# Returns and Standard Deviations

Consider the following information:

Rate of Return if State Occurs

State of Economy Probability of

State of Economy Stock A Stock B Stock C

Boom .20 .37 .41 .42

Good .30 .17 .12 .13

Poor .17 .11 .06 .05

Bust .33 .05 -.05 -.04

Requirement 1:

Your portfolio is invested 16 percent each in A and C, and 68 percent in B. What is the expected return of the portfolio? (Do not round your intermediate calculations.)

(select one)

10.85%

12.05%

12.65%

8.53%

13.26%

Requirement 2:

(a) What is the variance of this portfolio? (Do not round your intermediate calculations.)

HINT: It is best if you first calculate the return on the portfolio in all 4 states. You will need those numbers in the next part of the problem.

(select one)

.0269

.0232

.0349

.0244

.0081

(b) What is the standard deviation? (Do not round your intermediate calculations.)

NOTE: The standard deviation is the square root of the variance. It tells us on average, how far away the return will be from the expected return.

(select one)

18.69%

14.85%

16.42%

9.03%

15.64%

#### Solution Preview

See the attached file.

Consider the following information:

Rate of Return if state occurs

State of the economy Probability Stock A Stock B Stock C

Boom 0.20 37.0% 41.0% 42.0%

Good 0.30 17.0% 12.0% 13.0%

Poor 0.17 11.0% 6.0% 5.0%

Bust 0.33 5.0% -5.0% -4.0%

Expected Return ...

#### Solution Summary

The returns and standard deviations are determined.