Question

Consider the following information: Rate of Return If State Occurs State of Probability of State of Economy Economy Stock A Stock B Stock C .58 Boom Bust .07 .15 .33 .42 .16 .06 -.06 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 20 percent each in A and B and 60 percent in C? (Do not round intermediate calculations and round your answer to 6 decimal places, e.g., 161616.)

Answer 1

a)

Expected Expected Rate of returns if state Weighted returns if state portfolio Probability State of return [rxP(r)= µ] occurs (WeightxReturn) return (r) [(P(r)] economy occurs A A B 5.00% 11.00% 2.00% -2.00% 0.07 2.33% 18.33% 0.58 10.63% Boom 0.15 0.33 5.33% Normal (0.06) 5.33% 0.42 2.24% 0.16 0.06 Expected return 12.87% 33.33% 33.33% Weights 33.33%

Hence, expected return is 12.87%

b)

fx =H3-$J$6 КЗ A Н K M Expected Expected Rate of returns if state Weighted returns if state portfolio Probability State of return [(P(r)] [rxP(r)= µ] occurs (WeightxReturn) return (r) (r-µ)^2 P(r)x(r-u)^2 economy occurs r-p A A 3.00% 19.80% 1.20% -3.60% 14.04% 3 Boom 1.40% 24.20% 9.83% 0.97% 0.56% 0.07 0.15 0.33 0.58 1.84% (0.06) 3.20% 0.34%|-13.57% Normal 0.80% 0.77% 0.16 0.06 0.42 6 Weights Expected return (u) 20% 20% 60% 14.37% Variance (0^2) 0.013339

Hence, variance is 0.013339

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