Suppose that the bivariate random vector (R_1, R_2) represents the yearly rate o

Question

Suppose that the bivariate random vector (R_1, R_2) represents the yearly rate of return on assets 1 and 2. Further, suppose that E(R_1) = 0.04, E(R_2) = 0.06, SD(R_1) = sigma_1 = 0.15, SD(R_2) = sigma_2 = 0.30, and Cor(R_1, R_2) = rho_12 = 0.6. An investor creates a portfolio by putting $500 in asset 1 and $500 in asset 2. Express the portfolio's arithmetic return R_P in terms of R_1 and R_2. Compute E(R_P). Compute Var(R_P). Next, suppose the investor decides to invest $x in asset 1 and $(1000 - x) in asset 2. Express the portfolio's arithmetic return R_MV in terms of R_1, R_2, and x. Compute E(R_MV). Compute Var(R_MV). How much should the investor put into each asset to minimize the risk (i.e., variance) of the portfolio?

Explanation / Answer

a) The arithmetic return of the portfolio is the simple average of all the returns.

   Arithmetic return of portfolio = 0.04 + 0.06 / 2 = 0.10 / 2 = 0.05 i.e., 5 %.

b) Expected return of portfolio = Weighted average return of all the assets in the portfolio

   = 0.04 * 500 / 1000 + 0.06 * 500 / 1000

   = 0.04 * 0.50 + 0.06 * 0.50

= 0.05 [ 5 %]

c) Variance of portfolio = (0.50)2* (0.15)2 + (0.50)2 * (0.30)2 * 2 * (0.50) * (0.50) * (0.6)

   = 0.0005625 + 0.0225 + 0.30

   = 0.328125 [ 32.8125 %]

     

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.