et X and Y represent the rates of return (in percent) on two stocks. You are tol
ID: 1190983 • Letter: E
Question
et X and Y represent the rates of return (in percent) on two stocks. You are told that X ~ N(20,9) and Y ~ N(15, 4), and that the correlation coefficient between the two rates of return is -0.8. Suppose you want to hold the two stocks in your portfolio in equal proportion. [a] What is the probability distribution of the return on the portfolio? [b] Is it better to hold this portfolio or to invest in only one of the two stocks? Why? et X and Y represent the rates of return (in percent) on two stocks. You are told that X ~ N(20,9) and Y ~ N(15, 4), and that the correlation coefficient between the two rates of return is -0.8. Suppose you want to hold the two stocks in your portfolio in equal proportion. [a] What is the probability distribution of the return on the portfolio? [b] Is it better to hold this portfolio or to invest in only one of the two stocks? Why?Explanation / Answer
Solution :
The expected return on a portfolio is found using the formula :
E(Rp ) = W1 E(R1 ) + W2 E(R2 )
W1 = W2
E(R1 ) = 20% ; E(R2 ) = 15%
E(Rp ) = 0.5 X 0.2 + 0.5 X 0.15
E(Rp ) = 17.50 %
It is better to invest in stock X only because it has a higher return when compared to the portfolio of two stocks X &Y which has a lesser return .
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