Efficient Frontier
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William J. Bernstein

When Risk and Return Become the Same

One of the hoariest bits of conventional financial wisdom is that over the long run, the probability that stocks will outperform bonds approaches unity—that is, as your time horizon grows, stocks actually become less risky than bonds or even T-bills.

Wharton finance professor Jeremy Siegel, author of the classic Stocks for the Long Run, is largely responsible for this agreeable state of affairs. The good professor examined stock performance over time periods of different lengths and found that over progressively longer periods, the odds of stocks having a negative return or of underperforming bonds and T-bills gradually decreases to zero. He pointed out that from 1802 to 1997, stocks outperformed bills in 97% of 30-year periods and after 1871, they outperformed in 100% of 30-year periods. He concluded:

Although it might appear to be riskier to hold stocks than bonds, precisely the opposite is true: the safest long-term investment for the preservation of purchasing power has clearly been stocks, not bonds.

The fallacy here is subtle and requires some explanation. Consider the investor who checks the stock page each day or imports his Yahoo! portfolio into a spreadsheet once every hour. For him, risk and return are entirely different things. Risk is the knot in his stomach as he sees his wealth slipping away in dribs and drabs, and occasionally in large jagged chunks during a bad market. Return, on the other hand, is what he is going to retire on 30 years hence.

Now, consider the investor who has been left a portfolio by an abusive uncle and, because of unpleasant memories, never looks at it until he needs the money. For him, risk and return are experienced at exactly the same moment—when the portfolio is liquidated. In other words, for the investor who never checks his portfolio, risk and return are the same.

This is not trivial sophistry. The reason that stocks are less risky than bonds and T-bills over long time periods is precisely because their returns have been much higher. The emphasis here is on the past tense: if in the future, stocks do not best bonds and bills by very much, then stocks will retain their risk. Or, as put to me by Cliff Asness, "With a big cushion (risk premium) even a bad draw probably doesn't get you less than bond performance over the long term."

Let’s analyze this using some basic statistics. From 1802 until 1997, the period covered in Stocks for the Long Run, the return of stocks was 8.4% with a standard deviation of 17.5%. The laws of statistics tell us that the probability of a return worse than two standard deviations (2SD) below the mean is 2.3%. What does that mean?. At one year, we’re talking about a return worse than -26.6% (8.4% minus 17.5% x 2) occurring about once every 43 calendar years.

What happens at ten years? Again, the laws of statistics tell us that with a random walk, the annualized standard deviation will be 17.5%/sqrt(10) = 17.5%/3.16 = 5.54%. So a minus-2SD ten-year annualized return is –2.68% (8.4% minus 5.54% x 2). And at 30 years, the minus-2SD return is +2%. So if the T-bill return is 3%, stocks will indeed underperform bills at the minus-2SD level over 30 years.

For those of you who are interested, I’ve made available an Excel spreadsheet that uses this method to calculate the theoretical probability that stocks will underperform T-bills. It requires four inputs: stock and T-bill returns, the stock-return SD, and time horizon. I’ve included the 1802-1997 Siegel summary data for reference. Using the historical data, the "theoretical" versus actual percentages that stocks have outperformed T-bills are plotted below:

Care is needed in interpreting these data since at the long end there have been only six non-overlapping 30-year periods. Siegel uses overlapping time periods—not kosher, but necessary—to produce the required data density. Still, the agreement is quite good. Incidentally, the vaunted mean-reversion tendency of the stock market, which shows up as the black-over-red gap at the right side of the curve, is shown to be a minor player in this act; the closeness of the fit confirms the random-walk behavior of market returns.

I strongly doubt that future stock returns are going to be 5.5% higher than T-bills, as they were from 1802 through 1997, or 7% higher than T-bills, as they were in this century. A reasonable case can be made that the equity risk premium going forward may be very small. If stock returns are approximated as the sum of earnings (or dividend) growth plus the dividend yield, then the gap between stock and bond returns may be only a few percent. What if it’s only 2%? Maybe a little higher or lower? I’ve plotted a range of possible equity risk premia below… no matter how you slice it, things look ugly:

Suddenly, stocks aren’t so safe; even at a 30-year time horizon, in addition to their breathtaking short-term volatility, stocks run a significant risk of underperforming T-bills once the risk premium falls below 4%.

This exercise neatly outlines the gross internal inconsistency of the Glassman and Hassett argument in Dow 36,000. The authors’ hypothesis is that stocks, because they are less risky than bonds, should have higher prices and lower returns. But, as we’ve just shown, if they have lower returns, then their long-run risks will be much higher.

Yes, the long-term risks of equities were lower than that of T-bills and bonds. But the good news is already out about the stock market and totally discounted into its present price. Going forward, stocks will be riskier than bonds and T-bills, no matter how you measure it. And the rewards for bearing that risk will be lower.

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