By John H. Huston and Roger W. Spencer
The "Fed Model" got its name when the documents accompanying Alan Greenspan's July 1997 Humphrey-Hawkins report to Congress contained a comparison between price-earnings ratios and Treasury yields as a means of gauging stock market over or under valuation. In fact, the comparison had been discussed by Fed officials, as reflected in FOMC transcripts, as a measure of disequilibrium at least a decade before that time. (Huston and Spencer, 2009) The "Fed Model" has also attracted some academic attention. For example, Burton Malkiel (2004) demonstrated its superiority over other "mean reversion" models in predicting long-run returns. The Fed Model compares the long-term bond yield (i) with the earnings yield on stocks (e/p). Using the data on Standard and Poor's Composite Index (SPY), earnings and the yield on the ten year treasury bonds generates figure 1 below.1
Expressing the comparison as a ratio gives i/(e/p).2 A higher value means that bond yields are large relative to stock earnings yields. Thus, peaks in the ratio such as those in 1929 and 1999 indicate equity prices that are high relative to bond prices.
The June 2012 value for this measure is .29 which is below the long term average of .75 and well below the average for the past 40 years of 1.2. In fact, values this low are somewhat uncommon with the only sustained periods below this level appearing in 1918-19, 1920-22, 1932-33, 1940-45 and 1946-50.
So does this imply that stocks are currently undervalued? The short answer is yes - statistically speaking this is a stationary series suggesting that the ratio's value should rise back to more familiar levels in the long run. However, just because it is mean reverting doesn't imply that over or undervalued stocks won't become more over or undervalued before returning to equilibrium. Someone using this tool as a trading signal could have sold in the early 80s as stocks reached 1929 valuation levels only to see them continue to rise for the next two decades. In addition, the fact that current equity prices are low relative to bonds may simply reflect greater risk. The prior periods matching our current low ratio include World Wars I and II and the Great Depression; periods which could have led investors to demand a greater risk premium. Finally, the ratio could return to its mean without an equity price increase due to a rise in long-term interest rates or a fall in earnings. One could certainly justify predictions of either of those.
With those caveats in mind, however, stock returns following periods of low ratios have been impressive. 160 months in the sample had ratios below the June, 2012 levels. The average annual rate of return including dividends for the five years following each of those months was 13.3% and the average annual return for the following ten years was 13.9%. For months with ratios above June 2012 levels, the average annual rate of return for the following 5 and 10 year periods was only 7.4%.
Huston, J.H. and R.W. Spencer 2009, "Speculative Excess and the Federal Reserve's Response," Studies in Economics and Finance, Vol. 26 No. 1, pp. 1086-7376.
Malkiel, B.G. 2004, "Models of stock market predictability," The Journal of Financial Research, Vol. 27, 4, pp. 449-59.
1 All data is from Robert Shiller's web site. Shiller uses the 10 year average of historic earnings to "cyclically adjust" his p/e.
2 This can be rewritten as (p/e)/(1/i), which is the price-earnings ratio for stocks divided by the equivalent concept for bonds or p/(e/i), which is the price of equities divided by the present value of an infinite stream of fixed earnings, e.