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Medium · Conditional Probability · Quant Trader interview question · portfolio-optimization, am-gm-inequality, geometric-mean, asset-allocation
You are managing a portfolio of two assets. Asset A has an expected return of $x$ and Asset B has an expected return of $y$, where $x, y > 0$. You want to allocate your capital to maximize the geometric mean return of your portfolio over a long period. Let $w$ be the proportion of your capital allocated to Asset A, and $1-w$ be the proportion allocated to Asset B, where $0 \le w \le 1$. Assuming returns are independent, what allocation, w, maximizes the geometric mean return of your portfolio?