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What Is the Fair Value of the S&P? Ask Baa Long-Term Corporate Bonds

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Here's the math: Calculations suggest the stock market needs to go up 33% before it hits fair value.

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MINYANVILLE ORIGINAL Since October 6, 2011 we have looked at a dozen indicators which suggested stocks will go considerably higher. But if someone follows the indicators, is he or she buying a piece of paper merely on the sole basis of technical analysis? What about the fundamentals? Let's see if we can figure out how much the S&P (INDEXSP:.INX) is really worth.

What is the fair value of the stock market? This is one of the more basic questions in finance. Over the last century there have been a wide variety of attempts made to value stocks using all sorts of different methodologies. Where to begin?

The first step is to figure out the earnings yield of the S&P. In order to do this one has to figure out what the S&P's earnings are. These days when most people quote the earnings of the S&P, they are referring to operating earnings. Reported earnings more accurately reflect reality because there are less expenses written off as "one-time" events than is the case when using operating earnings.

The next step is, do you use trailing earnings or future earnings? The answer is use trailing earnings. Why? In recent years there has been an increased tendency for Wall Street to use the higher forward estimated earnings yields and then compare them to historical trailing earnings yields. It is fine to use forward estimates but they must be compared to past forward estimates average valuations as well. This is done about 1% of the time. Therefore, comparing future estimates earnings yields to historical actual earnings yields causes overestimation of fair value since forward estimate historical earnings yields are considerably higher than trailing historical earnings yields. In addition, courtesy of Robert Shiller's work, we have trailing earnings going back to 1871. What was Wall Street's consensus earnings forecast for 1872 in 1871? Using trailing earnings allows for a considerably more robust dataset.

So as of November 18, 2012, reported earnings on the S&P were at $87.92 and the S&P was 1359. This gives us an earnings yield of 6.47%.

There is one dimension which we have not addressed yet. What discount rate should one use to calculate the net present value of future income streams?

One popular valuation technique is the Fed Model which uses the 10-year note. But stocks have an infinite income stream, not 10 years. The 30-year bond is much better fit for our purpose. However, there are still two problems with using the 30-year bond in our model. The first problem is the government did not always issue the 30-year bond so the data can get a bit dodgy pre-1977. The second problem is the government can print money and companies can't. Corporate bonds would appear to be a better fit than treasuries for valuing stocks. Let's look at the relationship between earnings yield and long term corporate bonds.
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No positions in stocks mentioned.
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