Learning Unit #16Law of One Price

and Derivative Markets

Objectives of Learning Unit

• Law of One Price• Types of Financial Derivatives

– Forwards – Futures– Options– Swaps

• Benefits and Danger of Derivatives

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 SaleEcon415Text for

$40Call A&T

WantedEcon415Text for

$50Call UNCG

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.

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.

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.

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.

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.

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!

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.

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.

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).

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).

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.

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.

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.

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).

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).

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

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

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

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

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.

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.

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.

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).

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.

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.

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.

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)

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.

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.

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.

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

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.

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.

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.

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)

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.

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.

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.

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.

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.

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).

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.

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.

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.

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().

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

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

Disclaimer

Please do not copy, modify, or distribute this presentation without author’s consent.

This presentation was created and owned byDr. Ryoichi Sakano

North Carolina A&T State University