Question

28. An investor invests 30% of his wealth in a risky asset with an expected rate of return of 0.15 and a variance of

0.04 and 70% in a T-bill that pays 6%. His portfolio's expected return and standard deviation are __________

and __________, respectively.

Answer Below:

E(r P) = 0.3(15%) + 0.7(6%) = 8.7%; sP = 0.3(0.04)^1/2 = 6%.

Question:

Could someone please explain why the sP formula is ^1/2? All the other formulas I have seen are ^2. What is happening here?

Please explain formula and also conceptually please!

Answer 1

Variance is the average of the squared differences from the mean

Here variance of the risky asset is given as 0.04

Standard deviation shows the amount of deviation of the returns of the risky asset from the mean return

Standard deviation is the square root of variance or variance^1/2

Since the weight of the risky asset is 30% in the portfolio and standard deviation of a risk free investment like T-bill is zero,

The Portfolio standard deviation is given as 30% * variance^1/2 = 0.3 * 0.04^1/2 = 0.3*0.2 = 6%