Suppose we have the following projects on two stocks. Assume the correlation among the two assets returns is 0.8

State of Economy	Probability	Stock A	Stock B
Recession	0.4	-3%	-6%
Slow	0.1	5	10
Average	0.3	12	9
Good	0.2	8	3

a. Find the expected return of shares A and B.

b. Find the standard deviation of shares A and B.

c. Find the investment percentage needed in A and B shares to create the minimum variance portfolio.

a-

Expected return of stock A = .4*-3% + .1*5% + .3*12% + .2*8% = 4.5%

Expected return of Stock B = .4*-6% + .1*10% +.3*9% +.2*3% = 1.9%

b.

Variance of stock A = .4*(-.03-.045)^2 + .1*(.05-.045)^2 + .3*(.12-.045)^2 + .2*(.08-.045)^2. = .004185

Standard deviations of stock A = √.004185 = 6.47%

Variance of stock B = .4*(-06-.019)^2 + .1*(.10-.019)^2 + .3*(.09-.019)^2 + .2*(.03-.019)^2 = .004689

Standard deviations of stock B = √.004689 = 6.85%

c-

Investment percentage Stock a= (σb²-ρabσaσb) / (σa² + σb² – 2ρabσaσb)

Investment percentage of Stock A = (.0685^2 - .8*.0647*.0685)/(.0647^2+.0685^2-2*.8*.0647*.0685) = .64

Investment percentage of Stock A = .64

Investment percentage of Stock B = 1-.64 = .36