0. Derivatives and Hedging Risk
CHAPTER 25
Derivatives and Hedging Risk

1. Chapter Outline 25.1 Forward Contracts 25.2 Futures Contracts
25.3 Hedging
25.4 Interest Rate Futures Contracts
25.5 Duration Hedging
25.6 Swap Contracts
25.7 Actual Use of Derivatives
25.8 Summary & Conclusions

2. 25.1 Forward Contracts
A forward contract specifies that a certain commodity will be exchanged for another at a specified time in the future at prices specified today.
Its not an option: both parties are expected to hold up their end of the deal.
If you have ever ordered a textbook that was not in stock, you have entered into a forward contract.

3. 25.2 Futures Contracts: Preliminaries
A futures contract is like a forward contract:
It specifies that a certain commodity will be exchanged for another at a specified time in the future at prices specified today.
A futures contract is different from a forward:
Futures are standardized contracts trading on organized exchanges with daily resettlement (“marking to market”) through a clearinghouse.

4. Futures Contracts: Preliminaries
Standardizing Features:
Contract Size
Delivery Month
Daily resettlement
Minimizes the chance of default
Initial Margin
About 4% of contract value, cash or T-bills held in a street name at your brokerage.

5. Daily Resettlement: An Example
Suppose you want to speculate on a rise in the $/¥ exchange rate (specifically you think that the dollar will appreciate).
Currently $1 = ¥140.
The 3-month forward price is $1=¥150.

6. Daily Resettlement: An Example
Currently $1 = ¥140 and it appears that the dollar is strengthening.
If you enter into a 3-month futures contract to sell ¥ at the rate of $1 = ¥150 you will make money if the yen depreciates. The contract size is ¥12,500,000
Your initial margin is 4% of the contract value:
$3, = 0.04 × ¥12,500,000 ×
¥150 $1

7. Daily Resettlement: An Example
If tomorrow, the futures rate closes at $1 = ¥149, then your position’s value drops.
Your original agreement was to sell ¥12,500,000 and receive $83,333.33:
$83, = ¥12,500,000 ×
¥150 $1
But ¥12,500,000 is now worth $83,892.62:
Optimists may wish to work this example from the counterparties point of view.
$83, = ¥12,500,000 ×
¥149 $1
You have lost $ overnight.

8. Daily Resettlement: An Example
The $ comes out of your $3, margin account, leaving $2,774.05
This is short of the $3, required for a new position.
$3, = 0.04 × ¥12,500,000 ×
¥149 $1
Your broker will let you slide until you run through your maintenance margin. Then you must post additional funds or your position will be closed out. This is usually done with a reversing trade.

9. Selected Futures Contracts

10. Futures Markets
The Chicago Mercantile Exchange (CME) is by far the largest.
Others include:
The Philadelphia Board of Trade (PBOT)
The MidAmerica Commodities Exchange
The Tokyo International Financial Futures Exchange
The London International Financial Futures Exchange

11. The Chicago Mercantile Exchange
Expiry cycle: March, June, September, December.
Delivery date 3rd Wednesday of delivery month.
Last trading day is the second business day preceding the delivery day.
CME hours 7:20 a.m. to 2:00 p.m. CST.

12. CME After Hours
Extended-hours trading on GLOBEX runs from 2:30 p.m. to 4:00 p.m dinner break and then back at it from 6:00 p.m. to 6:00 a.m. CST.
Singapore International Monetary Exchange (SIMEX) offer interchangeable contracts.
There’s other markets, but none are close to CME and SIMEX trading volume.

13. Wall Street Journal Futures Price Quotes
Highest price that day
Highest and lowest prices over the lifetime of the contract.
Opening price
Closing price
Daily Change
Lowest price that day
Number of open contracts
Expiry month

14. Basic Currency Futures Relationships
Open Interest refers to the number of contracts outstanding for a particular delivery month.
Open interest is a good proxy for demand for a contract.
Some refer to open interest as the depth of the market. The breadth of the market would be how many different contracts (expiry month, currency) are outstanding.

15. 25.3 Hedging
Two counterparties with offsetting risks can eliminate risk.
For example, if a wheat farmer and a flour mill enter into a forward contract, they can eliminate the risk each other faces regarding the future price of wheat.
Hedgers can also transfer price risk to speculators and speculators absorb price risk from hedgers.
Speculating: Long vs. Short

16. Hedging and Speculating Example
You speculate that copper will go up in price, so you go long 10 copper contracts for delivery in 3 months. A contract is 25,000 pounds in cents per pound and is at $0.70 per pound or $17,500 per contract.
If futures prices rise by 5 cents, you will gain:
Gain = 25,000 × .05 × 10 = $12,500
If prices decrease by 5 cents, your loss is:
Loss = 25,000 ×( –.05) × 10 = –$12,500

17. Hedging: How many contacts?
You are a farmer and you will harvest 50,000 bushels of corn in 3 months. You want to hedge against a price decrease. Corn is quoted in cents per bushel at 5,000 bushels per contract. It is currently at $2.30 cents for a contract 3 months out and the spot price is $2.05.
To hedge you will sell 10 corn futures contracts:
10 contracts =
5,000 bushels per contract
50,000 bushels
Now you can quit worrying about the price of corn and get back to worrying about the weather.

18. 25.4 Interest Rate Futures Contracts
Pricing of Treasury Bonds
Pricing of Forward Contracts
Futures Contracts
Hedging in Interest Rate Futures

19. Pricing of Treasury Bonds
Consider a Treasury bond that pays a semiannual coupon of $C for the next T years:
The yield to maturity is r … T C F +
Value of the T-bond under a flat term structure
= PV of face value + PV of coupon payments ú û ù ê ë é + - = T r C F PV ) 1 (

20. Pricing of Treasury Bonds
If the term structure of interest rates is not flat, then we need to discount the payments at different rates depending upon maturity … T C F +
= PV of face value + PV of coupon payments T r F C PV ) 1 ( 2 3 + = L

21. Pricing of Forward Contracts
An N-period forward contract on that T-Bond …
0 N N+1 N+2 N N+2T
forward P - C F +
Can be valued as the present value of the forward price. N
forward r P PV ) 1 ( + = N T r F C PV ) 1 ( 2 3 + = L

22. Pricing of Forward Contracts: Example
Find the value of a 5-year forward contract on a 20-year T-bond.
The coupon rate is 6 percent per annum and payments are made semiannually on a par value of $1,000. N
40 = 20 × 2
The Yield to Maturity is 5 percent.
First, set your calculator to 2 payments per year.
Then enter what you know and solve for the value of a 20-year Treasury bond at the maturity of the forward contract.
I/Y 5
–1,125.51 PV PV
30 = 2
1,000 × .06
PMT FV
1,000

23. Pricing of Forward Contracts: Example
First, set your calculator to 1 payment per year.
Then, use the cash flow menu: 5
CF0 I
CF1
881.86
NPV F1 5
–1,125.51
CF2 F2 1

24. Pricing of Futures Contracts
The pricing equation given above will be a good approximation.
The only real difference is the daily resettlement.

25. Hedging in Interest Rate Futures
A mortgage lender who has agreed to loan money in the future at prices set today can hedge by selling those mortgages forward.
It may be difficult to find a counterparty in the forward who wants the precise mix of risk, maturity, and size.
It’s likely to be easier and cheaper to use interest rate futures contracts however.

26. 25.5 Duration Hedging
As an alternative to hedging with futures or forwards, one can hedge by matching the interest rate risk of assets with the interest rate risk of liabilities.
Duration is the key to measuring interest rate risk.

27. 25.5 Duration Hedging
Duration measures the combined effect of maturity, coupon rate, and YTM on bond’s price sensitivity
Measure of the bond’s effective maturity
Measure of the average life of the security
Weighted average maturity of the bond’s cash flows

28. Duration Formula å = + N t T r C D PV 1 2 ) ( L

29. Calculating Duration
Calculate the duration of a three-year bond that pays a semi-annual coupon of $40, has a $1,000 par value when the YTM is 8% semiannually?

30. Calculating Duration
Duration is expressed in units of time; usually years.

31. Duration The key to bond portfolio management Properties:
Longer maturity, longer duration
Duration increases at a decreasing rate
Higher coupon, shorter duration
Higher yield, shorter duration
Zero coupon bond: duration = maturity

32. 25.6 Swaps Contracts: Definitions
In a swap, two counterparties agree to a contractual arrangement wherein they agree to exchange cash flows at periodic intervals.
There are two types of interest rate swaps:
Single currency interest rate swap
“Plain vanilla” fixed-for-floating swaps are often just called interest rate swaps.
Cross-Currency interest rate swap
This is often called a currency swap; fixed for fixed rate debt service in two (or more) currencies.

33. The Swap Bank
A swap bank is a generic term to describe a financial institution that facilitates swaps between counterparties.
The swap bank can serve as either a broker or a dealer.
As a broker, the swap bank matches counterparties but does not assume any of the risks of the swap.
As a dealer, the swap bank stands ready to accept either side of a currency swap, and then later lay off their risk, or match it with a counterparty.

34. An Example of an Interest Rate Swap
Consider this example of a “plain vanilla” interest rate swap.
Bank A is a AAA-rated international bank located in the U.K. and wishes to raise $10,000,000 to finance floating-rate Eurodollar loans.
Bank A is considering issuing 5-year fixed-rate Eurodollar bonds at 10 percent.
It would make more sense to for the bank to issue floating-rate notes at LIBOR to finance floating-rate Eurodollar loans.

35. An Example of an Interest Rate Swap
Firm B is a BBB-rated U.S. company. It needs $10,000,000 to finance an investment with a five-year economic life.
Firm B is considering issuing 5-year fixed-rate Eurodollar bonds at percent.
Alternatively, firm B can raise the money by issuing 5-year floating-rate notes at LIBOR + ½ percent.
Firm B would prefer to borrow at a fixed rate.

36. An Example of an Interest Rate Swap
The borrowing opportunities of the two firms are:

37. An Example of an Interest Rate Swap
Bank
The swap bank makes this offer to Bank A: You pay LIBOR – 1/8 % per year on $10 million for 5 years and we will pay you 10 3/8% on $10 million for 5 years
10 3/8%
LIBOR – 1/8%
Bank A

38. An Example of an Interest Rate Swap
½% of $10,000,000 = $50,000. That’s quite a cost savings per year for 5 years.
Here’s what’s in it for Bank A: They can borrow externally at 10% fixed and have a net borrowing position of
-10 3/ (LIBOR – 1/8) =
LIBOR – ½ % which is ½ % better than they can borrow floating without a swap.
Swap
Bank
10 3/8%
LIBOR – 1/8%
Bank A
10%

39. An Example of an Interest Rate Swap
The swap bank makes this offer to company B: You pay us 10½% per year on $10 million for 5 years and we will pay you LIBOR – ¼ % per year on $10 million for 5 years.
Swap
Bank
10 ½%
LIBOR – ¼%
Company B

40. An Example of an Interest Rate Swap
Here’s what’s in it for B:
½ % of $10,000,000 = $50,000 that’s quite a cost savings per year for 5 years.
Swap
Bank
10 ½%
They can borrow externally at
LIBOR + ½ % and have a net
borrowing position of
10½ + (LIBOR + ½ ) - (LIBOR - ¼ ) = 11.25% which is ½% better than they can borrow floating.
LIBOR – ¼%
Company B
LIBOR + ½%

41. An Example of an Interest Rate Swap
The swap bank makes money too.
¼% of $10 million = $25,000 per year for 5 years.
Swap
Bank
10 3/8%
10 ½%
LIBOR – 1/8%
LIBOR – ¼%
Bank A
Company B
LIBOR – 1/8 – [LIBOR – ¼ ]= 1/8
10 ½ /8 = 1/8

42. An Example of an Interest Rate Swap
The swap bank makes ¼%
Swap
Bank
10 3/8%
10 ½%
LIBOR – 1/8%
LIBOR – ¼%
Bank A
Company B
A saves ½%
B saves ½%

43. An Example of a Currency Swap
Suppose a U.S. MNC wants to finance a £10,000,000 expansion of a British plant.
They could borrow dollars in the U.S. where they are well known and exchange for dollars for pounds.
This will give them exchange rate risk: financing a sterling project with dollars.
They could borrow pounds in the international bond market, but pay a premium since they are not as well known abroad.

44. An Example of a Currency Swap
If they can find a British MNC with a mirror-image financing need they may both benefit from a swap.
If the spot exchange rate is S0($/£) = $1.60/£, the U.S. firm needs to find a British firm wanting to finance dollar borrowing in the amount of $16,000,000.

45. An Example of a Currency Swap
Consider two firms A and B: firm A is a U.S.–based multinational and firm B is a U.K.–based multinational.
Both firms wish to finance a project in each other’s country of the same size. Their borrowing opportunities are given in the table below.

46. An Example of a Currency Swap
Bank
$8%
$9.4%
£11%
£12%
Firm A
Firm B
$8%
£12%

47. An Example of a Currency Swap
A’s net position is to borrow at £11%
Swap
Bank
$8%
$9.4%
£11%
£12%
Firm A
Firm B
$8%
£12%
A saves £.6%

48. An Example of a Currency Swap
B’s net position is to borrow at $9.4%
Swap
Bank
$8%
$9.4%
£11%
£12%
Firm A
Firm B
$8%
£12%
B saves $.6%

49. An Example of a Currency Swap
The swap bank makes money too:
1.4% of $16 million financed with 1% of £10 million per year for 5 years.
Swap
Bank
$8%
$9.4%
£11%
£12%
Firm A
Firm B
$8%
At S0($/£) = $1.60/£, that is a gain of $64,000 per year for 5 years.
£12%
The swap bank faces exchange rate risk, but maybe they can lay it off (in another swap).

50. Variations of Basic Swaps
Currency Swaps
fixed for fixed
fixed for floating
floating for floating
amortizing
Interest Rate Swaps
zero-for floating
Exotica
For a swap to be possible, two humans must like the idea. Beyond that, creativity is the only limit.
It gets complicated in a hurry.

51. Risks of Interest Rate and Currency Swaps
Interest Rate Risk
Interest rates might move against the swap bank after it has only gotten half of a swap on the books, or if it has an unhedged position.
Basis Risk
If the floating rates of the two counterparties are not pegged to the same index.
Exchange Rate Risk
In the example of a currency swap given earlier, the swap bank would be worse off if the pound appreciated.

52. Risks of Interest Rate and Currency Swaps
Credit Risk
This is the major risk faced by a swap dealer—the risk that a counter party will default on its end of the swap.
Mismatch Risk
It’s hard to find a counterparty that wants to borrow the right amount of money for the right amount of time.
Sovereign Risk
The risk that a country will impose exchange rate restrictions that will interfere with performance on the swap.

53. Pricing a Swap
A swap is a derivative security so it can be priced in terms of the underlying assets:
How to:
Plain vanilla fixed for floating swap gets valued just like a bond.
Currency swap gets valued just like a nest of currency futures.

54. 25.7 Actual Use of Derivatives
Because derivatives don’t appear on the balance sheet, they are present a challenge to financial economists who which to observe their use.
Survey results appear to support the notion of widespread use of derivatives among large publicly traded firms.
Foreign currency and interest rate derivatives are the most frequently used.

55. 25.8 Summary & Conclusions
This chapter shows a number of hedging strategies.
A short hedge involves an agreement to sell the underlying asset in the future.
A long hedge involves an agreement to buy the underlying asset in the future.
Swaps can also be used to hedge; a swap can be viewed as a portfolio of futures with different maturities.