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 .16 .357 .457 .337 Good .44 .127 .107 .177 Poor .34 .017 .027 .057 Bust .06 .117 .257 .097 Requirement 1: Your portfolio is invested 32 percent each in A and C and 36 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) Expected return of the portfolio % Requirement 2: (a) What is the variance of this portfolio? (Do not round intermediate calculations. Round your answer to 5 decimal places (e.g., 32.16161).) Variance of the portfolio (b) What is the standard deviation of this portfolio? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) Standard deviation %

Explanation / Answer

Expected return of the portfolio:

Variance of the portfolio:

Variance of stock A is calculated as below:

Varinace of stock B:

Variance of Stock C:

Variance of the portfolio:

Formula for variance of the portfolio is as follows:

WeightA2* Varinace of Stock A+WeightB2* Varinace of Stock B+WeightC2* Varinace of Stock C+2* Covariace of Stock A*Stock B*Stock C

Substituting the values in the formula:

=(.32)^2*0.0314486+(0.36)^2*0.0338589+(0.32)^2*0.0321092+2*0.32*0.36*0.32*-0.00012355

=0.01088732

Standard deviation of the portfolio is nothing but squareroot(0.01088732)

=10.43%

=10.44%.

Weighted State of economy Weight Boom Good poor Bust Boom Good poor Bust Total A 32% 0.357 0.127 0.017 -0.117 0.11424 0.04064 0.00544 -0.03744 B 36% 0.457 0.107 0.027 -0.257 0.16452 0.03852 0.00972 -0.09252 C 32% 0.337 0.177 -0.057 -0.097 0.10784 0.05664 -0.01824 -0.03104 Total return 0.3866 0.1358 -0.00308 -0.161 Probability 0.16 0.44 0.34 0.06 Expected return 0.061856 0.059752 -0.0010472 -0.00966 0.1109008

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