FUTURES

1. FUTURES

2. Definition • Futures are marketable forward contracts. • Forward Contracts are agreements to buy or sell a specified asset (commodities, indices, debt securities, currencies, etc.) at an agreed-upon price (f) for purchase or delivery on a specified date (delivery date: T).

3. Futures Exchanges • Futures are traded on organized exchanges: • CBOT • CME • NYFE • The exchanges provide marketability: • Listings • Standardization • Position Traders • Clearinghouse

4. Futures Positions • Long Position: Agreement to buy. • Short Position: Agreement to sell. • Long Hedge: Taking a long position in futures to protect against a price increase. • Short Hedge: Taking a short position in a futures to protect against a price decrease.

5. Clearinghouse Like the OCC, the futures clearinghouse guarantees each contract (both long and short positions) and acts as an intermediary, breaking up each contract after it has been established.

6. Example • Suppose A buys a September Wheat Futures contract (5,000 bu.) from B for fo = $2.50/bu. • A is long; B is Short • After the contract is established, the CH steps in and breaks up the contract.

7. CH Records • A agrees to buy at $2.50. • B agrees to sell at $2.50.

8. Example Continued • Suppose the price of wheat increases, causing the September futures price to increase to ft = $3.00. • Suppose A decides to close by going short. • New Contract: A agrees to sell September Wheat futures at $3.00 to C. • A is short; C is long. • After the contract is established, the CH breaks it up.

9. CH Records • A agrees to buy at $2.50. • B agrees to sell at $2.50. • A agrees to sell at $3.00. • C agrees to buy at $3.00.

10. At Expiration • In the absence of arbitrage, the price on an expiring futures contract must be equal to the spot price.

11. Example Continued • At the September expiration, suppose the spot price of wheat is at $3.50/bu. • B is short and needs to close by going long (B is not a farmer). • C is long and needs to close by going short (C does not need 5000 bu of wheat). • New Contract: B agrees to buy September Wheat (that is expiring) from C for $3.50. • CH breaks up the contract.

12. CH Records • B agrees to sell at $2.50. • C agrees to buy at $3.00. • B agrees to buy at $3.50. • C agrees to sell at $3.50.

13. Long Futures Hedge • Take long position in futures to protect against an increase in the spot price. • EXAMPLE: • OJ distributor plans to buy 15,000 lbs of frozen OJ in September. To protect against an increase in the spot price of OJ, the distributor goes long in one OJ futures contract (size = 15,000 lbs) at fo = $0.96/lb. • At delivery, the distributor buys OJ on the spot market at the spot price and closes the futures position by going short in the expiring futures at a futures price equal to the spot price.

14. Cost at T

15. Short Futures Hedge • Take short position in futures to protect against a decrease in the spot price. • EXAMPLE: • Wheat farmer plans to sell 5000 bu. of wheat in September. To protect against a decrease in the spot price, the farmer goes short in a September wheat futures at fo = $2.40 • At delivery, the farmer sells wheat on the spot market at the spot price and closes the futures position by going long in the expiring futures at a futures price equal to the spot price.

16. Revenue at T

17. Hedging Risk Quantity Risk Quality Risk Timing Risk

18. Speculative Positions • Pure Outright Position: • Long Position (Bullish) • Short Position (bearish) • Spread • Intracommodity Spread: long and short in futures on the same underlying asset but with different expirations. • Intercommodity Spread: Long and short in futures with different underlying assets but the same expiration.

19. Initial Margin Requirements • Initial Margin: Cash or RF securities that must be deposited with the broker to secure the position. Initial margin (Mo) is equal to a porportion (m) times the contract value. • Example: September wheat contract at fo = $2.40 (long or short) with m = .10:

20. Maintenance Margin Requirements • Maintenance Margin: Keep the equity value of the commodity account (Eq) equal to a proportion (90% to 100%) of initial margin.

21. Example • September wheat prices increase from $2.40 to $2.42. With a 100% maintenance margin requirement, a long position would be overmargined and a short position would be undermargined:

22. Undermargined Positions • If an account is undermargined, the investor must deposit additional funds to satisfy the maintenance margin requirement. If the investor does not do this, then she will receive a margin call from the broker instructing her that her account will be closed unless she deposits the requisite funds. • When the equity value of the account meets the maintenance margin requirement, the account is said to be marked to market.

23. Other Points • Equity accounts are adjusted daily. • Futures Funds are often set up where the funds of investors are used to buy RF securities which the fund uses to satisfy the margin requirements for the futures. Such funds can be viewed as overmargined futures positions.

24. Futures Pricing • Basis (B): • Carrying Cost Model: Equilibrium futures price is equal to the net cost of carrying the underlying asset to expiration. This relation is governed by arbitrage.

25. Pricing Futures on PDB • Let So = spot price of PDB with maturity of 91 days + T; Rf = RF rate or repo rate with maturity of T; fo = price of PDB futures expiring at T.

26. Example • Price on spot PDB maturing in 161 days is So = 97.5844; 70-day RF rate is 6.38%. • Equilibrium price of PDB futures with expiration of 70 days (or T= 70/365):

27. Arbitrage • Overpriced: • If the market price of PDB futures is at 99, an arbitrageur could earn a riskless profit of 99-.98.74875 = 0.25125 (times $1M) by: • Borrowing $97.5844 at Rf = 6.38% , then buying 161-day SPOT PDB at So = 97.5844; • taking short position in a PDB futures expiring in 70 days at fm = 99. • At T, the arbitrageur would sell the spot PDB on the futures (it would now have a maturity of 91 days) and pay off her loan.

28. Arbitrage • Underpriced: • If the market price of PDB futures is at 98, an investor holding 161-day spot PDB could earn a riskless profit of 98.74875-98 = 0.74875 (times $1M) by: • Selling the PDBs for $97.5844, then investing the proceeds in RF security for 91 days at Rf = 6.38%; • taking long position in a PDB futures expiring in 70 days at fm = 98. • At T, the arbitrageur would buy the spot PDB on the futures (it would now have a maturity of 91 days) for 98 and receive 98.74875 from her investment.

29. Pricing Futures on Stock Portfolio • Carrying Cost Model:

30. Pricing Commodity Futures • Carrying Cost Model:

31. Example: Pricing Commodity Futures • In June, the spot price of a bushel of wheat is $2.00, the annual storage cost is $0.30/Bu, Rf = 8%, and transportation cost of transporting wheat from the destination point on the futures contract to a grain elevator is $0.01/bu. The equilibrium price of a September wheat futures (T = .25) is $2.124/bu:

32. Pricing Relation Between Futures with Different Expirations • Carrying Cost Model:

33. Financial Futures • Stock Index Futures • Foreign Currency Futures • Debt Securities

34. Stock Index Futures • Types: • SP 500 (CME, Multiplier = 500) • MMI (CBT, Multiplier = 250) • SP OTC (CME, Multiplier = 500) • Cash Settlement Feature • Multiplier • Use: Speculation, hedging, and portfolio management.

35. Hedging Portfolio Future Value Example: • Portfolio manager plans to liquidate a $50M portfolio in September. The portfolio is well-diversified with a beta of 1.25. The current S&P 500 is at 1250 and there is a September S&P 500 futures index trading at fo = 1250. (Note futures and spot prices are usually not equal.) • Hedging Strategy: Go short in 100 September index futures contracts:

36. Hedged Value at T

37. Portfolio Uses • Speculating on Unsystematic Risk • Market Timing • Dynamic Portfolio Insurance

38. Pricing Stock Index Futures • Let So = spot price of stock index (S&P 500); Rf = RF rate or repo rate with maturity of T; D = dividend per share on portfolio underlying the index which can be estimated from a proxy portfolio; fo = price of index future expiring at T.

39. Proxy Portfolio • Stock Index futures are often priced in terms of a proxy portfolio. A Proxy portfolio is a portfolio which is highly correlated with the index (could be 30-stock portfolio or a MF). This portfolio can be viewed as equivalent to holding hypothetical shares in the index. • For example, if the S&P 500 is at 1200, a $10M well-diversified portfolio with a beta of 1 and expected dividends at T worth $250,000 could be viewed as owning 8333.333 hypothetical index shares that are selling at $1200 per share and paying a dividend per share of $30.

40. Example • Spot index (S&P 500) is at 1200 and RF rate is 8% for RF securities maturing in 180 days. • Using the proxy portfolio, the equilibrium price S&P 500 futures with expiration of 180 days (or T= .5 per year:

41. Index Arbitrage • Overpriced: • If the futures were priced at fm = 1245, an arbitrageur could earn a riskless profit by going long in the proxy portfolio and short in the futures: • Borrow $10M and buy portfolio. • Go short in 8333.333/500 = 16.6667 futures.

42. CF at T

43. Foreign Currency Futures • Traded on the IMM. • Futures on major currencies: • DM (125,000) • BP (25,000) • FF (250,000) • Use: Hedging and speculation.

44. Pricing Currency Futures • Carrying cost for currency futures is the interest rate parity model discussed in many international text:

45. Pricing Currency Futures

46. Pricing Currency Futures • Covered Interest Arbitrage:

47. IRPT and Cutoff Exchange Rate • Use the IRPT to determine the cutoff expected exchange rate for determining whether to invest in domestic or foreign RF security.

48. IRPT and Cutoff Exchange Rate • Example:

49. IRPT and Cutoff Exchange Rate • Use Ef from IRPT as curtoff rate:

50. Cross Exchange Rate Relation • Cross Rates: