Equity Correlation Risk - Quant Trader Interview Question
Difficulty: Medium
Category: Probability & Statistics
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Topics: correlation, risk-management, normal-distribution, probability
Problem Description
A portfolio manager at a hedge fund holds a long position in 100 shares of Stock A and wants to hedge their exposure. Stock A's daily returns are normally distributed with mean 0 and standard deviation of 1%. They decide to use Stock B to hedge, but Stock B's daily returns are derived from Stock A: specifically, Stock B's daily return is equal to the square of Stock A's daily return.
What is the approximate correlation between the daily returns of Stock A and Stock B?
Assume that the number of s
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