Math

StatisticsSTATISTICS F/BUSINESS+ECONOMICS-TEXTA person is interested in constructing a portfolio. Two stocks are being considered. Let x = percent return for an investment in stock 1, and y = percent return for an investment in stock 2. The expected return and variance for stock 1 are E ( x ) = 8.45% and Var ( x ) = 25. The expected return and variance for stock 2 are E ( y ) = 3.20% and Var ( y ) = 1. The covariance between the returns is σ xy = −3. a. What is the standard deviation for an investment in stock 1 and for an investment in stock 2? Using the standard deviation as a measure of risk, which of these stocks is the riskier investment? b. What is the expected return and standard deviation, in dollars, for a person who invests $500 in stock 1? c. What is the expected percent return and standard deviation for a person who constructs a portfolio by investing 50% in each stock? d. What is the expected percent return and standard deviation for a person who constructs a portfolio by investing 70% in stock 1 and 30% in stock 2? e. Compute the correlation coefficient for x and y and comment on the relationship between the returns for the two stocks.BuyFind*arrow_forward*

13th Edition

Anderson

Publisher: CENGAGE L

ISBN: 9781305881884

Chapter 5.4, Problem 26E

Textbook Problem

A person is interested in constructing a portfolio. Two stocks are being considered. Let *x* = percent return for an investment in stock 1, and *y* = percent return for an investment in stock 2. The expected return and variance for stock 1 are *E*(*x*) = 8.45% and *Var* (*x*) = 25. The expected return and variance for stock 2 are *E*(*y*) *=* 3.20% and *Var* (*y*) = 1. The covariance between the returns is *σ _{xy}* = −3.

- a. What is the standard deviation for an investment in stock 1 and for an investment in stock 2? Using the standard deviation as a measure of risk, which of these stocks is the riskier investment?
- b. What is the expected return and standard deviation, in dollars, for a person who invests $500 in stock 1?
- c. What is the expected percent return and standard deviation for a person who constructs a portfolio by investing 50% in each stock?
- d. What is the expected percent return and standard deviation for a person who constructs a portfolio by investing 70% in stock 1 and 30% in stock 2?
- e. Compute the correlation coefficient for
*x*and*y*and comment on the relationship between the returns for the two stocks.

STATISTICS F/BUSINESS+ECONOMICS-TEXT

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