## The Future of the Equity Premium: SUMMARY: PRELIMINARY AND INCOMPLETE

Konstantin Magin and I are closing in on the first draft of our "Future of the Equity Premium" paper...

SUMMARY: PRELIMINARY AND INCOMPLETE: DRAFT

The Future of the Equity Premium

J. Bradford DeLong and Konstantin Magin

December 2006

Suppose that, at the start of some year since the beginning of the twentieth century, you had taken $1,000,000 that you had invested in bonds and believed you would not want to touch for twenty years, and invested it insteade in a diversified portfolio of equities. (Or suppose you had been able to borrow$1,000,000 at the long-term government bond rate). And suppose you had then let both legs of that investment ride for twenty years. What would have been the results in dollars (adjusted for inflation) twenty years later?

The figure above tells you the answer, for each year from 1901, the start of the twentieth century, until 1986--twenty years ago.

In two years you lose: $50,000 if you invest in 1913, and$150,000 if you invest in 1929. In both years, you would have done better to invest in bonds. In all the other years--all 84 of them, 97.7% of the time--you win.

Often you win big. The average return is $4,356,000: more than four times the value of the initial long equity leg of the portfolio. 93% of the time you are up more than$500,000. 80% of the time you are up more than $1,000,000. 59% of the time you are up more than$2,000,000. 42% of the time you are up more than $4,000,000. 19% of the time you are up more than$8,000,000. And the champion moment to go long stocks and short bonds was 1942, just after Pearl Harbor, when your portfolio held until 1962 would have given you an edge of $15,600,000. This is, in brief, the equity premium puzzle of Mehra and Prescott (1985). Throughout the twentieth century anybody with some initial wealth devoted to bonds and with a twenty-year or more time horizon had a near money machine at his or her disposal. And not a nickel-and-dime money machine either. Rietz (1988) and Barro (2005) attribute the apparent equity premium to serious and severe risks of equity ownership that do not show up in the twentieth-century sample. The problem is that it is hard to think of what such risks might be. We have one Great Depression in the sample. Isn't that enough? And when the Day of the Revolution comes and the red flag flies from the towers of the Loop, investors in U.S. government bonds will be in no better shape than investors in corporate equities. At a more subtle level, Weitzman (2006) argues that the equity premium is generated by unknown unknowns--risks that we cannot characterize and that have the potential to have any conceivable effect on our expected utility. In Weitzman's framework, the anomaly is not that stock prices are so low but that they are so high: that the equity premium return is not still bigger than it has been. But once again there is the question of just what these risks are, and why they depress the relative price of stocks rather than bonds. Once you put the possibility that the ex ante distribution of stock relative to bond returns had a big, important, substantial lower tail that just does not show up in the data ex post, attempts to explain the equity premium return as some kind of rational-expectations equilibrium for investors with reasonable degrees of risk aversion are likely to be in vain. You have to construct a scenario in which investors and markets are such that investors do not turn the crank on a money machine. And that is very, very hard to do. An enormous variety of institutions and investors ought to have taken advantage of this money machine--sold their bonds and put their money in stocks: young parents of newborns looking forward to their children's college, the middle-aged looking at rapidly-escalating health-care costs, the elderly looking forward to bequeathing some of their wealth to their descendents or to worthy causes, workers with defined-contribution pensions, businesses with defined-benefit pensions, life insurance companies, the Social Security Trust Fund, the reserve accounts of the world's central banks, businesses with reputational capital that do not expect to be blindsided by new technologies, hedge funds, and so on. On the other side of the market, there are all the companies that appear underleveraged: replacing high-priced equity capital with low-priced debt capital would seem to have been as profitable a strategy for a long-lived company as investing in high-return equity rather than low-return debt is for a long-lived investor. Yet they have not done so, or have not done so on a sufficient scale to pick up all the$4,356,000 checks and the occasional $15,600,000 check left on the sidewalk. We can explain why any one particular group might have good reason not to try to take advantage of the equity premium, but it is much harder to come up with the many good reasons why all of the groups of potential investors, and institutions, and organizations passed the$4,356,000 checks by.

It's not that the existence of an equity premium return is a new discovery. In 1923 financial analyst Edgar L. Smith pointed out that diversified investments in American equities had far outperformed bonds of all types. Edgar Smith's (1923) Common Stocks as Long-Term Investments was not the first publication to point out that stocks earned higher returns than bonds on average-—that was well-known. But investments in equities were viewed then as the domain of the risk-loving and the entrepreneurial. Speculators—-either possessing inside information about fundamentals or market microstructure, risk-loving, or naïve—owned stocks. But prudent investors did not: the risk of ruin was seen as too high. What Smith did was to publicize the fact that equity diversification worked: diversified stock portfolios produced higher rates of return without bearing higher systematic risk than bond portfolios, especially once one took inflation risk into proper account. A portfolio invested in one or two individual stocks was overwhelmingly risky: "subject," Smith wrote, "to the temporary hazard of hard times, and [might] be permanently lost as a result of a radical change in the arts or of poor corporate management." But, Smith pointed out, these risks could be diversified away: "effectively eliminated through the application of the same principles which make the writing of fire and life insurance policies profitable." By contrast, portfolio diversification did not work for bonds, which were all "subject to the same hazards" which were "not reduced by increasing the number of different bonds held."

Some economists--Blanchard (1993) is probably the best advocate for this position--see the large premium equity return in the past as a mistake on the part of the market, a mistake that the market should be correcting. They anticipate that the equity premium is smaller in the present than it was in the past and that it will vanish or nearly vanish in the future. Blanchard sees the high equity premiums of the 1950s and the 1970s as a combination of excessive salience of the memory of the Great Crash and the Great Depression in investors' minds, and as the result of simple money illusion a la Modigliani and Cohn (1979).

But we do not see any signs that Ms. Market has moved to eliminate past mistakes. The real return on the 20-year U.S. Treasury inflation-protected bond is 2.1%, while the current annual earnings yield on the S&P composite stock market index is 5.7%. These numbers suggest an expected equity premium today of 3.6%, lower than the 6% premium equity return of Mehra and Prescott (1985), but far, far higher than the value of 0.25% per year of Mehra's (2003) baseline representative-agent model for a coefficient of relative risk aversion of 2. and an equity premium of 3.6% per year is enough to double your relative wealth over twenty years, and quadruple it over forty. Plus you get substantial immunity from long-run inflation risk as well.

The equity premium remains a puzzle. And there is no reason to think that it is a puzzle about to vanish. As Rajnish Mehra (2003) wrote:

The data used to document the equity premium over the past 100 years are as good an economic data set as analysts have, and 100 years is a long series when it comes to economic data. Before the equity premium is dismissed, not only do researchers need to understand the observed phenomena, but they also need a plausible explanation as to why the future is likely to be any different from the past. In the absence of this explanation, and on the basis of what is currently known, I make the following claim: Over the long term, the equity premium is likely to be similar to what it has been in the past and returns to investment in equity will continue to substantially dominate returns to investment in T-bills for investors with a long planning horizon.

Or as Warren Buffett wrote twenty years ago:

[T]he secret has been out for fifty years, ever since Ben Graham and Dave Dodd wrote Security Analysis, yet I have seen no trend toward value investing in the 35 years I have practiced it. There seems to be some perverse human characteristic that likes to make easy things difficult. The academic world, if anything, has actually backed away from the teaching of value investing.... It's likely to continue that way.... [T]hose who read their Graham and Dodd will continue to prosper.