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) = 3.40% and Var(y) = 1. The covariance between the returns is σxy = −3. (a) What is the standard deviation (as a percent) for an investment in stock 1? % What is the standard deviation (as a percent) for an investment in stock 2? % Using the standard deviation as a measure of risk, which of these stocks is the riskier investment? An investment in stock 1 ---Select--- would would not be risky compared with an investment in stock 2. (b) What is the expected return and standard deviation, in dollars, for a person who invests $400 in stock 1? expected return$ standard deviation$ (c) What is the expected percent return and standard deviation (as a percent) for a person who constructs a portfolio by investing 50% in each stock? (Round your answer for standard deviation to four decimal places.) expected return %standard deviation % (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? (Round your answer for standard deviation to four decimal places.) expected return %standard deviation % (e) Compute the correlation coefficient for x and y. Comment on the relationship between the returns for the two stocks. There is ---Select--- a strong positive a strong negative not a relationship between the variables.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 2AGP

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Question

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) = 3.40%

and

Var(y) = 1.

The covariance between the returns is

σ_xy = −3.

(a)

What is the standard deviation (as a percent) for an investment in stock 1?

What is the standard deviation (as a percent) for an investment in stock 2?

Using the standard deviation as a measure of risk, which of these stocks is the riskier investment?

An investment in stock 1 ---Select--- would would not be risky compared with an investment in stock 2.

(b)

What is the expected return and standard deviation, in dollars, for a person who invests $400 in stock 1?

expected return$ standard deviation$

(c)

What is the expected percent return and standard deviation (as a percent) for a person who constructs a portfolio by investing 50% in each stock? (Round your answer for standard deviation to four decimal places.)

expected return %standard deviation %

(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? (Round your answer for standard deviation to four decimal places.)

expected return %standard deviation %

(e)

Compute the correlation coefficient for x and y.

Comment on the relationship between the returns for the two stocks.

There is ---Select--- a strong positive a strong negative not a relationship between the variables.

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