Chapter 6 The Wide World of Futures Contracts
Currency Contracts Widely used to hedge against changes in exchange rates WSJ listing Figure 6.1 Listings for various currency futures contracts from the Wall Street Journal, August 10, 2007. 6-2
Currency Contracts: Pricing Currency prepaid forward Suppose you want to purchase 1 one year from today using $s Where x 0 is current ($/ ) exchange rate, and r y is the yen-denominated interest rate Why? By deferring delivery of the currency one loses interest income from bonds denominated I that currency Currency forward F P 0,T = x 0 e r y T F 0,T = x 0 e (r r y )t r is the $-denominated domestic interest rate F 0, T > x 0 if r > r y (domestic risk-free rate exceeds foreign risk-free rate) 6-3
Currency Contracts: Pricing (cont d) Example 6.1 -denominated interest rate is 2% and current ($/ ) exchange rate is 0.009. To have 1 in one year one needs to invest today 0.009/ x 1 x e -0.02 = $0.008822 Example 6.2 -denominated interest rate is 2% and $-denominated rate is 6%. The current ($/ ) exchange rate is 0.009. The 1-year forward rate 0.009e 0.06-0.02 = 0.009367 6-4
Covered Interest Arbitrage Synthetically creating a yen forward contract by borrowing in dollars and lending in yen. The payoff at time 1 is 1 $0.009367. 6-5
Eurodollar Futures Contract Specifications Figure 6.3 Specifications for the Eurodollar futures contract. WSJ listing Figure 6.2 Listing for interest rate futures contracts, including the 1-month LIBOR and 3-month Eurodollar contracts, from the Wall Street Journal, August 10, 2007. 6-6
Introduction to Commodity Futures Different commodities have their distinct forward curves, reflecting different properties of Storability Storage costs Production Demand 6-7
The Commodity Lease Rate The lease rate is the difference between the commodity discount rate, α, and the expected growth rate of the commodity price, g δ l = α g For a commodity owner who lends the commodity, the lease rate is like a dividend With the stock, the dividend yield, δ, is an observable characteristic of the stock With a commodity, the lease rate, δ l, is income earned only if the commodity is loaned. It is not directly observable, except if there is a lease market 6-8
Forward Prices and the Lease Rate The lease rate has to be consistent with the forward price Therefore, when we observe the forward price, we can infer what the lease rate would have to be if a lease market existed The annualized lease rate δ l = r 1 T In (F 0,T / S) The effective annual lease rate δ l = (1 + r) (F 0,T / S) 1/T 1 6-9
The Commodity Lease Rate Contango occurs when the lease rate is less than the risk-free rate Backwardation occurs when the lease rate exceeds the risk-free rate 6-10
Energy Futures Corn, electricity, natural gas, and oil all have distinct forward curves, reflecting the different characteristics of their physical markets. When there are seasonalities in either the demand or supply of a commodity, the commodity will be stored (assuming this is physically feasible), and the forward curve for the commodity will reflect storage costs. 6-11
Electricity Because electricity cannot be stored, its price is set by demand and supply at a point in time. Table 6.2 Day-ahead price, by hour, for 1 megawatt-hour of electricity in New York City, October 1, 2007. 6-12
Natural Gas The natural gas futures contract is one of the most heavily traded futures contracts in the United States. Figure 6.5 Listing for the NYMEX crude oil, heating oil, gasoline, and natural gas futures contracts from the Wall Street Journal, August 10, 2007. 6-13
Crude Oil Both oil and natural gas produce energy and are extracted from wells, but the different physical characteristics and uses of oil lead to very different forward prices than for gas. Figure 6.7 Specifications for the NYMEX light sweet crude oil contract. 6-14
Weather Derivatives A heating degree-day is the maximum of zero and the difference between 65 F and the average daily temperature. A cooling degree-day is the maximum of zero and the difference between the average daily temperature and 65 F. 6-15
Table 6.3 Heating degree-day futures prices, October 1, 2007. Source: Chicago Mercantile Exchange In all three cities, the period December through February is expected to be the coldest, and the futures price rises with latitude. 6-16
Housing Futures Residential real estate futures, introduced by the CME in May 2006, are futures contracts that settle based on city-specific indexes of real estate prices. These contracts settle quarterly and are based on indexes constructed by S&P/Case-Shiller for 20 metropolitan areas in the United States. Figure 6.8 Specifications for the CME housing futures index contract. 6-17
Chapter 6 Additional Art
Equation 6.1 6-19
Equation 6.2 6-20
Equation 6.3 6-21
Figure 6.4 A hypothetical forward curve for corn, assuming the harvest occurs at years 0, 1, 2, etc. 6-22
Equation 6.4 6-23
Equation 6.5 6-24
Equation 6.6 6-25
Equation 6.7 6-26
Equation 6.8 6-27
Figure 6.6 Specifications for the NYMEX Henry Hub natural gas contract. 6-28
Equation 6.9 6-29
Table 6.4 Real estate futures prices for several cities, October 1, 2007. Source: Chicago Mercantile Exchange 6-30
Equation 6.10 6-31