Welcome to the help document of the calculator of the CGB futures contract!
The calculator identifies the cheapest-to-deliver bond of the Ten-year Government of Canada
Bond futures, CGB, and computes the following values :
 The implied repo rate;
 The net basis;
 The CGB theoretical price;
 The conversion factors.
The calculator is divided in three parts:
 CGB futures contract;
 Deliverable bonds of the CGB futures contract;
 Output results.
For additional informations on the futures contract CGB, please consult the reference manual on
http://www.m-x.ca/f_publications_en/interest_rate.pdf
N.B : It is necessary to use the comma in all inputs of the model where decimal numbers
are involved, for example: 0,01
1. CGB FUTURES CONTRACT
In this part, the user enters all of the following data concerning the futures contract :
Futures price : CGB market price.
Actual repo rate : Financing rate on the maturity period of the specific CGB contract.
Settlement date : Date when the calculation is performed plus 3 business days. For example,
if today’s date is August 05, 2003 and it is the date of computation, the settlement date is
August 08, 2003.
Last day of delivery of the CGB : the last business day of the delivery month.
For example, the last day of delivery of the September 03 CGB contract is September 30,
2003.
Present value factor : we use the factor «actual / 365» for the CGB futures contract.
2. BONDS
Coupon rate: the interest rate of the periodic coupon paid by the bond, in decimals terms.
For example, if the coupon rate of the Government of Canada bond maturing on June 1 2011
is 6%, write in decimals 0,06. Only semi-annual coupon-bearing bonds are considered in the
calculator.
Maturity date: date of maturity of the bond.
Market price of the bond
3. OUTPUT RESULTS
Implied repo rate : The risk-free rate used by market participants in the futures market. It is
computed using the following equation :
(P + A1) ( 1 + r D1 / FA)
= C (1 + r D2 / FA)
+ DP + A2
cost of buying and financing the bond = coupon and reinvestment
+cash-flows received from the delivery of the contract
In developing the above formula, we find the value of implied repo rate using
the following equation:
Implied repo rate = [ DP + A2 – ( P + A1) + C ] / [( P + A1) ( D1 / ACT ) – C ( D2 / ACT)]
Where :
P = purchase price of the bond.
A1 = accrued interest at the purchasing date.
D1 = number of days between the purchasing date and the date of delivery of the contract.
C = coupon.
D2 = number of days between the coupon date and the date of delivery of the futures contract.
DP = delivery price.
A2 = accrued interest of the bond at the delivery date of the futures contract.
Net basis : The difference between the theoretical price and the market price of the futures
contract.
Theoretical price of the futures contract : computed using the implied repo rate of the
chapeast-to-deliver bond.
The conversion factor : the conversion factor brings all eligible deliverable bonds on the
same footing at delivery. It is computed for each deliverable bond in determining the price at
which each bond will have a yield-to-maturity equal to the notional coupon of the underlying
bond of the CGB contract, i.e. 6%
Cheapest-to-deliver : The bond which has the highest implied repo rate (identified in grey
color).
REFERENCES :
 Bloomberg
 http://www.m-x.ca/f_publications_fr/taux_interet.pdf
 http://www.m-x.ca/invest_inst_cgb_fact_fr.php