I just need help on part d, my answer is wrong... show all steps please :) yea i
ID: 3216642 • Letter: I
Question
I just need help on part d, my answer is wrong...
show all steps please :)
yea i tried 0 but that was not correct.
no idea how to determine the value of r
Suppose that you wish to invest in two stocks which both have a current price of $1. The values of these two stocks in one month are described by two random variables, say, X_1 and X_2. Suppose that the expected values and standard deviation of X_1 and X_2 are mu_1, mu_2, sigma_1 and sigma_2, respectively. We also assume that the correlation between the stocks is given by rho. Let C denote your initial investment, which is to be invested in the stocks, and assume that shares can be bought up to any percentages. Let w denote the percentage of your investment in stock 1. Finally, let P denote the value of your portfolio (investment) after a month. Then we have that P = c (w X_1 + (1 - w) X_2), where 0 lessthanorequalto w lessthanorequalto 1. a. Find an expression for the expected value of your investment after one month. Enter a formula below. For simplicity, use m_1 for m_2 for mu_2, s_1 for sigma_1, s2 for sigma_2, and r for rho. Use * for multiplication, /for division and A for power. For example, c*(2*m1 + w*m2)/(5*s1^2 + r*s2^2) means c(2 mu_1 + w mu_2)/(5 sigma_1^2 + rho sigma_2^2). How do we go about solving for the correlation? you do not need to solve for corr (ie: r) directly. Instead find the Var(equally weighted portfolio) using part b. Then determine what value of r minimizes this keeping in mind r is between -1 to 1.Explanation / Answer
c^2(w^2*(s1^2 + s2^2 - 2*r*s1*s2) + 2*w*(r*s1*s2 - s2^2) + s2^2)
for w = 0.5
c^2(0.25*(s1^2 + s2^2 - 2*r*s1*s2) + (r*s1*s2)) = c^2(0.25*s1^2 + 0.25*s2^2 - 0.5*r*s1*s2 + r*s1*s2)
= c^2(0.25*s1^2 + 0.25*s2^2 + 0.5*r*s1*s2)
This is the variance of equally weighted portfolio and this equation needs to be minimized.
r varies from -1 to 1
since s1 and s2 are always positive, the term 0.5*r*s1*s2 can become a negative term if we substitute in -1 for r.
c^2(0.25*s1^2 + 0.25*s2^2 - 0.5*s1*s2).
r = -1 is the answer