Question

2. (13 points) The table below presents the returns on stocks ABC and XYZ for a five- year period. Year 1 2 ABC 0.14 0.43 -0.05 -0.26 0.44 XYZ 0.11 0.64 -0.27 -0.81 0.55 3 4. 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

Pg No- Solution :- Given data: ABC xyz 0.14 0:1] 0.43 0.64 Vi swe - -0.5 -0.27 -0.26 -0.81 0.44 0.55 Average Calso Expected 0.044 0405 Return 0.60 0.42 Sted deviation Correlation (ABC, Xy7) Convariunce Variance 24 / A) weight op a portfello :- → Expected return of portfolio - W * Erpreted return of ARC + (1-w) ► Expected return of xyz . = W *0.05+(1-w) x diony =. 20%

Pg No (2) → Solving Above Equalion : w (ABC)= 26- w (xyz) - 1-26.4 = 744 a) Std, Deviation of portfolio :- Std. Deviation of poilfolio = V(w (ABC)? ystod dev CABC* + WCx92)2 + Steld. $ (342)2+2* w CARC)y sto dv (ABC) + W1942) * Std Dew (x42) * Correlation (Abc, xy2)] → Std: Deviation of portfolio= (0.267 * 0.422) +(14762 ) + Rou2 x 0.268074 * 016*0186] = 54.16 3). Slope of the poitfolio :- Formula = ( portfolio Return - Risk Free Return) / Std Dev of poitfolio slope of the portfolio = (20 –6-4) 154,1- = 14•7/5411% 0.258

Pg No ③ 4). A) 5% VAR = -165 * 5414 = -89.12 B) 12%. VAR = -2,33 54.1-4. -126/