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

By James Debevec  NOV 19, 2012 12:40 PM

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


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. While there are a wide variety of corporate bonds, thanks to FRED we have long term data on AAA and Baa Long Term Corporate Bonds going back to January 31, 1919. Which one should we use? There are only four AAA companies left (Microsoft (NASDAQ:MSFT), Exxon Mobil (NYSE:XOM), Johnson & Johnson (NYSE:JNJ) and Automatic Data Processing (NASDAQ:ADP)). So Baa debentures income flows would seem to match up with the S&P better than the AAAs.

The average yield for Long Term Baa Corporates is 7.06%. Stocks’ earnings yield over the same time period is 7.43%.

Therefore, stocks have had an average earnings yield of 0.37% more than Baa Corporate Bonds. This seems to be a nice match. Let’s go to the chart.

You can see there was a very wide divergence from stock and corporate bond yields from around 1939 to 1958. However, when debt yields went up in the 1960s and 1970s earnings yields followed suit. And when debt yields came down from their early 1980’s highs, stocks were allowed to trade at below their historical average earnings yield.

So what is the final answer?

Using the current Baa yield of 4.48% and adding a 0.37% historical average premium spread gives us a fair value earnings yield of 4.85%. The calculation is 87.92 (earnings) / 0.0485  = 1,812. This method would suggest that the S&P would need to go up by a third to hit fair value.

So, in summary, we have determined that 1,812 is the current fair value for the S&P. What is interesting is the 252 Daily Rate of Change decline on the 30 year bond yield indicator suggested the S&P could go to 1800 as well. As Baa rates change, the fair value calculation will be modified accordingly.

But as of right now, it adds solid fundamental evidence to compliment the many quantitative indicators which are bullish on stocks.
No positions in stocks mentioned.

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