Question

There are two stocks in the market, Stock A and Stock B . The price of Stock A today is $85. The price of Stock A next year will be $74 if the economy is in a recession, $97 if the economy is normal, and $107 if the economy is expanding. The probabilities of recession, normal times, and expansion are .30, .50, and .20, respectively. Stock A pays no dividends and has a correlation of .80 with the market portfolio. Stock B has an expected return of 15.0 percent, a standard deviation of 35.0 percent, a correlation with the market portfolio of .34, and a correlation with Stock A of .46. The market portfolio has a standard deviation of 19.0 percent. Assume the CAPM holds. a-1. What is the return for each state of the economy for Stock A? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Return Recession % Normal % Expansion % a-2. What is the expected return of Stock A? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return % a-3. What is the variance of Stock A? (Do not round intermediate calculations and round your answer to 4 decimal places, e.g., 32.1616.) Variance a-4. What is the standard deviation of Stock A? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Standard deviation % a-5. What is the beta of Stock A? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.) Beta of Stock A a-6. What is the beta of Stock B? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.) Beta of Stock B If you are a typical, risk-averse investor with a well-diversified portfolio, which stock would you prefer? Stock A Stock B b-1. What is the expected return of a portfolio consisting of 75 percent of Stock A and 25 percent of Stock B? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return % b-2. What is standard deviation of a portfolio consisting of 75 percent of Stock A and 25 percent of Stock B? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Standard deviation % c. What is the beta of the portfolio in part (b)? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.) Beta of the portfolio

Answer #1

Current price = 85

a-1 Return for each state of economy : (Expected value - current price)/current price

Recession = (74-85)/85 = -12.94%

Normal = (97-85)/85 = 14.12%

Expansion = (107-85)/85 = 25.88%

a-2. Expected return of stock a =

=0.3 * -12.94% + 0.5*14.12% + 0.2*25.88% = -3.882 + 7.06 + 5.176 = 8.35%

a-3. Variance of stock A : (x - MEan X)/n-1

Prob | X | X- mean return | (x-meanX )^2 |

0.3 | -12.94 | -21.294 | 453.434436 |

0.5 | 14.12 | 5.766 | 33.246756 |

0.2 | 25.88 | 17.526 | 307.160676 |

Mean return | 8.354 | Total | 793.841868 |

Variance | 396.920934 |

a-4. Std dev = variance ^0.5

=19.92

a-5. Beta of stock A = correlation with market * std dev of stock / std dev of markt = 0.8 * 19.92 / 19 = 0.839

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