15-1

Chapter 15

Bond Futures

15-2

Treasury Bond Futures

Delivery date

at least 15 years

n0

$100,000 par per contract

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

15-4

Quoting Treasury Bond Futures

Quoted per $100 par in 32nds. Thus,

.25.31)1000(321

25.531,99$)1000(3217000,991799

15-5

Computing Changes in Futures Quotes

Transform to dollars and cents:

99 – 17 = 99,531.25– 99 – 15 = 99,468.75

$62.50Compute the change in 32nds and

multiply by $31.25:

99 – 17– 99 – 15 2 31.25 = $62.50

15-6

Futures Price on the Delivery Date

Converges to the Spot Price on the Delivery

Date.

15-7

Futures Price before the Delivery Date

15-8

Assume One Deliverable Bond with Maturity of 2 Years and Delivery Date in 1 Year

Delivery date

F

0

If R0,1 = 0.04, R0,2 = 0.08, f0,2 = 12.15%, C = $8, par = $100

1 2

.29.961215.1

1008F

F =

C + PARC + PAR

1 + f0,2

15-9

Express Futures Price in Terms of Spot Price

C

0 1 2

.C)R1(Pf1

PARCF 1,002,0

1 DEL

-C

C + PAR

C + PAR

-P0Long Spot

+C[PV1]Short C

Net -[P0 - C(PV1)] 0

-[P0 - C(PV1)](1 + R0,1)Time 1 Value

-[P0(1 + R0,1) - C]

15-10

Bond Maturity = 3 Periods, Delivery = Time 1

C

0 1 2

.)f1)(f1(

PARCf1

CF3,02,02,0

1 DEL

C + PAR-F

3Delivery date

15-11

In Terms of Spot Price

+C

0 1 2

.)f1)(f1(

PARCf1

CC)R1(PF3,02,02,0

1,001 DEL

+C + PAR

3

+C-C

+C + PAR

-P0Long Spot

+C[PV1]Short CNet -[P0 - C(PV1)] 0

-[P0 - C(PV1)](1 + R0,1)Time 1 Value =

=-[P0(1 + R0,1) - C]

+C

Delivery date

15-12

Bond Maturity = 3 Periods, Delivery = Time 2

0 1 2

.f1

PARCF3,0

2 DEL

C + PAR-F

3Delivery date

15-13

In Terms of Spot Price

C

0 1 2

.C)f1(C)R1(P

)R1)(PVA(C)R1(PF

2,02

2,00

22,02

22,002 DEL

C + PAR

3

C-C

C + PAR

-P0Long Spot

+C[PVA2]Short CouponsNet -[P0 - C(PVA2)] 0

-[P0 - C(PVA2)](1 + R0,2)2Time 2 Value =

0

Delivery date

-C

15-14

If Delivery is at Time d

.)R1)(PVA(C)R1(PF dd,0d,0

dd,00d DEL

15-15

Short Hedging with Financial Futures

15-16

Short Hedge

Net = [-P0 + P1] + [F0 - F1]= [Spot] + [F]= [-100 + 95] + [96 - 92]= [-5,000] + [4,000]= -1,000 = Net loss.

0Close

Time

Sell Spot+P1

Buy Spot-P0

ShortFutures

+F0

Deliverydate

LongFutures

-F1