Nastja Bethke, Senior Quantitative Research Analyst
December 7, 2022
Which strategy would you rather invest in? You can choose between Strategy 1 and Strategy 2. On down days, Strategy 1 has an average (risk-adjusted) return of -1.00, while on up days it has an average (risk-adjusted) return of 1.00. The figures for Strategy 2 are -0.71 and 1.08, respectively. It seems like an obvious choice: you decide to allocate money to Strategy 2.
You were missing an essential piece of information, however. How often do these strategies experience up and down days? With a fraction of positive returns of 53% for Strategy 1 and 42% for Strategy 2, it turns out that the overall return is 0.05 and 0.04, respectively. While Strategy 2 dominates Strategy 1 in each subcategory (conditional mean), overall, Strategy 1 beats Strategy 2.
This phenomenon is named Simpson’s Paradox after Edward H. Simpson, a British statistician, and there is a short white paper on the topic here.