D-Index: A Risk Measure in a New Dimension

In this article, we construct a risk measure of an investment, called the D-Index, which measures the fraction of time the investment is in a drawdown. The D-Index isolates the time dimension from the returns when measuring risk, and this property uniquely characterizes it from other performance measures. An explicit analytical form of the ex-ante D-Index is provided for the case of a buy-and-hold strategy with price dynamics following a Black-Scholes model. Numerical evidence based on 32,642 funds across three asset classes shows that the D-Index does not exhibit strong rank correlation with the Sharpe ratio across funds, in contrast with most other existing risk-measures. Coupled with evidence from experimental psychology, this new perspective motivates us to consider its importance in investment decision making in the real-world environment.