Lecture 11 Treasury Futures Topics Pricing Delivery Complications for both Multiple assets can be delivered on the same contractunlike commodities The deliverable assets all have different prices ID: 259791
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Slide1
Derivatives
Lecture 11Slide2
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 pricesSlide3
Treasury Futures Specs
Copyright: CME Group 2019Slide4
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 deliverySlide5
Cheapest to Deliver
Copyright: Bloomberg Financial Services 2015Slide6
Cheapest to Deliver
Copyright: Bloomberg Financial Services 2015Slide7
Cheapest to Deliver
Copyright: Bloomberg Financial Services 2015Slide8
Cheapest to Deliver
Copyright: Bloomberg Financial Services 2015Slide9
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 downSlide10
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 deliveredSlide11
Accrued InterestSlide12
Bond Price & Accrued Interest
Example
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%?
Price
FV = 1000
Pmt = 20
int
= 3.25
n = 24.50
Solve for PV = $781.20 Quoted Price = 78.12Slide13
Bond Price & Accrued Interest
Example (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 PriceSlide14
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. Slide15
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%?
Using exact dates on a HP12c provides 82.824Slide16
Futures “Cash Price”
Also called the Adjusted Futures price
Cash Price =
Futures Price x Conversion Factor
Futures Price =
Cash Price / Conversion FactorSlide17
Invoice Amount
(also called Delivery Cost)
Invoice Amount =
Futures Price
x Conversion factor
x Contract Size
+ accrued Interest
Total amount of money exchanged at deliverySlide18
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 Slide19
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%.Slide20
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%.
Price
FV = 1000
Pmt = 25
int = 2.4
n = 18
Solve for PV = $1014.48 Quoted Price = 101.45Slide21
Futures Price
Example (continued)
Compute the price of the 9 month futures contract. Remember the next coupon payment will be made in 6 months.Slide22
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 costSlide23
Cheapest to Deliver
The CTD can be found three ways
Quoted Bond Price – (Futures Price x CF)
Also called the “Gross basis”
Select the lowest
Invoice Amount (lowest)
Also called the “Delivery Cost”
Highest Repo Rate
The interest rate earned by short selling a security and buying it back later. Slide24
Cheapest To Deliver
Theoretical Futures Price (FP)?
3 Ways to Derive CTD
1 – Highest Repo Rate
(
The interest rate earned by short selling a security and buying it back later. )
2 - Calculate Futures Delivery Spot Price
3 - Cost of Delivery (“Gross Basis”)
Accrued interest and others itemsSlide25
Cheapest To Deliver
Example
Two 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 bondSlide26
Q: If YTM = 5%, which will you deliver and what is its price?
A:
CF Bond Price FC Spot Price
9.875Nov38 1.51 171.05 113.28
7.25May39 1.17 133.09 113.75
Deliver 9.875 Nov38
Cheapest To DeliverSlide27
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 72.03
7.25May39 1.17 82.36 70.39
Deliver 7 1/4 May39
Cheapest To DeliverSlide28
Cheapest To Deliver
Q: 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) = -32.47
7 1/4May39 CTD = 103.00 - (110.5 x 1.17) = -26.29
Implied Repo Rate
Cost of Carry