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B School
 
STRATAGEM B-SCHOOL COLUMN LUBOS PASTOR
“Uncertainty compounds overtime”
Lubos Pastor, Charles P. McQuaid Professor of Finance and Robert King Steel Faculty Fellow at the University of Chicago Booth school of Business, believes that contrary to conventional wisdom, stocks are riskier in the long run. Therefore, it makes sense to hold fewer stocks as investors get older, but the reduction in the stock allocation should not be as steep as conventional wisdom suggests.
Issue Date - 30/05/2012
 
Investors are often told that stocks are highly risky for anyone investing for a period of five years or less. Extend that horizon to 15 years or more, however, and the risk of owning stocks falls dramatically – they are told – because a longer investment period allows more time for a bull market to cancel out a bear market. Thus, investors who hold on to stocks for a long time can expect to earn high real returns with low risk. This conventional wisdom has become the cornerstone of long-term investing. Popular target date mutual funds, for instance, start with a high allocation in stocks and glide toward a lower stock allocation as investors move closer to retirement.

The idea that stocks are less risky in the long run is supported by the historical performance of stocks. Indeed, the classic book, Stocks for the Long Run, by University of Pennsylvania professor Jeremy J. Siegel, shows that stocks have consistently outperformed bonds over various 30-year periods since the early 19th century. Investors might use this evidence as reason to put more stocks in their long-term portfolio. But according to a recent study, “Are Stocks Really Less Volatile in the Long Run?” undertaken by me along Prof. Robert F. Stambaugh of the University of Pennsylvania, investors should pay attention not only to historical estimates, but also to the uncertainty associated with those estimates.

What matters to investors is a measure of volatility that captures the uncertainty about whether the average future stock return will resemble its historical counterpart. This uncertainty compounds over time, so that its effect on the volatility of stocks increases with the investment horizon. In fact, the volatility of stock returns over long periods of time can be so high that it can overturn the conventional view, which is exactly what we find. When investors take the uncertainty associated with historical estimates into account, they discover that stocks are riskier in the long run.

Uncertainty Trumps Mean Reversion
From the 1950s to the 1980s, the view that dominated investors’ understanding of stocks was that stock prices followed a random walk; that is, stock price changes cannot be predicted based on past price movements. Because changes in stock prices are independent from one another, the volatility of stock returns is expected to be equal at all investment horizons. In other words, a person who invests in stocks for one year and another who invests for 30 years would face the same amount of risk on a per-year basis.

Beginning in the 1980s, people started to realise that it was somewhat possible to forecast stock prices – just enough to induce a slight “mean reversion” in stock returns. The idea is that bull markets tend to be followed by bear markets, so that stock returns end up close to the historical average. The concept of mean reversion makes stocks less volatile in the long run, a powerful idea that was popularized by Siegel’s book, which presents evidence of mean reversion using more than 200 years of stock returns. Today, almost anyone who wants to save for retirement or their children’s college tuition is given the same advice – to load up on stocks and hold on to them for a long time, because stocks are safer and the returns higher than bonds over comparable periods.

This conventional wisdom, however, is based on backward-looking historical measures of volatility, which we feel are only somewhat relevant to forward-looking investors. The reason we arrive at a different conclusion is that we take the investor’s perspective. Mean reversion is only one of a handful of components in measuring long-run volatility. In particular, there are three types of uncertainties that pull in the opposite direction of mean reversion.

 
The first is the uncertainty about the current equity premium, which is the expected stock market return in excess of the Treasury bill rate. The equity premium is one of the most important numbers in finance and also one of the hardest to pin down. Investors have diverse views on what the equity premium is today and what it will be in the future, which is the second type of uncertainty that makes stocks more volatile in the long run. The third involves all the other parameters that affect stock market returns that, like the equity premium, may be very different from historical estimates.

We find that these uncertainties rise rapidly as the investment horizon lengthens. As a result, the combined effect of these three forces outweighs mean reversion, making the volatility of stock returns higher in the long run.

Taking Stock
To find out if investors share our views, we analysed a series of surveys that asked Chief Financial Officers (CFOs) where they think stock market returns are headed, particularly in the next year and in the next 10 years. We inferred from the results that the typical CFO views the annual variance of 10-year stock returns to be at least twice the variance of one-year stock returns. In other words, CFOs seem to perceive stocks as more volatile at longer investment horizons.

If stocks are more volatile in the long run, then those who have been investing based on the conventional wisdom should consider adjusting their portfolios. If on a scale of one to 10 you thought the risk of investing in stocks was only three, and you put half of your money in stocks based on that view, then you should probably reduce your stock allocation if I tell you the risk is actually five.

In fact, the study reveals that investors in target date mutual funds would find the predetermined asset mix typically offered by this investment strategy less appealing if they took parameter uncertainty into account. In particular, investors with sufficiently long horizons would choose an asset mix with initial and final stock allocations that are lower than those of investors with shorter horizons.

These results also have implications for how investors should change their mix of assets as they get older. Financial advisors often tell investors to start with a high stock allocation when they are young and to reduce it over time for two reasons: first, younger investors have mean reversion on their side – that is, they have more time to go through the ups and downs of the stock market; second, they have more human capital – that is, they can look forward to a long stream of income. But if mean reversion’s contribution to the measurement of volatility is overcome by the various uncertainties investors face, as the study shows, then the first reason ceases to be a good argument for reducing stock allocations as investors get older.
          

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