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 X 1 ,X 2 ,X 3 Initially, $2500, $3000, and $4500 are allocated to each one, respectively After one year, the distr...

Let Y be the rate of return for the entire investment after one year a b c The covariance does no ...

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

Question:

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 with rates of returns X₁,X₂,X₃. Initially, $2500, $3000, and $4500 are allocated to each one, respectively. After one year, the of the rate of return for each is normally distributed with the following parameters:

Î¼₁ = 0.12,Ïƒ₁ = 0.14,Î¼₂ = 0.04,Ïƒ₂ = 0.02,Î¼₃ = 0.07,Ïƒ₃ = 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 ˆ’0.005. Repeat part (a).

between the assets.

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