More leverage, higher Sharpe? A pooled-data trap
An analyst pools daily records from two funds and regresses Sharpe ratio on leverage across all the pooled points. The fitted line slopes up: more leverage seems to go with higher Sharpe. But when you fit the two funds separately, each has a downward slope: within a fund, adding leverage lowers its Sharpe.
How can the pooled slope be positive while both within-fund slopes are negative? Which relationship should guide a leverage decision?
Show a hint
This is Simpson's paradox for a continuous predictor. Ask what separates the two funds besides leverage.
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.