Question

Consider an economy where a one-factor APT holds. All portfolios are well diversified. Portfolio A has an expected return of 10% and its factor beta is 1. Portfolio F has an expected return of 8% and its factor beta is 0.6. Suppose another portfolio E is well diversified with a beta of 0.8 and an expected return of 10%. Does an arbitrage opportunity exist in this case?

Answer 1

Expected return

Beta

Portfolio A

10%

1

Portfolio F

8%

0.6

Portfolio E

10%

0.8

To find: Arbitrage opportunity exists

Step 1:-

We need to choose the portfolio with highest and lowest beta.

In this case,

Highest Beta

Portfolio A

Lowest Beta

Portfolio F

Step 2:-

Construct a hypothetical portfolio say Portfolio B in this case, combining Portfolio A and F with Beta equal to that of Portfolio E

Let the weight of Portfolio A be Wa

so weight of portfolio F= (1-Wa)

We know,

Beta of portfolio= Weighted average

Wa*1+(1-Wa)*0.6= 0.8

Wa+0.6-0.6Wa= 0.8

0.4Wa= 0.2

Wa= 0.5

Weight of portfolio A= 0.5

Weight of portfolio F= (1-0.5)=0.5

Step 3:-

Expected return from the hypothetical portfolio i.e Portfolio B= Weighted average

0.5*10+0.5*8

9%

Step 4:-

Comparing Portfolio B so created with Portfolio E we get,

Potfolio

Beta

Return

B

0.8

9%

E

0.8

10%

The above results violate the law of one price i.e. stocks with equal risk should provide equal return. Hence there is an arbitrage opportunity:-

Short sell Portfolio B and invest the proceeds in Portfolio E

Arbitrage profit= (10-9)%

jeff jeffy Next > < Previous Related Solutions Consider the following data on a one-factor economy. All portfolios are well-diversified. Portfolio A has a... Consider the following data on a one-factor economy. All portfolios are well-diversified. Portfolio A has a beta of 1.0 and an expected return of 11%, while another portfolio B has a beta of 0.75 and an expected return of 8%. The risk-free rate is 2%. In this scenario, an arbitrage opportunity exists and a strategy to take advantage of it would be: To short B and use 3/4 of the proceeds to invest in A and borrow the other ¼... Consider the multifactor APT with two factors. Portfolio A has a beta of 1.5 on factor... Consider the multifactor APT with two factors. Portfolio A has a beta of 1.5 on factor 1 and a beta of 0.45 on factor 2. The risk premiums on the factor 1 and 2 portfolios are 12% and 5%, respectively. The risk-free rate of return is 3%. The expected return on portfolio A is Answer if no arbitrage opportunities exist. Consider a single factor APT. Portfolio A has a beta of 1.5 and an expected return... Consider a single factor APT. Portfolio A has a beta of 1.5 and an expected return of 24%. Portfolio B has a beta of 0.9 and an expected return of 13%. The risk-free rate of return is 4%. An arbitrage portfolio in which you take a position in a combination of the highest beta portfolio and the risk-free asset, and an opposite position in the other risky portfolio would generate a rate of return of ______%. Consider the single factor APT. Portfolio A has a beta of 1.1 and an expected return... Consider the single factor APT. Portfolio A has a beta of 1.1 and an expected return of 23%. Portfolio B has a beta of .6 and an expected return of 19%. The risk-free rate of return is 6%. If you wanted to take advantage of an arbitrage opportunity, you should take a short position in portfolio __________ and a long position in portfolio _________. A;B B;A B;B A;A In the APT model, what is the nonsystematic standard deviation of an equally-weighted, well diversified portfolio... In the APT model, what is the nonsystematic standard deviation of an equally-weighted, well diversified portfolio of 170 securities that has an average value (across securities) of nonsystematic standard deviation, σ(ei), equal to 22%? (Round your answer to 2 decimal places.) Suppose Emma holds a well-diversified stock portfolio. Her son, Andrew, who is a portfolio manager, has... Suppose Emma holds a well-diversified stock portfolio. Her son, Andrew, who is a portfolio manager, has just advised her not to invest in stocks of oil refining industry because their prices tend to have much higher volatility relative to other stocks. Is Andrew’s advice sound? Explain. Suppose Emma holds a well-diversified stock portfolio. Her son, Andrew, who is a portfolio manager, has... Suppose Emma holds a well-diversified stock portfolio. Her son, Andrew, who is a portfolio manager, has just advised her not to invest in stocks of oil refining industry because their prices tend to have much higher volatility relative to other stocks. Is Andrew’s advice sound? Explain. Karen currently has $5 million invested in a long-term bond fund which has an expected return of 7% and a standard deviation of 18%. Her son, Michael, recommends her to consider changing to invest... Suppose Emma holds a well-diversified stock portfolio. Her son, Andrew, who is a portfolio manager, has... Suppose Emma holds a well-diversified stock portfolio. Her son, Andrew, who is a portfolio manager, has just advised her not to invest in stocks of oil refining industry because their prices tend to have much higher volatility relative to other stocks. Is Andrew’s advice sound? Explain. Karen currently has $5 million invested in a long-term bond fund which has an expected return of 7% and a standard deviation of 18%. Her son, Michael, recommends her to consider changing to invest... Suppose Emma holds a well-diversified stock portfolio. Her son, Andrew, who is a portfolio manager, has... Suppose Emma holds a well-diversified stock portfolio. Her son, Andrew, who is a portfolio manager, has just advised her not to invest in stocks of oil refining industry because their prices tend to have much higher volatility relative to other stocks. Is Andrew’s advice sound? Explain. Well-diversified portfolio A has a beta of 1.0 and an expected return of 12%. Well-diversified portfolio... Well-diversified portfolio A has a beta of 1.0 and an expected return of 12%. Well-diversified portfolio B has a beta of 0.75 and an expected return of 9%. The risk-free rate is 4%. a. Assuming that portfolio A is correctly priced (has ?? = 0), what should the expected return on portfolio B be in equilibrium? b. Explain the arbitrage opportunity that exists and explain how an investor can take advantage of it. Give specific details about what to buy... ADVERTISEMENT Subjects Accounting Advanced Math Anatomy and Physiology Biology Chemistry Civil Engineering Computer Science Economics Electrical Engineering Finance History Math Mechanical Engineering Operations Management Physics Psychology Statistics and Probability Nursing Other ADVERTISEMENT Latest Questions Consider a project generating the following cash flows over six years: Year Cash Flow (R in... Please explain why it is important to determine early and late, start and finish schedules? 8. if the project duration needs to be reduced then a. the activity with the lost... Part 4: CLO 4 Question 1 What are the factors that project manager need to consider... I need this in Java please: Behaviors. In the context of OOP, functions are called methods... Emotional Intelligence (EI) includes both personal and social competence. In the personal realm, a person with... How "democratic" is the U.S. democracy? What is "limited government" and how are the various levels... ADVERTISEMENT About @ 2020 WizEdu