Question

a)Suppose A and B are disjoint events where A has probability 0.5 and B has probability 0.4. The probability that A or B occurs is

B)

The expected return of a kind of stock is 12% with standard deviation 10%. The expected return of a kind of bond is 4% with standard deviation 2%. The covariance of the return of the stock and of the bond is -0.0016. What is the standard deviation of a portfolio of 20% invested in the stock and 80% invested in the bond.

Answer 1

a)

P(A) = 0.5, P(B) = 0.4

P(A intersect B) = P(A)*P(B) --- as A and B are independent

so P(A int B) = 0.2

So P(A U B) = P(A) + P(B) - P(A intersect B) = 0.5 + 0.4 - 0.2 = 0.7.

So P(A or B occur) = 0.7

b) Let A be the return of the stock and B be the return of bond

Need to find SD(0.2A + 0.8B)

First we will find Var(0.2A + 0.8B) = Var(0.2A) + Var(0.8B) + 2Cov(0.2A * 0.8B)

Now Var(0.2A) = 0.04*Var(A) = 0.04*0.01. --- (Since SD = 10% = 0.1, so var = 0.01). = 0.0004

Now Var(0.8B) = 0.64*Var(B) = 0.64*0.0004 = 0.000256

and Cov(0.2A * 0.8B) = 0.2*0.8*Cov(A, B) = 0.16*(-0.0016) = -0.000256

So Var(0.2A + 0.8B) = 0.0004 + 0.000256 - 2*0.000256 = 0.000144

So SD(0.2A + 0.8B) = sqrt(0.000144) = 0.012 Ans