Do Financial Markets Reward Buying or Selling Insurance and Lottery Tickets?

Selling financial investments with insurance or lottery characteristics should earn positive long-run premiums if investors like positive skewness enough to overpay for these characteristics. The empirical evidence is unambiguous: Selling insurance and selling lottery tickets have delivered positive long-run rewards in a wide range of investment contexts. Conversely, buying financial catastrophe insurance and holding speculative lottery-like investments have delivered poor long-run rewards. Thus, bearing small risks is often well rewarded, bearing large risks not.See comments and response on this article.Financial markets are full of strategies that resemble insurance or lotteries. It seems worth asking whether investors maximize long-term expected returns by buying or selling financial investments that have insurance-like or lottery-like characteristics. This question is related to economists’ long-standing puzzle about consumers’ simultaneous demand for insurance and lottery tickets, which appears to be inconsistent with rational behavior and standard risk preferences in a mean–variance world.The answer depends on the market pricing of skewness: how investors trade asymmetry against mean return. If most investors prefer positive skewness, investments with positively asymmetric payoffs tend to be highly priced and offer relatively low long-run returns. However, this outcome is not a foregone conclusion. Conceivably, for a given mean return, investors may prefer to suffer losses in one big hit instead of a slow trickle, implying a preference for negative skewness.Separately discussing these patterns on the left and right tails of the return distribution can enhance our intuition. Positive skewness may reflect a truncated/thinner left tail or a thicker/longer right tail—that is, a lesser likelihood of large losses or a greater possibility of outsized gains. Both characteristics can increase skewness and can be appealing, but their psychological drivers seem quite different. The left tail concerns demand for insurance, and the emphasis is on systematic risk and limiting the downside, especially in financial crises. The right tail concerns demand for lottery tickets, and the emphasis is on idiosyncratic opportunities to enhance the upside. Both types of demand for positive skewness can lead to “overpricing” and thus to long-run rewards for sellers of insurance and lottery tickets.This article surveys rational and behavioral theories on the pricing of asymmetric payoffs and presents wide-ranging empirical evidence in highly diverse contexts. Theoretical predictions differ on whether skewness is priced and, if so, with what sign. The empirical evidence is much more consistent. I found broadly similar patterns in diverse contexts.First, selling volatility on either the left tail (insurance) or the right tail (lottery tickets) earns profits in the long run. Conversely, buying option-based tail risk insurance against financial catastrophes and holding lottery-like high-volatility investments can result in poor long-run returns.Second, the evidence is not restricted to option trading. Carry-seeking and other strategies with asymmetric payoffs are close cousins of volatility selling; they are all variants of selling tail risk insurance and have earned positive long-run returns. Moreover, speculative, lottery-like investments have delivered lower risk-adjusted returns than their defensive peers within all major asset classes. In general, accepting small risks has been well rewarded, but taking further large risks has been poorly rewarded. Thus, levering up low-volatility opportunities appears to boost long-run returns.To interpret the long-run gains from selling financial catastrophe insurance as rational risk premiums seems natural. In contrast, the gains from lottery selling seem better explained by investor irrationality or by such nonstandard preferences as lottery seeking or leverage aversion.