Sign-flip Simpson: volatility and returns across sectors

Question

Over your sample, plotting each stock's volatility against its return gives an upward slope across the whole market: higher-volatility stocks had higher returns. Yet within each sector taken separately, the slope is downward: higher-volatility stocks had lower returns.

Reconcile the positive market-wide slope with the negative within-sector slopes. Which relationship should guide stock selection inside a sector?

Accepted Answer

This is Simpson's paradox in continuous form. The confounder is sector. What is happening. Suppose in your sample a high-volatility sector (say, technology) also happened to post high returns, while a low-volatility sector (say, utilities) posted low returns. Then across the market, "high volatility" travels with "the sector that did well," so the pooled slope is positive, driven by which sectors led during the period, not by volatility as such. Within any one sector, where the sector effect is fixed, the more volatile names underperformed the calmer ones: a negative slope. Which slope to tru…

Sign-flip Simpson: volatility and returns across sectors

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