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CONCEPTS IN THIS CASE

expected return
risk
portfolio choice
diversification
systematic risk
nonsystematic risk
beta
capital asset pricing model
arbitrage pricing

Your supervisor has asked that you quantify the effects of diversification using three potential portfolios. The information given regarding each portfolio is as follows:

Probability

Return (%) on
Security A

Return (%) on
Security B

Return (%) on
Security C

.20

8

24

16

.30

10

16

10

.30

12

12

12

.20

14

17

6

Using the information above, calculate the following for each individual security:

What is the expected return for security A?

What is the expected return for security B?

What is the expected return for security C?

What is the variance of the return for security A?

What is the variance of the return for security B?

What is the variance of the return for security C?

Using the information above, calculate the following for each pair of securities:

What is the covariance of securities A and B?

What is the covariance of securities A and C?

What is the covariance of securities B and C?

If your firm makes equal investments in securities A and B (50% in each):

What is the expected return of the portfolio that combines A and B?

What is the variance of the portfolio that combines A and B?

If your firm makes equal investments in securities A and C (50% in each):

What is the expected return of the portfolio that combines A and C?

What is the variance of the portfolio that combines A and C?

If your firm makes equal investment in securities B and C (50% in each):

What is the expected return of the portfolio that combines B and C?

What is the expected variance of the portfolio that combines B and C?

Given the results of your work in questions 3, 4, and 5 above, which portfolio would you recommend to your supervisor? Explain.

You have searched online resources and found the beta of each security. Security A has a beta of 1.0, security B has a beta of .50 and security C has a beta of 1.50. If the risk-free interest rate is 5% and the expected return for the market portfolio is 12%:

What is the CAPM risk premium for security A?

What is the CAPM risk premium for security B?

What is the CAPM risk premium for security C?

How would your definition of the risk premium change if you used the Arbitrage Pricing Theory (APT) equation?

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Elin Hessel
Elin HesselLv2
28 Sep 2019

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Related questions

There are three securities available for investment: Security A has an expected return of 10% and standard deviation of 20%; Security B has an expected return of 15% and standard deviation of 25%; Security C expected return of 8% and standard deviation of 0%. The covariance between the returns on the Security A and the Security B is -0.05.

a)What is the lowest level of risk (standard deviation) you can achieve by investing in the Security A and the Security B only? Show how you can create such portfolio.

b)What is the equation of the CAL connecting Security A and Security C? What is the reward-to-variability (Sharpe) ratio associated with this CAL?

c)If you decide to invest $50 in Security A and $150 in Security B, what are the expected return and the standard deviation of the resulting portfolio?

d)What should be a degree of risk aversion of an investor who is indifferent between investing in the Security A and the Security B?

1. Security C has an expected return of 6% and a standard deviation of 3% while security D has an expected return of 10% and a standard deviation of 7%. The correlation of returns between the two securities is –1.

a) If you place half of the money in each stock, then what is the expected return of this portfolio?

b) If you place 20% of the money in stock C and the remaining in stock D, then what is the expected return of the portfolio?

c) What is the portfolio standard deviation in b above?


2. a) A security has a beta of 1.5 when the risk-free rate is 2.6 percent and the expected return on the market is 12 percent. Calculate the expected return on the security.

b) If the beta on the security in a) increases to 2.5, what is the new expected return? Why does the expected return increase as the beta increases?

Additional Requirements

Level of Detail: Show all work

Suppose that the return on a risk-free security is 5 percent. The expected return on the market portfolio is 16 percent and the volatility of the market portfolio is 22 percent

(a) Write down the equation for CML.

(b) Consider a portfolio on CML such that the expected return on the portfolio is 14 percent. What is the volatility of this portfolio? What percentages of your portfolio you need to invest on the risk-free security and the market portfolio in order to create this portfolio (i.e., the portfolio on the CML with expected return equal to 14 percent).

c) What is the volatility of the risk-free security? What is the correlation of the return on the risk-free security and the market portfolio? Show that the beta of the risk-free security is zero.

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