9. You are currently holding portfolio M. You are considering combining M with se-curity X, Y, or Z. There are three possible scenarios listed in the table below. (Forinstance, in scenario 1 which happens with 20% probability, M will deliver a returnof -20%).Scenarios13Probability20%50% 30%Return of M -20%0% 30%15%5%-5%Return of X -10%0%5%5%5%0%Return of YReturn of Z(a) Which of X, Y, and Z is a risk-free security when considered on a standalonebasis?(b) Now, you are considering investing 90% in your current portfolio M and in-vesting 10% into X, or Y, or Z.' Suppose your goal is only to reduce portfoliorisk and you do not care about portfolio return. Which of X, Y, or Z will youchoose, and why?(c) Recall that you can short securities in forming your new portfolio. Is it pos-sible to reduce portfolio risk by combining M and X by choosing appropriateportfolio weights? If so, please give examples of such portfolio weights.'For instance, if you choose X, then your final portfolio will be 90% invested into M and 10% investedinto X.

Portfolio is the collection of securities or investments. The return on portfolio is the weighted average of the return of the individual securities. The weight of the portfolio is the percentage of investment made in portfolio. Expected return is the return that an investor expects from those securities in which their investment has been made. It can be calculated using the following equation: Rp = ∑t=1nxiri Where, Rp = Return on the portfolio xi = Proportion of total portfolio invested in security 1 ri = Expected return of security 1 Lets consider an example that a Portfolio M with return 20%. Consider another securities X,Y,Z with their respective probabilities are given below. X Y Z Probabilities -10 5 5 20 0 5 0 50 15 5 -5 30 Expected return on X =((-10×0.2)+(0×0.5)+(15×0.3)) = -2+4.5 =2.5%Expected return on Y =((5×0.2)+(5×0.5)+(5×0.3)) = 1+2.5+1.5 = 5%Expected return on Z= ((5×0.2)+(0×0.5)+(-5×0.3)) = 1+(-1.5) =-0.5% The expected return on Portfolio Y is higher and it is more risk free.

Answered: (a) Which of X, Y, and Z is a risk-free…

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(a) Which of X, Y, and Z is a risk-free security when considered on a standalone basis?

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

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Concept explainers

Risk and return

Before understanding the concept of Risk and Return in Financial Management, understanding the two-concept Risk and return individually is necessary.

Capital Asset Pricing Model

Capital asset pricing model, also known as CAPM, shows the relationship between the expected return of the investment and the market at risk. This concept is basically used particularly in the case of stocks or shares. It is also used across finance for pricing assets that have higher risk identity and for evaluating the expected returns for the assets given the risk of those assets and also the cost of capital.

Question

9. You are currently holding portfolio M. You are considering combining M with se-
curity X, Y, or Z. There are three possible scenarios listed in the table below. (For
instance, in scenario 1 which happens with 20% probability, M will deliver a return
of -20%).
Scenarios
1
3
Probability
20%
50% 30%
Return of M -20%
0% 30%
15%
5%
-5%
Return of X -10%
0%
5%
5%
5%
0%
Return of Y
Return of Z
(a) Which of X, Y, and Z is a risk-free security when considered on a standalone
basis?
(b) Now, you are considering investing 90% in your current portfolio M and in-
vesting 10% into X, or Y, or Z.' Suppose your goal is only to reduce portfolio
risk and you do not care about portfolio return. Which of X, Y, or Z will you
choose, and why?
(c) Recall that you can short securities in forming your new portfolio. Is it pos-
sible to reduce portfolio risk by combining M and X by choosing appropriate
portfolio weights? If so, please give examples of such portfolio weights.
'For instance, if you choose X, then your final portfolio will be 90% invested into M and 10% invested
into X.

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