OLS Beta Impact on Hedging - Quant Trader Interview Question
Difficulty: Medium
Category: Data Science
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Topics: linear-regression, ols, beta, hedging, statistics
Problem Description
You are tasked with hedging a portfolio of stocks against market movements. You have a portfolio, $Y$, and a market index, $X$. You run an Ordinary Least Squares (OLS) regression to estimate the beta of your portfolio with respect to the market, using the standard linear model $Y = X\beta + \epsilon$. Assume $X^T X$ is invertible. You use the estimated beta, $\hat{\beta}$, from the OLS regression to construct a hedge. If you incorrectly calculate $\hat{\beta}$ as $(X^T X)^{-1} X Y$ instead o
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