illusion.

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