Rajnish Mehra is Professor of Finance and Chair of the Department of Economics at the University of California. He is a visiting professor at the Graduate School of Business, Chicago, and is an associate editor of The Journal of Economic Dynamics and Control.
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The equity premium - what is it?
For over a century, stock returns have been considerably higher than those for T-bills. The average annual real return (that is to say, the inflation adjusted return) on the U.S. stock market over the last hundred and ten years has been about 7.9%. Over the same period, the return on a relatively riskless security, like a government bond was a paltry 1%. The difference between these two returns, 6.9 percent, is termed the 'equity premium'. This statistical difference is even more pronounced over the post war period, with the premium of stock returns over bonds being almost 8%.
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What is the equity premium puzzle?
Since stocks are 'riskier' than bonds, investors require a larger premium for bearing this additional risk; and indeed, the standard deviation of the returns to stocks (about 20% per annum historically) is larger than that of the returns to T-bills (about 4% per annum), so, obviously they are considerably more risky than bills! But are they?
Stocks and bonds pay off in approximately the same states of nature or economic scenarios and hence according to standard asset pricing theory they should command approximately the same rate of return, or at most, a 1% return premium over bills! Since the observed mean premium on stocks over bills is considerably and consistently higher, we have a puzzle on our hands.
The equity premium puzzle is a quantitative puzzle in that standard theory is consistent with our notion of risk that, on average, stocks should return more than bonds. The puzzle arises from the fact that the quantitative predictions of the theory are an order of magnitude different from what has been historically documented.
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Statistics, damn statistics . . .
The observed premium is not just a statistical artifact. Given that we have over a hundred years worth of good data, it is highly unlikely that the 'true' premium is small or zero when the observed premium is 7%.
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The US and other markets.
The pattern of excess returns to equity holdings is not unique to U.S. capital markets. Equity returns compared to the return to debt holdings in other countries also exhibit this historical regularity. The annual return on the British stock market was 5.7% over the post war period, an impressive 4.6% premium over the average bond return of 1.1%. Similar statistical differentials are documented for France, Germany, Italy and Spain.
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Great fluctuations of the equity premium year-by-year.
The 'ex-post', or 'realized', equity premium is the actual, historically observed difference between the return on the market, as captured by a stock index, and the risk free rate, as proxied by the return on government bills. This premium has varied considerably over time, being positive in some years and negative in others.
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Investment planning with the equity premium.
The related concept, the 'ex-ante' equity premium, is a forward-looking measure of the premium - that is, the equity premium that is expected to prevail in the future or the conditional equity premium given the current state of the economy.
To elaborate, after a bull market, when stock valuations are high relative to fundamentals, the ex-ante equity premium is likely to be low. However, it is precisely in these times, when the market has risen sharply, that the ex-post, or the realized premium is high. Conversely, after a major downward correction, the ex-ante (expected) premium is likely to be high while the realized premium will be low.
The ex-post premium (i.e. the realized) premium can be negative. However, the forward-looking premium MUST be positive. If it were negative investors would not hold stocks and perhaps even short them. Can the whole market do that? No. What will happen is that the price would go down so that, looking ahead, the premium is positive.
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Investment planning horizons are key!
The documented equity premium is for very long investment horizons. It has very little to say about what the premium is going to be over the next couple of years. Market watchers and other professionals who are interested in short term investment planning, will wish to project the conditional equity premium over their planning horizon. This is by no means a simple task.
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Time and tide . . .
The ex-post equity premium is the realization of a stochastic process over a certain period and it has varied considerably over time. Furthermore the variation depends on the time horizon over which it is measured. There have been periods when it has even been negative. It is important to remember that not only is the mean 7% but it comes with a standard deviation of almost 20%!
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The equity premium is dead! Long live the equity premium!
There is the point of view, held by a group of academicians and professionals who claim that at present there is no equity premium and by implication no puzzle. Before we dismiss the premium we need to examine the evidence. The data used to document the equity premium over the past hundred years is probably as good as any economic data we have - and a hundred years is long series when it comes to economic data. Even if the conditional equity premium, given the current market conditions is small, this in itself does not imply that either the historical premium was too high or that the equity premium has diminished.
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Stocks payoff in the long run.
Based on what we know, we can make the following claim: over the long investment horizon the equity premium is likely to be similar to what it has been in the past and the returns to investment in a diversified equity portfolio will continue to substantially dominate that in bills for investors with a long planning horizon.