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 State
Economy of Economy Stock A Stock B Stock C
  Boom .72               .10         .04         .30       
  Bust .28               .19         .25         –.10       

Required:

(a)

What is the expected return on an equally weighted portfolio of these three stocks? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).)

  Expected return %

(b)

What is the variance of a portfolio invested 27 percent each in A and B and 46 percent in C? (Do not round intermediate calculations. Round your answer to 5 decimal places (e.g., 32.16161).)

  Variance of a portfolio   

Explanation / Answer

Calculation of portfolio return Probability of state Security rate of return 0.72 A 0.1 B 0.04 C 0.3 0.72 0.146666667 Rate of return under state of Boom 10.56 10.56% Probability of state Security rate of return 0.28 A 0.19 B 0.25 C -0.1 0.28 0.113333333 Rate of return under state of Boom 3.173333333 3.17% Total return on Portfolio 13.73% variance of portfolio Probability of state Security rate of return weight Weight * Rate Return* probability of state Final return 0.72 A 0.1 0.27 0.027 0.01944 1.944 B 0.04 0.27 0.0108 0.007776 0.7776 C 0.3 0.46 0.138 0.09936 9.936 0.72 0.146666667 Rate of return under state of Boom 10.56 10.56% 0.1758 Probability of state Security rate of return weight Weight * Rate Return* probability of state Final return 0.28 A 0.19 0.27 0.0513 0.014364 1.4364 B 0.25 0.27 0.0675 0.0189 1.89 C -0.1 0.46 -0.046 -0.01288 -1.288 0.28 0.113333333 Rate of return under state of Boom 3.173333333 3.17% Total return on Portfolio 13.73% Company return(sum of return under boom state + sum of return under bust state A 3.3804 B 2.6676 Company return C 8.648 A 3.3804 Variance 10.67014629 B 2.6676 C 8.648 Variance 10.67015

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