Blog - Investing Notes

December 6, 2007 - Update: What Would the Fed Model Do?

The differences between the aggregate stock forward earnings yield and the yields on Treasury instruments are at present extraordinarily large. What are the current outputs of the the Fed Model based on these differences? To calculate Fed Model valuation benchmarks, we use daily data for the 13-week Treasury bill (T-bill) yield, the 10-year Treasury note (T-note) yield and the S&P 500 forward operating earnings yield (E/P) derived from our Real Earnings Yield Model over the period 1/2/90-12/5/06. To generate projections, we use the current Standard and Poor’s S&P 500 operating earnings forecast for the fourth quarter of 2007 through the third quarter of 2008. Using these data series, we find that:

The average spread between E/P and the T-bill (T-note) yield over the benchmark period is +1.48% (-0.29%). Standard and Poor's currently projects S&P 500 operating earnings of $98.15 for the next four quarters (9.6% growth over the prior four quarters). The current E/P for an S&P 500 index level of 1485 is 6.61%, and the current T-bill (T-note) yield is 2.98% (3.91%).

The following chart depicts the combinations of the S&P 500 index and T-bill/T-note yields that produce the average (E/P - T-bill) and (E/P - T-note) yield spreads for the benchmark period. Reciprocal analyses are as follows:

The red dashed lines project the levels of the S&P 500 index based on current Treasury yields, as indicated by the benchmark relationships. These projections are 2201 based on the current T-bill yield and 2709 based on the current T-note yield. (The disparity in these projections reflects an historically unusual spread between T-bill and T-note yields.) In other words, if Treasury yields do not change, then stock prices must rise substantially for stock-Treasuries yield spreads to revert to the benchmarks.

The green dashed lines project T-bill and T-note yields based on the current level of the S&P 500 index, indicating yields of 5.7% for the T-bill and 7.4% for the T-note. In other words, if stock prices do not change, then the yields on Treasuries must rise substantially for stock-Treasuries yield spreads to revert to the benchmarks.

Of course, the earnings forecast could be wrong, and the forecast has recently declined substantially. The following table shows the effects on Fed Model projections of the S&P 500 index, based on current Treasury yields, for various decrements of the current operating earnings forecast. (Such decrements move the blue curves down and to the left.) The table shows that the Fed Model projects large gains for the stock market even if the earnings forecast declines further.

In summary, the Fed model says that substantial movements of stock prices (up), earnings (down) and/or T-bill and T-note yields (up) must occur to produce "normal" stock-Treasuries yield spreads.

For related research, see Blog Synthesis: Gunning for the Fed Model?.