Volatility-Adjusted Performance An Alternative Approach to Interpret Long-Run Returns

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