Returns and Standard Deviations [LO1] Consider the following information: Rate o

ID: 2729121 • Letter: R

Question

Returns and Standard Deviations [LO1]

Consider the following information:

Rate of Return If State Occurs

State of Economy Probability of State Economy Stock A Stock B Stock C

Boom .15 .32 .42 .33

Good .45 .19 .13 .12

Poor .30 -.05 -.08 -.06

Bust .10 -.16 -.28 -.09

A. Your portfolio is invested 30 percent each in A and C, and 40 percent in B. What is the expected return of the portfolio?

B.-1. What is the variance of this portfolio?

B.-2. What is the standard deviation?

Answer A.

Expected Return in Boom = 0.30 * 0.32 + 0.40 * 0.42 + 0.30 * 0.33

= 0.363

Expected Return in Good = 0.30 * 0.19 + 0.40 * 0.13 + 0.30 * 0.12

= 0.145

Expected Return in Poor = 0.30 * -0.05 + 0.40 * -0.08 + 0.30 * -0.06

= -0.065

Expected Return in Bust = 0.30 * -0.16 + 0.40 * -0.28 + 0.30 * -0.09

= -0.187

Expected Return of Portfolio = 0.15 * 0.363 + 0.45 * 0.145 + 0.30 * -0.065 + 0.10 * -0.187

= 0.0815 = 8.15%

Answer B.

Variance of the Portfolio = 0.15 * (0.363 - 0.0815)^2 + 0.45 * (0.145 - 0.0815)^2 + 0.30 * (-0.065 - 0.0815)^2 + 0.10 * (-0.187 - 0.0815)^2

= 0.02735

Answer C.

Standard Deviation = Sqrt(0.02735) = 0.16538

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