1. 1 Finance School of Management Chapter 14: Forward & Futures Prices Objective How to price forward and futures Storage of commodities Cost of carry Understanding financial futures

2. 2 Finance School of Management Chapter 14: Contents  Distinction Between Forward & Futures Contracts  The Economic Function of Futures Markets  The Role of Speculators  Relationship Between Commodity Spot & Futures Prices  Extracting Information from Commodity Futures Prices  Spot-Futures Price Parity for Gold  Financial Futures  The “Implied” Risk-Free Rate  The Forward Price is not a Forecast of the Spot Price  Forward-Spot Parity with Cash Payouts  “Implied” Dividends  The Foreign Exchange Parity Relation  The Role of Expectations in Determining Exchange Rates

3. 3 Finance School of Management  Two parties agree to exchange some item on a specified future date at a delivery price specified now.  The forward price is defined as the delivery price which makes the current market value of the contract zero.  No money is paid in the present by either party to the other.  The face value of the contract is the quantity of the item specified in the contract times the forward price. Features of Forward Contracts

4. 4 Finance School of Management Features of Forward Contracts  The party who agrees to buy the specified item is said to take a long position, and the party who agrees to sell the item is said to take a short position.  “Customization”, difficulty of “closing out” positions, low liquidity  The risk of contract default, credit risk

5. 5 Finance School of Management Characteristics of Futures  Futures are – standard contracts – immune from the credit worthiness of buyer and seller because exchange stands between traders contracts marked to market daily margin requirements (enough collateral)

6. 6 Finance School of Management Terms  Futures List Open High Low Settle Change Lifetime High Lifetime Low Open Interest 292 294 1/2 289 294 3/4 -7 1/4 326 258 16.168 Monday Aug.5,2007 WHEAT(CBT)5,000bu; cents per bu  Mark-to-market  Margin requirement  Margin call

7. 7 Finance School of Management An Illustration  You place an order to take a long position in a September wheat futures contract on August 4, 1991.  The broker requires you to deposit an initial margin of $1,500 in your account.  On August 5, the futures price closes 7 1 / 4 cents per bushel lower. – You have lost 7 1 / 4 cents*5,000 bushels = $362.50 that day. – Marking to Market: the broker takes that amount out of your account and transfers it to the future exchange, which transfers it to one of the parties who was on the short side of the contract. – If you do not have enough money in your account to meet the margin requirement (variation / maintenance margin), you’ll receive a margin call from the broker asking you to add money. – If you do not respond immediately, then the broker liquidates your position at the prevailing market price.

8. 8 Finance School of Management Spot-Futures Price Parity for Gold  There are two ways to invest in gold. – buy an ounce of gold at S 0, store it for a year at a storage cost of $hS 0, and sell it for S 1. – invest S 0 in a 1-year T-bill with return r f, and purchase a 1-ounce of gold forward, F, for delivery in 1-year.

9. 9 Finance School of Management  The spot price of gold is $300, the storage costs is 2% per year, and the risk-free rate is 8%. – If the forward price is $340 (too high) Arbitrage Opportunities of Forwards: An Illustration

10. 10 Finance School of Management – If the forward price is $320 (too low)

11. 11 Finance School of Management Spot-Futures Price Parity for Gold  A contract with life T: – This is not a causal relationship, but the forward and current spot are jointly determined in the market. – If we know one, then the law of one price determines that we know the other.

12. 12 Finance School of Management Implied Cost of Carry  Implied cost of carry = F − S 0 = (r f + h) S 0  The implied cost of storing the gold (per $spot) is h = (F − S 0 )/S 0 − r f  Suppose F = $330, S 0 = $300, and r f = 8%, then – Implied cost of carry = $330 − 300 = $30 – Implied storage cost = (330 − 300)/300 − 8% = 2%

13. 13 Finance School of Management Financial Futures  Financial futures contracts are usually settled in cash.  With no storage cost, the relationship between the forward and the spot is – Any deviation from this will result in an arbitrage opportunity.

14. 14 Finance School of Management Replication of Non-Dividend-Paying Stock Using a pure Discount Bond and a Stock Forward Contract

15. 15 Finance School of Management Arbitrage in Stock Futures  The spot price of a stock is $100, and the risk-free rate is 8%.  The forward price is $109.

16. 16 Finance School of Management The “Implied” Risk-Free Rate  Rearranging the formula, the implied interest rate on a forward given the spot is – This is reminiscent of the formula for the interest rate on a discount bond.

17. 17 Finance School of Management Replication of a Pure Discount Bond Using a Stock and a Forward Contract

18. 18 Finance School of Management The Forward Price is not a Forecast of the Spot Price  Following the diagrams in Chapter 13 we might suppose that the expected price of a stock is  If this is indeed correct, then the forward price is not an indicator of the expected spot price at the maturity of the forward.

19. 19 Finance School of Management Forward-Spot Parity with Cash Payouts  The S − F relationship becomes – Note: (forward price > the spot price) if (D < r f S) – Because D is not known with certainty, this is a quasi-arbitrage situation.

20. 20 Finance School of Management Replication of Dividend-Paying Stock Using a Pure Discount Bond and a Stock Forward Contract

21. 21 Finance School of Management “Implied” Dividends  From the last slide, we may obtain the implied dividend

22. 22 Finance School of Management Exchange Rate Example Time 15450 ¥ (Repaid) 3% ¥/¥ (direct) 3% ¥/£/£/¥ £109 (Matures) 9%£/£ Forward ¥/£ 15000 ¥ (Borrowed) £100 (Invested) 150 ¥/£ JapanU.K. 15450 ¥ (Repaid) 3% ¥/¥ (direct) 3% ¥/£/£/¥

23. 23 Finance School of Management The Foreign Exchange Parity Relation  We used the diagram to show that