Investing

Is the market overvalued?

Probably yes, very slightly.

To answer that question from a fundamental point of view we need to have a look at a stock market valuation model. One of the most popular valuation models is known as the Fed model. This model asserts that the earnings yield on stocks should equal the yield on a 10 year Treasury. There is both a descriptive and mathematical basis for the model. The reason it's called the Fed model is that it first turned up in the report that the Federal Reserve Open Market Committee receives from its staff.

The underlying descriptive reason for it is based on opportunity cost. Basically investors will place their money wherever they can get a better yield on a risk adjusted basis. Given that the S&P 500 (S&P) is so diversified and has a 100 year track record (or at least the Dow Jones index does) it is not perceived to be riskier than treasuries over a long period of time. Therefore if 10 year Treasuries offer a higher yield than stocks then money will flow into them, deflating the value of the S&P and raising the S&P yield, creating equilibrium. Correspondingly if the S&P offers a better yield, then money will leave treasuries and enter the stock market, depressing the price of bonds and raising the yields.

I was a little dubious about the assertion that investors consider them equal on a risk adjusted basis so I looked at the correlation between the 30 year treasury yield (which closely tracks the 10 year with a relatively constant spread) and the S&P 500 yield over 27 years. I also looked at the fed funds rate yield versus the S&P 500 yield over 50 years. The correlation was .71 and .74 respectively, where 1 would mean that they moved completely in harmony. My reason for testing the 30 year treasury is that stocks are valued based on their long term ability to generate cash and that 30 years seemed a better valuation period than 10 years. Even if that didn’t hold I thought that 30 year bonds may better reflect the difference between 10 year bond's risks and the S&P (the 10 year/30 year spread may account for the risk difference between bonds and stocks). It turns out that the relationship between 30 year bonds and the S&P yield that the S&P yield has been about .91 percentage points below the 30 year bonds and therefore the ten year bond is the better measure.

This led me to develop a similar model to the fed, specifically to develop a linear equation for the relationship between the Fed Funds rate and stocks as well as the 30 year Treasury and stocks.

So what does this model say about the value of securities today.

With the fed funds rate so low, I'm inclined to disregard those results but they show a 38% under valuation of the S&P 500. The 30 year Treasury equation shows a 30% under valuation of the S&P. This looks very promising, right....

Well the problem is that interest rates tend to revert to the mean and that the fed is guaranteed to raise rates at some point in the next 12 months. The Fed model is relatively useful at providing a snap shot of expected valuation at a point in time but is not necessarily effective at looking into the future.

Therefore I also calculated the value of the S&P 500 based on the long term averages of the Fed Funds rate and the 30 year Treasury bond. These show the S&P 500 as overvalued by 20% and 25% respectively.

I then propose that the average of these two probably makes for a reasonable approximation for the fair value of the S&P 500 today. According to the Fed Funds rate average we are 1.4% undervalued (remember this series had 50 years of data but is more volatile). The 30 year Treasury has the S&P 500 4.5% overvalued. By further taking the average of these two valuations I would suggest that the S&P 500 is slightly overvalued.

Given this along with the fact that we are a few percentage points ahead of the expected Dow Jones at this point in a bull market I'm inclined to say that it is time to move into more defensive positions. I don't expect that we have seen the peak of the bull market, but whole of market returns from this point on are not going to be spectacular. If interest rates move back to their long term average then we are not going to see any growth in the S&P 500 for 3-5 years and may even see a 20-25% drop.