Using Price-Earnings Ratios to Time the Market

(This does not work either!)

Professor Matthew Spiegel

August 3, 2005

The press loves to discuss whether stocks are "expensive" or "cheap" based on price-earnings ratios. Type "price earnings ratio S&P" into Google news and you are almost guaranteed to find recent articles.  Alas, from what I can tell, most of the dedication to analyzing the price-earnings ratio comes from people believing, "Gee, this must be a good idea" rather than any hard evidence.  But, fortunately, it is easy to pull up the evidence and see if there is anything to this line of analysis.  The bad news follows.

Origins of the Price-Earnings Stock Selection Model

Using the price-earnings ratio to value stocks has a long tradition.  The idea behind this investment strategy comes from a few simple and seemingly compelling principles.  A security’s value derives from the cash it will generate for its owner. Since the money does not arrive all at once, it is necessary to adjust each payment’s value in order to determine how much the asset is worth to an investor today.  The number that this generates is called the "present value" of the cash flows.  If you are willing to put up with a little mathematics you can express it in a reasonably straightforward manner.  Imagine that in period t the security will pay C_t dollars.  If the interest rate equals r then the present value (PV) of the security equals

The ellipses at the end (the ···) mean to keep going until you run out of cash flows. 

While in general the only way to calculate the PV is with a computer there is one particularly useful exception.  Imagine there exists a security that pays $100 in period 1 and in each subsequent period its payout grows by 1%.  Thus, in period two you will get $101, and in three $102.01.  A security that does this forever is called a growing perpetuity. Perhaps the best thing about a growing perpetuity is the simplicity of its valuation formula:

where g is the growth rate.  In the case of our example, if the interest rate equals 8% then the growing perpetuity’s value is $100/(.08-.01) or $1,428.57.

Perhaps the second best thing about a growing perpetuity is that it resembles what you might imagine to be the expected payoff from holding the entire stock market. In this case C₁ equals the total dividends and other payouts from the set of stocks traded on various exchanges and g the rate at which you expect these payouts to increase over time.  All of this seems pretty sensible and forms the basis for using the price-earnings ratio to value the market.  Earnings are presumably the cash flows available to investors.  While not exactly what investors can expect to receive each period it is probably not a bad proxy. If you are willing to further assume that the cash received by investors equals some fixed fraction of earnings then it is a perfect proxy!  With all of these assumptions we can now conclude that the value of the overall market is proportional to overall earnings.  (See the box for additional details.)  The exact proportion depends on the interest rate; the earning’s growth rate, and what fraction of earnings is paid out to investors. But, if the proportionality factor is constant you now have a powerful investment tool.  Assuming that the interest rate, and growth rate are also constant into the foreseeable future high price-earnings ratios imply the market is over valued. The opposite should hold when the price-earnings ratio is too low.

Now that we know where the price-earnings ratio investment rule comes from the next question is, “Does it work?”  That is, if you invest in bonds when the ratio is high and in stocks when it is low do you earn more than you would with some other reasonable strategy?

Historical Returns to a Portfolio Using the Price-Earnings Ratio

Before you can test the performance of a strategy you first need to determine what the strategy is. One very tempting, but very misleading, line of analysis begins with some average value to date, in this case the price-earnings ratio.  With this starting point you can then look up what the returns would have been from a strategy that invests in the market when the ratio is below its current historical average and in bonds when it is above.  While this may produce respectable looking returns they are worthless. Consider an investor in 1960 trying to decide where his money should be invested.  Could he have used the data you plan to use in your test?  If our strategy uses the average price-earnings ratio to date clearly the answer is no.  Nobody in 1960 had access to the market’s price-earnings ratio in the years 1961 through today.  At best they could have used the historical price earnings ratio up to 1960. 

With the above in mind, one workable strategy suggests itself.  If the market’s price-earnings ratio in a particular year is above the historical average, up to that date, invest in bonds otherwise invest in stocks. This is pretty much what financial commentators often recommend.  They first compare today’s ratio with the historic average and then determine if the market is “cheap” or “expensive.”  So, how would a portfolio like this have done?  As the graph shows, really badly!

The pink line shows how much money you would have if you initially invested $1 in the stock market at the end of 1946 and kept it in until the end of 2004.  The blue line is how much you would have today if you invested in one year government bonds when the market’s price-earnings ratio was above its historical average and in the market otherwise.  Following the price-earnings ratio strategy essentially leaves you in bonds quite a bit of the time; in 38 out of 58 years to be exact.  This might be acceptable if it meant that you could avoid major market downturns.  But you do not.  For example, the strategy has you in the market in 1974 when it went down 28%! You also miss quite a number of years with exceptional returns.  While the market lost a lot of ground in 2000 and 2001 (years where the model had you in bonds) it did quite well through most of the 1990s.  So well in fact that if you invested in the market starting in 1990 and kept your money there until the end of 2004 you more than tripled your initial holdings.  Alas, for those using the price-earnings ratio strategy, their money was parked in bonds the whole time.

Beating the Market:  Good is Not Good Enough

If you seek a higher expected return on your portfolio by jumping from the stock market to the bond market, then being a good forecaster is not good enough.  Historically, stocks have returned about 8% per year more than bonds.  Now imagine your forecasting tool is pretty good.  When it issues a “sell” recommendation that means the stock market will (on average) return only 4% more than bonds.  That is indeed a pretty good forecaster in this business!  But, it is not good enough.  By moving into bonds you actually expect to generate a 4% lower return than you would have by just leaving your money in the stock market. Worse yet, by moving in and out of the market you incur transactions costs which further reduce your portfolio’s expected value.

The price-earnings ratio, alas, has not been that good a forecasting tool.  Historically, when it signals “sell” that has not meant bonds would in fact outperform stocks.  Worse yet, holding bonds when the price-earnings ratio is above its historical mean leaves you invested in bonds most of the time.  But why?  You would think that buying stocks when the price-earnings ratio is below its historical average would leave you in stocks about half the time. What causes this very reasonable conjecture to fail is that the price-earnings ratio appears to have been on a long run upward trend. 

While the trend is very gradual it is there.  Something called the Lehmann rank-ordered trend test indicates that there is approximately a 98% chance that the price-earnings ratio is slowly moving upward over time. That is it seems unlikely that the slow move upward in the price-earnings ratio is just random chance.

What do all of these results mean for investors?  It is hard to say.  Clearly using the price-earnings ratio to time the market has not worked in the past. The fact that it has generally “recommended” investors stay out of the market has been due to its long upward drift over time.  Will the price-earnings ratio continue to go up?  I have no idea.  I cannot even tell you why it has been trending up to date.  The only thing I do know is that historically, at least in terms of total average return, using the price-earnings ratio as a guide to investing in the stock market has not done as well as a mindless buy and hold strategy.

© Matthew Spiegel