Question

An investor plans to divide $200,000 between two investments. The first yields a certain profit of 10%, whereas the second yields a profit with expected value 18% and standard deviation 6%. If the investor divides the money equally between these two investments, find the mean and standard deviation of the total profit.

Answer 1

mean = 14%; standard deviation = 3%

Step-by-step explanation:

We treat the combined investment as a portfolio, with 50% each of the portfolio size invested in each asset.

Asset A: return (r) = 10%; standard deviation (s) = 0

Asset B: return (r) = 18%; standard deviation (s) = 6%

Portfolio mean (R) =

`(w_(1)*r_(1))+(w_(2)*r_(2))\\=(0.5*0.1)+(0.5*0.18)\\=0.05+0.09\\=0.14`

Therefore, portfolio mean = 14%.

Portfolio standard deviation (S) =
`[(w_(1)^(2)*s_(1)^(2))+(w_(2)^(2)*s_(2)^(2))+(2w_(1) w_(2)COV_(12) )]^{(1)/(2)}`

Since no information was given about portfolio covariance, we will assume it is zero.

`S=[(w_(1)^(2)*s_(1)^(2))+(w_(2)^(2)*s_(2)^(2))]^{(1)/(2)}\\=[(0.5^(2) *0^(2) )+(0.5^(2) *0.06^(2) )]\\=0.25*0.0036\\=0.03`

Therefore, portfolio standard deviation = 3%.