Variance-minimizing hedge

You hold one share of A and short hh shares of B to minimize the variance of rA−h rBr_A - h\,r_B. With σA=30%\sigma_A = 30\%, σB=20%\sigma_B = 20\% and correlation ρ=0.5\rho = 0.5, what is the optimal hh? (to 2 decimals)

Show hints (2)+
  1. Differentiate the variance with respect to hh.
  2. h∗=ρσA/σBh^* = \rho\sigma_A/\sigma_B.

Answer

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0.75 (± 0.01)

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