? asked in 社會與文化語言 · 1 decade ago


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

  • Edov
    Lv 5
    1 decade ago
    Favorite 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



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


    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!

Still have questions? Get your answers by asking now.