Hi. I read the book of M. Schap ('The complete guide to spread trading'), and I tried to check if I could trade some credit spreads, beginning with a 5-30 spread (NOB). I followed Scharp's explanations but the market did not give me what I looked for, even if I was true on the yield spread change. Here is the beginning situation: October 10th, 2006 Rate Future Price(Z06) DV01 5y: 4.68% 105+3.5/32 $40.20 30y: 4.86% 111+8/32 $117.10 So the spread was equal to 0.18%. Here is the final situation: November 24, 2006 Rate Future Price (Z06) 5y: 4.53% 105+21,5/32 30y: 4.61% 112+21/32 So the spread was equal to 0.08%, thus the spread has tightened by 0.10%. I used the classic formula to calculate the ratio, that is to say that I divided the DV01 of the 30years by the DV01 of the 5years, which gave 2.9129. Thus about 10 US futures (long) and 29 FV futures (short). However, even if the leading futures has not changed since (Dec06 contract), and the CTD of both futures did not changed either, I should have earned much more than what I got. As the volume was 10 US futures and 29 FV futures, I should have earn about 117.10*10 = $1,171 per basis point, thus about $11,710 on the 10-points change. But I earned only $7,750. If I did not do a rounding (thus playing 10 US futures and 29.129 FV futures), I would have earned only $7,677.24. And I doubt the daily precise adjustements of the DV01s could explain the $4,000 difference. So what did I forget to manage? I know that several things are to be considered in addition: 1. The CTD If the CTD changes, we have to change the ratio, as a CTD change can have a dramatic impact on the DV01. However, I really do not think the CTD have changed on the 5 and 30 years since the 10/10/06. Am I correct? 2. The DV01 changes each day: if the future is much higher or much lower than the preceding day, the DV01 can change even if the CTD does not change. However, I do not think it was really important, as the rounding numbers remained 10 US against 29 FV. 3. I also understand that the change in the leading future contracts (from Dec06 to March07 for instance) could also change the DV01 (conversion factors), thus change the behaviour of the credit spread. But that was not the case in this trade on both Dec06 contracts. So the 3 points above do not seemingly explain the difference between the theorical gain and the real P&L. What are the other factors that may change the behaviour of the spread so much? I think of these 2 other explanations: 1. The convexity bias difference can change the spread ratio, as the low number of long 30years would not profit much of the convexity bias whereas that is not the case for the 5years (short) which would suffer from losses. But I do not think it can change so much the results, and I thought the DV01 should also have taken that into account. 2. The yield difference between the implied yields of the futures (or the YTM of the CTD) and the current forward rates. I understand we would have to pay for the difference between the 30y YTM and the current forward rates each day (as the 30y ITM is LOWER than current forward rates), and we would receive the difference between the 5y YTM and the current forward rate also. However, I would have thought that it should have been a "positive yield" in that spread, as: + the difference between the 5y YTM and the forward rates was not much lower than the difference between the 30y YTM and the forward rates + I had almost 3 times more 5y futures than 30y futures I thought this "financing yield" should have added a premium to the P&L of the trade, so I really do not understand what I miss here, as that would mean I should have earn EVEN MORE than the $11,710, instead of $7,750. What did I forget or misunderstand? Many thanks.
Thanks for your reply. Hum, ok, the difference is the "carry", but "carry" is a word that is used for different purposes. For instance, the "yield differences" (the difference between Forward rate and the Treasury rate) is in the global "carry" of the spread. Or the "carry" could be the difference between a future rate and a forward rate... Would you mind be more precise? Which "carry" did I forget? Do you know how to calculate this additional carry?
I don't know the exact formula for calculating the carry for you problem but re check your calculation. cash bonds & notes versus note & bonds futures your cost of carry would realized cash spread versus futures spread.
Ok so your "carry" is the difference between cash bonds and futures on bonds. To my mind, this difference was given by the current forward rate. (forward rate - YTM = "yield difference" = "your carry", which is applied to the exact number of days from the open to the close of the spread) Do you think that it is more complex than that?
Is this right? Or should it be 117.10-40.20 * 10 = 769 per basis point, or $7690 for the 10-point change? I have no idea if I'm right--my knowledge of bonds and EDs is still in the "dangerous" phase, rather than the "useful" phase.
FullyArticulate, thanks for your answer, but that cannot be the difference. The DV01 difference between the 2 treasury futures HAS to be compensated, that is the reason why I had to invest in 2.91 FV contracts for each US contract (117.10/40.20 = 2.91...) So in my spread, the 5Y futures should have earn about $1,170/basis point (because I had 29 FV contracts) and the 30Y futures should also have earned about $1,170/basis point (because I had 10 US contracts) That is the reason why that is a "credit spread", as it aims at isolating the "credit spread" thanks to the ratio. However, my issue is that I did not manage to isolate correctly the "credit spread", which is obviously a real issue. Does anyone think of something else? I will check the bond/future discrepancy again...
I apologize if this isn't helpful, but let me take one more naive crack at this. On the 5yr, the price change was actually .5625, or $562.50. Assuming a flat DV01, the yield change of 15bp would have resulted in a price change of $603 which is pretty close. On the 30yr, the price change was actually 1.40625, of $1406.25. Assuming a flat DV01, the yield change of 25bp would have resulted in a price change of $2927.50, which isn't even close. I'll yield the floor to someone who is actually helpful.
FullyArticulate, Thanks for your new answer. This one is more helpful. 1. Please excuse-me, I made a COPY error: the close of the US future was 113+21/32, not 112+21/32!!! 2. Even if we change the price (now that is 2.40625 or $2,046.25), the difference remain with the theoric price of $2927.50. So there may be an issue ONLY on the DV01 of the 30y T-Bonds futures (error in the DV01 calculation? Rounding?...) and not on the whole spread. I would have to check again more specifically the DV01 and the YTM of the 30years on October 10th. Thanks for your useful help, FullyArticulate. Please do not hesitate to add something if you think it could be useful...