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(+4) Applications of the concepts of covariance and correlation have been extremely important in the field of finance. The purpose of this question is to illustrate one such application, which is the value of maintaining a diversified portfolio. To that end, let X and Y denote the (unknown) future returns associated with two stocks. A stock is most attractive to an investor if its payoffs are expected to be high, and have low risk-that is, a high mean and low variance. For simplicity, suppose that two stocks are equally attractive, with E(X) = E(Y) = μ and V(X) = V(Y) = 1. Note that having a variance of one implies that the standard deviation is equal to Tz = ơy-1 as well, and therefore that the correlation and covariance are the same (a) (+1) Find the mean and variance of the returns associated with a portfolio consisting of two shares of stock X.(b) (+2) As a function of the correlation coefficient p between the two stock returns, find the mean and variance of the returns associated with a diversified portfolio, consisting of one share of stock X and one share of stock Y. (c) (+1) Under what conditions ist unambiguously better to have a diversified portfolio? That is, when E(X +Y) 2 E(2X) and V(X +Y) s V(2.x)?

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Solution from the given information @ E (2x) = 2 E (x) = 24 V (2x) = 2 ² v(x) = 4 v(x) = 4 b E(x+4)= E(x) + E(Y) = 24. So, EThank you.

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