1. Futures Introduction

2. Futures Usage Usage Hedgers Hedgers Speculators Speculators Trading Environment Trading Environment Open-Outcry Auction Open-Outcry Auction CBOT, CME, NYMEX, NYBOT, Intls. CBOT, CME, NYMEX, NYBOT, Intls.

3. Marking-to-market & Margin Marking-to-market is daily settling up: Marking-to-market is daily settling up: Margin: Initial vs Maintenance Margin Margin: Initial vs Maintenance Margin

4. Convergence of Futures to Spot Time (a)(b) Futures Price Futures Price Spot Price

5. Forwards Specifications: Specifications: Contract Size, delivery date, trading and delivery location and timetables, pricing, cash flows, and deposits All aspects negotiable! Contract Size, delivery date, trading and delivery location and timetables, pricing, cash flows, and deposits All aspects negotiable! Pricing Relation with Futures: Pricing Relation with Futures: Arbitrage Pricing as sequence of daily rolled futures Arbitrage Pricing as sequence of daily rolled futures If Interest Rates are known then Arbitrage holds If Interest Rates are known then Arbitrage holds If Rates are unknown, then relation is floor If Rates are unknown, then relation is floor

6. Pricing and Examples Basis: Spot Price - Futures Price Basis: Spot Price - Futures Price Cash and Carry (Reverse Cash and Carry) Cash and Carry (Reverse Cash and Carry) Examples Examples

7. Futures Pricing Pricing is a result of convergence to the future spot price and arbitrage relations. Pricing is a result of convergence to the future spot price and arbitrage relations. In general: F 0 = S 0 (1 + r) T F 0 = Futures Price at time 0 S 0 = Spot Price at time 0 r = cost of carry (risk-free) T = Time to expiration (Add Storage and Transportation for commodities!)

8. Futures Pricing Example Current Gold Price is $400 per ounce. Risk-free rate is 5%. Time to expiration of futures contract is 3 months. F 0 = S 0 (1 + r) T F 0 = $400(1+.05) (3/12) F 0 = $404.91

9. Cash and Carry Back to Gold Example: Expected Futures was $404.91. What if futures in market is $410, and gold is still on spot market at $400? Assume r=5%, and T=3 months. Back to Gold Example: Expected Futures was $404.91. What if futures in market is $410, and gold is still on spot market at $400? Assume r=5%, and T=3 months. Borrow $400. Buy Gold. Store it. Sell Futures at $410. Borrow $400. Buy Gold. Store it. Sell Futures at $410. Expiration: Expiration: Spot Gold is $425. Sell Gold, get $425. Pay Loan:$400(1+.05) (3/12) = $404.91. Net $20.09 on Gold and Loan. Short Futures Lost $15, Overall Net = $5.09. Spot Gold is $425. Sell Gold, get $425. Pay Loan:$400(1+.05) (3/12) = $404.91. Net $20.09 on Gold and Loan. Short Futures Lost $15, Overall Net = $5.09. Spot Gold is $375. Sell Gold, get $375. Pay Loan:$400(1+.05) (3/12) = $404.91. Net Loss $29.91 on Gold and Loan. Short Future Gains $35, Overall Net = $5.09 Spot Gold is $375. Sell Gold, get $375. Pay Loan:$400(1+.05) (3/12) = $404.91. Net Loss $29.91 on Gold and Loan. Short Future Gains $35, Overall Net = $5.09

10. Reverse Cash and Carry Again the Gold Example: Expected Futures was $404.91. What if futures in market is $390, and gold is still on spot market at $400? Assume r=5%, and T=3 months. Again the Gold Example: Expected Futures was $404.91. What if futures in market is $390, and gold is still on spot market at $400? Assume r=5%, and T=3 months. Short Gold at $400. Buy $400 in T-Bills. Buy Futures at 390. Short Gold at $400. Buy $400 in T-Bills. Buy Futures at 390. Expiration: Expiration: Spot Gold is $450. Short Gold lost $50, but T-Bills returned $4.91 and Expiring Futures racked up $60 marking-to-market. Net Gain $14.91. Spot Gold is $450. Short Gold lost $50, but T-Bills returned $4.91 and Expiring Futures racked up $60 marking-to-market. Net Gain $14.91. Spot Gold is $350. Short Gold gained $50 and T- Bills returned $4.91, but Expiring Futures lost $40 marking-to-market. Net Gain $14.91. Spot Gold is $350. Short Gold gained $50 and T- Bills returned $4.91, but Expiring Futures lost $40 marking-to-market. Net Gain $14.91.

11. Other Futures Pricing T-Bond Futures Pricing T-Bond Futures Difference between 2 T-Bond Futures Prices should be accrued interest and Cost-of-Carry Difference between 2 T-Bond Futures Prices should be accrued interest and Cost-of-Carry Cost of Carry = 3 month T-Bill = 5.25% (yrly) Cost of Carry = 3 month T-Bill = 5.25% (yrly) June T-Bond Fut = Mar T-Bond Fut *(1+CofC) - Accrued Interest = 120 14/32 * (1+.0525).25 -.075*100*1/4 = 120.12 Note: Quote was 120 3/32Difference due to current 3 mo T-Bill and AI June T-Bond Fut = Mar T-Bond Fut *(1+CofC) - Accrued Interest = 120 14/32 * (1+.0525).25 -.075*100*1/4 = 120.12 Note: Quote was 120 3/32Difference due to current 3 mo T-Bill and AI

12. Other Futures Pricing Stock Index Futures: Pricing Stock Index Futures: Futures = Current Index*(1+CofC) - Sum Discd Divs Futures = Current Index*(1+CofC) - Sum Discd Divs Div Yield on S&P 500 is 1.5% Div Yield on S&P 500 is 1.5% CofC is 5.25% CofC is 5.25% Current Index = 969.02 Current Index = 969.02 969.02*(1+.0525).33 -.015/3*969.02 /(1+.0525).33 = 980.76; 983.2 969.02*(1+.0525).33 -.015/3*969.02 /(1+.0525).33 = 980.76; 983.2