Question

Stocks 1 and 2 are selling for $100 and $125, respectively. You own 200 shares of stock 1 and 100 shares of stock 2. The weekly returns on these stocks have means of 0.001 and 0.0015, respectively, and standard deviations of 0.03 and 0.04, respectively. Their weekly returns have a correlation of 0.35. Find the correlation matrix of the weekly returns on the two stocks and the mean and standard deviation of the weekly returns on the portfolio.

Answer 1

Answer: covariance matrix is

(0.00090 0.00042)

(0.00042 0.00160)

Mean of weekly return = 0.00119

Standard deviation = 0.0279

VaR(0.05) = $1450.73

Explanation:

> S1 = 200*100

> S2 = 100*125

> w1 = S1/(S1+S2)

> w2 = 1 - w1

> w = c(w1,w2)

> means = c(0.001, 0.0015)

> sd = c(0.03, 0.04)

> rho = 0.35

> multiply = w %*%

means> round(mutiply by 5)=0.00119

> cov = matrix(c(sd^2, sd[1]*sd[2]*rho,sd[1]*sd[2]*rho,sd[2]^2),nrow=2) = 0.00090, 0.00042, 0.00042, 0.00160

> sdp = sqrt( w %*% cov %*% w )> round(sdp,4)=0.0279

> VaR = -(S1+S2)*(mup+sdp*qnorm(.05))

=1450.73