Question

5. Assume that an investment is forecasted to produce the following returns: a 20% probability of a 12% return; a 50% probability of a 16% return; and a 30% probability of a 19% return. What is the standard deviation of return for this investment? A) 5.89% B) 16.1% C) 2.43% D) 15.7% 6. Answer the questions below using the following information on stocks A, B, and C. Expected Return Standard Deviation Beta 20% 12% 1.8 21% 10% 2.2 10% 10% 0.8 Assume the risk-free rate of return is 3% and the expected market return is 12%. If returns are normally distributed, then approximately two-thirds of the time the return on each stock will be?

Answer 1

Let R_i be the Return for Probability P_i

Given, R₁ = 0.12 for P₁ = 0.20
R₂ = 0.16 for P₂ = 0.50
R₃ = 0.19 for P₃ = 0.30

Average Return ER = ΣP_iR_i = 0.20*0.12 + 0.50*0.16 + 0.30*0.19 = 0.161

Standard Deviation = sqrt [ ΣP_i(R_i - ER)² ]

= sqrt [0.20(0.12 - 0.161)² + 0.50(0.16 - 0.161)² + 0.30(0.19 - 0.161)² ]

= 0.0243 or 2.43%