Question

Find the weights for the optimal risky portfolio. Assuming risk-free rate is 3%.

E(rs) =10%

E(rB )= 5%

σs = 15%

σB = 6%

PBS = 0.3

Answer 1

In Optimal Portfolio the Capital Allocation Line(CAL) is tangent to the efficient frontier of portfolio frontier. At this point CAL is maximum, thus returning maximum return for per unit additional risk.

Since, W(s) + W(b) = 1 ......(1)

where W(s) & W(b) are the respective weights of assets in an optimal portfolio.

and this W(rs) is calculated as,

W, = (Ers – Rp) - (Ero - Rj)phs0301 (Ers - Rio + (Erb - Rp)o} - (Erb - Rp + Erb - Rp)pós0300

substituting the values in the above equation:

= $\frac{(0.10-0.03)0.06^2-(0.05-0.03)0.3*0.15*0.06}{(0.10-0.03)0.06^2+(0.05-0.03)0.15^2-(0.10-0.03+0.05-0.03)0.3*0.15*0.06}$

= 0.4313 or 43.13%

Therefore,

$W_{b}$ = 1 - $W_{b}$

= 1 - 0.4313

= 0.5687 or 56.87%