Calculation of Conversion Factor [ New study notes Hull ]

[srini]

Hi @David Harper CFA FRM
page: 89

I can't get the bond price for the bond#2 $123.99.
FV = $100
PMT = 8/2 = 4
I/Y = 6/2 = 3
N = 18.250 * 2 = 36.5
CPT PV = 122.0009817

Am i missing something here? please clarify.

thanks

 

[David Harper CFA FRM]

Hi @srini Per the notes (I though Deepa did a great job of summarizing here!) the calculation of the conversion factor (CF) is a special situation of applying the specific rules due to need of the exchange to produce comprehensive tables. Please note the test (at the top of age 89):

• If, after rounding, the bond lasts for an exact number of 6-month periods, the first coupon is assumed to be paid in 6 months.
• If, after rounding, the bond does not last for an exact number of 6-month periods (i.e., there are an extra 3 months), the first coupon is assumed to be paid after 3 months and accrued interest is subtracted.

In the case of the bond with 18 years and 4 months to maturity, therefore, we are applying the second rule ("the first coupon is assumed to be paid after 3 months and accrued interest is subtracted"). First, the bond is rounded down to the nearest three months (ie, 0.25 years), which is 18.250 years (as displayed). Then it is priced as a bond in three months (+ 0.25 years) but where the first coupon is also paid immediately (in three months), so the price is the $4.00 coupon plus (+) $121.83 <-- N = 18*2 = 36, I/Y = 6/2 = 3, PMT = 8/2 = 4, FV = 100 and CPT PV = $121.83 such that the price in three months = $121.83 + $4.00 = $125.83; but that is three months forward, so it is discounted to today with $125.83/(1+6.0%/2)^(0.25*2) = $123.9862 (displayed as price $123.99). Accrued interest is subtracted to produced $121.99 and CF = 1.2199. I hope that clarifies!

 

[srini]

thanks @David Harper CFA FRM . i will go through this calculation one more time.

 

[Scopur]

Hi @srini Per the notes (I though Deepa did a great job of summarizing here!) the calculation of the conversion factor (CF) is a special situation of applying the specific rules due to need of the exchange to produce comprehensive tables. Please note the test (at the top of age 89):


In the case of the bond with 18 years and 4 months to maturity, therefore, we are applying the second rule ("the first coupon is assumed to be paid after 3 months and accrued interest is subtracted"). First, the bond is rounded down to the nearest three months (ie, 0.25 years), which is 18.250 years (as displayed). Then it is priced as a bond in three months (+ 0.25 years) but where the first coupon is also paid immediately (in three months), so the price is the $4.00 coupon plus (+) $121.83 <-- N = 18*2 = 36, I/Y = 6/2 = 3, PMT = 8/2 = 4, FV = 100 and CPT PV = $121.83 such that the price in three months = $121.83 + $4.00 = $125.83; but that is three months forward, so it is discounted to today with $125.83/(1+6.0%/2)^(0.25*2) = $123.9862 (displayed as price $123.99). Accrued interest is subtracted to produced $121.99 and CF = 1.2199. I hope that clarifies!

This was really helpful. Perhaps in the note you could change it to [if three] PV + Coupon Payment? The 0.25 was confusing.

 

[David Harper CFA FRM]

Hi @Scopur Yes, good point (I myself couldn't now recall what the +0.25 signified, and I wrote it). Tagged as such for non-urgent revision

 

[ktrathen]

I was wondering if this calculation has ever come up in actual exam. All the practice exams seem to give you a few bonds and their conversion factors, and ask us to calculate the CTD. What's the chance we'll have to do the whole thing on the exam given that it is quite tedious?

 

[David Harper CFA FRM]

@ktrathen I do agree with your inference but GARP has decided to write the LO in this way ...

Explain and calculate a US Treasury bond futures contract conversion factor.

... and they've had ten years to change it. Ten years of deciding to retain the "calculate". Would I write different LOs? Yes I would!

 

[ktrathen]

@ktrathen I do agree with your inference but GARP has decided to write the LO in this way ...

... and they've had ten years to change it. Ten years of deciding to retain the "calculate". Would I write different LOs? Yes I would!

Thanks. I think the most likely two questions are 1) choosing the CTD bond from a list of alternatives with their CF, and 2) explaining what type of bond will be CTD given yields lower/higher than 6%.