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Chapter 15

Chapter 15. Bond Futures. Treasury Bond Futures. 0. Delivery date. n. at least 15 years. $100,000 par per contract. Cheapest to Deliver. There are many deliverable bonds. This prevents anyone from buying up all the deliverable bonds (cornering the market) and manipulating prices.

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Chapter 15

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  1. Chapter 15 Bond Futures

  2. Treasury Bond Futures 0 Delivery date n at least 15 years $100,000 par per contract

  3. Cheapest to Deliver 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.

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

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

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

  7. Futures Price before the Delivery Date

  8. Assume One Deliverable Bond with Maturity of 2 Years and Delivery Date in 1 Year Delivery date 0 1 2 F C + PAR C + PAR1 + f0,2 F = If R0,1 = 0.04, R0,2 = 0.08, f0,2 = 12.15%, C = $8, par = $100

  9. Express Futures Price in Terms of Spot Price 0 1 2 Long Spot -P0 C C + PAR Short C +C[PV1] -C Net -[P0 - C(PV1)] 0 C + PAR Time 1 Value -[P0 - C(PV1)](1 + R0,1) -[P0(1 + R0,1) - C]

  10. Bond Maturity = 3 Periods, Delivery = Time 1 Delivery date 0 1 2 3 -F C C + PAR

  11. In Terms of Spot Price Delivery date 0 1 2 3 +C +C + PAR Long Spot -P0 +C Short C +C[PV1] -C Net -[P0 - C(PV1)] 0 +C +C + PAR Time 1 Value = = -[P0 - C(PV1)](1 + R0,1) -[P0(1 + R0,1) - C]

  12. Bond Maturity = 3 Periods, Delivery = Time 2 Delivery date 0 1 2 3 -F C + PAR

  13. In Terms of Spot Price Delivery date 0 1 2 3 C C + PAR Long Spot -P0 C Short Coupons +C[PVA2] -C -C Net -[P0 - C(PVA2)] 0 0 C + PAR Time 2 Value = -[P0 - C(PVA2)](1 + R0,2)2

  14. If Delivery is at Time d

  15. Short Hedging with Financial Futures

  16. Short Hedge Close Deliverydate 0 Time Buy Spot-P0 Sell Spot+P1 ShortFutures +F0 LongFutures -F1 Net = [-P0 + P1] + [F0 - F1] = [Spot] + [F] = [-100 + 95] + [96 - 92] = [-5,000] + [4,000] = -1,000 = Net loss.

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