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# Adjusted Sport Price, another way to identify the CTD bond?

#### Steve Jobs

##### Active Member
I was reviewing few questions on the CTD, the solution provided for of them does not calculate the:
=Quoted Bond Price - (Settlement price x CF)

=Quoted Bond Price / CF
and the lowest is selected as CTD

I solved some questions using both ways and the result sometimes is matching and sometimes no. Is this another way to identify the CTD bond or am I missing something here? Have you heard about Adjusted Spot Price before?

#### Steve Jobs

##### Active Member
Hi David,

Thanks, so solving the same question with the correct formula gives the following results:

a ----------b -------c (CF) --d=b*c ---a-d
102.44 ----103.53 ---0.98 ---101.46 ---0.98
106.59 ----103.53 ---1.03 ----106.64 --(0.05)
98.38 -----103.53 ----0.95 ---98.35 ----0.03

Here, is the CTD the second row? and does it the matter if the result of one row is positive while another is negatives?

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi Steve,

Yes, yours is correct (answer B is coincidentally correct). The +/- sign doesn't matter, it's a cost/benefit. You either want to minimize (cost - benefit) or maximize (benefit - cost). Your expression is (cost - benefit): The short position pays the quoted price of 106.59 and then delivers that purchased bond and receives 104.53*1.03 = 106.64, for a net cost of (-0.05) = spend \$106.59 - receive 106.64, which is the lowest cost, in the form of a small profit. Thanks,

#### Steve Jobs

##### Active Member
Thanks David, the CTD identification is clarified but I still don't understand the the whole CTD process and who pays to who and how much. I need to review more practice questions before being able to phrase my confusion.

#### Rolme

##### Member
Subscriber
A question that popped up regarding this exercise was under what circumstances we would have to account for accrued interest.

I realize we are given spot prices already including accrued interest and no settlement date so we couldn't really calculate accrued interest unless we arbitrarily picked a random date - I guess that would work as it'd be the same multiplier for all bonds and therefore CTD relations would remain unchanged? Or are conversion factors not fixed over time so arbitrarily picking a date would not be realistic anyway?

If we were given Quoted price we would have to calculate accrued interest - correct?

thanks,
Roland

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#### ShaktiRathore

##### Well-Known Member
Subscriber
Hi
Different bonds have different CFs associated with them. Under bond futures contract a dealer can deliver any bond with a paeticular CF that minimizes his cost,first dealer shall buy bond to deliver in mkt for Qouted price +AI and deliver it under contract at price CF*settlement price+AI so net cost is Qouted price +AI -( CF*settlement price+AI ) ,AI cancels out to give net cost of Qouted futures price-CF*settlement price. There is no need of AI calculation to get cost and I think CF factor for a bond is fixed remains same over time.

#### Fisuca

##### New Member
Subscriber
Hi Steve, That's an error sourced in a 2011 sample paper, we notified GARP almost two years ago. As i recall, like you suggest, the answer is correct by coincident but not necessarily and that division does not really make sense; e.g.,
Hi David,
Why would that be wrong? Minimizing CF×Settlement-quoted price should be equivalent to maximizing quote price divided by CF right? (As settlement price is like a constant and we divide the whole equation by cf...

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi David,
Why would that be wrong? Minimizing CF×Settlement-quoted price should be equivalent to maximizing quote price divided by CF right? (As settlement price is like a constant and we divide the whole equation by cf...
Yes, you are correct, but the OP refers to GARP's mistake in a prior practice paper where they used the formula Quoted Bond Price / CF to determine the CTD. It's easy to show this is often gives the wrong result. He is referring to their formula as below: