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 M26:p61 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

    Thanks in advance,
  2. Paul_G


    Dunno if the XL file got attached....
  3. The geeks at can answer "that" if nobody can provide an answer here. :cool:
  4. Paul_G



    Thanks for your reply but I got an answer from - it's a quality site!

    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 :)

  5. As long as you're able to somehow, someway, make money trading bonds with that info, then it's okay. :)
  6. 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:,3206,1413+20356,00.html
  7. Paul_G



    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.