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Date Submitted: 03/23/2009 05:43 AM
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...