Question

1) Suppose you have $100,000 to invest in a PORTFOLIO OF TWO stocks: Stock A and Stock B. Your analysis of the two stocks led to the following risk -return statistics:

Expected Annual Return | Beta | Standard Deviation | |

A | 18% | 1.4 | 25% |

B | 12% | 0.6 | 16% |

The expected return on the market portfolio is 7% and the risk free rate is 1%. You want to create a portfolio with NO MARKET RISK.

a) How much (IN DOLLARS) should you invest IN EACH OF THE TWO STOCKS in order to achieve your goal?

b) What is the expected return of this portfolio?

2) Stocks A and B are currently selling for $75 and $42, respectively. Assume the expected return and the standard deviation of the market portfolio is 10% and 12%, respectively and the risk-free rate is 0.5%. The standard deviation for A and B are 18% and 14%, respectively; and the correlation of each stock with the market portfolio is 0.35 and 0.65. Suppose that you estimate a year-end target price of $78 and $46 for these stocks (NO DIVIDENDS ARE EXPECTED). Using CAPM as a benchmark, calculate the alpha for each stock and state whether the stocks are underpriced or overpriced.

Answer #1

Expected Annual Return | Beta | Standard Deviation | |

A | 18% | 1.4 | 25% |

B | 12% | 0.6 | 16% |

Let Wa be weight of A in portfolio

Wb be weight of B in portfolio

Market Return Rm =7%

Risk free return Rf = 1%

For No market risk , beta protfolio should be 0

βa | 1.4 |

βb | 0.6 |

βp = Wa*βa + Wb*βb

0 = Wa*1.4 + Wb*0.6

Wa=(Wb*0.6)/1.4 =0.43 Wb

Also Wa + Wb =1 (sum of weights should be 1)

.0.43Wb+Wb=1

1.43*Wb=1

Wb= 0.7

Wa=0.3

Thus amont to be invested in A = Wa * Total amount= 0.3*100,000 = $ 30,000

Amount invested in B = 1000,000-Amount in A = 100,000-30,000= $ 70,000------Answer 1

Portfolio return = waRa+WbRb=0.3*0.18+0.7*0.12 = 0.138 = 13.8%

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