1. There are four stocks XI, X2, X3 and X4. Each share of Xi, X2, X3 and X4 has
ID: 2649232 • Letter: 1
Question
1. There are four stocks XI, X2, X3 and X4. Each share of Xi, X2, X3 and X4 has a payoff of 0 with probability 0.5 and 2 with probability 0.5. The payoffs of XI, X2, X3 and X4 are independent. (a) What is the mean and standard deviation of each stock? (b) Suppose you buy 1/2 share of Xi and X2, what is the mean and standard deviation of the portfolio? (c) Suppose you buy 1/3 share of XI, X2 and X3, what is the mean and standard deviation of the portfolio? (d Suppose you buy 1/4 share of XI, X2, X3 and X4, what is the mean and standard deviation of the portfolio?Explanation / Answer
Answer:(a)Calculation the mean and standard deviation of each stock:
Mean = E(r) = ? ?s * rs
= ?1*r1 + ?2*r2
Mean = 0.50*0 + 0.50*21 = 1
StDev = ? ?s [rs-E(r) ]2
StDev = 0.50*(2-1)2+0.50*(0-1)2 = 1
Answer: (b) Calculation the mean and standard deviation of each stock:
Mean = E (rp) = ? wi*E (ri)
=
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