Question

State of Nature 1 Probability 0.25 0.4 0.35 Investment A Return 6% 9% 5% Investment B Return 15% 12% -3% III Given the above information on two investments A and B, calculate the statistics below. The correlation coefficient between A and B is 0.6472. Note that since the correlation is given, you do not have to do the long calculation for covariance, just use the shortcut = PA00,- E. The covariance between A and B F. The expected return for a portfolio consisting of 60% A and 40% B G. The standard deviation of a portfolio consisting of 60% A and 40% B.

Not supposed to be done in excel.

Answer 1

Solution:

Expected return of A = 0.25*6 + 0.4*9 +0.35*5 = 6.85%

Expected return of B = 0.25*15 + 0.4*12 +0.35*-3=7.50%

Standard deviation of A = Sqrt((0.25*(6%-6.85%)^2)+(0.4*(9%-6.85%)^2)+(0.35*(5%-6.85%)^2)) = 0.01797

Standard deviation of B =Sqrt((0.25*(15%-7.5%)^2)+(0.4*(12%-7.5%)^2)+(0.35*(-3%-7.5%)^2)) = 0.7794

E)

Correlation between A and B = 0.6472

Covariance between A and B = Correlation between A and B * standard deviation of A * Standard deviation of B = 0.6472* 0.01797*0.07794= 0.000906243

F)

Weight of A = 60%

Weight of B = 40%

Expected Return of portfolio = Weight of A* Expected Return of A + Weight of B*Expected return of B = (0.6*6.85)+(0.4*7.5)= 7.11%

G)

Weight of A = 60%

Weight of B = 40%

Standard deviation of portfolio = Sqrt((((Weight of A)^2)*((Standard deviation of A)^2))+(((Weight of B)^2)*((Standard deviation of B)^2))+(2*Weight of A*Weight of B* Covariance of A and B)) = Sqrt((((0.6)^2)*((0.01797)^2))+(((0.4)^2)*((0.07794)^2))+(2*0.6*0.4*0.000906243)) = 0.039028 or 3.90%