Question

2. You are given annual returns for stocks ABC and XYZ from the last 5 years: Return on Stock ABC (in %) Return on Stock XYZ (in %) Year 1 11 9 2 12 7 13 6 4 15 5 5 14 11 a. What is your estimate of expected return for each of the stocks? b. What is your estimate of return standard deviation for each of the stocks? c. What is your estimate of the correlation between the returns of stock ABC and stock XYZ? d. Consider a portfolio invested 70% in stock ABC and 30% in stock XYZ - what would its expected return and volatility be? e. What is the minimum varian ce portfolio comprised of these two stocks? f. Plot the investment opportunity set for stock ABC and stock XYZ. (You can use the spreadsheet 'corr.xls' on the course website: substitute the expected return, variance and correlation values with the ones in the question.)

Answer 1

a. Expected return for ABC (MA) = 0.11 + 0 12 + 0.13 +0.15 +0.14 - 50.13 Expected return for XYZ ay = 0.09+0.07 +0.06 + 0.00+ 0.11 = 0.076 b. Std. der for ABC (TA) = {(24-MA) ² n-1 ICO./-0.13) + (0-12-0:13) + ... + (O)-0-13) = 0.015811 Std. de for xyz (G) = {( x M.)2 n- 10.09-0.070)2+(0.07 -0.076)?.... + (0.18-0.070) 0.024083 = 0.024083 c. Correlation (8) è cov (ABC, x42) n-i con (ABC, XYZ) = { (RA-MA) (2x - M) = [(0.11 -0.13) (0.09 -0.0Ft) +(012-0:13)(0.07-0.070)+. +40-1-0-13) (0./- 0.070)] -0.00010

-D.ODOLO 0.01581) X 0.024083 I - 0.2626 d. & std. der be op Let the return be np weight of ABC (WA) = D. 7. weight of XYZ (Wx) = 0.3 p = WA MA + Wyx E 0.7 x 0.13 + 0.3x 0.076 E 0.1138 Spa (wet w x + 2 WA WAxS)" Y2 (0.72 0.0158112 + 0.3? x 0.024083 + 2x0.7x0.3 x 0-01 581)x 0.024 083 x (-0.2626))X2 (0.00013270)/2 0.01152 = =