People who buy lottery tickets know that those are poor investments.
Specifically, they have negative expected returns, paying out perhaps 50 percent of the proceeds from sales. Lottery tickets have another very specific feature—the distribution of returns isn’t “normal,” like the well-known bell curve. Instead, the distribution exhibits what is called “excess kurtosis” and “positive skewness.” Some definitions will be helpful.
Kurtosis is the degree to which exceptional values, much larger or smaller than the average, occur more frequently (high kurtosis) or less frequently (low kurtosis) than in a normal distribution. High kurtosis results in exceptional values called “fat tails.” Low kurtosis results in “thin tails.”
Skewness is a measure of the asymmetry of a distribution. Negative skewness occurs when the values to the left of (less than) the mean are fewer but farther from the mean than values to the right of the mean. For example, the return series of –30 percent, 5 percent, 10 percent and 15 percent has a mean of 0 percent. There’s only one return less than zero, and three higher; the negative one is much farther from zero than the positive ones. Positive skewness occurs when the values to the right of (more than) the mean are fewer but farther from the mean than are values to the left of the mean.
Playing The Investment Lottery
Lottery tickets exhibit both a fat tail (high kurtosis) and positive skewness. Given their negative return, it must be that this feature is what’s attracting people to buy lottery tickets. Even though the likelihood of winning is small, if you win, you win a very large amount.
Academic research has discovered that investors have a preference for investments that exhibit the same characteristics as lottery tickets; namely, high kurtosis and positive skewness. Just as is the case with lottery tickets, this preference leads them to overinvest in the most highly skewed securities, with values to the right of the mean. The increased demand leads to higher prices, with the consequence that those securities will have lower subsequent average returns.
The research has found that there is a strong negative relationship between the skewness of an investment and subsequent returns—firms with less negative or positive skewness earn lower returns. Investments with high kurtosis and positive skewness have poor returns, similar to most lottery tickets.
On the other hand, investments with high kurtosis but negative skewness—with values to the left of and less than the mean that are fewer but farther from the mean than values to the right of the mean—have high returns.
The big difference, as you probably noticed, is that investments with fat tails and positive skewness have the potential, but small likelihood, for large gains. One example of investments that exhibit lotterylike characteristics are IPOs. Research has found that IPOs experience significantly greater first-day returns (at least if you’re lucky enough to buy at the initial offering price), followed by substantially greater negative abnormal returns in the subsequent three to five years.
Other examples of investments with lottery-like characteristics are extreme small-growth stocks, “penny” (low-priced) stocks, and stocks in bankruptcy. The evidence demonstrates that investors would improve their performance if they avoided these investments instead of preferring them.
The potential for one big payout—or jackpot—is not a solid investment plan. Think of how much you’ll lose between now and your “big win.”
On the other hand, investments with fat tails and negative skewness have the potential for huge losses, losses that tend to appear at the wrong time. Investors have a preference for avoiding such investments, leading to their having low valuations, and, therefore, high expected returns.
Two investment strategies that exhibit these characteristics are momentum and what is known as the carry trade (borrowing (going short) a currency with a relatively low interest rate and using the proceeds to purchase (going long) a currency yielding a higher interest rate, capturing the interest differential).
While the returns have been high, it’s important you also consider that there is the potential for large losses. In fact, the high returns can be seen as compensation for accepting the risks of large losses, losses that have a nasty tendency to appear at the wrong time.
The authors of the study “Ex Ante Skewness and Expected Stock Returns,” which appears in the February 2013 issue of the Journal of Finance, added to the literature on this issue. They found that there is “a significant negative relation between firms’ risk-neutral skewness and subsequent returns, that is, more negatively skewed securities have higher subsequent returns.”
They also found that these relations persist after controlling for firm characteristics, such as beta, size and book-to-market ratios. The data was both statistically and economically significant. The authors cited prior research that confirmed the preferences of individual investors.
Don’t Stay Positive
Everyone dreams of that big win—the big check, the balloons, the financial security, but that’s a pipe dream. In the meantime, investors (and lotto players) have to deal with reality, and the evidence is piling up that human behavior has a significant impact on investment returns. The preference for positive skewness in their investments is negatively impacting returns of those who buy securities with that characteristic. Perhaps it’s time to check your portfolio to see if your portfolio has been influenced by a preference for skewness. Remember, a lottery ticket that only costs you around $2.00, an investment based on the appeal of a potential big return, could cost you a great deal more.
Larry Swedroe is director of Research for the BAM Alliance, which is part of St. Louis-based Buckingham Asset Management.
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