Expected returns and predictability

For most of the twentieth century, finance treated the return you could expect from the stock market as a fixed number. Seven percent, eight percent, whatever the long average said. Prices moved every day, but the expected return sat still underneath them, like the bottom of a lake under waves. That belief made life simple. If the expected return never changes, there is nothing to forecast, and the only sensible question is how much of the market you want to own.

Then the data started saying something else. When stocks were cheap relative to what they earned and paid, the following years tended to be good; when they were expensive, the following years tended to be poor. The expected return, it seemed, moved. That raised the obvious question: if expected returns move, can an investor use the movement? Two papers answer it, and they appear to disagree. One says no, quite firmly. The other says yes, and explains what the first one was measuring. Reading them together is the whole lesson.

Goyal and Welch, 2008

Amit Goyal and Ivo Welch ran an audit. By the middle of the 2000s the academic literature had proposed dozens of variables that were supposed to forecast the market’s return over the coming year: the dividend yield, earnings relative to price, book value relative to price, interest rates, inflation, the spread between safe and risky bonds, and more. Each had a paper behind it and a table of statistics that looked convincing. Goyal and Welch asked a plainer question. Suppose an investor had used each of these predictors as it became available, with only the data known at the time. Would it have helped?

The answer was no. Almost none of the predictors would have beaten the simplest possible forecast, which is the historical average return, and many would have done worse. Variables that looked powerful over the full sample fell apart when you were only allowed to know what a real investor could have known. Their conclusion was blunt for an academic paper: these models would not have helped an investor.

I have built versions of these models myself, and the paper describes my experience exactly. A valuation model tells you the market is expensive. You reduce. The market rises for three more years. The model was not wrong about the long run, as we will see, but you were asked to act on it one year at a time, and one year at a time it was noise. The most useful thing in the paper is the benchmark it forces on you. Before trusting any forecast of next year’s return, ask whether it would have beaten the dumbest forecast available, which is the long average. In real time, almost nothing does.

The episode I keep in mind is December 1996. Alan Greenspan, the head of the American central bank, said in a speech that stock prices might be carried away by what he called irrational exuberance. He had a point: compared with what the companies earned, stocks were more expensive than they had been in decades. Many people sold. Over the next three years the market roughly doubled, and they missed it. But measured from the peak in 2000, the following ten years returned almost nothing. So the warning was right about the decade and wrong about the year, three years in a row.

Cochrane, 2011

John Cochrane took all of this apart in his address as president of the American Finance Association, and his title was the whole argument: discount rates. Here is the plain version. A price is a stream of future cash, discounted at the rate investors demand for waiting and for bearing risk. So a price can move for only two reasons: either the expected cash changed, or the rate changed. The old view of finance held that almost all movement was cash news. Companies would earn more or less than expected, and prices adjusted. The rate, which is another name for the expected return, was assumed constant.

Cochrane’s claim, resting on thirty years of evidence, is that the old view had it backwards. Most of the movement in prices comes from the rate. When the market falls hard, it is usually because investors have started demanding a higher return, and the arithmetic of that demand is a lower price today and higher returns afterward. The evidence is consistent across every place anyone has looked. Cheap markets are followed by high returns and expensive markets by low ones, in stocks, in bonds, in currencies, in houses. And the forecast gets stronger with distance: a valuation measure explains little of next year, and a large share of the next decade.

Why would the rate move? Cochrane’s answer is about people in bad times. When the economy turns and incomes are threatened, people cannot bear as much risk as they could before, so they demand more return to hold risky things. Prices fall to deliver it. High expected returns are therefore a symptom of fear, and they arrive when most investors are least able to take advantage of them. This is what reconciles the two papers. Expected returns do vary, and valuation does forecast them, at the horizon of years. But the variation is a payment for holding risk at the moments when holding risk is hardest, and it is available only to investors who differ from the average, who can buy when the average investor is selling. Goyal and Welch showed that the signal is useless as a trading rule for next year. Cochrane showed why it is nevertheless the organizing fact of modern finance.

Planning and timing

What I keep from these two papers is a separation I did not have before reading them. There are two uses for a forecast of returns.

The first use is planning. How much do we need to save. What can this portfolio support in spending. What is reasonable to promise a family over the next ten or fifteen years. For that, valuation is the best information available, and using the long average instead, when prices are far from normal, is a way of lying to yourself. When stocks are expensive I plan for less. When they are cheap I plan for more, and I say so in writing, so that when the cheapness feels like catastrophe there is a page telling me it was expected.

The second use is timing: moving in and out of the market according to what the forecast says about the coming year. For that, valuation is close to worthless, and Goyal and Welch showed it. Over a year the signal is drowned by everything else, and the person acting on it pays in taxes, in costs, and in the years he spends out of a market that kept rising. I do not do it. The few times I have, the result was a lesson I could have read for free.

So the habit is one sentence. Use the price you paid to set what you expect over a decade, and never to decide what you do this year. That way the plan stays realistic and the money stays invested.

Gala: the price you pay for something tells you roughly how well it will do over the next ten years, and almost nothing about next year. Use it to plan for the long run. Do not use it to guess what happens next.