DejaVu & Fed Model

One of the most popular and enduring market relationships in recent years is the so-called “Fed Model.” This model evaluates market P/Es as high or low relative to interest rates.  In a typical formulation, the trailing P/E of the S&P 500 is “high” when it is greater than the inverse of the yield on 10-year Treasury note, or “low” when it is lower.  Various refinements have been postulated, both in earnings measures and in choice of interest rate benchmark. Some such suggestions may be durable improvements, but the basic Fed model is illustrated here.

In a 2002 study covering the prior decade, DejaVu showed the Fed model to have real value. That is, extremely low stock pricing by Fed Model standards is significantly associated with above-average returns, and very high stock pricing is significantly associated with below-average returns. The effect is persistent and consistent and acceptably significant. The table below summarizes Fed Model outcomes as measured forward from every one of the more than 2500 market days.

(The value in each cell is a difference between S&P returns ensuing from days meeting a given Fed Model condition vs returns ensuing from “all other” days.  Other DejaVu data show outcomes and significance from each first day of consecutive qualifying days. “First occurrence” analysis can be useful, but tends to foster a “signals” mindset over a “conditions” mindset.)

Fed Model Outcomes Summary
7/29/92 - 7/29/02

1-Mon 3-Mo 6-Mo 12-Mo
Top Decile  +1.57*  +2.87* +2.15 +3.69
   Quintile 1 +0.95 +1.88 +0.98 +0.02
   Quintile 2 +0.42 +2.23 +3.04 +7.86
   Quintile 3 +0.26 +2.00 +5.5 +12.76
   Quintile 4 -0.46  -2.07* -1.42 +0.79
   Quintile 5  -1.14*  -3.83*  -7.65*  -19.23*
Bottom Decile -0.56  -3.56*  -7.36*  -23.61*


Low Fed Model values lead to above-average returns, and high values lead to below-average returns, as expected.  But DejaVu shows effects that most investors never see.  First, the effect is only significant (*) when the Fed valuation reaches the 1st or 5th quintiles (with a single exception at 4th Quintile and 3 months lookahead).

DejaVu also provides a profile of time horizons. For low P/E conditions, most of the positive price response comes early. The highest per-day gains come in the first month. But for high-P/E conditions, most of the effect comes late, with the greatest effect (both cumulative and monthly rate) coming a year or more out. Overall the most consistent and significant effects are realized at about three months.

Expected values aren’t sufficient for the risk-averse investor, even when statistically significant.  Thus DejaVu also estimates probability of gain (loss) from given market state.  In the Fed Model example, the probabilities associated with three-month lookahead (2nd data column) are like this:

Fed Fractile Prob(gain) Prob(loss)
     Decile 1 (Cheap) .84 .16
Quintile 1 .78 .22
Quintile 2 .79 .21
Quintile 3 .70 .30
Quintile 4 .53 .47
Quintile 5 .45 .55
     Decile 10 (Dear) .43 .57
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