Quantitative Methods for Finance

MASTER OF FINANCE (26020)

AF5343 QUANTITATIVE METHODS FOR FINANCE

HOMEWORK #2

Prepared By:

PART I

|1. |D |

|2. |A |

|3. |D |

|4. |A |

|5. |A |

|6. |E |

|7. |B |

|8. |D |

|9. |A |

|10. |C |

PART II

Question 1

(1)

The probability function of the EPS of the firm:

|f(x) |= { |1/2 for -0.5< x 8%) = P(Y > (8% '' 11%) / 33.71%) = P(Y > -0.09) = 0.5359

(3)

Let the weight of stock 1 be w, then the weight of stock 2 be (1 '' w),

σp2 = w2σ12 + (1-w)2σ22 + 2w(1 '' w) ρ12σ1σ2

= (0.15)2w2 + (0.2)2(1 '' w)2 + 2w(1 '' w)(-0.4)(0.2)(0.15)

= 0.0865w2 '' 0.104w + 0.04

= (0.2941w)2 '' 2(0.052)w + 0.04

= (0.2941w '' 0.1768)2 + 0.04 '' 0.0313

= (0.2941w '' 0.1768)2 + 0.0087

If the portfolio has minimum variance, 0.2941w '' 0.1768 = 0

w = 0.6012 = 60.12%

If the portfolio has minimum variance, stock 1 should be weighted 60.12% and stock 2 should be weighted 39.88%

Question 3

Sample mean = 0.74%, sample standard deviation = 8.09%, n = 132

95% confidence intervals:

0.74% ± 1.96 (8.09% / √132) = 0.74% ± 1.38%

The confidence interval for the population mean span -0.64% to 2.12%. It can be confident at the 95% level that this range includes the population mean.

99% confidence intervals:

0.74% ± 2.58 (8.09% / √132) = 0.74% ± 1.82%

The confidence interval for the population mean span -1.08% to 2.56%. It can be confident at the 99% level that this range includes the population mean.

We construct the confidence intervals based on the standard normal distribution since the sample size was large enough & the use of z distribution also acceptable regardless the population variance was unknown in this case.

Question 4...