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Minimum-variance weights

MediumStatisticsFinance & Derivatives~6m

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

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  1. Differentiate the two-asset variance and set it to zero.
  2. wA=(σB2−ρσAσB)/(σA2+σB2−2ρσAσB)w_A = (\sigma_B^2-\rho\sigma_A\sigma_B)/(\sigma_A^2+\sigma_B^2-2\rho\sigma_A\sigma_B).

Answer

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85.7 (± 0.5)

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Asked at: Citadel, Two Sigma

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