Fed Model Update, from Alex Castaldo

January 4, 2008 |

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 December 31, the S&P was at 1468.36 and expected forward S&P 500 earnings for the next 12 months were 101.86, making the forward earnings yield 6.94 percent (101.86/1468.36). The yield on the 10-year T-note was 4.02 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 10 occasions when this differential has been greater than 1 percent, the S&P 500 has risen ten out of ten times for an average of 13.5 percent in the subsequent 12 months. (This differential currently stands at 2.92 percent, which the highest it has ever been at year end).

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] = 0.082 + 4.172 * ( Forward Earnings Yield[t+1]  -   10 Year Yield[t] )

t-stat     2.66      1.85

p-values   1.32%     7.53%```

The R-Squared of 0.12 is quite high for a predictive regression in the financial markets and indicates that 12 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 12/31/07) stands at 1468.36
Forward Earnings = 12 months consensus forward earnings for the S&P 500 = 101.86
Forward Earnings Yield = Forward Earnings / S&P = 101.86/1468.36 = 6.94 percent
10.Year.Yield = The Current Yield on 10-Year government note is 4.02 percent
The Differential (Earnings Yield - 10.Year) = 2.92 percent
Substituting these numbers into the regression formula :
0.082 + 4.172 * (0.0694 – 0.0402 ) = 0.203
Therefore, Fed Model yields a forecast of 20.3 percent for next 12 months.

How does Dr. Castaldo counter the failings of the Fed model in other G10 countries? Japan has been horrible under that model. Germany has been OK, barely statistically significant. UK has been good, like the US.

Alex Castaldo replies:

I believe Mr.Humbert is referring to the paper "The Fed Model: A Note" FRL (2006) by Javier Estrada who tested the Fed model in a number of foreign markets.   I have exchanged Emails with the professor but neither one of us was convinced by the other's arguments; we will just have to disagree.

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