Question

The following equally likely outcomes have been estimated for the returns on Portfolio P and Portfolio Q:

Scenario Portfolio P Portfolio Q

1 4% 11%

2 7% -7%

3 -3% 15%

4 9% -9%

Which of the two portfolios is riskier?

Answer 1

Mean = $\sum_{i=1}^{n}$ [Ri] / n

E(rP) = [4% + 7% + (-3%) + 9%] / 4 = 17% / 4 = 4.25%

E(rQ) = [11% + (-7%) + 15% + (-9%)] / 4 = 10% / 4 = 2.50%

To find the riskier portfolio, we need to find the standard deviation of each portfolio:

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

$\sigma$p = [{0.25 x (4% - 4.25%)²} + {0.25 x (7% - 4.25%)²} + {0.25 x (-3% - 4.25%)²} + {0.25 x (9% - 4.25%)²}]^1/2

= [0.0156%² + 1.8906%² + 13.1406%² + 5.6406%²]^1/2 = [20.6875%²]^1/2 = 4.55%

$\sigma$q = [{0.25 x (11% - 2.50%)²} + {0.25 x (-7% - 2.50%)²} + {0.25 x (15% - 2.50%)²} + {0.25 x (-9% - 2.50%)²}]^1/2

= [18.0625%² + 22.5625%² + 39.0625%² + 33.0625%²]^1/2 = [112.7500%²]^1/2 = 10.62%

As the standard deviation of Portfolio Q is higher, hence, it is riskier.