A Better Way Of Determining If Market P/E Is Too High Or Low

The price-earnings ratio, P/E, of the S&P 500 (SPY) currently stands at 14.1 based on year-end estimates for 2011 S&P 500 operating earnings. P/E is often compared to a historical average to determine if the market is over or undervalued. The idea is that it if it is above the average, then the market is overvalued. If it is under the average, then the market is undervalued.

There is also much debate of what to use for earnings. The leading contenders are reported earnings and operating earnings. Some, like Robert Shiller, building off the work of Benjamin Graham, suggest taking a 10-year average, often called "P/E10." I use the most recent trailing four quarters of operating earnings because they eliminate non-recurring items and I believe that current earnings are usually the best basis for predicting future earnings. (We can save the debate on P/E 10 for the comments section or another day, but taken to the extreme, does it make sense that Apple's (AAPL) 10 year average is a better reflection of its future potential than today's earnings?)

The market P/E is volatile. Since 1986 it has ranged from a low of 11.5 in December 1988 to a high of 29.6 in December 1999 with an average of 18.8. Using the average as a benchmark implies that, other than anticipated changes in earnings, there is no reason that P/E should ever change and no cause for the rise and fall. My research says otherwise and suggests that the market P/E is driven by long-term interest rates and their relationship to the cost of capital.

The Risk Premium Factor (RPF) Model is a simple approach for understanding intrinsic value of the market and expected P/E. The model shows that two factors drive the market: Earnings and interest rates (30 year Treasury yields), which drives the equity risk premium and cost of capital and embody inflation. And for individual companies, there is a third factor: Growth. I introduced the model to Seeking Alpha here in 2010. Earnings were discussed in my October 25, 2011 article. This article focuses on interest rates as the driver of P/E.

The RPF Model is built on a simple constant growth equation where P = E / (C - G), and explains S&P Index levels with good accuracy for 1960 - present using only the long-term Treasury yields, S&P 500 operating earnings and some simplifying assumptions. P is predicted price for the index, E is index earnings, C the cost of capital, and G, the expected long-term growth rate.

The charts below shows actual versus values predicted by the RPF Model for the S&P 500 since 1986. (I'll discuss the references to normalized Treasury yields later.)

right click to enlarge

The cause of the relationship between interest rates and P/E becomes apparent when with the terms are rearranged:

P/E = 1 / (C - G)

Looking at this equation, you can see the relationship between C and P/E ratio. If C increases, then P/E gets smaller and vice versa. This next chart shows predicted versus actual P/E based on the model. Treasury yields drove changes in the cost of capital, C, resulting in the volatility in P/E.

The chart below compares predicted P/E to a range of interest rates:

As interest rates increase, the expected P/E falls. As the chart below demonstrates, this relationship has held since at least 1960.

Looking at the past 50 years, you can see where the rise in interest rates caused the P/E compression between 1960 and 1980, while interest rates falling from historic highs resulted in the P/E multiple expansion that followed.

For a more complete discussion of the assumptions and derivation of the formula see this article on Seeking Alpha or my book, "The Risk Premium Factor."

Now you're probably wondering, if this really works, with the 10 and 30-year Treasuries trading at historic low yields, why isn't the market trading at a much higher multiple? As I've discussed in several other articles (here), interest rates are being artificially depressed by the Federal Reserve. I use a normalized Treasury yield of 4.5% base on a real rate of 2% plus 2.5% long-term inflation. Using the normalized Treasury yield with S&P 500 earnings of $96.47, the S&P 500 Index which closed Wednesday at 1,358 is still undervalued by 17% with a predicted value of 1,650 and a predicted P/E of 16.5.

Investors know that once the artificial controls are removed, interest rates will return to a normalized level, so these artificially low yields are not reflected in equity prices.

One big note of caution, this valuation assumes that earnings hold and continue some growth which is very dependent on the outcome of macro factors like the Sovereign debt problems with Greece and other European Union countries.

Disclosure: I am long SPY and short long-term Treasuries.