Question 9.4: Determine optimal weights, at zero correlation, for the data......

Optimal weights are:
\qquad\,w^*_L = [(20)^2 – (0) \,(16) \,(20))]/[(16)^2_ 1 + (20)^2 – 2 \,(0)\, (16)\, (20)]
\qquad\quad = (400)/(256 + 400) = (400)/(656) = 0.61 = 61 per cent
\qquad\,w^*_H = 1 – 0.61 = 0.39 = 39 per cent
\,  The portfolio standard deviation with these weights is smaller than the standard deviations of assets included in the portfolio. This may be verified using Equation 9.4

\sigma^2_p = (w_1 \sigma_1)^2 + (w_2 \sigma_2)^2 + 2 w_1 w_2 (\rho_{12} \sigma_1 \sigma_2 )          (9.4)

\qquad\,\sigma^2_p = (0.61 × 16)^2 + (0.39 × 20)^2 + 2\,(0.61)(0.39) [(0)(16 × 20)]
\qquad\quad= 95.26 + 60.84 = 156.1
\qquad\,\sigma_p= 12.5 per cent