Question

Consider the following information: Rate of Return if State Occurs Probability of State of Economy .74 26 Stock A Stock B State of Economy Boom Bust Stock C .06 32 21 27 -12 a. What is the expected return on an equally weighted portfolio of these three stocks? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What is the variance of a portfolio invested 29 percent each in A and B and 42 percent in C? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.) a. Expected return b. Variance of portfolio

Answer 1

(a) Expected return

Calculate the expected return of each individual portfolio

Stock A = ( 0.74 * 0.12 ) + ( 0.26 * 0.21 ) = 0.0888 + 0.0546 = 14.34 %

Stock B = ( 0.74 * 0.06 ) + ( 0.26 * 0.27 ) = 0.0444 + 0.0702 = 11.46 %

Stock C = ( 0.74 * 0.32 ) + ( 0.26 * - 0.12 ) = 0.2368 - 0.0312 = 20.56 %

Multiply each expected return with equal weight

Stock A = 14.34 % * ( 1 / 3 ) = 4.73 %

Stock B = 11.46 % * ( 1 / 3 ) = 3.78 %

Stock C = 20.56 % * ( 1 / 3 ) = 6.78 %

Expected Return Portfolio = 4.73 % + 3.78 % + 6.78 % = 15.29 %

(b) Variance of Portfolio

Calculate the expected return for the booms and bust

Boom = ( 0.29 * 0.12 ) + ( 0.29 * 0.06 ) + ( 0.42 * 0.32 ) = 0.0348 + 0.0174 + 0.1344 = 18.66 %

Bust = ( 0.29 * 0.21 ) + ( 0.29 * 0.27 ) + ( 0.42 * -0.12 ) = 0.0609 + 0.0783 - 0.0504 = 8.88 %

Total portfolio expected return

= ( 0.74 * 18.66 % ) + ( 0.26 * 8.88 % ) = 13.81 + 2.31 = 16.12 %

Deviation of boom and bust from total expected portfolio

Boom = 18.66 % - 16.12 % = 2.54 %

Bust = 8.88 % - 16.12 % = 7.24 %

Square of Deviation

Boom = 2.54 * 2.54 = 0.000645

Bust = 7.24 * 7.24 = 0.005242

Multiply square deviation with probability

Boom = 0.000645 * 0.74 = 0.0004773

Bust = 0.005242 * 0.26 = 0.0013629

Sum of Product for variance

0.0004773 + 0.0013629 = 018 %