DerivativesLecture 11

Treasury Futures

Topics Pricing Delivery

Complications for both Multiple assets can be delivered on the

same contract…unlike commodities The deliverable assets all have different

prices

Treasury Futures Specs

Copyright: CME Group 2011

Product“Eligible” Maturity

Face Amount

Min. TickValues

Treasury Futures Pricing

Cheapest to Deliver Delivery = Treasury futures allow the short

position to select which bond to deliver (or sell) to the long futures position.

The short will deliver the bond which is the least costly for the short position to purchase.

This occurs since only 4 contracts are used to hedge all interest rate instruments. Thus, a real underlying asset does not exist.

Certain bonds are “eligible” for delivery

Cheapest to Deliver

Copyright: Bloomberg Financial Services 2015

Cheapest to Deliver

Copyright: Bloomberg Financial Services 2015

Cheapest to Deliver

Copyright: Bloomberg Financial Services 2015

Cheapest to Deliver

Copyright: Bloomberg Financial Services 2015

Cheapest to Deliver

Conversion Factor Bond prices vary for many reasons

◦ Higher coupons have higher prices◦ Lower coupons have lower prices◦ Longer maturities have higher prices◦ Shorter maturities have lower prices

If you deliver a more expensive bond, the amount you receive at delivery goes up

If you deliver cheap bond, the amount you receive at delivery goes down

Cheapest to Deliver Quoted price = Price of the bond as quoted

in the paper Accrued interest = amount of coupon

earned on a bond since the last coupon payment

Bond Cash Price = (Quoted price of bond X notational amount) + accrued interest

Invoice Amount = Amount of money that is exchanged when a futures contract bond is delivered

Accrued Interest

period during paid Couponperiod in days Total

couponlast since Days Interest Accrued

Bond Price & Accrued InterestExample What is the cash price of a bond that pays a 4%

semiannual coupon and matures in 12 years and three months, if the YTM is 6.5%?

PriceFV = 1000Pmt = 20int = 3.25n = 24.50 Solve for PV = $781.20 Quoted Price = 78.12

Bond Price & Accrued InterestExample (continued) What is the cash price of a bond that pays a 4%

semiannual coupon and matures in 12 years and three months, if the YTM is 6.5%?

Accrued Interest Bond Cash Price

10

20180

90

20.791$

1081.207 Price

Treasury Futures Pricing

Conversion Factor Since the bond we deliver is not specified in the

futures contract, the price of the bond must be standardized.

The conversion factor converts the futures price into a settlement or invoice price.

The conversion factor is the present value of $1 at YTM=6%, assuming coupons are paid semiannual.

Repo Rate Difference between the conversion factor yield of

6% and the coupon on the bond.

Conversion Factor Used to convert futures prices to bond

prices

What is the cash price of a bond that pays a 4% semiannual coupon and matures in 12 years and three months, if the YTM is 6.5%?

100

6%= YTM@ bond of PriceQuotedCF

81837.0100

81.837CF

Using exact dates on a HP12c provides 82.824

Futures “Cash Price” Also called the Adjusted Futures price

Cash Price =Futures Price x Conversion Factor

Futures Price = Cash Price / Conversion Factor

Invoice Amount (also called Delivery Cost)

Invoice Amount = Futures Price x Conversion factorx Contract Size+ accrued InterestTotal amount of money exchanged at delivery

Futures Price Calculation The price of a treasury futures contract. The price is merely the future value of the spot

price of the treasury, less PV of the coupons. This assumes a flat yield curve.

I = present value of coupons

rTeISF )( 00

Futures Price

Example Compute the conversion factor of a bond with

exactly 9 years to maturity a 5% coupon, paid semiannually, and a YTM of 4.8%.

9312.100

12.93100

6%=YTM @ bond of Price Quoted

CF

Futures Price

Example (continued) Compute the quoted price of the bond with exactly

9 years to maturity a 5% coupon, paid semiannually, and a YTM of 4.8%.

PriceFV = 1000Pmt = 25int = 2.4n = 18 Solve for PV = $1014.48 Quoted Price = 101.45

Futures Price

Example (continued) Compute the price of the 9 month futures contract.

Remember the next coupon payment will be made in 6 months.

44.2

5.2 )50.048(.

eI

64.102

)44.245.101( 75.048.0

eF

Cheapest To Deliver

How To Calculate Delivery Cost (steps)1 - Look up the price (FP)2 - Compute “Conversion Factor” (CF)3 - CF x FP x (contract size) + (accrued

interest) = Delivery cost

Cheapest to Deliver

The CTD can be found three ways

1. Quoted Bond Price – (Futures Price x CF)Also called the “Gross basis”Select the lowest

2. Invoice Amount (lowest) Also called the “Delivery Cost”

3. Highest Repo Rate The interest rate earned by short selling a security

and buying it back later.

Cheapest To DeliverTheoretical Futures Price (FP)?

3 Ways to Derive CTD1 – Highest Repo Rate (The interest rate earned by short selling a

security and buying it back later. )

2 - Calculate Futures Delivery Spot Price3 - Cost of Delivery (“Gross Basis”)

FPCF

Price of bond

?

Accrued interest and others items

QPCF

QP FP CF[ ]

Cheapest To DeliverExampleTwo bonds are eligible for delivery on the June 2012 T

Bond Futures K

1 - 9.875Nov38 deliveries on 15th of maturity month

2 - 7.25May39

On June 12, you announce to deliver a bond

Q: If YTM = 5%, which will you deliver and what is its price?

A:CF Bond Price FC Spot Price

9.875Nov38 1.51 171.05 113.287.25May39 1.17 133.09 113.75

Deliver 9.875 Nov38

Cheapest To Deliver

Q: If YTM = 9%, which will you deliver & what is its price?

A:CF Bond Price FC Spot Price

9.875Nov38 1.51 108.76 72.037.25May39 1.17 82.36 70.39

Deliver 7 1/4 May39

Cheapest To Deliver

Cheapest To DeliverQ: If YTM = 7% and the listed futures price is 110.50, which

bond is CTD?

A:9 7/8Nov38 CTD = 134.39 - (110.5 x 1.51) = -32.477 1/4May39 CTD = 103.00 - (110.5 x 1.17) = -26.29

Implied Repo Rate

Cost of Carry