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# Working out conversion factors for Treasury Bond Futures.

Discussion in 'Trading' started by Paul_G, Feb 16, 2009.

1. ### Paul_G

Hi all,

There's something that I just can't make sense of and would appreciate some help.

When calulating the conversion factor for a Treasury Bond Future, we round down the maturty date to the nearest 3 months period. So we can have the situation where there is an extra 3 months when we semi annualize the bonds present value.

Now the example in Hull is confusing me. I've attached a spreadsheet that shows the present value of the bond. This is in cells M2661 on sheet1. I've scanned in the formula that hull uses from his book and placed it on the sheet. Both prices are the values of \$125.83

However, the things I don't understand are:
1. The pricing of the bond, according to the Hull text, is to 3 months time. I believe that the bond is actually calculated to discount to the present time not 3 months!

For example the 1st coupon payment is worked out to be discounted to a factor 0.9708 for a 0.5 period to the present day.

4, 0.5, 0.970873786, 3.883495146

How can Hull work this out to be 3 months??
Surely the 1st time period used for calculating the price would be 0.25 - i.e. 3 months (0.25). This would yield a different price.

2. If you look at the formula scanned in the spreadsheet, he deals with the extra 3 months coupon by simply adding the a coupon payment of 4. How on earth does that add up? Wouldn't the extra 3 months 'at the maturity' of the bond need to be discounted back to a price today?? How can you just add an additional coupon payment not pv'ed or anything.

I can't make head or tails of this.
Any help is really appreciated

Paul

2. ### Paul_G

Dunno if the XL file got attached....

File size:
40.5 KB
Views:
517
3. ### nazzdack

The geeks at wilmott.com can answer "that" if nobody can provide an answer here.

4. ### Paul_G

Hi,

Basically, Hull is examining the cash flows from the 1st coupon payment and so the \$4 is that coupon payment.

If you do the ALL cash flows again and include the \$4 coupon i.e. 37 in total then pv the bond, and then compound it forward 3 months you'll get the price that Hull does. Hull works it out to the 3 months then discounts it back. Effectively the same just one easier to understand

Thanks,
Paul

5. ### nazzdack

As long as you're able to somehow, someway, make money trading bonds with that info, then it's okay.

6. ### EquityGuy4321

Working them out yourself is an pedagogical exercise since it won't help you make money directly. Your time is better spent on other aspects of the futures/cash dynamic. Here is a link to the CBOT/CME website that does the conversion factor calculation for you:

http://www.cbot.com/cbot/pub/cont_detail/0,3206,1413+20356,00.html

7. ### Paul_G

Hi,

I'm just working through Hull to understand how these things are priced etc. I'm not going to trade these instruments, although I'm a believer in knowing the details of how things are calculated.

Thanks
Paul

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