1. (4 Points) Stock X has an expected return of 8% and the standard deviation of
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Question
1. (4 Points) Stock X has an expected return of 8% and the standard deviation of the expected return is 9%. Stock Z has an expected return of 10% and the standard deviation of the expected return is 7%. The correlation between the returns of the two stocks is +0.5. These are the only two stocks in a hypothetical world.
A. What is the expected return and the standard deviation of a portfolio consisting of 100% Stock X? Will any rational investor hold this portfolio (in this hypothetical two stock world)? Explain why or why not.
B. What is the expected return and the standard deviation of a portfolio consisting of 75% Stock Z and 25% Stock X? Will any rational investor hold this portfolio (in this hypothetical two stock world)? Explain why or why not. (You might want to do Part D first).
C. What is the expected return and the standard deviation of a portfolio consisting of 25% Stock Z and 75% Stock X? Will any rational investor hold this portfolio (in this hypothetical two stock world)? Explain why or why not.
D. What is the maximum amount of Stock X a rational investor will hold in his or her portfolio? What is the expected return and the standard deviation of this portfolio? The maximum amount is a percentage between 0% and 100%, and to receive full credit your answer should be within 2 percentage points of the correct answer. (Hint: Set up Excel to calculate the portfolio expected return and standard deviation as a function of the portfolio weights, which must sum to 100%. You can find the correct answer to this part by manually changing the portfolio weights, or by using the Solver function on Excel).
Explanation / Answer
Formula for expected return =Weight of stock 1*Expected return of stock 1+weight of stock 2*Expected return of stock 2.
Formula for standard devition of portfolio=Weight of stock1^2*Standard deviation of stock 1^2+Weight of stock2^2*Standard deviation of stock 2^2+2*Weight of stock1*Weight of stock 2*Co varinace of stock 1 and stock 2.
Answer for question no.A:
When the portfolio has only one stock i.e., 100% of stock X is as follows:
The investor would not prefer to invest 100 % in stock X, as the expected return is less than that of Stock Z and also the standard deviation of expected return of stock X is more than that of Stock Z. Therefore, one would prefer to invest in Stock Z rather than in stock X.
Answer for question no.B:
Answer for question no.C:
Answer for question no.D:
Variours combnationso stock X and Stock Y is as follows:
From the above table it is clear that weight of stock X is 0 where the expected return is more and the standard deviation is less.
Particulars Weight(1) Expected return(2) Weighted return(3)=(1)*(2) Standard deviation (4) Variance of the portfolio Calculations for portfolio standard deviation Stock X 100% 8% 0.08 9% 0.0081 (Weight of stock X^2)*(Standard deviation of Stock X)^2=(A) Stock Z 0 10% 0 7% 0 (Weight of stock Z^2)*(Standard deviation of Stock Z)^2=(B) Expected return of the portfolio 8.00% 0 2*Weight of Stock X*Weight of Stock Z*Covariance of stock X and Stock Z=(C ) Variance of the portfolio 0.0081 (D) =(A)+(B)+(C ) Standard deviation of the portfolio 0.41% Square root of (D)Related Questions
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