Forward and Futures: Treasury bond futures

Question 1

What makes bond futures different from stock index futures?

Answer 1

1. The underlying asset is not a basket of securitites, but one bond in a basket of relatively similar bonds
2. The contract is settled through physical delivery rathen than cash settlement
3. At maturity the seller decides which bond (within the set of deliverable bonds) he wants to deliver to the buyer
4. Since the actual bond that will be delivered is not known and deliverable bonds are different, the futures price is referred to an ideal(non-existing!) bond with certain characteristics (notional bond)…
5. …so when “real” bonds are delivered, the price paid by the buyer must be adjusted by a conversion factor

Question 2

What is the EDSP?

Answer 2

The EDSP is the exchange delivery settlement price, or the “final” price in the last trading day for a bond futures contract

Question 3

What is the invoice price for a bond future?

Answer 3

1. At delivery the buyer pays the invoice price IP, which is given by”
   IP = EDSP * CF + AI
   where
   EDSP = Exchange delivery settlement price
   CF = conversion factor
   AI = acrrued interest at delivery date

The CF should be:
>1 if delivered bond value is higher than notional bond value
‘<1’ in the opposite case

Question 4

What are the key factors in determining the conversion factor used in calculating the invoice price for a bond future?

Answer 4

Key factors: coupon + (as a second-order factor) time to maturity

Question 5

How is the conversion factor used in invoice price calculated?

Answer 5

CF = P_{deliverable bond}(DD, r)/P_{notional bond}(DD, r)

P is forward price calculated at each delivery date (DD) of the future, r is the rate equal to the coupon rate of the notional bond

Question 6

What is CTD in a bond future?

Answer 6

CTD stands for cheapest to deliver for the seller.

DD stand for delivery date
S_DD,i is the clean price at delivery of bond i

Question 7

How to find the CTD bond at maturity date?

Answer 7

The cheapest bond at maturity is the one maximizing:
Invoice price (IP_i) - P_DD,i (Price on delivery date)
Simplified maximize:
EDSP * CF_i - S_DD,i

DD stand for delivery date
S_DD,i is the clean price at delivery of bond i

Question 8

How to find the CTD bond before maturity date?

Answer 8

Before the delivery date the CTD bond is the one that maximizes
F * CF_i - S_T,i

Where F is the future price
CF is conversion factor
S_T,i is the clean price of the forward

Question 9

How to see if there are arbitrage opportunities for bond futures in terms of value basis?

Answer 9

Value basis:
S_T - F * CF
Value (net) basis equal to zero -> future trading at its fair value (S_T - F * CF = 0)
Value basis < 0 overvalued

S_T is the clean price of the forward

Question 10

How do we tell the cheapest to deliver bond with repo rate?

Answer 10

The CTD bond is the one maximizing the implied repo rate.

Repo rate is precise and theoretically correct measure.

Question 11

What is the min S_T/CF method?

Answer 11

We can find the cheapest to deliver bond by seeing the bond that minimizes S_T/CF