The minimum-variance portfolio of two assets
You allocate between two risky assets and with weights and (long only, summing to one). Their volatilities are and , with correlation .
What weight in minimizes the portfolio's volatility, and what is that minimum volatility?
Show a hint
Write the portfolio variance as a function of , differentiate, and set it to zero. The algebra mirrors the hedge-ratio derivation.
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.