1. Futures Hedging Examples

2. Hedging Examples  T-Bills to Buy with T-Bill Futures  Debt Payment to Make with Eurodollar Futures  Futures in Portfolio Hedging

3. T-Bills, Notes & Bonds  Treasury Securities: < 1 yr. Maturity: T-Bills, Discount Basis >1 yr., < 10 yr. Maturity: T-Notes, Coupon Bond >10 yr. Maturity: T-Bonds, Coupon Bond

4. T-Bills  Pricing (Discount Basis)  (1 - discount*(91/360))*$1million  Mar 19 w/ 27 days to Maturity priced at a discount of 4.68. Price on $1 million Face: (1-.0468(27/360))*$1 million = $996,490

5. T-Bill Futures  Delivery of 91-day T-Bill at maturity date. So, a March futures delivers a June T-Bill.  Pricing on a discount basis, but quoted %.  Feb. 19, March 95.02 ==> discount = 4.98 100 - (4.98*91/360) ----------------------- * $1 million = $987,412 100

6. Hedging a $25MM T-Bill Purchase  Previous T-Bill futures has us buy: $25mill / $987,412 = 25.3187 contracts  If rates at delivery are 5.5%, T-Bills cost: (1-(.055*91/360))*$1mill = $986,097  Futures lost: (986,097 - 987,412)*25.3187 = (33294), leaving $24,966,706 for T-Bills, but this still buys us: $ 24,966,706 / $986,097 = 25.3187 $1mill. T-Bills

7. Hedging a T-Bill Purchase  If rates at delivery are 4.5%, T-Bills cost: (1-(.045*91/360))*$1mill = $988,625  Futures gained: (988,625 - 987,412)*25.3187 = +30,712, leaving $25,030,712 for T-Bills, but this just buys us: $25,030,712/ $988,625 = 25.3187 $1mill. T-Bills  So, whether rates go up or down, buying March T-Bill futures locks in delivery.

8. Eurodollar Futures  Among the most liquid and actively traded futures contracts in the world  Eurodollar: a dollar deposit in a U.S. or foreign bank outside the U.S.  The contract: Underlying: 90-day hypothetical Eurodollar CD Contract Size: $1 mm face value One basis point (.01%) is worth $25 Contract Months: March, June, Sep, Dec, serial months, spot month Maturities: Available through 10 years

9. Hedge Floating Rate Payment  Assume an unknown Floating Rate to be paid in 3-months on $100,000,000.  Short 100 ($1,000,000) Euro$ Futures today at 94.555 (or Yield of 5.445%).  Settle in 3-months at 94.35 or 94.75. Use proceeds from futures to make debt payment.

10. Hedge Floating Rate Payment  Futures settles at spot of 94.35 (5.65%). Floating Payment is.0565*.25*100M = $1,412,500  Futures settles for 94.555-94.35 =.205 (where each.01 = $25), for a gain of 20.5*$25*100 contracts = $51,250  Net Debt Payment = $1,412,500 - $51,250 = $1,361,250

11. Hedge Floating Rate Payment  Futures settles at spot of 94.75 (5.25%). Floating Payment is.0525*.25*100M = $1,312,500  Futures settles for 94.555-94.75 = -.195 (where each.01 = $25), for a loss of -19.5*$25*100 contracts = - $48,750  Net Debt Payment = $1,312,500 + $48,750 = $1,361,250

12. Hedging: Futures  No up front transfer of funds, but daily marking-to-market.

13. Hedging: Futures  Number of Futures Contracts to Hedge is a function of Relation of Portfolio Returns with Index Returns (Portfolio Beta with Index).  Assume a $7 mill. Portfolio that has a Beta of 1.40 with some Index. The Index Futures is currently at 600 and it trades for $500 per Index point. Value portfolio $7,000,000 -------------- *  contracts, or, -------------- * 1.40 = 32.67 contracts Value futures $300,000

14. Hedging: Futures