The link between stocks and lottery tickets
- When evaluating risk, people have different attitudes toward gains and losses, generally caring more about potential losses than potential gains -- the pain of a loss is worse than the joy of an equal gain. Put simply, they're risk-averse.
- People tend to overweight extreme, but unlikely, events, but underweight "average," and more common, events.
- People can be risk-averse or risk-tolerant depending on the level of risk involved and on whether the gamble relates to becoming better off or worse off. This explains why the same people may buy both insurance policies and a lottery tickets.
- People place much more weight on outcomes that are certain relative to outcomes that are merely probable. The most extreme outcomes -- the outcomes in the statistical "tails" -- are therefore overweighted.
- People like positively-skewed, or lottery-like, distributions of returns.
Since Kahneman's and Tversky's groundbreaking work in 1979, researchers have accumulated a large body of evidence on attitudes to risk. This evidence reveals that when people evaluate risk, they often depart from the predictions of expected utility.
In a 2007 paper, Nicholas Barberis of the Yale School of Management and Ming Huang of Cornell University's Johnson Graduate School of Management studied the asset pricing implications of Tversky and Kahneman's theories. The following is a summary of their findings and conclusions:
- Investors have a preference for securities that exhibit positive skewness (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). Such investments offer a small chance of a huge payoff (winning the lottery). Investors find this small possibility attractive. The result is that positively skewed securities tend to be "overpriced" -- they earn negative average excess returns.
- The preference for positively skewed assets explains the existence of several anomalies (deviations from the norm) to the efficient market hypothesis, including the low average return on IPOs, private equity, and distressed stocks, despite their high risks.
- The preference for portfolios with positive skewness can also explain the lack of diversification in most individuals' portfolios. Concentration adds skewness, making the distribution of potential returns more lottery-like. Thus, investors prefer a large, undiversified portfolio to a diversified one, preferring one (or a few) stock that is positively skewed to two (or many) with the same distributions. For example, the authors of the study "Equity Portfolio Diversification" found that the vast majority of investors held portfolios that concentrated in just a few stocks -- the average investor holds a portfolio consisting of just four stocks. Less than 5 percent of investors held at least 10 stocks. And studies have found that the stocks held by undiversified investors have greater return skewness than those held by diversified investors.
- The preference for positive skewness can also explain the pricing of out-of-the-money options (which act like lottery tickets).
In theory, we would expect anomalies to be arbitraged away by investors who don't have a preference for positive skewness. They should be willing to accept the risks of a large loss for the higher expected return that shorting overvalued assets can provide.
However, in the real world, anomalies can persist because there are limits to arbitrage. First, many institutional investors -- such as pension plans, endowments and mutual funds -- are prohibited by their charters from taking short positions. Second, the cost of borrowing a stock in order to short it can be expensive, and there can also be a limited supply available to short. Third, investors are unwilling to accept the risks of shorting because of the potential for unlimited losses -- prospect theory at work. The pain of a loss is much larger than the joy of an equal gain. Fourth, short sellers run the risk that the borrowed securities are recalled before the strategy pays off, as well as the risk that the strategy performs poorly in the short run, triggering an early liquidation.
Taken together, these factors suggest that investors may be unwilling to trade against the overpricing of skewed securities. This allows the anomaly to persist.
There's one more observation we need to cover. Since investors have a preference for positive skewness, it's no surprise that they dislike assets with negative skewness. The overall stock market exhibits negative skewness, which helps explain why investors have historically demanded a high premium for accepting the risks of equities.
The findings from the research demonstrate investors would earn superior returns if they avoided assets with positive skewness. However, if you find that you're tempted by the lure of assets with positive skewness, you should do what Ulysses did in "The Odyssey" to resist the sirens' irresistible song -- tie yourself to the mast. In this case, the equivalent of a mast is an investment policy statement that includes the principles of broad diversification.
Image courtesy of Flickr user Robert Couse-Baker
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