3.4 Arbitrage and the Law of One Price
1) Which of the following statements regarding arbitrage is the most correct?
A) Any situation in which it is possible to make a profit without taking any risk is known as an
arbitrage opportunity.
B) Any situation in which it is possible to make a profit without making any investment is known as an
arbitrage opportunity.
C) We call a competitive market in which there are no arbitrage opportunities an arbitrage market.
D) The practice of buying and selling equivalent goods in different markets to take advantage of a price
difference is known as arbitrage.
2) Which of the following statements regarding the Law of One Price is INCORRECT?
A) At any point in time, the price of two equivalent goods trading in different competitive markets will
be the same.
B) One useful consequence of the Law of One Price is that when evaluating costs and benefits to
compute a net present value, we can use any competitive price to determine a cash value, without
checking the price in all possible markets.
C) If equivalent goods or securities trade simultaneously in different competitive markets, then they
will trade for the same price in both markets.
D) An important property of the Law of One Price is that it holds even in markets where arbitrage is not
possible.
Use the table for the question(s) below.
Consider the following prices from a McDonald’s Restaurant:
Big Mac Sandwich
$2.99
Large Coke
$1.39
Large Fry
$1.09
3) A McDonald’s Big Mac value meal consists of a Big Mac Sandwich, Large Coke, and a Large Fry.
Assuming that there is a competitive market for McDonald’s food items, at what price must a Big Mac
value meal sell to ensure the absence of an arbitrage opportunity and uphold the law of one price?
A) $4.08
B) $4.38
C) $5.47
D) $5.77
4) A McDonald’s Big Mac value meal consists of a Big Mac Sandwich, Large Coke, and a Large Fry.
Assume that there is a competitive market for McDonald’s food items and that McDonald’s sells the Big
Mac value meal for $4.79. Does an arbitrage opportunity exists and if so how would you exploit it and
how much would you make on one extra value meal?
A) Yes, buy extra value meal and then sell Big Mac, Coke, and Fries to make arbitrage profit of $0.68.
B) No, no arbitrage opportunity exists.
C) Yes, buy Big Mac, Coke, and Fries then sell value meal to make arbitrage profit of $1.09.
D) Yes, buy Big Mac, Coke, and Fries then sell value meal to make arbitrage profit of $0.68.
5) Walgreen Company (NYSE: WAG) is currently trading at $48.75 on the NYSE. Walgreen Company is
also listed on NASDAQ and assume it is currently trading on NASDAQ at $48.50. Does an arbitrage
opportunity exists and if so how would you exploit it and how much would you make on a block trade
of 100 shares?
A) No, no arbitrage opportunity exists.
B) Yes, buy on NASDAQ and sell on NYSE, make $25.
C) Yes, buy on NYSE and sell on NASDAQ, make $25.
D) Yes, buy on NASDAQ and sell on NYSE, make $250.
6) You are up late watching TV one night and see an ad from Ronco for the Dial-o-matic food slicer.
You learn that the Dial-o-matic sells for $29.95. But wait, there is more. Ronco is also including in this
deal a set of Ginsu steak knives worth $10.95 and another free gift worth $7.95. Assuming that there is a
competitive market for Ronco items, at what price must Ronco be selling this three item Dial-o-matic
deal to insure the absence of an arbitrage opportunity and uphold the law of one price?
7) Advanced Micro Devices (NYSE: AMD) is currently trading at $20.75 on the NYSE. Advanced Micro
Devices is also listed on NASDAQ and assume it is currently trading on NASDAQ at $20.50. Does an
arbitrage opportunity exists and if so how would you exploit it and how much would you make on a
block trade of 1000 shares?
3.5 No-Arbitrage and Security Prices
1) Which of the following statements regarding arbitrage and security prices is INCORRECT?
A) We call the price of a security in a normal market the no-arbitrage price for the security.
B) In financial markets it is possible to sell a security you do not own by doing a short sale.
C) When a bond is underpriced, the arbitrage strategy involves selling the bond and investing some of
the proceeds.
D) The general formula for the no-arbitrage price of a security is Price(security) = PV (All cash flows
paid by the security).
2) Consider two securities, A & B. Suppose a third security, C, has the same cash flows as A and B
combined. Given this information about securities A,B, & C, which of the following statements is
INCORRECT?
A) If the total price of A and B is cheaper than the price of C, then we could make a profit selling A and
B and buying C.
B) Price(C) = Price(A) + Price(B).
C) Because security C is equivalent to the portfolio of A and B, by the law of one price they must have
the same price.
D) The relationship known as value additivity says that the value of a portfolio is equal to the sum of
the values of its parts.
3) Which of the following statements regarding value additivity is FALSE?
A) The value of a portfolio is equal to the sum of the values of its parts.
B) The price or value of the entire firm is equal to the sum of the values of all projects and investments
within the firm.
C) To maximize the value of the entire firm, managers should make decisions that maximize NPV.
D) Value additivity does not have important consequences for the value of the entire firm, only on
portfolios of firms.
4) Which of the following statements is FALSE?
A) Financial transactions are not sources of value, but merely serve to adjust the timing and risk of the
cash flows to best suit the needs of the firm or its investors.
B) The NPV of trading a security in a normal market is zero.
C) We cannot separate a firm’s investment decision from the decision of how to finance the investment.
D) In normal markets, trading securities neither creates nor destroys value.
5) Suppose that Bondi Inc. is a holding company that owns both Pizza Hut and Kentucky Fried Chicken
Franchised Restaurants. If the value of Bondi is $130 million, and the Pizza Hut Franchises are worth
$70 million, then what is the value of the Kentucky Fried Chicken Franchises?
A) $60 million
B) $70 million
C) $130 million
D) Unable to determine with the information provided
6) Without issuing the new security, the NPV for this project is closest to what amount? Should the film
maker make the investment?
A) $1.7 million; Yes
B) $1.7 million; No
C) $2.7 million; Yes
D) $2.7 million; No
7) Assuming that the film maker issues the new security, the NPV for this project is closest to what
amount? Should the film maker make the investment?
A) $1.7 million; Yes
B) $1.7 million; No
C) $2.7 million; Yes
D) $2.7 million; No
8) What is the NPV of this project if the film maker invests his own money and does not issue the new
security? What is the NPV if the film maker issues the new security?
A) $1.7 million; $1.7 million
B) $1.7 million; $2.7 million
C) $2.7 million; $1.7 million
D) $2.7 million; $2.7 million
Use the table for the question(s) below.
Security
Cash flow
today
Cash flow
in one year
A
0
100
B
100
0
C
100
100
9) If the risk-free rate of interest is 7.5%, then the value of security “A” is closest to:
A) $91.00
B) $92.50
C) $93.00
D) $100.00
10) If the risk-free rate of interest is 7.5%, then the value of security “B” is closest to:
A) $91.00
B) $92.50
C) $93.00
D) $100.00
11) If the value of security “C” is $180, then what must be the value of security “A“?
A) $80
B) $90
C) $100
D) Unable to determine without the risk-free rate.
Use the information for the question(s) below.
An exchange traded fund (ETF) is a security that represents a portfolio of individual stocks. Consider
an ETF for which each share represents a portfolio of two shares of International Business Machines
(IBM), three shares of Merck (MRK), and three shares of Citigroup Inc. (C). Suppose the current market
price of each individual stock are shown below:
Stock
Current Price
IBM
$121.57
MRK
$36.59
C
$3.15
12) The price per share of the ETF in a normal market is closest to:
A) $161.31
B) $322.62
C) $362.36
D) $483.93
13) Suppose that the ETF is trading for $362.36; you should:
A) sell the EFT and buy 2 shares of IBM, 3 shares of MRK, and 3 shares of C.
B) sell the EFT and buy 3 shares of IBM, 2 shares of MRK, and 3 shares of C.
C) buy the EFT and sell 2 shares of IBM, 3 shares of MRK, and 3 shares of C.
D) do nothing, no arbitrage opportunity exists.
14) Suppose a security with a risk-free cash flow of $1000 in one year trades for $909 today. If there are
no arbitrage opportunities, then the current risk-free interest rate is closest to:
A) 8%
B) 10%
C) 11%
D) 12%
15) An American Depository Receipt (ADR) is a security issued by a U.S. bank and traded on a U.S.
stock exchange that represents a specific number of shares of a foreign stock. Siemens AG has an ADR
that trades on the NYSE and is equivalent to one share of Seimens AG trading on the Frankfurt Stock
Exchange in Germany. If Seimens trades for $95.19 on the NYSE and for €64.10 on the Frankfurt Stock
Exchange, then under the law of one price, the current exchange rate is closest to:
A) $0.6744/€
B) €0.6734/$
C) €1.4850/$
D) $1.5274/€
Use the following information to answer the question(s) below.
An exchange traded fund (ETF) is a security that represents a portfolio of individual stocks. Consider an
ETF for which each share represents a portfolio of two shares of Apple Inc. (APPL), one share of Google
(GOOG), and ten shares of Microsoft (MSFT). Suppose the current stock prices of each individual stock
are as shown below:
Stock
APPL
GOOG
MSFT
16) The price per share of this ETF in a normal market is closest to:
A) $800
B) $1001
C) $1067
D) $1267
17) Suppose that a security with a risk-free cash flow of $1000 in one year trades for $930 today. If there
are no arbitrage opportunities, then the current risk-free rate is closest to:
A) 6.0%
B) 6.5%
C) 7.0%
D) 7.5%
Use the information for the question(s) below.
An exchange traded fund (ETF) is a security that represents a portfolio of individual stocks. Consider
an ETF for which each share represents a portfolio of two shares of International Business Machines
(IBM), three shares of Merck (MRK), and three shares of Citigroup Inc. (C). Suppose the current market
price of each individual stock are shown below:
Stock
Current Price
IBM
$121.57
MRK
$36.59
C
$3.15
18) Assume that the ETF is trading for $366.00, what (if any) arbitrage opportunity exists? What (if any)
trades would you make?
19) The price per share of the ETF in a normal market is:
Use the following information to answer the question(s) below.
An exchange traded fund (ETF) is a security that represents a portfolio of individual stocks. Consider an
ETF for which each share represents a portfolio of two shares of Apple Inc. (APPL), one share of Google
(GOOG), and ten shares of Microsoft (MSFT). Suppose the current stock prices of each individual stock
are as shown below:
Stock
APPL
GOOG
MSFT
20) If the ETF is currently trading for $1200, what arbitrage opportunity is available? What trades would
you make?
21) If the ETF is currently trading for $1300, what arbitrage opportunity is available? What trades would
you make?
3.6 Appendix: The Price of Risk
1) Which one of the following statements is FALSE?
A) When we compute the return of a security based on the average payoff we expect to receive, we call
it the expected return.
B) The notion that investors prefer to have a safe income rather than a risky one of the same average
amount is call risk aversion.
C) Because investors are risk averse, the risk-free interest rate is not the right rate to use when
converting risky cash flows across time.
D) The more risk averse investors are, the higher the current price of a risky asset will be compared to a
risk-free bond.
2) Pfizer Inc. (PFE) stock is currently trading on the NYSE with a quoted bid of $18.35 and an ask price
of $18.40. At the same time NASDAQ dealers are posting for following bid and ask prices for PHE:
Dealer
Bid
Ask
1
$18.38
$18.43
2
$18.30
$18.34
3
$18.36
$18.39
Trading with which of these NASDAQ dealers provides an arbitrage opportunity when compared to
the NYSE quotes?
A) Only NASDAQ dealer #1
B) Only NASDAQ dealer #2
C) Only NASDAQ dealer #3
D) Both NASDAQ dealer #1 and dealer #3
E) None of the above
Use the table for the question(s) below.
Market Price
Cash Flow in One Year
Security
Today
Poor
Economy
Good Economy
A
200
840
0
B
600
0
840
C
???
840
4200
3) Based upon the information provided about securities A, B, and C, the risk-free rate of interest is
closest to:
A) 4%
B) 5%
C) 8%
D) 10%
4) What is the no-arbitrage price for security C?
A) $800
B) $1600
C) $3200
D) $4000
5) Suppose a risky security pays an average cash flow of $100 in one year. The risk-free rate is 5%, and
the expected return on the market index is 13%. If the returns on this security are high when the
economy is strong and low when the economy is weak, but the returns vary by only half as much as the
market index, what risk premium is appropriate for this security?
A) 4%
B) 6.5%
C) 9%
D) 11%
6) Suppose a risky security pays an average cash flow of $100 in one year. The risk-free rate is 5%, and
the expected return on the market index is 13%. If the returns on this security are high when the
economy is strong and low when the economy is weak, but the returns vary by only half as much as the
market index, then the price for this risky security is closest to:
A) $88
B) $92
C) $93
D) $95
Use the table for the question(s) below.
Market Price
Cash Flow in One Year
Security
Today
Poor
Economy
Good Economy
A
200
840
0
B
600
0
840
C
???
840
4200
7) Suppose that security C had a risk premium of 30%, describe what arbitrage opportunity exists and
how you would exploit it.
3.7 Appendix: Arbitrage with Transaction Costs
1) Which of the following statements is FALSE?
A) No arbitrage opportunities will exist until the underlying prices diverge by more than the amount of
the transaction costs.
B) Because you will generally pay a slightly lower price when you buy a security (the ask price) than
you receive when you sell (the bid price) you will pay the bid–ask spread.
C) The price of a security should equal the present value of its cash flows, up to the transaction costs of
trading the security and the cash flows.
D) In most markets, you must pay transactions costs to trade securities.
2) Consider a bond that pays $1000 in one year. Suppose that the market interest rate for savings is 8%,
but the interest rate for borrowing is 10%. The price range that this bond must trade in a normal market
if no arbitrage opportunities exist is closest to:
A) $909 to $917
B) $909 to $926
C) $917 to $926
D) $909 to $1000
Use the table for the question(s) below.
Security
Bid
Ask
IBM
123.20
123.25
MRK
36.50
36.55
C
3.15
3.20
3) Consider an ETF that is made up of one share each of IBM, MRK, and C. The minimum bid price for
this ETF in a normal market is closest to:
A) $162.85
B) $163.00
C) $168.00
D) $168.10
4) Consider an ETF that is made up of one share each of IBM, MRK, and C. The minimum ask price for
this ETF in a normal market is closest to:
A) $162.85
B) $163.00
C) $168.00
D) $168.10
5) In a normal market with transactions costs, is it possible for different investors to place different
values on an investment opportunity? Are there any limits on the amount that their values can differ?
Use the table for the question(s) below.
Security
Bid
Ask
IBM
123.20
123.25
MRK
36.50
36.55
C
3.15
3.20
6) Consider an ETF that is made up of one share each of IBM, MRK, and C. The current quote for this
ETF currently is $162.75 (bid) $162.80 (ask). What should you do?
7) Consider an ETF that is made up of one share each of IBM, MRK, and C. The current quote for this
ETF currently is $162.85 (bid) $163.00 (ask). What should you do?
8) Consider an ETF that is made up of one share each of IBM, MRK, and C. The current quote for this
ETF currently is 163.15 (bid) $163.20 (ask). What should you do?