Forward and Futures Contracts Innovative Financial Instruments Dr. A. DeMaskey Chapter 23

An Overview of Forward and Futures Trading u Forward contracts are negotiated directly between two parties in the OTC markets. – Individually designed to meet specific needs – Subject to default risk u Futures contracts are bought through brokers on an exchange. – No direct interaction between the two parties – Exchange clearinghouse oversees delivery and settles daily gains and losses – Customers post initial margin account

Futures vs. Forward Contracts

Hedging With Forwards and Futures u Create a position that will offset the price risk of another holding. – Short hedge supplements a long commodity holding with a short forward position – Long hedge supplements a short commodity holding with a long forward position

Relationship Between Spot and Forward Prices u The basis is the spread between the spot and futures price for the same asset at the same point in time T: – B t,T = S t - F t,T – Initial basis – Maturity basis – At maturity, the forward price converges to the spot price (F T,T = S T )

Basis Risk u Profit from short hedge: – B t,T - B 0,T = (S t - F t,T ) - (S 0 - F 0,T ) – Terminal value of hedge equals cover basis minus initial basis. u Real exposure is correlation between future changes in the spot and forward contract prices u Basis risk is small if price movements are highly correlated – Basis risk = 0 for forwards – Basis risk > 0 for futures

Optimal Hedge Ratio Net profit of short hedge position: Variance of this value: Minimizing and solving for N:

Valuing Forwards and Futures The value of unwinding a forward position early: The value of a futures, which are marked-to-market is: * = the possibility that forward and futures prices for the same commodity at the same point in time might be different.

The Cost of Carry Model u If you buy a commodity now for cash and store it until you deliver it, the price you want under a forward contract would have to cover: – the cost of buying it now – the cost of storing it until the contract matures – the cost of financing the initial purchase u These are the cost of carry necessary to move the asset to the future delivery date.

The Relationship Between Spot and Forward Prices u Contango – high storage costs and no dividends u Premium for owning the commodity – convenience yield – results from small supply at time 0 relative to what is expected at time T (after the crop harvest) u Backwarded market – future is less than spot

Relationship Between Futures Price and Expected Future Spot Price u Pure Expectations Hypothesis – F 0,T = E(S T ) u Normal Backwardation – F 0,T < E(S T ) u Normal Contango – F 0,T > E(S T )

Applications and Strategies u Interest Rate Forward and Futures – Short-term – Long-term u Equity Index Futures u Currency Forward and Futures

Long-Term Interest Rate Futures u Treasury bond and note contract mechanics – CBT $100,000 face value – T-bond >15 year maturity – T-note 10 year - bond with 6.5 to 10 year maturity – T-note 5 year - bond with years – Delivery any day during month of delivery – Last trading day 7 days prior to the end of the month – Quoted in 32nds – Yield quoted is for reference – Treasury bonds pay semiannual interest – Conversion factors for differences in deliverable bonds

A Duration Based Approach to Hedging

Treasury Futures Application u A T-Bond/T-Note (NOB) Futures Spread – expecting a change in the shape of the yield curve – unsure which way rates will change – long one point on curve and short another point

Short-Term Interest Rate Futures u Eurodollar and Treasury bill contract mechanics – Chicago Mercantile Exchange (CME or “Merc”), International Monetary Market (IMM), LIFFE – LIBOR u Altering bond duration with futures contracts u Creating a synthetic fixed-rate funding with a Eurodollar strip u Creating a TED spread

Stock Index Futures u Intended to provide a hedge against movements in an underlying financial asset u Hedging an individual stock with an index isolates the unsystematic portion of that security’s risk u Stock index arbitrage – prominent in program trading

Currency Forwards and Futures u Currency quotations – Direct (American) quote in U.S. dollars – Indirect (European) quote in non U.S. currency – Reciprocals of each other u Interest rate parity and covered interest arbitrage

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