1. Module 8: Futures, Forwards, and Swaps

2. Reading 8.1: Futures and Forwards

3. Definitions for futures and forwards
Derivative – An asset whose value is derived from the underlying asset or some other asset.
Futures – An agreement to trade an asset on a specified date at a specified price. Futures contracts are traded on an organized exchange.
Forward – Also an agreement between two parties to trade an asset on a specified date at a specified price. Forwards do not trade on an exchange: they are negotiated agreements between two parties.
Spot market – Transactions where commodities are sold for immediate delivery.
Strike price – Price at which the asset is to be delivered at a specified future date.

4. Definitions for futures and forwards
Cash price – Price at which the asset can be bought today.
Short position – Party which agrees to sell the asset at a specified future date. Party expects the asset price to fall.
Long position – Party which agrees to buy the asset at a specified future date. Party expects the asset price to rise.
Physically delivered - The other party agrees to deliver that item at the stipulated price.
Cash-settled - The difference between the strike price and the cash price of the underlying asset at the expiry of the contract is paid in cash by one party to the other.

5. Differences between futures and forwards

6. Example:
On November , a mid size canola processor enters into a canola futures contract on the ICE Futures Canada with the following details:
Contract size: 20 tonnes
Strike price: $425 tonne
Delivery date in May 2012
Current canola cash price: $430 tonne
On May , cash price for canola is $400.
- Long position has a loss of $500 [( ) x 20]

7. Clearing house
The clearing house guarantees the futures contracts. The clearing house faces default risk if one party can’t pay.
The clearing house reduces its risk by requiring parties to post collateral (margin).

8. Margin requirements
Initial margin – Collateral required when contract signed.
Maintenance margin – Minimum balance a brokerage firm (clearing house) will allow a margin account to fall to.
Marking to market – Updating margin accounts on a daily basis to reflect the market value of position.

13. Covering a futures or forward position
Daily price limits
Daily price limits specify range of prices around the opening price within which trading can take place. Trading can’t take place above the upper limit, or below the lower limit.
This doesn’t reduce a trader’s risk, it allows the clearing house time to determine and enforce margin calls.
Covering a futures or forward position
A trader can cover/close a futures position before the delivery date with an offsetting position (a trader can close a long position by entering into a corresponding short position).

15. Reading 8.2: Valuation of Futures and Forwards

16. Law of one price
The law of one price states that the futures price of an asset is determined from the spot price. The futures price should be derived from spot price and included costs such as storage and/or carrying costs.

18. General model for futures and forward prices
The law of one price states that the futures price of an asset is determined from the spot price.
The futures price should be derived from spot price and included costs such as storage and/or carrying costs. This is more relevant for commodities than for financial assets.
Futures price for financial futures

19. Futures price for non - financial futures

20. Pricing interest rate futures
Most common are U.S treasury bonds, Government of Canada bonds, bankers’ acceptances, and eurodollar deposits.
Spot price of interest rate futures reflects expectations about future prices, which is based on the term structure of interest rates.

21. Pricing stock-index futures
Most common are the S&P 500. In Canada, the most common are based on S&P/TSX 60.
Stock-index futures have an index multiplier – for the S&P/TSX 60 contracts it is 200.
Stock-index futures also have to account for dividends paid.

22. The annual 3 month treasury bill is 5.21%
Minicase 8-3 & 8-4:
March 16, 2010, Jim buys futures contract on S&P/TSX 60 for delivery June for $600.20
The annual 3 month treasury bill is 5.21%
Annual rate of dividends is 4.63%
Required: A) If the S&P/TSX 60 index closes at , what is the value of the futures contract? B) When the futures contract expires the index closes at $625. How is the futures contract settled on June 15? A)

23. B)
When the futures contract expires the index closes at $625. How is the futures contract settled on June 15?

24. Pricing currency futures: Interest rate parity
The forward exchange rate is determined by the spot rate and the domestic and foreign interest rates. The domestic rate contributes positively, while the foreign rate contributes negatively.
Equation 8-5

27. Reading 8.3: Hedging with Futures and Forward Contracts

28. The basics of hedging with futures and forwards
Direct hedge – Asset underlying a futures/forward contract is the same as the asset being hedged.
Cross hedge – The asset underlying a futures/forward contract is different from the asset being hedged.

29. Calculating the hedge ratio
Number of futures contracts required to be purchased or sold in order to hedge and cover all risk safely.
Naïve hedge is a hedge ratio of 1:1 – position in futures market is equal to position in spot market. Very rarely can you achieve this.
Duration-based hedge ratio – Change in value of futures position will offset change in value of spot position for a small change in interest rates.
Estimate hedge ratio by comparing the changes in volatility of the hedging instrument to changes in volatility of underlying asset.
ρ = sensitivity of changes in volatility of interest rate to be hedged to changes in volatility of rate on asset underlying futures contract.

30. Mf and Ff are standardized in a futures contract, but negotiated in a forward contract
Equation 8-6
Could try to calculate ρ like you do for β (remember Module 1) more likely a subjective guesstimate
Basis risk – when the values of the spot and futures contracts do not move together perfectly.

31. Canadian T-bills

35. Pricing bankers’ acceptances using futures contracts
Calculating the price of a BA with $100 face value:
Calculating the price of a 3month BA with $100 face value at 0.75%:

36. Hedging strategy for interest-rate changes

42. From Mach 2014:

52. Reading 8.4 : Swaps
A swap is an agreement between two parties to exchange future cash flows, such as interest payments on debt obligations.

53. Currency swaps
PPC – Canadian company looking to expand into Britain, needs access to British pounds.
ITC – British company operating in Canada that needs Canadian dollars

54. Interest-rate swaps

55. Reading 8.4-2 : Hedging with Swaps
Currency swap – Enter a swap to exchange cash flows in different currencies.
Interest rate swap – Enter a swap to exchange a fixed for floating rate payments or visa versa.