1. Financial Risk Management for Insurers
1. Futures Contracts
2. Interest Rate Futures 1

2. Overview What is a futures contract?
How does a futures contract differ from a forward contract?
What is the basis and what determines the relationship of the spot and futures price?
What types of interest rate futures exist?
How do we price interest rate futures?
How do we determine the best hedge? 2

3. Futures Contract Basics
Similar to a forward, a future obligates one party to buy and another to sell a specified asset in the future at a price agreed on today
Futures can be cash settled or require physical delivery of underlying asset
Most contracts are closed out before maturity 3

4. What is the use of a futures contract?
Help reduce uncertainty in future spot price
Agricultural futures were one early contract
Farmer can lock in future price of corn before harvest (protect against drop in price)
User of corn can protect against rise in price
Futures are now available on many assets
Agricultural (corn, soybeans, wheat, etc.)
Financial (interest rates, FX, and equities)
Commodities (oil, gasoline, and metals) 4

5. Differences between Forwards and Futures
Features reducing credit risk
Daily settlement or mark-to-market
Margin account
Clearinghouse
Features promoting liquidity
Contract standardization
Traded on organized exchanges 5

6. Daily Settlement
Recall that forward contracts have no settlement until maturity
Futures contracts settle every day
Like a series of one day forward contracts
At end of trading day, any contract value must be paid
Contract is “marked-to-market”
Risk is reduced to daily price movement 6

7. Margin Requirements Remaining risk is one day price movement
To use futures markets, party must post collateral called margin
Daily gains/losses posted to margin account
Initial margin is amount to open contract
If account balance drops below maintenance margin, customer receives margin call
If not met, customer position is closed out 7

8. Margin Account Example
P/C insurer has agreed to buy ¥ 10 million through the futures market at $1.25/¥100
The following prices represent closing futures prices (per ¥100) for the next five days: $1.22, $1.23, $1.21, $1.19, $1.24
What is the value of the margin account if the initial margin is $5,000 and the maintenance margin is $3,000 8

9. Margin Account Example Solution9

10. Clearinghouse
Even with daily settlement and margin accounts, there are default risk costs
Margin may not be enough if prices move a lot
Clearinghouse becomes counterparty to every trade
Counterparty credit analysis is not needed
Default risk is spread across the entire market
Daily price movement limits 10

11. Liquidity Enhancements of Futures Contracts
Forward contracts are negotiated by contracting parties
Futures are standardized contracts
Asset type, quantity, maturity
Futures are traded on organized exchanges

12. Interest Rate Futures Contracts
Most popular contracts divided by the type of interest rate exposure
Short term interest futures
Treasury Bill (T-bill)
Eurodollar CD (or just Eurodollar futures)
Intermediate or long term interest futures
Treasury bond or note (T-bond or T-note)
Municipal index

13. T-bill Futures
At maturity, short position must deliver $1 million of T-bills with 13 weeks to maturity
Either a new issue or an existing issue
Essentially, a T-bill future can be used to hedge the future interest rate
90 or 91 day forward rate beginning at the maturity date of the futures contract
Smallest change (one tick) in value is $25

14. T-bill Futures Value Remember T-bills are a discount security
Index price is quoted price (in WSJ)
Invoice price is amount long position must pay to short position

15. Example of T-bill Future Price
Index price = 94.50

16. Eurodollar Futures Underlying rate is 90-day future LIBOR
London InterBank Offered Rate
Has some credit risk
Cash settled (no delivery of some financial instrument)
Most heavily traded futures contract in the world
Used to hedge future interest rates

17. T-bond Futures
Underlying instrument is hypothetical bond with $100,000 face value and 8% coupon
Seller has option to deliver a number of bonds at maturity
Settlement value is adjusted based on actual bond delivered
Seller will evaluate which bond is cheapest to deliver

18. Before Pricing Futures Contracts: A side comment
Pricing of derivatives usually uses arbitrage arguments
Arbitrage is present if:
A zero net investment can generate a non-zero cash flow (cash flow must have no uncertainty)
The return of a cash investment exceeds the risk-free rate, assuming there is no uncertainty in the return 11

19. Futures Prices
At maturity, the spot price and futures price must be equal
If not, an arbitrage opportunity exists (Why?)
Before maturity, the spot price and futures price need not be equal due to cost of carry
Cost of carry reflects the benefit or cost of holding the asset vs. the benefit or cost of using the futures market 12

20. Cost of Carry Holding the asset Using futures
We must pay storage and insurance costs
Using futures
We earn interest on our money until maturity
For commodities: Ft(1+rf)<P0+c, where c is the storage and insurance costs
If inequality goes is reversed, sell the future and buy the asset in the spot market 13

21. Valuation of Interest Rate Futures
There should be no benefit from using cash market or futures market
Compare outlays at maturity
Tradeoff: Buy now (P) or later (F)
Lose interest on spot price P for t years
Earn coupon before futures maturity

22. Forwards Prices vs. Futures Prices
Margin payments are difference in value
We have ignored these cash flows
If interest rates increase, bond values decrease and short futures position has gain
Margin received earns higher interest rate
If rates decline, margin payments can be financed at lower interest
Short futures position is better than forward position in both cases
Opposite is true for long position

23. Futures Price Behavior
Expectations model says that the futures price is the expected future spot price
Expected profit on futures is zero
Futures price will only increase with the risk-free rate
For financial futures, expectations model is equilibrium price 14

24. Normal Backwardation Net long spot positions
e.g., farmers want to hedge future price risk
They are willing to sell futures at prices below the expected future spot price to entice investors
Long futures position receives a positive return 15

25. Normal Contango Net short spot positions
Users of oil may want protection against price increase
Willing to buy futures at prices above the expected future spot price to entice sellers
Short futures position receives a positive return 16

26. Uses of Futures Futures can be used to shed unwanted risk
Sell exposures that you don’t want
Buy back exposures that you have sold
Net position of exposure and futures contract is “riskless”

27. Determining the Required Hedge
Hedging is only “riskless” if underlying futures asset corresponds to exposure
Typically, futures contracts do not exist for every type of exposure
Decisions must be made
Which futures contract is best?
Which maturity is appropriate?
How many contracts to buy/sell?

28. Basis Basis is difference between spot price and futures price: F - P
Risk exposure becomes change in basis
If held to maturity, basis risk is zero
Factors affecting the basis
Futures price and spot prices converge
Cost of carry may change (e.g., interest rates)
If cross-hedging, spot price and futures price may not move together perfectly
Some other random and unpredictable factor 17

29. Maturity Mismatches Multiple exposures in the future
Strip hedge uses x contracts with maturity t1, y contracts with maturity t2, etc.
Rolling hedge aggregates all future exposure and uses only short-term contracts
Longer term contracts have less liquidity
At first exposure date, unwind position and use short term contracts again until next exposure
Assumes all contracts move together regardless of maturity

30. Selecting the Best Futures Contract
Frequently, there is no futures contract that matches the hedger’s exposure exactly
We want to determine the best cross-hedge
Use the most closely correlated future
Regress exposure against available futures contracts
Determine the appropriate number of contracts
Futures contract value may be more volatile than hedge required

31. Example
A life insurer needs to lock in the one month interest rate, 6 months from now
There is no futures contract which is based on the one-month rate
T-bills, Eurodollar futures are 3-month rates
The insurer regresses its exposure and finds that 50% of its exposure is explained by the 6-month Eurodollar futures contract
Insurer needs only a 16% hedge (Why?)

32. Next time... Swap contracts What are interest rate swaps?
What other kinds of swaps exist?
Why would someone use a swap?