Question

Suppose an investor has 50% of her portfolio invested in each stock. What is the standard deviation of the portfolio’s returns?

Returns State Probability Banger Mash Great 10% 75% 15% 40% 20% -20% 20% 15% 10% Average Bad

Answer 1

E(r) = $\sum_{i=1}^{n}$ [Pi x Ri]

$\sigma$ = $\sum_{i=1}^{n}$ [Pi x (E(r) - Ri)²]^1/2

E(r_Banger) = [0.10 x 40%] + [0.75 x 20%] + [0.15 x -20%] = 4% + 15% - 3% = 16%

E(r_Mash) = [0.10 x 20%] + [0.75 x 15%] + [0.15 x 10%] = 2% + 11.25% + 1.5% = 14.75%

E(r_P) = [0.50 x 16%] + [0.50 x 14.75%] = 8% + 7.375% = 15.375%

S.D. = [{0.5 x (15.375% - 16%)²} + {0.5 x (15.375% - 14.75%)²}]^1/2

= [0.20%² + 0.20%²]^1/2 = [0.39%²]^1/2 = 0.625%