Fed Model Update: Stocks Are Cheap Compared to Bonds

I thought that it would be good to compare the current bearish mood of the market with the Fed Model used by the Federal Reserve to measure the value of the stock market.

It is the uncertainty of stocks and the guarantee of the bond that creates the competition between stocks and bonds. If bond yields are higher than stock yields, investors will likely sell a portion of their stocks and move that money into bonds. When stock prices decline to the point that the SPX yield is higher than bonds, investors will allocate more capital back to stocks.

Bonds thrive in a weak economy because investors seek secure returns. But in an improving economy, money flows from bonds into stocks. At the prospect of a stronger economy, the yield on 10-year U.S. Treasury bonds rises sharply. As the yields rise, the value of the treasury bonds drop.

There is a long-term relationship of the 10-year Treasury yield running approximately equal to the forward earnings yield of the SPX. (The earnings yield is the inverse of the P/E).

The formula for the Fed Valuation Model is as follows:

(10 Year bond yield minus [-] SPX earnings yield) / SPX earnings yield). Where the SPX earnings yield = ( SPX earnings estimates/ SPX index price).

Currently, the S&P 500 is selling at 1370 and has projected 2008 operating earnings of $96.28 per share. Converting the $96.28 in S&P 500 earnings to an earnings yield gives us a fair comparison to the investment value of the bond yield. Dividing the S&P 500's earnings ($96.28) by the price of the index (1370), we get a yield of 7.03% ($96.28/1370 = 7.03%).

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Assume today's 3.48% yield on the 10 year treasury bond:

1. Convert this yield to a P/E multiple (100/3.48 = 28.74 P/E)

2. Take this 28.74 P/E and multiply it by the operating earnings of the SPX ($96.28) and you get a fair value of 2767 for the SPX 500.

With the 10-year note currently at 3.48%, stocks are undervalued by 50% for 2008 estimated operating earnings. The current operating P/E of 14.23 represents very good value given current interest rate levels. 2008 estimates are for a 7.03% SPX earnings yield compared to a 3.48% yield on the 10-year note leaving a spread of 355 basis points between the two yields. (rev. 4/5/08)

An additional calculation is also necessary. The yield on the Treasury bond is guaranteed, but it is also fixed. SPX earnings grow an average of 7% per year (the mean average for the last 60 years). If we project growth out into the future and take into consideration that inflation will decrease the value of that investment by (-3.5%) per year, the fixed yield on the bond is currently a negative return. The SPX earnings yield, however, is growing an average of 7% per year, more than compensating for the effects of inflation (7% - 3.5% = 3.5%).

In today's market environment, an investment in the SPX far exceeds the value of the Treasury bond for future returns. Common sense would lead an investor to place his money in equities because stocks are spectacularly undervalued in comparison to bonds. You have to go back to 1974 to find this degree of undervaluation. This is the exact opposite of stock/bond values at the height of the 2000 dotcom boom.

To put this in historical perspective, the Fed Model has only sold at a discount exceeding 20% four times in the last 26 years (1979, 1980, 1993, 2002). It is currently selling at a 50% discount and there has been only two times in 26 years that it has sold below a 25% discount (1979, 1980). This means that if the SPX were to rise to its Fed Fair Market value it would increase 50% from current levels. The risk premium for stocks in this environment is very favorable. With the forecasted 2008 SPX earnings, the upside potential clearly outweighs the downside risk. Stocks are cheap when compared to bonds; plus they beat inflation and yield more.

The Corp. AAA Indus. Bond rate [AAA] is currently about 5.4%. The earnings yield on the SPX is 7.03%. The growth of SPX cash earnings has averaged 3% to 7% over the past 50 years. The current cash earnings yield on SPX stocks is thus 1.6% higher than an AAA bond (the highest guaranteed corporate bond yield), plus you get the growth of cash earnings on the SPX (which next year is estimated at +9%).

Comments

[User 143167:]

You missed the risk premium there big time. Stocks are much more risky than the AAA bonds and you don't get earnings mailed in checks, so to compare these bonds yield to stock earnings yield is not right. That said, it is the case now that the T bonds are too expensive, not the stocks are cheap. You won't get a 50x PE market automatically even if the 10 year yield drops to 2%. You probably should invest money in other stock markets because the US stock is now among one of the "most expensive stock markets" in the world.

2008 Apr 07 09:48 AM

[greensleeves:]

I used to have a chart by Graham & Dodd showing the "fair" relationship between growth rates and P/E for stocks, and it had several lines, one for each of several rate environments. It seems to me that the real equity risk premium now is high - meaning risk adjusted returns will be better in stocks. The valuations are highly dependent on future growth rates, not 2008 rates, but the market is focusing on these. I'd also point out that the SPX would need to increase about 100% ( not 50% as you say) to get to the predicted value of the Fed model. But I guess that isn't important since as we now know from prior comment - stocks are risky and therefore way too expensive. In fact the US stock market is the most expensive in the world!

2008 Apr 08 11:33 AM