Question

Expected return and standard deviation. Use the following information to answer the questions: a. What is the expected return of each asset? b. What is the variance of each asset? c. What is the standard deviation of each asset? Hint: Make sure to round al intermediate calculations to at least seven (7) decimal places. The input instructions, phrases in parenthesis after each answer box, only apply for the answers you will type Core: i Data Table ou (Click on the following icon in order to copy its contents into a spreadsheet on 10 on 5 on 9 on 13 State of Economy Boom Normal Recession Probability of State 0.31 0.51 0.18 Return on Assol A in Slato 0.02 0.02 002 Roun on Asset B in Stato 0.21 0.08 -0.03 Rotun on Asset C in State 0.29 0.19 -0.27 Print Done

Answer 1

(a) Let the return be denoted by R_i and Probability by P_i for state of economy i

Expected Return = ER = ΣP_iR_i

Expected Return for A = ER_A = 0.31*0.02 + 0.51*0.02 + 0.18*0.02 = 0.02

Expected Return for B = ER_B = 0.31*0.21 + 0.51*0.08 + 0.18*(-0.03) = 0.1005

Expected Return for C = ER_C = 0.31*0.29 + 0.51*0.19 + 0.18*(-0.27) = 0.1382

(b) Variance = ΣP_i(R_i- ER)²

Variance for A = 0.31(0.02 - 0.02)² + 0.51*(0.02 - 0.02)² + 0.18(0.02 - 0.02)² = 0

Variance for B = 0.31(0.21 - 0.1005)² + 0.51*(0.08 - 0.1005)² + 0.18(-0.03 - 0.1005)² = 0.0069968

Variance for C = 0.31(0.29 - 0.1382)² + 0.51*(0.19 - 0.1382)² + 0.18(-0.27 - 0.1382)² = 0.0385048

(c) Standard Deviation = sqrt (variance)

Standard Deviation for A = sqrt(0) = 0

Standard Deviation for B = sqrt(0.0069968) = 0.0836469

Standard Deviation for C = sqrt(0.0385048) = 0.1962264