1. 15-1 Chapter 15 Bond Futures

2. 15-2 Treasury Bond Futures Delivery date at least 15 years n0 $100,000 par per contract

3. 15-3 There are many deliverable bonds. This prevents anyone from buying up all the deliverable bonds (cornering the market) and manipulating prices. But it adds a complication. The value of each bond in delivery must be specified by some formula. The “cheapest to buy” is the bond that would cost the least to buy and deliver. The cheapest to deliver sets the price of the futures contract. Cheapest to Deliver

4. 15-4 Quoting Treasury Bond Futures Quoted per $100 par in 32 nds. Thus,

5. 15-5 Computing Changes in Futures Quotes zTransform to dollars and cents: 99 – 17=99,531.25 – 99 – 15=99,468.75 $62.50 zCompute the change in 32 nds and multiply by $31.25: 99 – 17 – 99 – 15 2  31.25 = $62.50

6. 15-6 Futures Price on the Delivery Date Converges to the Spot Price on the Delivery Date.

7. 15-7 Futures Price before the Delivery Date

8. 15-8 Assume One Deliverable Bond with Maturity of 2 Years and Delivery Date in 1 Year Delivery date F 0 If R 0,1 = 0.04, R 0,2 = 0.08, f 0,2 = 12.15%, C = $8, par = $100 12 F = C + PAR C + PAR 1 + f 0,2

9. 15-9 Express Futures Price in Terms of Spot Price C 012 -C C + PAR -P 0 Long Spot +C[PV 1 ]Short C Net-[P 0 - C(PV 1 )]0 -[P 0 - C(PV 1 )](1 + R 0,1 )Time 1 Value -[P 0 (1 + R 0,1 ) - C]

10. 15-10 Bond Maturity = 3 Periods, Delivery = Time 1 C 012 C + PAR-F 3 Delivery date

11. 15-11 In Terms of Spot Price +C 012 +C + PAR 3 +C -C +C + PAR -P 0 Long Spot +C[PV 1 ]Short C Net-[P 0 - C(PV 1 )]0 -[P 0 - C(PV 1 )](1 + R 0,1 )Time 1 Value= = -[P 0 (1 + R 0,1 ) - C] +C Delivery date

12. 15-12 Bond Maturity = 3 Periods, Delivery = Time 2 012 C + PAR-F 3 Delivery date

13. 15-13 In Terms of Spot Price C 012 C + PAR 3 C -C C + PAR -P 0 Long Spot +C[PVA 2 ]Short Coupons Net-[P 0 - C(PVA 2 )]0 -[P 0 - C(PVA 2 )](1 + R 0,2 ) 2 Time 2 Value= 0 Delivery date -C

14. 15-14 If Delivery is at Time d

15. 15-15 Short Hedging with Financial Futures

16. 15-16 Short Hedge Net= [-P 0 + P 1 ] + [F 0 - F 1 ] = [  Spot] + [  F] = [-100 + 95] + [96 - 92] = [-5,000] + [4,000] = -1,000 = Net loss. 0 Close Time Sell Spot +P 1 Buy Spot -P 0 Short Futures +F 0 Delivery date Long Futures -F 1