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 July 2006 Are You Really Afraid of Beating the Market? What Does it Really Mean to Be “Risk Averse”?
In fact, most investors would probably say they’re “risk averse”. While they aren’t completely afraid of taking chances, they want to hedge their bets as much as possible. That’s why small investors purchase mutual funds instead of a handful of random stocks. It’s also why financial advisors are always preaching the virtues of diversification in an attempt to control the risk inherent in investing. But what exactly is this “risk” and what is this aversion to it? We all believe we’re risk-averse investors, but what does that really mean?
Above and Below This defines “risk” in terms of success or failure; it’s the probability of failure. Riskier endeavors have a higher likelihood of failure. But how do you apply that to investing? Certainly if you invest in X with the expectation that it will return 4% only to lose 2%, you’ve certainly failed to reach your goal. You’d probably be willing to say it’s a risky, especially since you’ve actually lost money. But what if you have a gain? Suppose investment Y has the same expected return of 4% but instead returns 12%? In a sense, you’ve still failed to meet your goal (4%). In fact, the difference from the expected return (8%) is greater for Y than it was for X (6%), suggesting Y is actually riskier. It’s hard to think of an investment that delivers a greater return than expected as “risky”, but when risk is defined in terms of success or failure even a positive surprise has to be considered a failure. Do you mind that type of failure? Are you averse to that type of “risk”?
Actually investment risk is often measured in a similar fashion. You’ve probably seen standard deviation used in this role. Essentially standard deviation is a measure of the average returns around the mean (expected return). The greater the standard deviation, the less likely you’ll get the average return in any given instance. For example, consider once again investments X and Y. Both have means of 4%, but if X’s standard deviation is 6% and Y’s is 8%, Y is riskier than X. In the earlier examples, both returns (4% - 6% = -2%) for X and (4% + 8% = 12%) are within their standard deviations. Indeed, that’s how standard deviation is used. For investment X, returns falling within one standard deviation of the mean would range from -2% (4% - 6% = -2%) to 10% (4% + 6% = 10%). Statistics tell us that 68% of X’s returns should fall within this range. Ninety-five percent should fall within two standard deviations (-10% to +16%). Standard deviation is clearly a good way to gauge the dispersion around expected returns. Again from the example, knowing that 95% of their respective returns will fall from -10% to +16% for X and -12% to +20% for Y may help you decide between the two potential investments. But is this really the way you think of risk?
Failure or Loss? To illustrate this point, consider two other investments. Investment A has an expected return of 3% and a standard deviation of 4%. Investment B’s expected return is 10% and its standard deviation is 5%. B’s standard deviation is higher (5% vs. 4%) so it’s riskier, right? Before you answer, consider where 95% of their returns will fall. For A the range runs from -5% to +11% while for B it’s 0% to +20%. Investment B won’t suffer any losses 95% of the time, or looking at it the other way, there’s only a 2½% chance it will ever be negative. Now which is riskier? Arguably, most investors don’t mind if returns occasionally fall below their average as long as they don’t actually lose money. Failure to meet the expected goal isn’t nearly as bad as actually incurring a loss. It’s the loss that’s the source of the aversion, not the fear of failing to achieve the average return. We’ve argued before that investors aren’t risk averse, they’re loss averse. They don’t want to minimize or even limit the opportunity to exceed the average on the upside. They don’t even mind the periodic miss on the downside as long as it doesn’t turn into a loss. It’s the downside risk -- or rather “risk of loss” – that investors want to cap. That’s why most of us would choose investment B over investment A in the earlier example – even though it had a higher standard deviation. It might have wider return swings, but rarely ends in a loss. The same can’t be said for investment A.
A Different Approach Instead, investors should look for ways to quantify risk of loss. Obviously the short end of standard deviation can give you an idea of the magnitude of potential losses, but the probability is also important.
It’s important to remember that if returns are normally distributed (see accompanying diagram for an illustration of a normal distribution), there’s little likelihood that the extreme returns will ever be achieved. Even investment B had a 2½% chance of a negative return, although positive results were substantially more likely. Alternatives whose mean is closer to 0 and with significant standard deviations (like investment A) have greater opportunities for negative outcomes and thus, greater risk of loss. These are truly the “riskier” investments. So stop fearing opportunities that can provide greater than average returns. Aside from a possible reversion to the mean in later periods, there’s nothing to fear about investments exceeding expectations. That’s not risk, that’s good fortune. You can also use downside risk to your advantage. Many investors choose their investments by concentrating solely on upside potential. If returns are normally distributed, investments with outsized upside deviations will have equally large swings to the downside. Any investor failing to realize that is probably in for a rude awakening. Instead, a risk averse investor should reverse the process. Rather than focusing on the investment’s upside potential, consider the downside risk. Would you be comfortable with it should that loss occur? If not, it doesn’t matter what the upside is, the investment isn’t for you. If you know the downside risk -- the worst-case scenario -- and you’re OK with it, that’s an investment you can hold through the ups and downs of a market cycle. Once you’ve found your comfort level, you should adjust your return expectations to its average. If it does better than expected, that’s great. When it falls below the mean, you won’t be surprised. Most investors really want to avoid the risk of loss, not the opportunity for outsized returns. Once you realize this, your investment decisions are sure to improve. Search this site! Just enter you key word or words:
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OST OF US AREN'T overly aggressive when it comes to investing. We all want to “beat the market” but we don’t want to lose the house in the process. Sometimes we get carried away (like the 1990’s tech craze), but in general, most investors aren’t out making wild bets.
