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What this minimum variance portfolio question tests

This is an easy portfolio theory question that appears frequently in quant interviews and asset management roles. It tests whether you understand how correlation and variance interact to shape optimal portfolio construction, and whether you can apply the minimum variance portfolio framework under a concrete constraint.

The question asks you to find the weight of one asset in a two-asset portfolio that minimizes total risk. Since both assets have identical expected returns and volatilities, the focus shifts entirely to how their correlation affects diversification. The no-leverage constraint (weights are non-negative and sum to 1) rules out short positions, which can change the optimal solution in corner cases.

• The role of correlation in portfolio diversification
• The minimum variance portfolio formula for two assets
• How boundary constraints (no short selling) affect the solution
• Perfect negative correlation and its theoretical implications