Fed model

The "Fed model" is a theory of equity valuation used by some security analysts that hypothesizes a relationship between long-term treasury notes and the expected return on equities.

According to this valuation model, in equilibrium the real yield on the 10-year U.S. Treasury Bonds should be similar to the S&P 500 earnings yield (that is, S&P forward earnings divided by the S&P level).^{[citation needed]} Differences in these yields identify an over-priced or under-priced equity market.

More specifically, if the S&P earnings yield is higher than the treasury yield investors should sell treasuries and buy stocks (i.e. stocks are undervalued), while if the S&P earnings yield is lower investors should sell stocks and buy the more attractive treasuries (i.e. stocks are overvalued).

The Fed Model was so named by Ed Yardeni of Prudential Securities based on the fact that some research at the Federal Reserve in the mid 1990's used similar ideas.^[1] But the model goes back much further than this and can be found in various forms in a number of security analysis books. In this sense, the term Fed Model is misleading, and the model is definitely not endorsed by the Fed.

The Gordon growth Model reduces to the Fed model if one assumes that the present value of growth opportunities is 0, and that the required rate of return on equities is equal to the real treasury rate. If growth opportunities are positive, that should lead to lower earnings yield. On the other hand, if there is a risk premium for equities, this should lead to a higher earnings yield. The Fed model assumes that the 2 effects balance each other. The Gordon model is itself an approximation which assumes that the growth rate will stay the same forever.

The data presented in the book Stocks for the Long Run shows that the Fed Model was not applicable before 1965. The data shows that the market was very expensive in 2000 but has been cheap since 2003^[2].

Example

Tom Lauricella applied the Fed Model to S&P500 index on January 19, 2008^[3]. He writes:

With the past week's downturn, stocks in the Standard and Poor's 500-stock index are trading at 13 times their expected earnings for 2008. Last June, when the S&P index was 12% higher than it is now, stocks were priced at 14.2 times this year's earnings. Meanwhile, with a U.S. recession now widely expected and the Federal Reserve thought likely to cut short-term rates further, U.S. Treasury yields have fallen sharply. The 10-year Treasury note is yielding 3.64%, its lowest level since July 2003, and down from 3.81% a week ago.

Thus S&P500 forward earning yield (1/13=7.69%) is higher than 10-year Treasury note yield (3.64%), suggesting S&P500 is significantly undervalued.

References

• Lander, Joel, Athanasios Orphanides, and Martha Douvogiannis, "Earnings, Forecasts and the Predictability of Stock Returns: Evidence From Trading the S&P", Journal of Portfolio Management, 23(4), 24-35, Summer 1997. [The research paper by three Federal Reserve economists that gave rise to the somewhat misleading name 'Fed Model' to describe the idea of comparing earnings yields to treasury yields].
• Asness, C., "Fight the Fed model: The relationship between future returns and stock and bond market yields", Journal of Portfolio Management, 30, 11-24, Fall 2003. [The case against the Fed Model, by one of its leading opponents].

External links

• The "FED Model" theory of equity valuation- A blog discussion of the "Fed model" and how to apply it to the S&P 500 index.
• Investopedia: The Fed Model and Stock Valuation