Traditional investment performance measures often fail to capture tail risk. The recent financial breakdowns demonstrate the necessity of including higher distributional moments in the performance appraisal process. The authors construct two indices to provide evidence that including higher moments allows investors to better understand a given investment scenario and to make more informed decisions.
The authors construct two performance indices and apply them to well-known investment strategies and anomalies to prove the significance of the third and fourth distributional moments relative to investment performance appraisal. They find that high moments can shift certain investment possibilities or strategies from being positive (based on traditional performance measures) to being neutral or even negative. An example of such a traditional measure is the Sharpe ratio, which underestimates tail risk and skewness because of the low probability assigned to distribution tails—that is, rare disasters. Recent turmoil in the financial markets, however, is proof that the effects of such low-probability events may be large enough to materially distort investment results.
How Is This Research Useful to Practitioners?
Rare disasters have been central to the most recent financial market breakdowns. The Sharpe ratio and other common performance measures typically focus on the first two moments of the distribution—that is, mean and variance—and neglect skewness and kurtosis. In normal times, because of the low probability of rare events, the low moments (i.e., mean and variance) seem to be adequate measures of financial performance. Taking rare disasters into account, however, is a crucial part of understanding a given investment strategy.
The main contribution of the authors is their demonstration of the importance of the higher distributional moments in the investment selection and appraisal processes. This contribution is beneficial to practitioners and academics.
How Did the Authors Conduct This Research?
Using prior research, the authors create two performance indices that capture high moments, and they apply the indices to popular investment strategies and well-known anomalies. They present a number of their findings.
First, they show that a momentum strategy, when appraised with skewness and kurtosis (i.e., high moments) in mind, does not outperform a simple buy-and-hold scenario. Second, when a momentum strategy is modeled with only the first two moments, the resulting distribution differs from the actual distribution in a manner that ignores the potential for a large loss, which is not to the investor’s advantage. Third, private equity investments, in spite of their profitability in many cases, are extremely right skewed and seriously biased with high volatility and tail risk, which effectively removes their advantage over public equity. Fourth, taken net of fees, active mutual fund management does not yield a surplus when compared with passive management. Fifth, the authors show that the two indices proposed may be used to identify investments with desirable moment properties.
Much of the testing was performed with monthly data between January 1962 and December 2009.
The authors’ empirical findings indicate the importance of high moments in performance evaluation. What seems to be an attractive investment may lose much of its glamour after accounting for high moments and the risk of disaster. The article is interesting and, when combined with the background literature, constitutes a significant contribution to both academic and practical knowledge. Its greatest value is in the examples of practical application of the methodology and reliance on quantitative techniques.