Risk Equity Prices and Excess Return

We noted above that, at least in the United Kingdom and the United States, the rate of return on equities over the last 100 years had, on average, substantially exceeded the rate of return available on government bonds. This makes perfect sense as long as the risk on equities substantially exceeds the risk of those other investments. But what do we mean by risk here, and how might we measure it? The answer to these questions matters a lot, because movements in the risk premium can dramatically affect stock prices. If people come to think of equities as much more risky, they might require that, on average, they yield 10% more than government bonds, rather than, say, 5% more. Discounting future dividends at a rate that is higher by 5% could easily generate 40% or 50% falls in the price of equities. We can see, in principle, why this is so if we look again at Figure 17.7. Anything that causes the required rate of return to increase will decrease share prices unless there are compensating shifts in future dividends. Therefore, increases in risk premiums will lead to sharp falls in share prices even if investor forecasts of future dividends do not change.

The simple dividend discount model for stock prices, combined with an assumption of anticipated steady dividend growth, generates a link between stock prices, the latest dividend payment, and the relative magnitudes of the overall required return and the expected growth in dividends

The required return on equities, r, is the sum of a safe rate and the risk premium. Let's consider some plausible magnitudes for a developed economy. The safe (real) rate might be around 3%. With a risk premium of 4%, r = 7%. If dividends grow in line with GDP, 2% a year might be plausible, giving a value for (r β€” g) of 5%, so that the price to dividend ratio is 20. Suppose that the risk premium falls to 2%; (r β€” g) is now 3% and the price to dividend ratio rises to 33β€”an increase in stock prices of 65%!

As long as investors perceive that equities are riskier than other assets, they will have to yield a higher rate of return. Can we therefore use this perspective to explain Figure 17.6, which shows by just how much equities have outperformed rates of return than other conventional assets? The first issue to consider here is whether equities really are riskier than most other investment categories.

It may seem obvious that equities are riskier than bank deposits or government bonds. But that is a hasty conclusion. What matters are real rates of returns, that is, the proportionate increase in the money value of the asset less the rise in the general cost of living. Most government bonds guarantee a nominal rate of return, and even then, that return is only guaranteed if you hold the debt until maturity and if the government has a zero probability of default. Holders of U.S., Italian, and U.K. government bonds found that those assets generated substantial negative real returns through much of the 1970s because inflation was higher than expected. Holders of Russian government bonds had a much nastier shock in 1998; their market value fell by about 80% during the year. Nor do bank deposits generate predictable real rates of return; inflation is unpredictable even over a five-month horizon, let alone over five or ten years. These facts should make us think harder about the relative riskiness of equities and other assets.

To gauge whether the extra return over bonds or bank deposits that investors in U.S. or U.K. equities have got over the last century is a fair compensation for risk, we need to use a more formal apparatus. In 1985, Raj Mehra and Ed Prescott published an influential paper on the "equity premium"; that is, the extra return that equities yield over risk-free assets.7 Using past data, Mehra and Prescott estimated that the U.S. risk

7 Mehra and Prescott, "The Equity Premium: A Puzzle," Journal of Monetary Economics (1985), vol. 15, pp. 145-161.

TABLE 17.1 The Equity Premium In the United States
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