After a brutal three-year bear market to begin the 21st century, US stock markets have done well for four consecutive years. Despite this fact, stocks (especially large-caps) remain a great buy.

I come to this conclusion for several reasons.

First, the valuation on the S&P 500 index has fallen for three consecutive years even though stock prices have risen. This is because earnings have risen faster than stock prices. According to Standard and Poor’s, the trailing 12-month price/earnings ratio on the operating earnings of the S&P 500 has fallen from 28 at the beginning of this century to 17 two years ago, to 16 today. The 12-month forward p/e stands at just 14.1, implying a 7.1 per cent earnings yield for stocks.

By contrast, the 10-year yield on US Treasury bonds is about 4.2 per cent. Not only are bond yields far lower than stock yields, but this yield is also the best you will ever get if you buy a Treasury bond, because bond interest payments do not rise over time.

Not true for stocks. The earnings yield on your original purchase price will rise over time, so the yield on today’s purchase price will be higher in the future than it is today. If you were to buy both an S&P 500 index fund and a US Treasury bond fund today, the discrepancy between the earnings yield on your stock portfolio and the interest yield on your bond portfolio would rise over time.

For example, say you buy the S&P 500 index at today’s earnings yield of 7.1 per cent, and the operating earnings of the companies in the S&P 500 rise 6 per cent a year, on average, over the next 10 years. By year 10, the earnings yield on your original purchase price will have risen to 12.7 per cent. The interest payments on the Treasury bond will stay the same, however, so the pre-tax yield on your cost basis will be the same: 4.2 per cent. It can never rise from that level. The discrepancy between the earnings yield and the bond yield will rise from 2.9 per cent today to 8.5 per cent in year 10.

In addition, stocks offer another advantage: the ability to defer capital gains taxes until a time of your choosing (this isn’t relevant if you’re a tax-exempt investor). Since most of the gain on stocks comes in the form of capital gains, you get to choose when to pay the taxman. Sell a stock, and you pay taxes on your gain. Hold on to it, and you don’t. Treasury bonds don’t give you this option. You have to pay taxes each year on the interest payments at ordinary income rates. If you’re in the 32 per cent tax bracket, the after-tax yield on a 4.2 per cent bond falls to 2.9 per cent. Subtract inflation and you get about 1 per cent real after-tax bond yield. Whoopee.

By contrast, the earnings yield on a stock is already converted to an after-tax yield because the earnings yield is calculated based on after-tax profits. And earnings tend to rise with inflation so that the earnings yield approximates a real (after-inflation) yield.

Some would argue that even at stocks’ current trailing p/e of 16, they are selling above their post-second-world-war average valuation of about 14.5. That’s true. However, there is good reason to believe that the long-term average is skewed low. Interest rates in the 1970s and 1980s were far higher than they are today, while confidence in the Federal Reserve’s ability to manage inflation was far lower. The Fed has gotten better at controlling inflation and telegraphing its thoughts on this subject to market participants. This has increased investor confidence in Fed policy, theoretically lowering the “risk premium” built into stocks. If investors don’t have to worry about runaway inflation, the future expected real (after-inflation) earnings yield on stocks should be higher. Runaway inflation is the killer of p/e ratios. Remove significant worries about inflation, and p/e ratios should be higher, all else equal.

Sure, there is always a risk of a recession, which would cause the “e” in the p/e ratio to decline temporarily. That risk is always with us, especially after several years of an expanding economy. This is why investors demand a higher after-tax yield on stocks than they do on Treasury bonds. As an exercise, let’s assume operating earnings of the S&P 500 fall 20 per cent over the next year, far below the current consensus. If that happened, the forward p/e would be 17 rather than 14, for an after-tax earnings yield of 5.9 per cent, still far higher than the yield on treasuries. You just can’t beat the yield on stocks. You have to be willing to live with the volatility, but the maths works in your favour the longer your time horizon.

Today’s large gap between bond and stock yields is excessive. Investors are being too cautious.

The writer is a former equities strategist at Morningstar who manages a hedge fund, Sellers Capital, in Chicago.

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