The Unlucky Trader

What this Bayesian inference interview question tests

This is a medium-difficulty probability question that probes your understanding of Bayes' theorem and how to reason about conditional probability when base rates matter. Quant firms use questions like this to see whether you can correctly update your belief about a hypothesis in light of new evidence—a core skill in quantitative trading and risk management.

The setup is deliberately realistic: you're given a prior probability (how rare alpha truly is), two conditional accuracies (the backtester's hit rate and false-positive rate), and a single positive signal. The trap is assuming the signal itself is reliable without accounting for how rare the underlying event is. Candidates who skip the base-rate reasoning often overestimate the posterior probability.

• Prior and posterior probabilities
• Sensitivity and specificity (true-positive and false-positive rates)
• The role of base rates in updating beliefs
• Constructing a probability tree or contingency table