Finance Chapter 3 Homework Default Risk Premium Maturity Risk Premium None The Above One Source Risk

Chapter 3

Risk

Chapter Overview

I. Introduction

a. Definition of risk

II. Relationship between rate of return and risk

a. Rate of return

b. Dollar return

c. Volatility

III. Measuring risk

a. Level of risk

iii. Liquidity premium

iv. Maturity risk premium

c. Reinvestment rate risk

V. Risk and investment returns

a. Investment risk

b. Stand-alone return and risk

i. Calculating expected rate of return

1. Probability distribution

2. Expected rate of return

3. Standard deviation

ii. Calculating stand-alone risk

1. Coefficient of variation

c. Portfolio return and risk

i. Calculating portfolio expected rate of return

1. Expected return on portfolio

ii. Calculating portfolio risk

1. Correlation coefficient

1. Capital asset pricing model (CAPM)

2. Beta coefficient

3. Security market line

VI. Sources of risk

1. Synthetic fixed-rate bonds

2. Auction-rate bonds

ii. Operating budgets

iii. League loan pools

b. Revenue sharing models

VIII. Conclusion

Key Concepts

When reading this chapter, students should focus on the following key concepts:

1. The impact of risk on the financial management of sport organizations

2. How to calculate and interpret stand-alone risk and portfolio risk

Quiz Questions

1. In general, the chances of receiving back an investment in a large market Major League

Baseball team is __________ that for a small market team.

a. Less than

c. Equal to

d. Greater than

e. None of the above

2. Risk increases as the length of time funds are invested increases. What is this known as?

a. Risk of time

b. Level of risk

3. Which of the following is the nominal or quoted risk-free rate of interest?

c. The real-risk-free rate plus a liquidity premium

d. The real-risk-free rate plus a maturity risk premium

e. None of the above

4. When calculating the nominal interest rate, which of the following premiums is added to

account for the risk of time and interest rate risk?

a. Inflation premium

b. Liquidity premium

c. Default risk premium

5. One source of risk is current economic conditions. Of the following, which is impacted

by changes in current economic conditions?

a. Capital finance

d. Both a and b

e. a, b, and c are all impacted

6. Which of the following was the first major professional sports team to declare

bankruptcy in the middle of a long-term facility lease?

a. New York Yankees

b. Phoenix Coyotes

7. What is determined by comparing the risk of one asset to another?

a. Risk of time

d. Liquidity premium

e. None of the above

8. Which of the following is the rate of return required over and above the risk-free-rate?

a. Risk of time

9. If it is expected that it will be hard to sell a security, which of the following will be

added?

c. Liquidity premium

d. Maturity risk premium

e. None of the above

10. For this type of bond, the annualized interest rate on the bonds is reset at auctions held

every 7 to 35 days.

a. General obligation bonds

b. Auction-rate bonds

Answers to Quiz Questions

1. d (answer is found throughout the chapter)

2. a (p. 63)

3. a (p. 64)

Responses

1. How does risk affect the financial management of sport organizations?

See pages 58 and 74–76. Risk affects the rate of interest, bond rates, estimates of cash

flows, the cost of capital, and the capital structure of sport organizations. Sport

organizations must understand how risk impacts their organization, especially in times

2. Describe the process of determining a nominal interest rate.

See pages 64–65. The nominal interest rate is the interest rate on a given debt security.

It is calculated by adding the real risk-free rate of interest to several risk premiums.

These risk premiums may include the inflation premium, default risk premium, liquidity

3. Of MLB, the NBA, or the NHL, which league has the most risk and which has the least?

Why?

See pages 74–81, 83–84. According to Fitch Ratings, factors affecting risk as reflected in

the firm’s credit ratings include risk to cash flows. Specifically, the agency looks at player

salary restraints, national television contracts, revenue sharing among member clubs,

league influence on team financial matters, debt limits, and a league’s relationship with

its player’s union. Based on recent credit ratings, MLB has slightly less risk than the NBA

4. What must players and agents understand about risk? How should agents structure a

player’s contract if it contains deferred compensation?

See Sidebar 3.A, p. 60–61. The risk of time must be understood; risk increases as the

length of time increases. As salary is deferred over time, risk increases proportionally to

the amount of time the salary is deferred. Importantly, although deferred salary may be

guaranteed, if a team declares bankruptcy the player becomes an unsecured creditor

and may then never be paid in full. If a player’s salary includes deferred salary, the agent

5. What risk factors should a team consider when deciding whether to build and fund a

new venue? How are the risk factors different if a municipality is funding the

construction?

See pages 75–76. Teams must understand the sources of risk they face when building

and funding a new venue. For example, capital finance was impacted with the collapse

of financial markets in 2008. Variable rate bonds that looked good a few years earlier

suddenly cost teams additional millions of dollars as rates skyrocketed. For example,

6. If you were advising an investor interested in purchasing a sport franchise, what advice

would you give?

See Concept Check 3. Generally the recommendation, if financial resources were of no

concern and a team could be freely purchased, would be to purchase a NFL franchise.

Partly because of the low risk of ownership, these franchises are by far the most

7. Among NCAA men’s basketball teams, which team would you expect to have the highest

value? Why? How do you think conference affiliation affects value among these teams?

See pages 83–85. I’d expect North Carolina or Duke to have the highest value (Forbes

publishes a list for men’s basketball, similar to the one shown in Exhibit 3.12 for football,

from time to time). Three of the five highest rated ESPN basketball games (of all levels)

Responses

1. You have the opportunity to purchase NFL Franchise A. The probability distribution of

expected returns for the franchise is as follows:

Probability

Rate of Return

0.1

–20%

0.2

0%

0.4

7%

0.2

0.1

What is the expected rate of return for your investment in Franchise A? What is the

standard deviation?

See pages 66–68 in the text.

Expected rate of return =

𝐾

̂𝐹𝑟𝑎𝑐ℎ𝑖𝑠𝑒 𝐴 = 0.1(–20%) + 0.2(0%) + 0.4(7%) + 0.2(15%) + 0.1(25%)

Variance (𝜎2) = 0.1(–0.20 – 0.063)2 + 0.2(0.0 – 0.063)2 + 0.4(0.07 – 0.063)2

Standard Deviation = √0.0127

2. An owner of several sport assets holds the following portfolio:

Asset Investment Beta

Team A $100,000,000 0.5

What is the beta of this portfolio?

See page 73 in the text.

βp =

3. Boggs Sports Holdings has a total investment of $500 million in five companies:

Company

Investment ($MM)

Beta

A

130

0.3

B

160

1.5

C

70

3.2

D

90

2.0

E

50

1.0

500

See page 73 in the text.

βp =

4. For the portfolio described in Practice Problem 3, if the risk-free rate is 10% and the

market risk premium is 5%, what is Boggs’ required rate of return?

See page 72 in text.

Note: market risk premium = kM – kRF, where kM is the expected average stock market

return and kRF is the risk free rate of interest (see page 62for related discussion on total

risk).

5. You have been hired as the manager of a portfolio of ten sport assets that are held in

equal dollar amounts. The current beta of the portfolio is 1.9, and the beta of Asset A is

2.1. If Asset A is sold and the proceeds are used to replace a replacement asset, what

does the beta of the replacement asset have to be to lower the portfolio beta to 1.6?

See page 73 in the text.

First, find the beta of the remaining nine stocks:

1.90 = 0.9(𝛽𝑅) + 0.1(𝛽𝐴)

1.90 = 0.9(𝛽𝑅) + 0.1(2.1)

Next, find the beta of the new stock that produces 𝛽𝑃 = 1.6

1.60 = 0.9(1.88) + 0.1(𝛽𝑁)

1.60 = 1.69 + 0.1(𝛽𝑁)

6. The Sports Investment Fund has a total investment of $5 million in the following

portfolio:

Asset Investment ($) Beta

A 900,000 1.2

B 1,100,000 –0.4

The market required rate of return is 10% percent, and the risk-free rate is 4%. What is the

required rate of return?

See pages 70 to 73 in the text.

Determine the weight each stock represents in the portfolio:

Asset

Investment ($)

wi

Beta

wi  Beta

A

900,000

0.18

1.2

0.216

B

1,100,000

0.22

–0.4

–0.088

C

1,000,000

0.20

1.5

0.300

D

2,000,000

0.40

0.9

0.360

Substitute known values into SML equation, including the portfolio beta. Solve for the

required portfolio return.

kp = kRF + (kM – kRF)βp

= 4% + (10% – 4%)0.788

7. Following is a distribution of returns:

Probability

Return ($)

0.4

35

0.1

What is the coefficient of variation of the expected dollar returns?

See pages 66 to 69 of the text.

First, find the expected rate of return (𝑘

̂):

𝑘

̂ = .4($35) + .5($24) + .1(–$15)

Second, calculate list of deviations:

Deviationi = ki – 𝑘

̂

Deviation1 = $35.0 – $24.5 = $10.5

Third, calculate the variance of the probability distribution:

σ2 = .4($10.5)2 + .5(-$0.5)2 + .1(v$39.5)2

Fourth, take the square root of the variance to get the standard deviation (σ):

Responses to Questions

1. What current economic conditions might impact the credit rating of a team or league?

Anything that might impact cash flows or the consistency of cash flows could impact the

2. Which teams’ credit ratings might be most negatively impacted during a recession?

Teams with little contractually obligated income will be most negatively impacted. As

more cash flow is guaranteed through contracts over long periods of time, changes in

3. What must the NFL do to maintain its high credit rating?

The NFL has controlled player costs and shared a majority of its revenue over time. A

hard salary cap and revenue sharing among all owners and players should continue if

the league wishes to maintain its high credit rating.

4. What can MLB do to improve its credit rating?

MLB has lower national television revenues as compared to the NFL. Increases in

national contracts would help increase ratings; this may be offset by the financial

Additional Classroom/Exam Problems

1. What is the nominal interest rate (k) of a 5-year U.S. Treasury bond with a real risk-free

rate of interest of 1% and inflation expected to be at 3.5% per year? Assume that the

maturity risk premium is zero.

See pages 64–65 of the text.

k* = 1%, I=3.5%, MRP=0%; kT-5=?

DRP and LP = 0 as these are treasury securities.

kT-5 = k* + IP + DRP + LP + MRP

2. Refer to Additional Classroom Problem 1. What would kT-5 be if the inflation was

expected to be 3.5% over the next two years, 4.0% the two years after that, and 4.25%

in the fifth year?

See pages 64–65 of the text.

k* = 1%, I1=3.5%, I2=3.5%, I3=4.0%, I4=4.0%, I5=4.25%, MRP=0%; kT-5=?

IP5 = (3.5% + 3.5% + 4.0% + 4.0% + 4.25%)/5

kT-5 = k* + IP5 + DRP + LP + MRP

3. For a given bond, you have the following information: Real risk-free rate (k*)=3%,

inflation premium = 8%, default risk premium = 2%, liquidity premium = 2%, and

maturity risk premium = 1%. What is the nominal risk-free rate (kRF)?

See page 64 of the text.

kRF = k* + IP

4. A 30-year Treasury bond has a yield of 5%. A 30-year corporate bond has a yield of 6.5%.

Assume the liquidity premium on the corporate bond is 1.0%. What is the default risk

premium on the corporate bond?

See pages 64–65 of the text.

kT-30 = 5%; kC-30 = 6.5%; LP = 1.0%; DRP = ?

Note: Because both bonds are 30-year bonds, the inflation premium and

maturity risk premium on both are equal. The only difference between the two

are the liquidly and default risk premiums.

From kT-30 = 5% = k* + IP + MRP it is known that k* + IP + MRP = 5%, so