The rate of return of an asset is the change in price divided

by the initial price (denoted as r ). Suppose that $10,000 is used

to purchase shares in three stocks with rates of returns X₁,X₂ ,X₃.

Initially, $2500, $3000, and $4500 are allocated to each one,

respectively. After one year, the distribution of the rate of return

for each is normally distributed with the following parameters:

μ₁ = 0.12,σ₁ = 0.14,μ₂ = 0.04,σ₂ = 0.02,μ₃ = 0.07,σ₃ = 0.08.

(a) Assume that these rates of return are independent. Determine

the mean and variance of the rate of return after one year for

the entire investment of $10,000.

(b) Assume that X₁ is independent of X₂ and X₃ but that the

covariance between X₂ and X₃ is −0.005. Repeat part (a).

(c) Compare the means and variances obtained in parts (a) and

(b) and comment on any benefits from negative covariances

between the assets.

B B -D- A -A- C