Question: heview Question for chapter 1 Two assets have the outcomes detailed below Proba Asset bility Y Initial value $1000 $2000 ._ $800 52200 $1200 $1500

heview Question for chapter 1 Two assets have the outcomes detailed below Proba Asset bility Y Initial value $1000 $2000 ._ $800 52200 $1200 $1500 1000 2500 a. What is the expected return of each asset? b. What is the variance of each asset? c. What is the covariance between asset returns? d. What is the correlation coefficient between asset returns? e. What is the expected return on an equal-weighted portfolio? Asset X Asset Y Outcome 1 800/1000 -1 = -20% 2200/2000 - 1 = 10% Outcome 2 1200/1000-1 = 20% 1500/2000-1 =-25% Outcome 3 1000/1000 - 1 = 0% 2500/2000 - 1 = 25% a E(r) of X = .40 x (-.20) + .25 x .20 + .35 x 0 = -.03 E(r) of Y = .40 x .10 + .25 x (-.25) + .35 x .25 = .065 b Variance of X = .40 x (-.20-(-.03))^2 +.25 x (.20-(-.03))^2 +.35 x (0-(-.03))^2 = .40 x -.17^2 + .25 x .23^2 +.35 x .03^2 = .40 x .0289 + .25 x .0529 + .35 x .0009 = .0116 + .0132 + .0003 = .0251 Variance of Y = .40 x (.10-.065)^2 + .25 x (-.25-.065)^2 + .35 x (.25-.065)^2 = .037275 c Covariance = .40 x (-.20-(-.03)) x (.10-.065) + .25 x (.20-(-.03)) x ((-.25-.065) + .35 x (0-(-.03)) x (.25-.065) = .40 x -.17 x .035 + .25 x .23 x -.315 + .35 x .03 x .185 = -.002380 + -.018113 + .001943 = -.01855 d Correlation = -.01855/(.0251^.5 x .037275^.5) = -.61 e Equal-weighted return = .5 x (-.03) + .5 x .065 = .0175

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