Chapter 10Forwards and FuturesRoad MapPart A Introduction to finance.Part B Valuation of assets, given discount rates.Part C Determination of risk-adjusted discount rate.Part D Introduction to derivatives.• Forwards and futures.• Options.• Real options.Main issues• Forwards and Futures• Forward and Futures Prices• Hedging Financial Risks Using Forwards/FuturesChapter 10 Forwards and Futures 10-11 Forward ContractsDefinition: A forward contract is a commitment to purchase at afuture date a given amount of a commodity or an asset at a priceagreed on today.-0 T timeagreement settlement• The price fixed now for future exchange is the forward price.• The buyer obtains a “long position” in the asset/commodity.Features of forward contracts:• traded over the counter (not on exchanges)• custom tailored• no money changes hands until maturity• non-trivial counter-party risk.Example. Consider a 3-month forward contract for 10,000 bushelsof soybean at a forward price of $3.5/bushel. The long side iscommitted to buy 10,000 bushels of soybean from the short sidethree months from now at the price of $3.50/bushel.Fall 2006cJ. Wang 15.401 Lecture Notes10-2 Forwards and Futures Chapter 102 Futures ContractsForward contracts have two limitations:(a) illiquidity(b) counter-party risk.Futures contracts are designed to address these limitations.Definition: A futures contract is an exchange-traded, standard-ized, forward-like contract that is marked to the market daily.Futures contract can be used to establish a long (or short) posi-tion in the underlying commodity/asset.Features of futures contracts:• Standardized contracts:(1) underlying commodity or asset(2) quantity(3) maturity.• Traded on exchanges.• Guaranteed by the clearing house — little counter-party risk.• Gains/losses settled daily—marked to market.• Margin account required as collateral to cover losses.15.401 Lecture NotescJ. Wang Fall 2006Chapter 10 Forwards and Futures 10-3A Forward ContractA Futures ContractFall 2006cJ. Wang 15.401 Lecture Notes10-4 Forwards and Futures Chapter 10Example. Yesterday, you bought 10 December live-cattle con-tracts at CME, at the closing price of $0.7455/lb.• Contract size 40,000 lbs.• Agreed to buy 400,000 pounds of live cattle in December.• Value of position yesterday:(0.7455)(10)(40, 000) = $298, 200.• No money changed hands.• Initial margin required (5%-20% of contract value).Today, the futures price closes at $0.7435/lb, 0.20 cents lower.The value of your position is(0.7435)(10)(40, 000) = $297, 400a loss of $800.Forward and futures contracts are derivative securities because• payoffs determined by prices of the underlying asset• zero net supply.15.401 Lecture NotescJ. Wang Fall 2006Chapter 10 Forwards and Futures 10-53 Forward and Futures PricesQuestion: What determines forward and futures prices?Answer: Forward/futures prices are linked to spot prices.Contract Spot at t Forward FuturesPrice StFHIgnoring differences between forwards and futures, we haveF  H.Two ways to buy the underlying for date T :1. Buy forward or futures contract of maturityT .2. Buy the underlying now and store it untilT .Difference between buy-and-store from forward/futures:a. Cost of storing (for commodities).b. Benefits from storing:• Convenience yield (for commodities).• Dividends/interests (for financials).By arbitrage, the costs of these two approaches must equal:F  H =(1+rF)S0+ FV (net cost of storing).Fall 2006cJ. Wang 15.401 Lecture Notes10-6 Forwards and Futures Chapter 103.1 Commodities1. Gold.• Easy to store—negligible cost of storage.• No dividends or benefits.Two ways to buy gold forT :• Buy now for S0and hold until T .• Buy forward, pay F and take delivery at T .No-arbitrage requires thatF = S0(1 + rF)T H.Example. Gold quotes on 2006.08.21 are• Spot price $625.70/oz• 2007 February futures (CMX) $641.40/oz.The implied 6-month interest rate isrF=5.08%.15.401 Lecture NotescJ. Wang Fall 2006Chapter 10 Forwards and Futures 10-72. Oil.• Costly to store.• Additional benefits, convenience yield, for holding physicalcommodity (over holding futures).• Not held for long-term investment (unlike gold), but mostlyheld for future use.Let the percentage holding cost bec and convenience yield bey.WehaveF = S0[1+rF− (y − c)]T= S0(1 + rF− y)T Hwherey = y − cis the net convenience yield.Example. Prices on 2006.08.21 are• Spot oil price 72.45/barrel (light sweet)• Nov 06 oil futures price 74.22/barrel (NYM)• 3-month interest rate is 5.40% (LIBOR).Annualized net convenience yield is: y = −4. 74%.Fall 2006cJ. Wang 15.401 Lecture Notes10-8 Forwards and Futures Chapter 10For commodity futures:1. Contango means:(a) spot prices are lower than futures prices, and/or(b) prices for near maturities are lower than for distant.2. Backwardation means:(a) spot prices are higher than futures prices, and/or(b) prices for near maturities are higher than for distant.Backwardation occurs if net convenience yield exceeds interestrate:y − rF= y − c − rF> 0.Crude oil forward price curves for selected dates15.401 Lecture NotescJ. Wang Fall 2006Chapter 10 Forwards and Futures 10-93.2 FinancialsFor financial futures, the underlying are financial assets. Financialshave the following features:• No cost to store (the underlying asset).• Dividend or interest on the underlying.1. Stock index futures.• Underlying are bundles of stocks — S&P, Nikkei, etc.• Futures settled in cash (no delivery).Let the dividend yield bed, then there is the following relationbetween the forward/futures price and spot price:F = S0(1 + rF− d)T H.Deviations from this relation triggers index arbitrage.Example. Prices on 2006.08.21 are• S&P 500 closed at 1,279.52• S&P futures maturing in December closed at 1,313.60.• 4-month interest rate is 5.42%.The annual dividend yield is:d =2.78%.Fall 2006cJ. Wang 15.401 Lecture Notes10-10 Forwards and Futures Chapter 10Note:• Since the underlying asset is a portfolio in the case of indexfutures, trading in the futures market is easier than tradingin cash market.• Thus, futures prices may react quicker to macro-economicnews than the index itself.• Index futures are very useful to market makers, investmentbankers, stock portfolio managers:– hedging market risk in block purchases & underwriting– creating synthetic index fund– portfolio insurance.15.401