Law of One Price and Derivative Market

1. Learning Unit #16
Law of One Price
and Derivative Markets

2. Objectives of Learning Unit
• Law of One Price
• Types of Financial Derivatives
– Forwards
– Futures
– Options
– Swaps
• Benefits and Danger of Derivatives

3. Arbitrage
• Arbitrage: Riskless activity to earn
profits from a price discrepancy of the
same assets in two different markets.
• Assets must be identical.
• They are traded in different markets.
• Market prices are different for some reasons in two
markets.
• Example: You see one flier at A&T and another at
UNCG. Can you make a profit?
For Sale
Econ415
Text for
$40
Call A&T
Wanted
Econ415
Text for
$50
Call UNCG

4. Example of Arbitrage in Foreign Exchange
Markets
• Foreign exchange rates between U.S.
dollar and euro are $1=€1 in NYC and
$1=€0.8 ($1.25=€1) in London.
• Values of U.S. dollar are different in two
markets.
• Arbitrage: Buy euro (€1) and sell dollar
($1) in NYC, then sell euro (€1) and buy
dollar ($1.25) in London to make 25¢
profit for each $1 transaction.

5. Demand-Supply Analysis of
Arbitrage
• Arbitrage causes changes in demand and
supply of items in two foreign exchange
markets, and their equilibrium prices.
• In a market where an item is priced low, an arbitrager
purchases the item, increasing its demand, while in a
market where the item is priced high, the arbitrager
sells the item, increasing its supply.
• Changes in demand and supply in two markets will
cause changes in equilibrium prices in two markets,
raising an equilibrium price in a low price market and
falling an equilibrium price in a high price market.
• Arbitrage eliminates any price discrepancy
of the same asset in two different
markets.

6. Example of Demand-Supply Analysis of
Arbitrage in Foreign Exchange Markets
• Example: Buy euro and sell dollar in
NYC where euro is priced low ($1=€1),
then sell euro and buy dollar in London
where euro is priced high (($1.25=€1).
• Supply of U.S. dollar and demand for
euro increase in NYC, while demand for
U.S. dollar and supply of euro increase
in London.

7. Demand-Supply Diagrams of Arbitrage in
Foreign Exchange Markets
U.S. dollar depreciates against euro to $1=€0.9 in
NYC, while it appreciates against euro to $1=€0.9 in
London.

8. Law of One Price
• Law of One Price: the price of a good in one
country must be equal to the price of the same
good in other country after taking account of the
exchange rate between two countries.
• Arbitrage guarantees that prices of identical goods
must be equal in two markets (countries) at
equilibrium.
• Of course from time to time prices could be
different. However, whenever such
discrepancy occurs, an arbitrage will take
places and equalize their prices.

9. Example of Law of One Price
• The price of BMW is $50,000 in U.S. and the
price of the same BMW is €100,000 in
Germany.
• The exchange rate between U.S. dollar and
euro is $1= €2.
• Then, the U.S. dollar price of German BMW
should be $50,000(= € 100,000/ €2).
• Law of one price holds!

10. Financial Derivatives
• Financial derivatives are contracts that are
linked to previously issued securities, used
as risk reduction tools.
• Financial derivatives derive their values
from the values of other underlying assets.
– Financial derivatives promise to deliver a
specific financial instrument at a future date.
– The financial instrument that a derivative
promises to deliver is called “underlying asset”
of the derivative.

11. Hedging
• Hedge: To engage in a financial
transaction that reduce or eliminate risk.
– protect oneself against risk
• When you own or owe a financial asset,
you are exposed to risk.
– If you own a bond, you face the default risk,
the interest rate risk, and the purchasing
power risk.
– If you borrow a loan, you face the purchasing
risk because the real interest rate on the loan
is not known.

12. Long & Short Position
• Long position: A contractual obligation to
take delivery of an underlying financial
instrument.
– Own bonds and stocks (You may actually own
now or will own near future).
• Short position: A contractual obligation to
deliver an underlying financial instrument.
– You promise to sell bonds or stocks in future date
(which you may or may not own now).

13. Long & Short Position and Profits
• Long position involves a (possible) sale of financial
assets in future at unknown price.
– If a price of financial assets rises in future, you will make
profits (since you can sell them at higher price).
– If the price falls, you will make losses (since you must sell
at lower price).
• Short position involves a purchase of financial assets
in future at unknown price.
– If a price of financial assets falls in future, you will make
profits (since you can purchase them at lower price).
– If the price rises, you will make losses (since you have to
pay more to get them).

14. Examples of Long & Short Position
• Long position examples:
– You own Econ415 textbook and plan to sell it at the end
of semester, but you do not know its price = you are in
a long position of textbook.
– You promise to purchase Google stocks at
predetermined price next month = you are in a long
position of Google stocks.
• Short position examples:
– You promise to sell AT&T bonds at predetermined price
next month that you do not own = you are in a short
position of AT&T bonds.
– You need to get gasoline tomorrow, but you do not
know its price = you are in a short position of gasoline.

15. Long and Short Positions and Risk
• When a saver is in a long position or a
short position, he faces risk (uncertainty).
• Example of risk in a long position
– Michael owns a Treasury bond and needs to
sell it next month. However, he doesn’t know
how much he will get.
• Example of risk in a short position
– Michelle needs to purchase a textbook next
semester, but she doesn’t know how much it
will cost.

16. How Hedging Works
• Risk arises when a saver is in either a
long or short position. By eliminating her
long or short position, she can eliminate
risk.
• Hedging risk involves engaging in a
financial transaction that offset a long
(short) position by taking an additional
short (long) position.

17. Example 1 of How Hedging Works
• Brian owns 10-year Treasury Note and plan to
sell one year later.
– Brian is in a long position and expose to an
interest rate risk.
• Brian can engage in a contract that promise to
sell the 10-year Treasury Note one year later at
a set price (e.g. $1,000).
– The contract creates a short position.
• This contract eliminates the interest rate risk on
the 10-year Treasury Note that Brian owns.
– Brian is sure how much he will get from his
10-year Treasury Note next year ($1,000).

18. Example 2 of How Hedging Works
• Kim needs ACCT221 textbook next semester.
– Kim is in a short position and exposes to risk
since she does not know how much she must
pay on the textbook next semester.
• Kim can contact her friend who is taking
ACCT221 and makes a contract that she will
purchase the book at the end of this semester at
a set price (e.g. $100).
– The contract creates a long position.
• This contract eliminates the risk on the textbook
that Kim must purchase.
– Kim is sure how much she will pay for the
textbook ($100).

19. Types of Financial Derivatives
• Financial derivatives, which promise to
deliver underlying financial assets, can
be used to create a long or short position
for hedging.
• Four types of financial derivatives: they
are different in terms of contracts.
– Forwards
– Futures
– Options
– Swaps

20. Forward Contracts
• Forward contracts: agreements to
engage in a financial transaction at a
future point in time.
– Ex. Forward exchange
– Ex. Today you promise your friend that you
will sell the textbook on the first day of the
next semester at $30 to her.
• Interest-rate forward contracts:
forward contracts that are linked to debt
instruments

21. Interest-Rate Forward Contracts
• Interest-rate forward contracts include
– specification of the actual debt instrument
that will be delivered at a future date
– amount of the debt instrument to be
delivered
– price (interest rate) on the debt instrument
when it is delivered
– date on which delivery will take place

22. Example of Interest-Rate Forward Contracts
• A contract which promises to sell total of
$100,000 face value of U.S. Treasury bonds,
with 10 year maturity and 8% coupon rate, on
May 25th, 2017 at $101,000.
– What is delivered: U.S. Treasury bonds with 10 year
maturity and 8% coupon rate
– How many: $100,000 face value
– How much: $101,000
– When delivered: May 25th
, 2017

23. Reasons for Forward Contracts
• Forward contracts are used to hedge
against risk.
– Without a forward contract, a saver who wants
to buy (sell) a financial instrument in future
does not know the price of the instrument
when he actually buys (sells) it.
• Forward contracts benefits both parties
involved in the contracts.
– Buyers of forward contracts know how much to
pay to get the financial instrument.
– Sellers (issuers) of forward contracts know
how much to get when they deliver the
financial instruments.

24. Limitation of Forward Contracts
• Forward contracts are flexible (any
date, any amount, and any financial
instrument), but not liquid due to a lack
of secondary market.
– Because each forward contract is unique,
there is no market mechanism to determine
a value of each contract like individual
mortgage loan which is not traded in
market.
– To be able to trade in market, it must be
standardized, that is, futures contracts.

25. Futures
• Futures contract: A contract in which
an issuer agrees to deliver a certain
standardized assets on a specified future
date at an agreed-upon price.
• Futures price is not specified in the
futures contract, but is determined by the
demand and supply in the futures
market.
– Futures price reflects an expected value of
underlying asset on the date of delivery.

26. Widely Traded Futures Contracts
• There are many varieties
of futures contracts which
promise to deliver
commodity and financial
instruments.
• Among financial futures
are Treasury securities,
stock indices, and foreign
currencies.
• Among commodity futures
are agricultural products
(e.g. corn, wheat, coffee,
orange juice, meat) and
basic commodities (e.g.
oil, metals).

27. Origin of Futures Market and Now
• Futures markets in the U.S. originated in 19th
century in Chicago where farmers could sell
contracts to deliver grains, meat, and livestock.
– When farmers plant their seeds in spring, they do not know
how much they can make in fall. It all depends on yield of
crops and prices in fall. To reduce some of risk, farmers
engage in futures contracts.
• In 1970s the Chicago Mercantile Exchange
introduced financial futures which became more
dominant in trading volumes.
– Financial futures are used by many financial institutions and
investors to reduce risk on their portfolio.

28. How Price of Futures Contract Determined
• Futures contract price is a price that a buyer
of the contract pays to the seller when a
specified financial instrument is delivered.
– An issuer of futures contract sells a futures
contract at $111,125, which promises to deliver
$100,000 face value T-bonds with 6% yield to
maturity in March.
– A buyer of the futures contract agrees to pay
$111,125 in March when the T-bonds are
delivered. The buyer is required to put a portion
of price in margin account (like down payment).
– Why would someone want to pay $111,125 on
$100,000 face value T-bonds? Because the
buyer expected T-bond price to go up by March.

29. Futures Contract Transaction
• Margin requirement: An initial deposit that
buyers of contract must put in a margin
account of brokerage firm.
– Margin rate is a fraction of total value that
must be put and is set by the Federal
Reserves.
• Marked to market: At the end of each
trading day the change in the value of the
contracts is added or subtracted from the
margin account.
• On the expiration date an issuer may purchase
back the futures contract to avoid a delivery of
the underlying assets.

30. Organizations in Futures Markets
• Brokerage houses
• Exchanges
– Chicago Board of Trade
– Chicago Mercantile Exchange
– New York Futures Exchange
• Regulatory agency
– Commodity Futures Trading Commission (CFTC)

31. Brokerage Houses in Futures Markets
• Brokerage houses
– Act as dealers and brokers to help sellers and
buyers of futures contracts.
– Maintain margin accounts for sellers and buyers
of futures contracts.
– Extend credits (provide loans) to sellers and
buyers of futures contract.

32. Exchanges in Futures Markets
• Futures contracts are traded in exchanges
– Chicago Board of Trade trades commodity and
financial futures (e.g. currencies, stock indices, T-
bonds, corn, milk, pork, gold)
– New York Board of Trade trades commodity
futures contracts (e.g. coffee & sugar)
– New York Mercantile Exchange trades commodity
futures contracts (e.g. oil, gasoline, copper, gold)
– Tokyo Commodity Exchange, London Metal
Exchange, Dubai Mercantile Exchange, etc.

33. Chicago Mercantile Exchange
• At Chicago Board of Trade, traders
trade futures contracts in a
“Trading Pit” through “open outcry”
– They stand at a trading floor and call
out orders with hand signs to make
deals.

34. Regulatory Agency in Futures Markets
• Futures exchanges and all trades in financial
futures are regulated by the Commodity
Futures Trading Commission (CFTC).
– Originally, the futures markets were regulated by
the Department of Agriculture until 1974.
• The role of the CFTC is similar to that of the
SEC.
– Oversee trading and pricing of futures contracts
– Register and audit the brokers, traders, and
exchanges
– Ensure the financial soundness of the exchange

35. Futures and Long & Short Positions
• Like any financial instruments, issuers and
buyers of futures contract are in a long or
short position.
• Issuers of futures contract in a short position
– Issuers have an obligation to deliver assets at set
prices.
– When a price of assets decreases, issuers benefit
from the futures contracts.
• Buyers of futures contracts in a long position
– Buyers have an obligation to take a delivery of
assets at set prices.
– When a price of assets increases, buyers benefit
from the futures contracts.

36. Hedging with Futures Contracts
• Because futures contracts create a long or
short position, they can be used for hedging.
• If a saver is in a long position, he may issue
a futures contract to create an offsetting
short position.
• If a saver is in a short position, she may
purchase a futures contract to create an
offsetting long position.

37. Options
• Options contract is another derivative.
• Options contract: A contract which gives
its holder the right to purchase (call
options) or sell (put options) an asset
at a specified price (strike
price/exercise price) on or before a
specified future date (expiration).
– American options can be exercised
(converted into the underlying assets) at any
time up to the expiration date.
– European options can be exercised only on
the expiration date.

38. Types of Options
• Stock options: options on individual
stocks
– often granted to CEO of corporations
– regulated by the Security and Exchange
Commission (SEC)
• Financial futures options: options
contracts on financial futures
– traded at options markets
– regulated by the Commodity Futures
Trading Commission (CFTC)

39. Long and Short Positions with Options
• Like futures contracts, options contracts can
create a long or short position.
– Buyer of put options contract in a long position:
He has a right to purchase and receive an
underlying asset at its strike price. If a price of
the underlying asset increases, he will make
profits.
– Buyer of call options contract in a short position:
He has a right to sell and deliver an underlying
asset at its strike price. If a price of the
underlying asset decreases, she will make profits.

40. Hedging with Options
• Since options contracts can create a long or
short position, they can be used for hedging
like futures contracts.
– If a saver is in a short position, he may purchase
a put options contract to create an offsetting long
position.
– If a saver is in a long position, she may purchase
a call options contract to create an offsetting
short position.

41. Futures vs. Options
• Unlike futures contracts, buyers of options
contract face limited loss.
– A buyer of futures contract, who agrees to
purchase, must pay and receive the underlying
asset on its settlement day, regardless of spot
price of the assets on that day. He may face a
loss if the spot price of the underlying asset is
less than the purchase price of futures contract.
– A buyer of call options contract, who has a right
to purchase, may choose not to pay or receive
the underlying asset on its expiration day. He can
avoid a loss if a spot price of the underlying asset
is less than the strike price of options contract.

42. Swaps
• Swaps: financial contracts that obligate
one party to exchange a set of
payments it owns for another set of
payments owned by another party.
• Why swap? A saver has a choice of
financial instruments which differ in
their yields and cash flows. He wants
one with higher yield, but prefers cash
flows of the other. What should he do?
He can purchase one with higher yield,
and swap cash flows with the other.

43. Swaps for Borrowers
• Swaps help both savers and borrowers.
• A borrower has a choice of loan contracts
which differ in their interest rates and
payment patterns. She wants one with
lower interest rate, but prefers payment
pattern of the other. What should she do?
She can borrow one with lower interest rate,
and swap cash flows with the other.

44. Long and Short Positions with Swaps
• Because swaps are contracts that both parties agree
to make and receive payments, they create both
short and long positions.
• Example: William gets a loan with $600 semiannual
payment.
– William is in a short position of delivering $600
semiannually.
• William swaps with $100 monthly payment loan.
– The swap eliminates his $600 semiannual payment by
creating a long position (another party will deliver $600
semiannually to him).
– The swap creates another short position (he agrees to
deliver $100 monthly).

45. Two Types of Swaps
• Currency swaps: the exchange of a
set of payments in one currency for a
set of payments in another currency.
• Interest-rate swaps: the exchange of
one set of interest payments for
another set of interest payments.

46. Example of Currency Swap
• Flow Honda purchases 50 Honda Accords from Honda
Japan and promises to pay ¥1,000,000 next month.
– Flow Honda faces a foreign exchange risk since it does not know
an exchange rate next month.
– Flow Honda can purchase a forward contract (derivative) to
eliminate a foreign exchange risk.
• Japan Tobacco Co. purchases Camel cigarettes from R.J.
Reynolds for $100,000 and promises to make a payment
next month.
• Then, Flow Honda makes a currency swap arrangement
with Japan Tobacco Co., in which Flow Honda pays
$100,000 to R.J Reynolds and Japan Tobacco Co. pays
sells ¥1,000,000 to Honda Japan next month.
– With swap, Flow Honda eliminates a foreign exchange risk since
it does not need to exchange U.S. dollar to Japanese yen.

47. Example of Interest-Rate Swap
• Fixed-rate loan and variable-rate loan
– Midwest Savings Bank provided a fixed-rate loan to Mr.
Smith, but it prefers to receive variable-rate interest
payments.
– Friendly Finance Company provided a variable-rate loan
to Ms. Brown, but it prefers to receive fixed-rate interest
payments.
• Exchange between fixed-rate loan and variable-
rate loan
– Midwest Savings Bank sells its fixed-rate loan to Friendly
Finance Company, while Friendly Finance Company sells
its variable-rate loan to Midwest Savings Bank, or
– Midwest Savings Bank swaps interest payments with
Friendly Finance Company, while each still holds original
loan.

48. Interest-Rate Swap Contracts
Midwest Savings Bank receives fixed rate payments on the
security that it holds and gives them to Friendly Finance
Company (→).
Friendly Finance Company receives variable rate payments on the
security that it holds and give them to Midwest Savings Bank(←).

49. Credit Derivatives
• Credit Derivatives: Contracts to separate
and transfer credit risk (default risk) of
underlying assets (previously issued
securities) to another party while keeping
the underlying assets.
─ A change in default risk may affect cash flows on
debt instruments. Credit derivatives protect
either holders or issuers of the securities from
potential losses caused by the credit risk.
• Types of credit derivatives
─ Credit Options
─ Credit-Linked Notes
─ Credit Swaps

50. Credit Options
• Credit options are options for receiving
profits that are tied either to the price of
underlying security or to an interest rate.
̶ When the price of underlying assets declines due
to (but not limited to) downgrading of their
rating, the holder of credit options can sell the
underlying securities at the predetermined price.
̶ Credit spread options grant the buyers to receive
cash flows if the credit spread between two
specific benchmarks widens or narrows. When a
corporation plans to issue new bonds with a
particular credit rating, it can protect from an
increased borrowing cost in case that the average
bond interest rate in the same rating increases.

51. Credit-Linked Notes
• Credit-linked notes: a combination of a bond
and a credit option.
̶ The coupon payments are usually determined at
time of issuance of the bond and will not change
over the life of bond.
̶ When the economic or market condition changes,
the market interest rate may fall, but the
borrower must continue to pay the fixed coupon
rate on the previously issued bond.
̶ Credit-linked notes include the credit option that
pays off to the issuer of bonds when the market
interest rate falls.
̶ Credit-linked notes act like adjustable-rate bond.

52. Credit Default Swap (CDS)
• Credit default swap is a swap contract in
which the buyer of the CDS pays premiums
over a period of time in return for a payoff if
a credit instrument is defaulted.
̶ CDS is like insurance for default.
̶ Holders of risky bonds may purchase CDS and
protect from loss of cash flows in case that the
risky bonds default.

53. Credit Default Swap (CDS)
• The buyer of the CDS swap the payments made
on the risky credit instrument (e.g. bonds,
CMOs, CDOs) that he holds with the payments
made on U.S. Treasury securities that the seller
of the CDS holds.
• Because the payments on the risky credit
instrument are always higher than the
payments on the U.S. Treasury securities, the
seller of the CDS simply receives the difference
between them (like insurance premium).
• When the risky credit instrument is defaulted,
the seller of the CDS is obligated to continue to
give the payments from the U.S. Treasury
securities to the buyer of the CDS.

54. Credit Default Swap Crisis
• In fall of 2008, the largest CDS issuer,
AIG, became insolvent.
̶ AIG sold the CDSs to many financial
institutions which purchased CDOs and
CMOs, directly or indirectly backed by the
sub-prime mortgage loans.
̶ AIG, believing that CDOs and CMOs are AAA-
rating, failed to hold enough Treasury
securities to meet its potential obligation on
the CDS contracts. Without holding Treasury
securities, AIG pocketed premium payments
from the buyers of the CDS as profits.
̶ When the sub-prime mortgage loans
began to default, AIG became obligated
to make payments of defaulted CDOs
and CMOs which exceeded its assets.

55. Benefits of Derivative Markets
• Derivatives and derivative markets are
beneficial for individuals and the society.
– Hedging: Reducing one’s exposure to risk by
receiving the right to sell or buy an asset at a
known price on a specified future date.
– Information about expectations of future prices.
Investors infer from derivative markets how
much a spot price will be in future.
 Ex. High price of oil futures contracts indicates that
the spot price of oil may increase near future.

56. Risk on Derivatives
• Although derivatives provide means of
hedging to investors, they can create risk to
investor.
• Derivatives create a long or short position.
If a long or short position created by
derivatives does not offset an existing short
or long position, the derivative not only fail
to eliminate the original risk, but also
potentially increase the risk exposure.

57. Risk on Derivatives: Fact
• Some financial institutions miss-managed
derivatives and failed.
– Ex. Enron, Barings Bank, Long-Term Capital Management,
and Orange County
• Derivatives allow financial institutions to increase
their leverage.
– they can control a proportion of the underlying asset that is
many times greater than the amount of money they have
had to put up (margin).
• Only nominal value of derivatives is shown in the
balance sheet of financial institutions.
– It is hard to detect derivatives on financial statements and
their full effects.

58. Derivatives and Arbitrage
• Because derivatives promise to deliver an
underlying asset, its price must be align to
the actual price of the underlying asset.
– If any discrepancy in prices between derivatives
and their underlying assets appears in market,
an arbitrage will take place.
– Brokerage firms use computer to trade financial
derivatives and financial instruments online.
• Two types of computer-directed
(automated) trading by brokerage firms
– Program trading
– Portfolio insurance

59. Program Trading
• Program trading: Computer-directed
trading of financial instruments for
arbitrage between the futures contracts and
the underlying assets.
– If any discrepancy in prices between derivatives
and their underlying assets appears in market,
the computer software at brokerage firms will
automatically place orders of buy and sell
futures and underlying assets.

60. Portfolio Insurance
• Portfolio insurance: Program trading
to reduce risk of portfolio through
hedging.
– When a price of assets in portfolio falls, a
computer software will automatically place
orders to sell the asset (before further fall of
price) and to purchase a futures contract (so
it will have the same asset).
– Portfolio insurance is NOT an insurance.
There is no guarantee that you will not loose
or will be compensated 100%. It is not
offered by insurance firms, but by brokerage
firms which manage portfolios of their
customers.

61. Disclaimer
Please do not copy, modify, or distribute this presentation
without author’s consent.
This presentation was created and owned by
Dr. Ryoichi Sakano
North Carolina A&T State University