I just wrote a paper with my friend James White which applies and extends the ideas of the paper Andy Morton and I published in December on Optimal Investment Sizing. In the December note we suggested that it can be simple, and better, to use Expected Utility rather than Expected Value to make investment decisions. In this note we give two examples that illustrate that Expected Utility is still practical, and perhaps even more useful, when considering investments that have attractive expected returns but asymmetric distributions of outcomes, such as investments in some hedge funds and short-term corporate bonds. We’re continuing to work on case studies to illustrate this framework, so if you have any suggestions for investment-sizing problems that would be interesting to explore, please send us an email.
The full paper can be downloaded from SSRN here.
Below is a brief excerpt to whet your appetite:
“In a world of low rates and high stock prices, it’s natural many investors are looking for ways to earn a good return with limited exposure to equities. However, many candidate strategies have return distributions which are significantly different from the Normal and Log-normal distributions that serve as reasonable approximations for the return profile of most typical portfolio asset classes.
Using the heuristic of expected return, or even the ratio of expected return to risk (Sharpe ratio), can lead to a significant mis-evaluation when applied to these cases. Neither metric gives us an adequate way to weigh the small risk of a large loss, nor do either tell us how much of these types of investments we should optimally hold. What’s needed is a more fundamental and versatile tool, a sharper lens for sizing up the proverbial nickels and steamrollers. Expected Utility fits the bill.
It’s a concept that’s been around for a long time, but surprisingly is hardly used by present-day analysts and investors. Tellingly, professional gamblers rely on it heavily (well, those who don’t tend to change profession quickly).
To a greater or lesser degree, many popular investment strategies, such as selling puts on the stock market, holding concentrated individual stock portfolios or investing in leveraged hedge fund strategies which don’t or can’t employ tight stop-loss limits, are also good candidates for the application of the Expected Utility framework. Our message here is not that utility is the only thing you need – but rather that for enterprising investors looking at potential investments with highly skewed and/or non-linear return distributions, the standard toolbox of Expected Return and Sharpe Ratio is inadequate. Although Expected Utility analysis is rarely seen in the mainstream, we hope we have illustrated that it is both practical and useful…”