Lecture 11

Topics  Pricing  Delivery Complications for both  Multiple assets can be delivered on the same contract…unlike commodities  The deliverable assets all have different prices

Copyright: CME Group 2011 Product “Eligible” Maturity Face Amount Min. Tick Values

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

Copyright: Bloomberg Financial Services 2015

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

 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

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 = Solve for PV = $ Quoted Price = 78.12

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 InterestBond Cash Price

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.

 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

 Also called the Adjusted Futures price  Cash Price = Futures Price x Conversion Factor Futures Price = Cash Price / Conversion Factor

Invoice Amount = Futures Price x Conversion factor x Contract Size + accrued Interest Total 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

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%.

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 = $ Quoted Price =

Example (continued)  Compute the price of the 9 month futures contract. Remember the next coupon payment will be made in 6 months.

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

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.

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 items

Example Two bonds are eligible for delivery on the June 2012 T Bond Futures K Nov38 deliveries on 15th of maturity month May39 On June 12, you announce to deliver a bond

Q: If YTM = 5%, which will you deliver and what is its price? A: CFBond PriceFC Spot Price 9.875Nov May Deliver Nov38

Q: If YTM = 9%, which will you deliver & what is its price? A: CFBond PriceFC Spot Price 9.875Nov May Deliver 7 1/4 May39

Q: If YTM = 7% and the listed futures price is , which bond is CTD? A: 9 7/8Nov38CTD = (110.5 x 1.51) = /4May39CTD = (110.5 x 1.17) = Implied Repo Rate Cost of Carry