Volatility-adjusted Performance: An Alternative Approach to Interpret Long-run Returns

This paper investigates long-run returns by utilizing log-normal distribution properties of cross-sectional buy-and-hold returns. We decompose expected cross-sectional buy-and- hold returns into transformed mean components and volatility components. This decomposition shows that the volatility component contributes positively to the right-skewed buy-and-hold returns due to Jensen's inequality. Given the log-normal distribution properties are fulfilled, the method can be applied to any type of long-horizon event study of security performance. We apply the method to IPO stocks and SEO stocks listed on the Copenhagen Stock Exchange. Using traditional standard techniques, we find that IPO stocks and SEO stocks under perform relative to the market after five years by 27.3 percent and 21.4 percent, respectively. However, the volatility-adjusted performance measure shows that the IPO stocks and SEO stocks under perform relative to the market after five years by 43.7 percent and 38.1 percent, respectively.