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# 急!!!!計量經濟學之~~簡易的統計學問題!!!

Let X and Y represent the rates of return (in percent) on two stocks. You are told that X~N(15,25) and Y~N(8,4) , and that the correlation coefficient between the two rates of return is -0.4. Suppose you want to hold the two stocks in your portfolio in equal proportion. What is the probability distribution of the return on the portfolio? Is it better to hold this portfolio or to invest in only one of the two stocks?Why?

### 1 Answer

- EdovLv 51 decade agoFavorite Answer
E(X)=15, Var(X)=25, so that standard deviation of asset X is 5

E(Y)=8, Var(Y)=4, standard deviation of asset Y is 2

we know the correlation between X and Y is -0.4

If you invest in X and Y with equal proportion (50%) to construct a portfolio P

E(P)=0.5*EX+0.5*EY=11.5

Var(Y)=0.5^2*Var(X)+0.5^2*Var(Y)+2*0.5*0.5*(-0.4)=5.25

The probaility distribution of the return on the portfolio N(11.5, 5.25)

ans:

X's return/stdev ratio is 3 (15/5=3), Y's return/stdev ratio is 4 (8/2=4)

and the P's return/stdev ratio is over 5 (11.5/sqrt(5.25))

therefore, investing in portfolio is the best choice!