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Futures Introduction

Futures Introduction. Futures. Usage Hedgers Speculators Trading Environment Open-Outcry Auction CBOT, CME, NYMEX, NYBOT, Int’ls. Marking-to-market & Margin. Marking-to-market is daily settling up: Margin: Initial vs Maintenance Margin. Convergence of Futures to Spot. Futures Price.

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Futures Introduction

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  1. Futures Introduction

  2. Futures • Usage • Hedgers • Speculators • Trading Environment • Open-Outcry Auction • CBOT, CME, NYMEX, NYBOT, Int’ls.

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

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

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

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

  7. Futures Pricing • Pricing is a result of convergence to the future spot price and arbitrage relations. In general: F0 = S0 (1 + r)T (Add Storage and Transportation for commodities!) F0 = Futures Price at time 0 S0 = Spot Price at time 0 r= cost of carry (risk-free) T = Time to expiration

  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. F0 = S0 (1 + r)T F0 = $400(1+.05)(3/12) F0 = $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. • Borrow $400. Buy Gold. Store it. Sell Futures at $410. • 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 $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. • Short Gold at $400. Buy $400 in T-Bills. Buy Futures at 390. • 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 $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 • 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) • 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 3/32 Difference due to current 3 mo T-Bill and AI

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

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