TL;DR
Simpson's Paradox: When Aggregation Reverses Trends: A canonical quantitative trading interview question at intermediate difficulty. Commonly asked at Two Sigma, Citadel, DE Shaw, Point72, WorldQuant.
By Valenke Exam Prep Team·Last updated 2026-06-01
intermediateStatistical Inference & Estimation
Simpson's Paradox: When Aggregation Reverses Trends
Asked at: Two Sigma, Citadel, DE Shaw, Point72, WorldQuant
Problem
Two trading strategies are backtested over two market regimes (bull and bear):
| | Strategy A Win Rate | Strategy B Win Rate |
|---|---|---|
| Bull market (800 trades for A, 200 for B) | 60% | 70% |
| Bear market (200 trades for A, 800 for B) | 30% | 40% |
| Overall | ? | ? |
(a) Compute the overall win rate for each strategy.
(b) Which strategy has the higher overall win rate? Does this contradict the per-regime results?
(c) Explain the paradox. Which strategy is truly better?
(d) A PM asks you to deploy Strategy B because "it wins more often." What do you say?
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