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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.

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
BuyFind

STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

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Chapter
Section
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 σxy = −3.

  1. 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?
  2. b. What is the expected return and standard deviation, in dollars, for a person who invests $500 in stock 1?
  3. c. What is the expected percent return and standard deviation for a person who constructs a portfolio by investing 50% in each stock?
  4. 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?
  5. e. Compute the correlation coefficient for x and y and comment on the relationship between the returns for the two stocks.

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Chapter 5 Solutions

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