Consider the following information: State of Probability of Rate of Return If St

Question

Consider the following information: State of Probability of Rate of Return If State Occurs Economy State of Economy Stock A Stock B Stock C Boom .16 .363 .463 .343 Good .44 .133 .113 .183 Poor .34 .023 .033 .075 Bust .06 .123 .263 .103 Your portfolio is invested 29 percent each in A and C and 42 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return % What is the variance of this portfolio? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.) Variance What is the standard deviation of this portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Standard deviation

Explanation / Answer

Calculation:

What is the expected return of the portfolio?

Expected return of the portfolio is 11.41 %

(a) What is the variance of this portfolio?

Variance of the portfolio is 2.29%

(b) What is the standard deviation of this portfolio?

Standard deviation of this portfolio is 15.12%

Rate of Return if State Occurs Probability of State of Economy (p) Stock A (rA ) Stock B (rB) Stock C (rC) Average return of stock (return * weight in the portfolio) Probability * Average return of stock Average return - expected return (Average return - expected return)^2 (Average return - expected return)^2 *p 0.16 0.363 0.463 0.343 0.3992 0.063872 0.2850988 0.0812813 0.013005 0.44 0.133 0.113 0.183 0.1391 0.061204 0.0249988 0.0006249 0.000275 0.34 0.023 0.033 -0.075 -0.00122 -0.0004148 -0.1153212 0.013299 0.0045217 0.06 -0.123 -0.263 -0.103 -0.176 -0.01056 -0.2901012 0.0841587 0.0050495 Weight in the portfolio 0.29 0.42 0.29 The expected return of the portfolio 0.1141012 variance of this portfolio 0.0228512 Sum of above The expected return of the portfolio (%) 11.41% variance of this portfolio (%) 2.29% standard deviation of this portfolio (%) 15.12% variance

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