Weights in optimal risky portfolio
wb = E[Rb ]σe^2 −E[Re ]σde / E[Rd ]σe^2 +E[Re ]σb^2 − (E[Rd ] +E[Re ])σ de
σ de= σ d x σ e x correlation
E[Rb] = Rb - rf = 0.21-0.06 = 0.15
E[Re] = Re - rf = 0.12-0.06 = 0.06
0.15x 0.18^2 - 0.06x (0.28x0.18x0.09) / 0.15x0.18^2 + 0.06x0.28^2 - (0.15 + 0.06)(0.28x0.18x0.09)
=0.00458784/0.00861144
=0.53
We= 1 - Wb
=0.47
Expected return = We x Re + Wb x Rb
= 0.47 x 21 + 0.53 x 12 = 16.23%
Variance = wb^ 2 σb^ 2 + We^ 2 σe^ 2 + 2WbWe X r X σe X σb
= 0.53^2 x 0.18^2 + 0.47^2 x 0.28^2 + 2 x 0.53 x 0.47 x 0.09 x 0.18 x 0.28
=0.0286
S.D = 0.1693
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