Jan

7

The Fed Model postulates that if the forward earnings yield of the S&P Index is higher than the 10-year treasury yield, stocks are “undervalued“, and vice versa. As of January 4, the S&P was at 1418.34 and expected forward S&P 500 earnings for the next 12 months were 90.38, making the forward earnings yield 6.37 percent (90.38/1418.34). The yield on the 10-year T-note was 4.6 percent.

Historically, subsequent market returns have been correlated with the differential between the S&P forward earnings yield (estimated 12 months earnings divided by the S&P 500 level) and the 10-year treasury yield. On the 9 occasions when this differential has been greater than 1 percent, the S&P 500 has risen nine out of nine times for an average of 14.7 percent in the subsequent 12 months. (This differential currently stands at 1.77 percent).

We have found that the best way to specify the Fed model relationship for forecasting purposes is with a linear regression in the form:

S&P Return[t+1] = a + b * ( Forward Earnings Yield[t+1] - 10 Year Yield[t] )

Estimating this regression using yearly data since 1980, we obtained the following equation:

S&P Return[t+1] = 0.0834 + 4.8839 * ( Forward Earnings Yield[t+1]  -   10 Year Yield[t] )

t-stat   2.72      2.05

p-values   1.17%     5.07%

The R-Squared of 0.14 is quite high for a predictive regression in the financial markets and indicates that almost 15 percent of variation in subsequent returns was explained by the independent variable over the time period studied.

To determine current Fed Model forecast:
Current S&P (as of 01/04/07) stands at 1418.34
Forward Earnings = 12 months consensus forward earnings for the S&P 500 = 90.38
Forward Earnings Yield = Forward Earnings / S&P = 90.38/1418.34 = 6.37 percent
10 Year Yield = The Current Yield on 10-Year government note is 4.6 percent
The Differential (Earnings Yield - 10 Year) = 1.77 percent
Substituting these numbers into the regression formula :
0.084 + 5.027 * (0.0637 – 0.046 ) = 0.173

Therefore, Fed Model yields a forecast of about 17.3 percent for next 12 months. See full details.


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2 Comments so far

  1. Philip Townsend OBE on January 13, 2007 4:06 am

    I think you do yourselves an injustice. As I recall, and I can’t check back because you new URL appears to have overwritten the 2006 update, the implied expected return for 2006 was +18% not +45% as shown in the new chart. Hence my earlier congratulations on having had it almost spot on for 2006. Am I missing something here?

  2. Eugene on January 23, 2007 10:12 am

    Factor in the volatility of the S&P and bond returns in your equation and you may see your R-Squared going way up from 0.14 to 0.8.

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