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Derivatives - PowerPoint Presentation

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Derivatives - PPT Presentation

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

bond price deliver futures price bond futures deliver cheapest delivery interest amount conversion factor ytm accrued coupon cash quoted treasury prices contract

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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