Why are my futures losses greater than the yield change implies?

[Brackers27]

Hi

I was hoping someone might be able to explain why my losses are greater than I had expected given the yield move.

I got short 2 Year Treasury futures on June 7th at a price of 109-025. Today the future is trading at 109-175. Thus I have losses of 15 ticks or $937.50. I think the cheapest to deliver throughout the period has been the 4.875% 6/30/12 bond.I calculated DV01 to be about $40 in June (which is what I'd expect with a 2 year)so my losses of $937.50 should equate to a move of about 23.5 ticks in terms of yield. However the yield on the CTD has only changed by about 18 ticks (yield on June 7th was about .66% and today its about .48% or so) which I thought would have lead to losses of approximately $720.

I'd like to know why my losses are over $200 dollars more than I predicted. I think this is way too big a discrepancy to be explained by convexity.

Any ideas?


Thanks

Brackers27

 

[arabianights]

Doesn't sound insane that it would be convexity, although I haven't run the numbers

 

[Martinghoul]

I don't think it's convexity... We're talking about a 2y note here, after all, not the ultra-long or something like that. I think it's the carry/roll, personally.

 

[Brackers27]

Hi Martinghoul

I was thinking that convexity wouldn't explain it. How does the carry/roll affect the futures price?

 

[Martinghoul]

Well, not directly, but think of the futures as a fwd, rather than spot, right? So on the 7th of Jun you're short the CTD's yield approx 4m fwd, while arnd here you're short the CTD yield 3m fwd. That roll, from what I can see, is worth arnd 5bps (looking at the generic treasury curve).

 

[Brackers27]

So what you're saying is, not only am I losing on yield changes in the underlying CTD (18BPs), I'm also making losses on the difference between the June 7th yield 4 months forward and today's yield 3 month's forward? Also you are estimating it by looking at the difference in yield between the 3 month and 4 month points on the treasury curve?

 

[Martinghoul]

So what you're saying is, not only am I losing on yield changes in the underlying CTD (18BPs), I'm also making losses on the difference between the June 7th yield 4 months forward and today's yield 3 month's forward? Also you are estimating it by looking at the difference in yield between the 3 month and 4 month points on the treasury curve?

Well, by selling the future you're short the fwd yield, rather than spot. So by looking at the spot yield, as you're doing, you're just getting a proxy to what happened to your position. If you want to do the right thing, you need look at the fwd yield out of the same delivery date on the two days in question. I am estimating it by looking at the current UST fwd curve and using the 2y 3m fwd vs 2y 4m fwd. As I said, the absolutely correct way to do this would be to use the right rates (where CTD repo is to delivery date) on the two days in question. If you want a somewhat quick 'n dirty way, you can easily calculate the fwd if you know a) the CTD spot yield and b) the 3m and 6m bill yields, for both dates. Does that help?

 

[Brackers27]

Very informative thanks. So I could use:

(1) the 2 year forward curve and the points 3 and 4 months out to estimate?
(2) Ideally I would compare the implied repo rate of CTD to delivery date?
(3) or use the spot yield and 3m and 6m bill yields for both dates?

I like your quick n dirty method as I have these figures already. How would I execute no. 3?

 

[Martinghoul]

Sorry, 1) is just using the fwd curve (it can be defined any which way). 2) is the technically correct way of figuring out the fwd yield for a bond. 3) is the quick and dirty way and is just based on the simple fwd rate equality: (1+r)^T = (1+f1)^T1 * (1+f2)^T2, where
T - time to maturity of the CTD from spot date
r - CTD spot yield
f1 - spot yield to delivery date
T1 - time to delivery date from spot date
f2 - fwd yield, the unknown quantity
T2 - time to maturity of the CTD from delivery date
Do that for the two spot dates in question to obtain the two fwd yields.

Hope that helps...

 

[Brackers27]

I think that should help alright, I know that equality alright, would have surely used the wrong input figures though. Thanks again Martin

 

[Brackers27]

Hi Martinghoul.

I have 2 quick questions if you don't mind. Firstly is it ok to estimate the spot yields to delivery date from the treasury yield curve? Assuming this is ok, I have calculated a difference of about 23BPS in forward yields between June 7th and July 23rd and my losses were $843.75. This equates to approx. $36/BP.

Secondly do the normal price sensitivity measures (i.e modified duration, convexity and DV01) still hold when we are talking about forward yields? If so, when adjusted for convexity I predicted a $41 change per BP change, greater than the $36/BP implied by the forward yield (Mod D =1.9514, Convex. = 5, CTD price = 108.36).

My goal ultimately is to be able to predict what my P/L will be with a certain yield change but judging by this formula, the 2 unknowns (spot yields) will make this difficult?

 

[Martinghoul]

brack, sorry, I didn't see this... You still looking for answers?

 

[Brackers27]

brack, sorry, I didn't see this... You still looking for answers?

Hi Martinghoul, yes still seeking answers.

My main goal is to predict what my losses or gains are likely to be given a certain interest rate change but I think I'm right in saying that it is impossible to predict my P&L in the future accurately because it will depend on an unknown forward yield at some date in the future? I'm long interest rates so I guess all I can say for sure is "today this is the forward yield (from delivery to maturity of CTD) and this is my maximum downside (assuming only positive rates)"? This all sound right?

One more thing, If I calculate a future DV01 for the CTD, will the value for DV01 hold for forward rates. For example if the DV01 is $40 and I lose 10BP in terms of forward yield, will I lose €400 roughly?

Thanks

Brack

 

[Martinghoul]

Hi Martinghoul, yes still seeking answers.

My main goal is to predict what my losses or gains are likely to be given a certain interest rate change but I think I'm right in saying that it is impossible to predict my P&L in the future accurately because it will depend on an unknown forward yield at some date in the future? I'm long interest rates so I guess all I can say for sure is "today this is the forward yield (from delivery to maturity of CTD) and this is my maximum downside (assuming only positive rates)"? This all sound right?

One more thing, If I calculate a future DV01 for the CTD, will the value for DV01 hold for forward rates. For example if the DV01 is $40 and I lose 10BP in terms of forward yield, will I lose €400 roughly?

Thanks

Brack

Yes, you're right, the whole point is that futures are priced (simplistically) as the CTD traded in fwd space. However, to calculate a fwd yield for a bond you need to know the repo rate, which, obviously, isn't applicable to futures. So the "implied repo rate" is the number that makes it equate in the end. Another set of all-inclusive numbers people use is basis (gross and net basis), which, again, is sorta the number that encapsulates the richness/cheapness of a bond in the basket vs the futures. Note that this gets more complicated if there's a meaningful probability of a CTD switch. So I agree that, in the end, you really can't predict your futures PNL knowing only how much the cash bonds have moved. As a great example of this, if you looked at these basis trades in 2008, you would have seen all sorts of VERY large deviations between the two. I am not sure what you mean by max downside.

As to DV01s, you're right. The future DV01 of the CTD is the "fwd DV01" and yes, it should be multiplied by the change in fwd yield.

In general, you should definitely get your hands on the Burghardt, Belton, et al book called "Treasury Bond Basis". It offers the best explanation of these issues that I know of.

 

[Brackers27]

Thanks Marthinghoul, I'll check that book out

 

[BIBIqqq]

I agree with Brackers27.

You should follow his advice.