Statistics for Management and Economics (Book Only)
11th Edition
ISBN: 9781337296946
Author: Gerald Keller
Publisher: Cengage Learning
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Question
Chapter 7.3, Problem 89E
(a)
To determine
Calculate mean and standard deviation of the portfolio of Bank of Montreal (BMO): 25%, MagnaInternational (MG): 25%, Power (POW): 25%, and Rogers Communication (RCL.B): 25%.
(b)
To determine
Calculate mean and standard deviation of the portfolio of BMO: 20%, MG: 60%, POW: 10%, and RCL.B: 10%.
(c)
To determine
Calculate mean and standard deviation of the portfolio of BMO: 10%, MG: 20%, POW: 30%, and RCL.B: 40%.
(d)
To determine
Portfolio that the investor would choose to gamble.
(e)
To determine
Portfolio that a risk-averse investor would choose.
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Students have asked these similar questions
Consider the expected return and standard deviation of the following two assets:
Asset 1: E[r1]=0.1 and s1=0.2
Asset 2: E[r2]=0.3 and s2=0.4
(a) Draw (e.g. with Excel) the set of achievable portfolios in mean-standard deviation space for the cases: (i) r12=-1, (ii) r12=0.
(b) Suppose r12=-1. Which portfolio has the minimal variance? What is the variance and expected return of that portfolio?
(c) Derive the formula for the variance of a portfolio with four assets.
QUESTION 2
Elizabeth has decided to form a portfolio by putting 30% of her money into stock 1 and 70% into stock 2. She assumes that the expected returns will be 10% and 18%, respectively, and that the standard deviations will be 15% and 24%, respectively.
Describe what happens to the standard deviation of the portfolio returns when the coefficient of correlation ρ decreases.
The standard deviation of the portfolio returns decreases as the coefficient of correlation decreases.
The standard deviation of the portfolio returns increases as the coefficient of correlation increases.
The standard deviation of the portfolio returns decreases as the coefficient of correlation increases.
The standard deviation of the portfolio returns increases as the coefficient of correlation decreases.
3. The risk free rate is 3%. The optimal risky portfolio has an expected return of 9% and standard deviation of 20%. Answer the following questions.
(a) Assume the utility function of an investor is U = E(r) − 0.5Aσ2. What is condition of A to make the investors prefer the optimal risky portfolio than the risk free asset?
(b) Assume the utility function of an investor is U = E(r) − 2.5σ2. What is the expected return and standard deviation of the investor’s optimal complete portfolio?
Chapter 7 Solutions
Statistics for Management and Economics (Book Only)
Ch. 7.1 - Prob. 1ECh. 7.1 - Prob. 2ECh. 7.1 - Prob. 3ECh. 7.1 - Prob. 4ECh. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Prob. 7ECh. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Prob. 10E
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