Question

State	Probability	Security X	Security Y
Recession	0.25	0.16	-0.08
Normal	0.4	0.07	0.15
Boom	0.35	0.02	0.25
E(Ri)		0.075	0.1275
σi		0.0536	0.1274

a. Calculate the rate of return of the portfolio if the portfolio weights are  Wx = .25 and Wy = .75. (2 points)

b. Calculate the covariance of two securities, X and Y, given the portfolio weights Wx = .25 and Wy = .75. (4 points)

c. Using the covariance calculated from part b, calculate the standard deviation of the portfolio,  σ_{p. (3 points)}

d. Calculate the correlation coefficient of two securities, X and Y, given the portfolio weights remained the same as part a. (Wx = .25 and Wy = .75. ) (3 points)

Answer 1

a) The formula for portfolio return is:

b) The formula for covaiance

c) The formula for standard deviation of the portfolio is:

Solving this, we get:

d) The formula for correlation coefficient is:

r = -0.0068 / 0.0536*0.1274 = -0.996

Correlation coefficient of x,y = -0.996