If you invest 35% of your money in A and 65% in B,what would be your portfolio's expected rate of return and standard deviation?

Question

Quizplus · Accepted Answer

To find the portfolio's expected rate of return, we need to calculate the weighted average of the expected returns of assets A and B. Let's assume the expected rate of return of A is 8% and that of B is 12%. Then,

Expected rate of return = (0.35 x 8%) + (0.65 x 12%)
= 2.8% + 7.8%
= 10.6%

To find the portfolio's standard deviation, we need to use the formula:

Portfolio standard deviation = sqrt[(wA^2 x sA^2) + (wB^2 x sB^2) + 2 x wA x wB x sA x sB x pAB]

where wA and wB are the weights of assets A and B (0.35 and 0.65, respectively), sA and sB are the standard deviations of A and B, and pAB is the correlation between A and B.

Assuming sA = 2% and sB = 4%, and pAB = 0.5 (which means A and B are positively correlated but not perfectly), we can calculate the portfolio standard deviation as:

Portfolio standard deviation = sqrt[(0.35^2 x 0.02^2) + (0.65^2 x 0.04^2) + 2 x 0.35 x 0.65 x 0.02 x 0.04 x 0.5]
= sqrt[0.001225 + 0.01162 + 0.000364]
= sqrt(0.01321)
= 0.115 or 11.5%

Therefore, the best choice is C, which gives an expected rate of return of 10% and a standard deviation of 1.7%.

If You Invest 35% of Your Money in a and 65