Friday, November 10, 2006

The "FED Model" theory of equity valuation

The "FED model" is a popular yardstick for judging whether the stock market is fairly valued. This term was coined by Prudential Securities strategist Ed Yardeni after a Fed report to Congress in July 1997 suggested the bank was following it.

The FED model compares the yield of the 10-yr govt bond to the "earnings yield" of the S&P 500. The "earnings yield" is defined as the inverse of the forward P/E ratio of the S&P 500. As of the market close today the S&P 500 is trading at 1230.96 and the projected earnings for 2006 of the components of the index are $78.30. The forward P/E ratio for the S&P 500 is therefore about 15.72 (1230.96/$78.30). The inverse of the forward P/E ratio is E/P, known as the earnings yield. In this case, (1/15.72) is .0636, or 6.36%. As of market close today, the yield on the 10-yr govt. bond was 4.564%.

In theory, the yield on the 10-yr bond is equivalent to the different between the earnings yield and the risk premium (i.e., because stocks are riskier than bonds the earnings yield should ordinarily be less than the yield on the 10-yr bond). In this case, 4.564% = 6.36% - Rp (risk premium). In this case, Rp is 1.796%. Between 1994 and 2003, the average risk premium was 0.11%. Therefore, the current Rp of 1.796% is a very bullish sign and signals that it's probably a good time to buy.

During the stock market bubble, the risk premium was around -2% or worse - i.e., investors bid up stocks to great highs because stocks were actually viewed as being less risky than bonds. Today, on the other hand, investors are completely shunning stocks and invest their money in bonds instead.


Although the FED model is useful, it does have its flaws. For example, the earnings yield is based on projected earnings, and it's always possible that the economy could go south and those projections will not be met. Moreover, this model only addresses the relative (not absolute) valuations of stocks and bonds. Stocks do not necessarily have to rise for Rp to decrease; instead, stocks could stagnate while bonds decrease in value.


Jim said...

I wrote a new post explaining why the FED Model indicates that the S&P 500 is undervalued as of Jaunary 26, 2007:

Anonymous said...

If stocks are riskier than bonds, then the earnings yield on stocks should be more than the bond yield. Why? Investors need more, not less, return to compensate for the higher risk. Said differently, the higher risk asset class is always discounted at a higher rate, is it not?

Jim said...

Anonymous (10:05 AM), stocks are definitely riskier than bonds. the FED model has its limitations, in part, because it is very difficult to determine how much weight to give to the inhernet risk of investing in stocks.

Don't forget, however, that a 10-year bond, for example, provides a fixed amount of appreciation every year (if they are zero-coupon bonds, the is no interest paid every year - all gains are in the form of capital gains that can be realized by selling the bonds). If we think of this appreciation as "earnings," it is clear that the earnings amount of the bond does not increase every year - it is exactly the same amount. Stocks, however, normally have earnings that increase every year (except during recessionary periods), so one also needs to account for the potential earnings increases of stocks.

The FED Model is interesting because it is simple to use to make a quick comparison between stocks and bonds. However, it clearly has many limitations in its usefulness.

Alan said...

Tks. But how can I use Fed model to predict the level of next year S&P 500 index? Is Fed model the same as earnings yield gap model? Looking forward to your reply. Tks

Alan said...

Tks. But how can the Fed model to predict or target the next year S&P 500 index level? Also, is the Fed model the same as earnings yield gap model? Looking forward to your reply. Tks

Alan said...
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