Consider the following information: Rate of Return If State Occurs State of Prob

Question

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

.33

.43

.23

  Good

.55

.18

.14

.12

  Poor

.25

.05

.08

.06

  Bust

.05

.13

.18

.10

b-1

What is the variance of this portfolio? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.)

b-2

What is the standard deviation? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Consider the following information:

Explanation / Answer

Expected Returns:

E(rA) = (.15 x .33) + (.55 x .18) + (.25 x -.05) + (.05 x -.13) = 0.1295 or 12.95%
E(rB) = (.15 x .43) + (.55 x .14) + (.25 x -.08) + (.05 x -.18) = 0.1125 or 11.25%
E(rC) = (.15 x .23) + (.55 x .12) + (.25 x -.06) + (.05 x -.10) = 0.0805 or 8.05%

Variance:

Stock A = [(.33-.1295)2x.15] + [(.18-.1295)2x.55] + [(-.05-.1295)2x.25] + [(-.13-.1295)2x.05] = 0.01885475

Stock B = [(.43-.1125)2x.15] + [(.14-.1125)2x.55] + [(-.08-.1125)2x.25] + [(-.18-.1125)2x.05] = 0.02907875

Stock C = [(.23-.0805)2x.15] + [(.12-.0805)2x.55] + [(-.06-.0805)2x.25] + [(-.10-.0805)2x.05] = 0.01077475

Standard Deviation:

Stock A = (0.01885475)1/2 = 0.1373126
Stock B = (0.02907875)1/2 = 0.170524925
Stock C = (0.01077475)1/2 = 0.103801493

Please provide the weight of each stock in the portfolio to calculate the variance of portfolio.

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