Testing the Fed Model
Posted in Fed Model
November 6, 2009
The key guiding belief of the Fed Model of stock market valuation is that investors use a Treasury note (T-note) yield as a benchmark for the expected (forward) earnings yield of the stock market. When the gap between the forward earnings yield and the T-note yield is positive (negative), stocks are relatively attractive (unattractive), and investors bid stocks up (down) to restore yield parity. To test that belief, we relate the gap between the S&P 500 1-year forward earnings yield and the 1-year T-note yield to future returns for the S&P 500 index. We calculate the 1-year forward earnings yield from the Earnings Forecast and the level of the S&P 500 Index. Using end-of-month data for the two yields over the period March 1989 (limited by availability of an input variable for the Earnings Forecast) through October 2009, we find that:
The following chart compares the behaviors of the S&P 500 Index and the gap between the S&P 500 forward real earnings yield and the 1-year T-note yield (Fed Model yield gap) over the available sample period based on monthly data. To convert from the quarterly earnings cycle to a monthly frequency, we assume new earnings data for a quarter becomes known as follows: 50% during the first month after quarter end; 40% during the second month after quarter end; and, 10% during the third month after quarter end. No consistent relationship is obvious.
For precision, we relate the Fed Model yield gap to stock market returns over fixed future intervals.
The following scatter plot relates the 6-month future return for the S&P 500 Index to the Fed Model yield gap over the available sample based on monthly data. The Pearson correlation between the two series is -0.02 and the R-squared statistic is 0.00, indicating no relationship between the two series.
Because the future return measurement interval (six months) is longer than the sampling frequency (monthly), the number of points on the scatter plot overstates effective sample size.
For a future return measurement interval of three (12) months, the Pearson correlation is -0.04 (-0.04) and the R-squared statistic is 0.00 (0.00).
To check for a possible non-linear relationship, we segment future returns by ranges of the Fed Model yield gap.
The final chart summarizes the average 3-month, 6-month and 12-month future returns for the S&P 500 Index by quintile of the Fed Model yield gap over the available sample period. There is no apparent systematic relationship across quintiles between future stock market returns and the Fed Model yield gap for any of the three return intervals. The average Fed Model yield gap is 0.00% for the best-performing quintile (2). The overall sample size is fairly small (based on return intervals) for a quintile breakdown.
For an additional robustness test, we look at two subperiods.
The R-squared statistics for the relationship between the 6-month future return for the S&P 500 Index and the Fed Model yield gap over two equal subperiods (3/89-3/99 and 4/99-4/09) are 0.01 (with negative slope) and 0.05 (with positive slope). The overall sample period is fairly short (compared to return intervals) for subperiod tests.
Finally, we repeat the above tests using the 10-year T-note yield rather than the 1-year T-note yield. All results are similar.
In summary, evidence from several simple tests does not support a belief that the Fed Model explains investor behavior over the past 20 years.
Some other method of forecasting earnings (rather than the Earnings Forecast) may produce different results.
