
Daily Speculations The Web Site of Victor Niederhoffer & Laurel Kenner Dedicated to the scientific method, free markets, deflating ballyhoo, creating value, and laughter; a forum for us to use our meager abilities to make the world of specinvestments a better place. 
Write to us at: (address is not clickable)
The “Fed Model”
Similar in spirit to the StockBond Ratio is the “Fed Model”, which postulates a relationship between market returns, P/Es, and bond market yields. It has been thought to be used by the Fed itself and was originally named and extended by Dr. Edward Yardeni, now at Oak Associates Ltd. Some (such as Clifford Asness, founder of the $23 billion AQR Capital Management in " Fight the Fed Model: The Relationship Between Stock Market Yields, Bond Market Yields, and Future Returns" assert that the Fed Model is theoretically unsound. While we think that the Fed Model is far from bulletproof, we feel that it is a useful tool in our market timing toolbox. The main point of the Fed Model is that, if the forward earnings yield of the S&P Index is higher than the 10year treasury yield, stocks are “undervalued“ and vice versa. If expected earnings yield is lower than what you can earn riskfree on a 10year note, it does not pay to hold stocks, while if S&P yield is higher than that of the 10year note, then investors are receiving a premium for taking the additional risk inherent in stocks.
Analysis
We used yearend 12 months “forward” earnings (available from Thomson via Prudential) and interest rates from 1980 through 2006 to study this relationship. A convenient way of looking at the relationship is to estimate the Fair Value of the S&P 500 by dividing forward S&P Earnings by the current 10 Year Yield. If this Fair Value is less than the current value of the index, then the S&P is considered overvalued and vice versa. For example, the current S&P is at 1418, expected aggregate 2007 earnings for the S&P 500 are $90.38 and the current yield on the ten year T bond is 4.60 percent. Use the T bond yield as the discount rate for Forward Earnings to calculate Fair Value: Fair Value = Forward Earnings/10 Year Yield = 90.38/.0460 = 1964. Then divide Fair Value by the current index reading to determine under/over valuation: 1964/1418  1 = 38 percent implied expected return.
This implied return cannot really be interpreted as an expected return for the market, because 'equilibrium' may also be brought about through adjustments to interest rates and expected earnings, not just stock prices themselves. Therefore, for forecasting purposes, we prefer to base our forecasts on the differential between the forward earnings yield on the S&P 500 and the 10year yield. Figure 1 below shows a scatterplot of Actual Return versus Fed Model Expectation. The correlation of this implied expected return and the subsequent actual return is 0.38. Encouragingly, splitting the data into two time periods (19801991 and 19922006 respectively) yield correlations of greater than 0.30 in each of the periods, indicating a relatively stable relationship through time.
Market Timing
Expected Returns implied by the Fed Model were generally positive throughout the 1980s, as were stock returns. The model turned negative in 1997 and indicated a particularly strong overvaluation in 2000, the year in which the tech bubble finally burst. If one were to have strictly adhered to the Fed Model as a market timing tool, one would have expected markets to rise in 2003 through 2006 and one would also have stayed away from the market in 2000, 2001, and 2002 thereby avoiding a 40 percent drawdown. But one would also have been out of the market in 19971999, when the S&P 500 returned 98 percent. Note that the Fed Model has correctly predicted the market's direction for seven years in a row (20002006).
We have found that the best way to specify the Fed model relationship for forecasting purposes is in the
form: S&P Return[t+1] = a + b * ( Forward Earnings Yield[t+1]  10 Year Yield[t] )
Estimating a linear regression of the form above, we obtained the following equation:
S&P Return[t+1] = 0.0834 + 4.8839 * ( Forward Earnings Yield[t+1]  10 Year Yield[t] )
Tstats 2.72
2.05
pvalues
1.17% 5.07%
The RSquared 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 10Year 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 ) = 17.3 percent
Therefore, Fed Model yields a forecast of about 17.3 percent for next 12 months.
T. Downing in collaboration with Victor Niederhoffer and Laurel Kenner
Manchester Trading
Data Sources:
* Forward Earnings from Bloomberg and Thomson via Oak Associates.
* 10 Year Treasury Yield obtained from Bloomberg ( USGG10YR Index )