U.S. Stock Market Valuation Using P/E

A discussion of relative U.S. stock market valuation over time using price-to-earnings (P/E) ratios of the Real S&P 500 Index and a number of relevant new charts.

The Real S&P 500 stock market index is a reasonable proxy for overall U.S. stock market performance. As the following chart shows, the stock market sometimes goes up a lot and sometimes it goes down a lot...for extended periods of time. (see 10/30/20 Post - Stocks Go Up...And Down) This implies that sometimes the stock market is significantly over or undervalued. That is, stock prices are sometimes significantly higher or lower than they should be. This becomes apparent in hindsight, as illustrated by this next chart. For example, lower stock market values for an extended time after 1929 demonstrate that the stock market of 1929 was significantly overvalued. The colored horizontal lines in this chart mark a number of times when, in hindsight, the stock market was overvalued.

It would be nice to have a way, besides waiting for the future, to gain some insight into the current over/undervaluation of the stock market. Ideally, a good valuation measure would have a history of being high when the stock market has been shown by history to have been overvalued and being low when the stock market has been shown to be undervalued. Many stock market valuation measures have been proposed. One well known measure is the ratio of a stock's price to its corresponding earnings. This is called the price-to-earnings ratio or P/E.

To understand why the P/E might be considered a kind of stock valuation measure, consider the following. The value of a stock is determined by the value of the future stream of dividends provided by this stock. Thus, a good valuation measure would be the price of a stock divided by some unit of its future dividend stream. Of course, the future dividend stream is unknown. Since dividends must be paid out of earnings, and earnings will either be paid out as dividends or reinvested in the company in hope of producing even greater dividends in the future, earnings might be an interesting representation of a unit of the future stream of dividends. Thus, the ratio of price-to-earnings (P/E), might be an interesting stock valuation measure.

The following charts characterize several versions of price-to-earnings stock valuation measures and demonstrate how they have performed historically. This next chart shows the simple current Real (inflation adjusted) P/E for the S&P 500 Index over time.

The average Real P/E for this data is about 16 as shown by the horizontal gray line. The colored horizontal lines represent one and two standard deviations from the average. By definition, around 68% of the data points are within one standard deviation of the average and 95% of the data points are within two standard deviations of the average. In using the P/E as a valuation measure, one might define times when the P/E is more than one standard deviation from the average as times when stocks are over/undervalued and times when the P/E is more than two standard deviations from the average as times when stocks are extremely over/undervalued. The next chart shows the Real S&P 500 index colored to denote when it is over/undervalued according to this definition.

A good valuation measure would tend to color the index yellow or red at major price peaks and light or dark green at major price valleys. Instead, the coloring of the index in the previous chart makes very little sense. This next chart will help identify the problem.

The P/E is graphed in blue. The numerator for this ratio (Real S&P 500) is graphed in dark gray, and the denominator (Real Earnings AR) is graphed in light gray. Notice the large P/E spike in 2009. This happened not because stock prices were rising but because earnings were falling rapidly only to then recover rapidly. In many places in this chart, rapid changes in the denominator causes the P/E value to be unstable and not very meaningful.

The instability of this ratio can be fixed by using a longer term earnings average in the denominator of the P/E ratio. The following chart again shows in blue the original P/E ratio denominator (Real Earnings AR) and in red a new, more stable denominator (10 Y Average Earnings).

When this 10 year rolling average of earnings is used as the denominator in this P/E ratio, the result is something called the Cyclically Adjusted Price-to-Earnings Ratio or CAPE. This stock market valuation measure was created by economist Robert Shiller, and it is shown in the next chart.

As with the simple P/E chart, the above CAPE chart is marked with horizontal lines denoting the average and the points that are one or two standard deviations above or below the average. As before, one might define times when CAPE is more than one standard deviation from its average as times when stocks are over/undervalued and times when CAPE is more than two standard deviations from its average as times when stocks are extremely over/undervalued. This next chart shows the Real S&P 500 with portions colored to illustrate over/undervaluation according to this definition.

The above chart shows that the stabilization of the denominator in CAPE has produce a much more useful valuation measure. The major stock market peaks are colored in yellow or red and the major stock market values are colored in light green.

The S&P 500 index only shows capital gains. As discussed in 11/09/20 Post - U.S. Stock Market: Real Total Returns, dividends play a significant role in total returns. The CAPE valuation measure does not consider the impact of dividends. It is reasonable to ask how consideration of dividends might change the valuation measure. To this end, economist Robert Shiller also created a TRCAPE valuation measure that is very similar to CAPE, but with price and earnings modified as they would be if all dividends were reinvested. The next chart shows the TRCAPE stock valuation measure, and it looks very similar to CAPE.

Once again, times when TRCAPE is more than one standard deviation from its average can be considered to denote times of over/undervaluation, and times when TRCAPE is more than two standard deviations from its average can be considered to denote times of extreme over/undervaluation. Using this definition, the next chart shows the Real S&P 500 Total Return Price (includes reinvested dividends) with portions colored to illustrate over/undervaluation. This chart looks very similar to the Real S&P 500 index marked with CAPE based valuations, so it appears that reinvesting dividends hasn't had too much of an impact on the CAPE valuation measure.

Price-to-earnings ratio based stock valuations measures CAPE and TRCAPE can provide useful context for to current stock market valuations. Specifically, they can say how over or undervalued the current stock market is by these measures relative to history. The better a stock market valuation measure has performed historically, the more confidence one might have in the current valuations. However, a word of caution is in order. There is no guarantee that the future will be like the past. To the extent that the future is different from the past, stock market valuation measures based on past behavior could prove to be less useful than anticipated.