One way to adjust earnings yield for interest rates is to simply subtract the yield on the 90 day Treasury bill. If lower interest rates justify lower earnings yields, then the two should have some equilibrium historically. The relationship between the two should have remained more or less constant - when one grew much greater than the other, corrective market action should have brought them back into synch.
As it turns out, the historical range of the earnings yield minus the 90 day Treasury bill yield was wide (from minus 1.44% to 15.34%), which is the first piece of evidence against this theory of an instantaneously correcting market. Clearly, the earnings yield is not tethered to the Treasury bill although it spends most of its time far above it; stock investors demand a far higher earnings yield than the risk free rate in T-bills[1].
| Earnings yield minus 90 day Treasury bill yield versus next 12 month change in the S&P 500 , January, 1945-May, 2007, n = 737: | ||||
| | | Earnings yield - Treasury bill yield: | Next 12 month return: | |
| Percentiles: | n | From: | To: | |
| Min-25% | 185 | -1.44% | 2.84% | 1.06% |
| 25-50% | 184 | 2.84% | 4.82% | 7.45% |
| 50-75% | 183 | 4.82% | 6.91% | 11.95% |
| 75-Max | 185 | 6.91% | 15.34% | 14.65% |
| | | Correlation: | 32.3% | |
| | | | | |
| All: | 737 | | Average: | 8.79% |
Note the very strong, stepwise relationship between earnings yield minus Treasury bill yield and the next 12-month change in the S&P 500. The market only had an above average return when the earnings yield exceeded the Treasury bill yield by 4.82% percent or more.
25% of the time, the earnings yield exceeded the 90 day Treasury bill yield by 6.91% or more; however, it tended not to drop much below it. In fact, the most the 90 day Treasury bill yield exceeded the earnings yield was 1.44%, meaning that whenever the earnings yield dropped too far below the 90 day Treasury bill yield, the market must have corrected to bring the yield in line with the 90 day Treasury bill yield (a falling stock market would increase the earnings yield). In fact, only 25% of the time was the earnings yield 2.84% or less greater than the 90 day Treasury bill yield, and 50% of the time, it was almost 500 basis points greater. This means that historically at least investors have demanded a risk premium of approximately 5.2% for owning stocks.
Now let's examine how stocks performed over the next 12 months given various strata of earnings yield minus 90 day Treasury bill yield. There is a strong, stepwise inverse relationship between these two variables. Only when the earnings yield was 4.82% or more above the Treasury bill yield did the market rise at an above average rate. In the 25% of cases when the market earnings yield was 6.91% or more above the Treasury bill yield, the S&P 500 rose an average 14.65%. Conversely, when the earnings yield was 2.84% or less above the Treasury bill yield (lowest quartile) the market rose a miserable 1.06%. The correlation was a relatively high (for financial data series) .323.
[1] Caveat: the same was once said of the dividend yield versus corporate bond yields, but this relationship changed in the late 1950s when the dividend yield dropped below the bond yield and has remained below every since. In other words, even very long-term historical relationships can experience dramatic, secular shifts. Such a shift could conceivable occur as investors realize that the so-called risk premium demanded of stocks is greater than the long-term historical return from stocks can justify, leading to a permanently higher plateau.
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