Review Question for chapter 1

Two assets have the outcomes detailed below

	Probability	Asset X	Asset Y
Initial value		$1000	$2000
Outcome 1	.40	$800	$2200
Outcome 2	.25	$1200	$1500
Outcome 3	.35	$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

In regards to questions d and e. Where exactly does the .5 come from in the equation?