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The Fed Model

In this post, we will describe an equity trading strategy called the “Fed Model”.  The Fed Model refers to a method of evaluating equity markets versus fixed income markets, which claims that earnings yield of the S&P 500 (predicted forward earnings divided by the current price) can be compared to the yield of the 10-year government bond. In theory, the yield of the equity market should be equivalent to the yield of the bond by offsetting the risk premium of equity markets with the earnings growth.

Basic Fed Model

Below is a Chart of the S&P 500 levels (green) and implied Fed Model S&P 500 levels (blue). The implied S&P 500 level is derived from a ratio of the S&P 500 earnings yield and the 10-Year Treasury.

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The theory behind the Fed Model is that these should move together, and therefore the difference between them will be constant.  To take advantage of this, we’ll trade when the difference series is much higher or lower than its moving average.

Our Strategy enters a trade when the difference of the two series reaches two standard deviations above its 50 day moving average, and exits the trade when it moves back to its moving average. There is also a stop-loss of 10% of total NAV, to prevent large losses in the case of a regime change.

The results are shown below:

The strategy performs poorly, especially during the market downturn in 2008, where it frequently went long the S&P 500. The 10% stop-loss was hit twice.

Using Twiddle we can examine the effect of varying the number of days used in the moving average or the number of standard deviations.

The strategy is fairly unsuccessful; however, it can be improved upon.

Exploring Credit Quality

One of the main problems with the Fed Model is that it assumes that the credit quality of the S&P 500 matches the credit quality of the 10-year treasury.  Rather than making this assumption, we can instead choose a bond index whose yield is most correlated to the S&P 500 forward earnings yield. Using that bond index, we can better predict the value of the S&P 500.

Using Instrument Explorer, we find the bond index with the highest correlation to our forward earnings yield, with daily correlations in differences. The bond indices used correspond to the Moody’s Corporate and Industrial bond indices.

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We can track the strongest bond Index quarterly:

Legend: Dark Green/Light Blue: BAA, Red: A, Light Green/Gold: AA, Orange: AAA

The time series shown here represents the yield of the bond index that was chosen for that quarter. As can be seen here, the indicative bond index during most of 2005-2008 was the BAA-rated Moody’s indices, while in late 2004 the S&P 500 moved more like a AAA-rated bond.

Then, we look at the Z-Score of the difference between the current bond index’s yield versus the S&P 500 forward earnings yield. This allows us to get a better idea of when the difference is at its extremes.

Similar to the Strategy above, we can create a Strategy that trades when the Z-Score crosses a certain threshold, and exits the trade when the z-Score crosses back to 0. There is also a stop loss if any position loses more than 10% of its value.

We can see that the strategy does consistently well during from mid-2002 until mid-2008, and the 10% stop-loss is hit once.

Again, this strategy can be tweaked to show which Z-Scores were most effective over our testing period.

This strategy performed considerably better than the traditional Fed Model strategy.

Conclusion

The Fed model can be greatly improved upon by introducing a more sophisticated model for the equity market credit quality.  Doing so allows the strategy to perform better during times like the market downturn in 2008.

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