Question

2._(13 points) The table below presents the returns on stocks ABC and XYZ for a five- year period. Year 1 2 3T 4 ABC 0.14 0.43 -0.05 -0.26 0.44 XYZ 0.11 0.64 -0.27 -0.81 0.55 a. (3 points) Assume that the average returns from the data equals the expected returns for the respective stocks. If you want to form a portfolio with expected returns of 20%, what proportion of your assets would you invest in each of these stocks? b. (3 points) What is the standard deviation of this portfolio? Remember to implement the degree of freedom adjustment (dividing by n-1) when computing variances and covariances. c. (3 points) Suppose the risk-free rate is 6%. Compute the slope of the capital allocation lines for ABC and XYZ. Which of these two stocks yields a higher reward-to-risk ratio? d. (4 points) Assume that returns are normally distributed. What is the 5% and 1% VaR?

2.   (13 points) The table below presents the returns on stocks ABC and XYZ for a five- year period.

Year                                        ABC                                        XYZ

1                                           0.14                                         0.11

2                                           0.43                                         0.64

3                                           -0.05                                        -0.27

4                                           -0.26                                        -0.81

5                                           0.44                                         0.55

a.   (3 points) Assume that the average returns from the data equals the expected returns for the respective stocks. If you want to form a portfolio with expected returns of 20%, what proportion of your assets would you invest in each of these stocks?

b.   (3 points) What is the standard deviation of this portfolio? Remember to implement the degree of freedom adjustment (dividing by n-1) when computing variances and covariances.

c.    (3 points) Suppose the risk-free rate is 6%. Compute the slope of the capital allocation lines for ABC and XYZ. Which of these two stocks yields a higher reward-to-risk ratio?

d.    (4 points) Assume that returns are normally distributed. What is the 5% and 1% VaR?

Answer 1

Year	ABC	XYZ
1	0.14	0.11
2	0.43	0.64
3	-0.5	-0.27
4	-0.26	-0.81
5	0.44	0.55
Average (Also Expected return)	0.05	0.044
Std Deviation	0.42	0.60
Correlation (ABC, XYZ)	86%
Convariance	17%
Variance	24%

a) Weight of a portfolio:

Expected return of Portfolio = W * Expected return of ABC + (1-W) * Expected return of XYZ

Expected return of Portfolio = W * 0.05 + (1-W) * 0.044 = 20%

Solving above equation:

W (ABC) = 26%

W (XYZ)= 1-26% = 74%

2) Std. Deviation of Portfolio

Formula

Std. Deviation of Portfolio = Sqrt [ W (ABC)^2 * Std Dev (ABC)^2 + W (XYZ)^2 * Std Dev (XYZ)^2 + 2* W (ABC) * Std Dev (ABC) + W (XYZ) * Std Dev (XYZ) * Correlation (ABC, XYZ)]

Std. Deviation of Portfolio = Sqrt [ (0.26^2 * 0.42^2) + (.74^2 * .6^2) + (2. 0.42 * 0.26 * 0.74 * 0.6 * 0.86)] = 54.1%

Slope of the portfolio:

Formula = (Portfolio Return - Risk Free Return)/ Std Dev of Portfolio

Slope of Portfolio = (20%- 6% ) / 54.1% = 0.258

4)

a) 5 % VAR= -1.65 * 54.1 % = -89%

b) 1 % VAR= -2.33 * 54.1 % = -126%