Question

I was stuck on the following review problem on variance and expected value. Could you please guide me on how to approach this type of problem? Thank you! EDIT: x is just some variable representing the amount invested, so distribution depends on this value.

You are investing your money in two hedge funds and want to split your cash among two funds, Fund A and Fund B. If you invest $x dollars in Fund A, its worth after one year is distributed as a Normal (µ_A = 1.05x, σ_A² = .02x² ). If instead you invest $x dollars in Fund B, its worth after one year is distributed as a Normal (µ_B = 1.05x, σ_B² = .03x² ). Suppose you invest $p in Fund A and $(100 - p) in Fund B where p ∈ [0, 100] and both funds are independent.

(a) What is the expected value of the total worth of your investment after one year?

(b) What is the variance of the total worth of your investment after one year?

(c) What is the value of p which minimizes the variance of the total worth of your investment after one year? (d) If you adopt the value of p you determined in part (c), what is the probability that after one year the total worth of your investment is more than $120?

Answer 1

Probabilities calculated using normal distribution calculator.