Minimum-variance weights

MediumStatistics Finance & Derivatives~6m

Two stocks have equal expected return, with $\sigma_A=20\%$ , $\sigma_B=30\%$ and correlation $\rho=0.5$ . What weight in stock A minimizes portfolio variance? (as a percent, to 1 decimal)

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Differentiate the two-asset variance and set it to zero.
$w_A = (\sigma_B^2-\rho\sigma_A\sigma_B)/(\sigma_A^2+\sigma_B^2-2\rho\sigma_A\sigma_B)$ .

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85.7 (± 0.5)

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Minimum-variance weights

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