Fecal_tdr, I used the following formula: CASH DV01 = 0.01 * ((0.01 * modified duration of the Cash bond (CTD)) * full price of the Cash bond (CTD)) Then I divided this CASH DV01 by the conversion factor related to the December futures to get the future DV01. Do you have another way to find the Future DV01? Do you find the same numbers?
Laurentc, Did either the 5yr basis or 30yr basis flatten/steepen during this time period (did cash vs. futures relationships reprice)? That should explain why your actual futures profit vs. the theoretical futures profit is different.
That may have been the issue. I do not receive real time Bloomberg data of the CTD, so I follow easily the "gross basis", but not the "net basis". However, I doubt this could have been the real issue, as the 30y is the future that did not move as forecasted, and the CTD of the 30y have not changed from 10/10/06 to November 24, 2006 (to my best knowledge however, as I checked the values only 1 time per day) Do you think of any other "basis move"? The "basis" could also have changed because of the change in forward rates, but without any Fed Fund rate change, the forward rate did not really move for the last 2 months. Do you know where I could get the daily historical forward rates, so that i could check my values? Do you think these little changes can be enough to change so much the results of the spread?
If you calculate the net from the prices you give you get a credit of 770 ticks from the bonds and a debit of 522 from the FV, leaving you with 248 ticks. That's $7750, and now that I stated the obvious, the only conclusion I can come up with is that the yields you calculated on the futures prices are incorrect and the spread must of narrowed a smaller amount than what you calculated.
Thanks fecal. I come to the same conclusion: the main issue is in the yields! I was told that from the close of 10/10/06 to the close of 11/24/06, the real yield (the CTD yields) have moved about 0.05%, not 0.10%! So it was the main reason for the high difference between my theorical profit and the real one. However, I was told there are 2 other incorrect numbers : the DV01 ratio and the "cost of carry" (financing both futures against the current forward rate) However, I was not told where I was incorrect in my calculations. What do you think? 1.About the future DV01 Future calculation : how do you calculate it? Here is was I did: a. Finding the CTD bonds (they were the 4.5%/Feb11 on the 5years, and the 7.25%/Aug22 on the 30y). I am sure of this, I got the confirmation. b. Using their CTD yields. Let's use the "real" yields of these days: 30y: (7.25% of Aug 22): 4.95% 5y : (4.5% of Feb 11) : 4.71% I would use these yields to calculate: c. the Price of the bond (using the MS Excel formula "Price") d. The DV01 of the bonds, sugin the formula described before: CASH DV01 = 0.01 * ((0.01 * modified duration of the Cash bond (CTD)) * full price of the Cash bond (CTD)) e. Then I divided this CASH DV01 by the conversion factor related to the December futures to get the future DV01. For instance, on the CASH 30Y on 10/10/06 for a yield of 4.95%, I found: - cash price: 125.046 - modified duration: 10.41 - CASH DV01: 130.17$ As conversion factor = 1.1250: - FUTURE 30Y DV01 : 115.70$ Do you find the same numbers? 2. The "cost of carry issue". I understand that if we buy a future US for instance, we would "earn" the 30Y coupon of the CTD (market to market, each day), but we would also PAY the current forward rate each day. That is the reason why there is a great difference between the prices of FVZ6 and FVH7 for instance (not only the CTD differences, but also the cost of carry). Could someone confirm me that this "cost" is SIMPLY the difference between the YTM of the current CTD and the current forward rate (rate for a forward which ends at the expiration of the future contract)? Thanks again for your help.