What are stock and bond prices predicting for growth?

In today’s confusing markets, many people are wondering whether stocks are cheap or dear, just as they wonder whether bonds represent great value or a massive bubble. The first question everyone needs to answer before making a trade is: what is already implied in the market price? My purchase of Sony stock was particularly ill-timed because I had yet to understand this concept.

Tonight I will look at what the relative yields on stocks and bonds tell us about the market’s expectations for real profit growth. If you have a strong opinion on the future profitability of American public companies, you can use this metric to help determine whether you should buy or sell shares.

A stock is a claim on a company’s profits. The price of the stock is determined by current earnings, a discount rate (your expected rate of return for holding the stock), and expected real earnings growth:

P = E/(D-G)

This can be rearranged to say:

G = D-(E/P)

In other words, the expected real growth rate is the discount rate minus the earnings yield (inverse of the PE ratio). This means that you can determine the market’s implied expectations for real corporate profit growth just by knowing the earnings yield for the S&P 500 and by plugging in an appropriate discount rate. The trick is picking the right numbers.

For earnings, there are three basic options.

Sell-side analysts (so-called because their job is to sell you stocks, whether or not you ought to be buying) like to use their projections for next year’s profits. This “forward PE” usually makes shares look cheap because sell-side analysts always predict that profits will rise rapidly. The Wall Street Journal reports that analysts calculate the forward PE ratio of the S&P 500 index to be 11.98, or a forward earnings yield of over 6%. That looks attractive compared to the yield on a 30-year government bond (3.3%), but it is misleading.

Trailing 1-year earnings are more standard. While better than forward earnings, the timeframe is still too short to provide a good perspective. Profits are highly cyclical, after all, so a 1-year trailing PE makes stocks look relatively cheap right before they start losing value.

My personal favorite option is to use a 10-year trailing PE adjusted by inflation. This is known as the cyclically-adjusted PE ratio and was made popular by Yale professor Robert Shiller. You can read more about its construction on his website.

The harder choice is which discount rate to use. Stocks are exposed to duration risk and credit risk. The appropriate discount rate incorporates these two factors. In principle, the best rate would be the yield on a perpetuity with the same credit risk as the general stock index. In practice, you might use the Baa long-duration corporate bond yield.

The problem with this approach is that the implied credit risk shrinks when times are good and widens when times are bad. This makes implied earnings growth look lower than it should when markets are about to peak and can snooker you into buying high. Likewise, you might think shares are unreasonably expensive if corporate funding costs surge during a financial crisis. That would make you miss a great buying opportunity.

How to get around this? One way is to create a synthetic discount rate that takes the yield on a government bond and then adds a fixed equity risk premium on top. I chose the 3-month t-bill because it moves up and down with the business cycle and because it has no duration risk.

Then I made a reasonable assumption, which is that the equity risk premium should be roughly equivalent to one-fourth the annualized volatility (1 standard deviation) of the excess returns above cash of holding the S&P 500. Why one-fourth? When I worked at a global macro fund, I spent a great deal of time studying how different asset classes performed over long periods of time. Historically, for almost any asset, the annualized excess returns above 3-month t-bills ended up being about one-fourth historic annualized volatility. There is no inherent magic in the number, except that investors across countries and across time seem to have been satisfied with that ratio of return to risk. If it has been good enough for them, it is good enough for tonight’s analysis. The long-run annualized volatility of the U.S. stock market is about 16%, so I concluded that 4% was a reasonable choice for the equity risk premium over t-bills.

You might be wondering, as I did, whether this measure of implied earnings growth is a good predictor of the real growth in corporate profits. Not really:

The market was pretty bad at predicting real corporate profits, at least over the past half-century. That makes sense, since there were plenty of times in the past 50 years when stocks were either wildly overvalued or aggressively undervalued. Those moments presented opportunities for the smart (and lucky) to make a lot of money while betting against the conventional wisdom.

It turns out that implied earnings growth does track the annualized 5-year price change of the S&P 500. In other words, the market’s expectations about the future are determined by the experience of the recent past:

This is not what you would expect from a rational and efficient market, which should be forward-looking rather than backward-looking.

What should you make of all this? For more than ten years, investors have been battered by a vicious bear market in equities punctuated by sharp crashes. To my eye, it looks like they expect even more of the same. Decide for yourself whether you agree or disagree. Do you want to buy stocks and sell bonds, sell stocks and buy bonds, or stay away? I am not going to pretend that I have the answer, but if you are feeling optimisitic, be sure to read this and this.


About Matthew C. Klein
I write about the economy and financial markets for Bloomberg View. Before that I wrote for The Economist on a fellowship provided by the Marjorie Deane Financial Journalism Foundation. I have worked at the world's largest hedge fund and read every FOMC transcript since May, 1987.

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