Question

# Rate of Return if State Occurs State of Economy Probability of State of Economy Stock A...

 Rate of Return if State Occurs State of Economy Probability of State of Economy Stock A Stock B Stock C Boom 0.30 50.0% 12.0% 20.0% Average 0.45 15.0% -5.0% 6.0% Recession 0.25 -8.0% 2.0% -3.2%

Your portfolio manager has invested 30% of your money in Stock A, 50% in Stock B, and the rest in Stock C.

1. What is the correlation coefficient between Stocks B and C?

2. What is the standard deviation of your portfolio? Hint: Instead of using the portfolio variance formula for three stocks, you can save time by calculating the return on the portfolio for all three states of the economy

1.

E(Rb) = 0.3*12% + 0.45*(-5%) + 0.25*2%= 1.85%

E(Rc) = 0.3*20% + 0.45*6% + 0.25*(-3.2%)= 7.9%

SD(Rb) = [0.3*(12%-1.85%)2 + 0.45*(-5%-1.85%)2 + 0.25*(2%-1.85%)2]0.5 = 7.213%

SD(Rc) = [0.3*(20%-7.9%)2 + 0.45*(6%-7.9%)2 + 0.25*(-3.2%-7.9%)2]0.5 = 8.7378%

COV(Rb,Rc) =  [0.3*(12%-1.85%)*(20%-7.9%) + 0.45*(-5%-1.85%)*(6%-7.9%) + 0.25*(2%-1.85%)*(-3.2%-7.9%)]

=0.42285%

Correlation(Rb,Rc) = COV(Rb,Rc) / [SD(Rb) *SD(Rc)] = 0.0042285/(0.07213*0.087378) = 0.6709

2. Weights of A, B, C given to be 30%, 50%, 20%.

Rp(Boom) = 30%*50% + 50%* 12%+ 20%*20% = 25%

Rp(Average) = 30%*15% + 50%* (-5%)+ 20%*6% = 3.2%

Rp(Recession) = 30%*(-8%) + 50%* 2%+ 20%*(-3.2%) = -2.04%

E(Rp) = 0.3*25% + 0.45*3.2% + 0.25*(-2.04%) = 8.43%

SD(Rp) = [0.3*(25%-8.43%)2 + 0.45*(3.2%-8.43%)2 + 0.25*(-2.04%-8.43%)2]0.5 = 11.0491%

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