Question

Problem 13-10 Returns and Standard Deviations [LO1]

Consider the following information:

  

Rate of Return If State Occurs

State of

Probability of

Economy

State of Economy

Stock A

Stock B

Stock C

Boom

.15

.36

.46

.26

Good

.45

.21

.17

.10

Poor

.35

−.03

−.06

−.04

Bust

.05

−.17

−.21

−.07

  

a.	Your portfolio is invested 22 percent each in A and C, and 56 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
b-1.	What is the variance of this portfolio? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., .16161.)
b-2.	What is the standard deviation? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

	a. Expected return % b-1. Variance b-2. Standard deviation %

Answer 1

weighted return (weight x return) Stock C deviation expected return (weighted returndeviation^2 expected return) probability state of economy deviation A 2x probability rate of return if state occurs weighted sum Stock B Stock C Stock A Stock B 7.920% 25.760% (sum of weighted return) Stock A 39.400% 28.704% 5.720% 5.91% 8.239196% 0.012358794 Boom 0.36 0.46 0.26 0.15 2.200% 4.620% 16,340% 7.35% Good 0.21 9.520% 0.45 5.644% 0.318547% 0.00143346 0.17 0.10 -0.660%|-3.360% -3.740%-11.760% Poor -0.880% -4.900% -1.72% -15.596% 2.432352% 0.00851323 0.03 -0.06 -0.04 0.35 -0.85% -0.17 -1.540% 7.692857% 0.00384643 Bust -0.21 -0.07 -17.040% 0.05 -27.736% 10.70% Expected return of portfolio Weight 22.00% 56.00% 22.00% Variance 0.02615 16.17% Standard deviation variance^0.5 10.70% a) Expected return Answers: b-1) 0.02615 Variance b-2) Standard deviation = 16.17%