Questions on Carry

I don't work for a BB, but I would be happy to respond... Would you like me to?

Firstly, the answer will depend on the specific approach practiced by the bank in question. A while ago, it was relatively common for there to be no balance sheet charges on bond shorts and longs used to be all that mattered. In that case, the negative carry can be estimated bŷ the difference between yield and repo (note that it's not the coupon). Nowadays, things are a lot more complicated, so you might get charged for your usage of scarce resources, whatever they might be. For instance, if you're charged haircut on your repo, the capital you end up using might have a cost associated with it. In general, given the recent regulatory changes, there are lots of charges and lots of fragmentation. So the specifics will vary.

With swaps, it's a very similar idea. Specifically, your carry is a function of the difference between the fixed rate and the floating fixing (e.g. 3M LIBOR). Whether or not there are charges in this case will vary as well. For instance, you will have to pay a fee to have the swap cleared at the exchange. The exchange obviously will require initial and variation margin, which might mean that you get charged for the capital you end up using. Then there's the carry that's associated with any derivative. So while a swap is, technically, an off-balance sheet instrument, that doesn't mean there are no charges.

As to funding more broadly, most banks have a treasury function which acts as sort of an internal marketplace for funding needs of different desks. They decide how to pass on the various money market rates, such as the unsecured O/N, repo etc to the desks and/or individual traders' books.

Martinghoul thanks for your help on this.. I think I'm comfortable with the numbers I have for carry now but I am having some trouble with rolldown. If I assume an unchanged yield curve then is my treasury and swap rolldown just (spot rate - fwd rate)*(dv01)? Also, even with a flat yield curve shouldn't there be some roll/slide element just because as a discount or premium bond approaches maturity it goes to par? So I would think a short UST position at 98 would have negative roll/slide even with a flat yield curve.

i saw some errors in what was said, so here is how carry is actually calculated on a UST book

UST carry for a leveraged book is actually pretty simple.

For a long position, you receive 1 day of coupon on face, and you pay the repo rate for 1 day on the dollar amount.

--Coupon Portion of carry-- So, if the coupon is 2.5%, then you receive 1/365 * 2.5% of coupon, for every day that you own the position. If you own the position over the weekend, then you get 3 days of carry. Long holiday weekend? Great, then you can get 4 days of carry. you would think that this gets baked into the market prices, but in practice it rarely does.

--repo portion of Carry-- If the bond/note price is 96-00 (current 30yr price), then you pay 1/365 * 30yr repo rate * dollar value (the on-the-runs tend to be special in repo, while everything else tends to be GC)

so, for 1mm (face) 30yr bonds, with a price of 96, you will pay 1/365* 30yr repo rate * 960,000 per day (if the repo rate is negative, then you get paid repo on your long bond position...if its positive, then you pay)

Total carry is the combination of coupon + repo.

The Short position is exactly the opposite.

Balance sheet usage is a separate calculation

Reg Cap is as follows 1mm 30yr = 60k 1mm 10yr = 40k 1mm 5yr = 30k 1mm 3yr = 20k 1mm 2yr = 15k

Reg Cap is like margin for US Treasuries. The 1mm is for dollar value (not face)...so 1mm face where the price is 96 = 960,000 of dollar value that you need to finance and hold the appropriate RegCap.

And similar to futures, longs and shorts offset for RegCap, but only if they are in the same maturity bucket.

i'm not sure about calculating carry for swaps, but i suspect it is pretty similar.

rolldown depends on what part of the curve you are looking at. The 5yr sector is different from the 10yr sector, which is different from the 30yr sector. You also have to add in the volatility of off-the-runs with different coupons (coupon effect)...so rolldown can be hard to isolate with all those moving pieces. You can do a DCF valuation to help with what rolldown should be...but the curve is not perfectly priced...and there aren't enough RV players to force the micro curves back into line, also the dealers don't have the balance sheet to force the issue...so unless an issue looks really wack on the curve...nobody cares anymore...off the run trading is pretty dead...sadly.

ironchef's method is fine for getting realized PnL on a book at EOD, but it ignores pull-to-par (also, very importantly repo is accrued on Act/360 basis, not Act/365). Martinghoul made no real errors, yield carry is much better for looking at intermediate horizon trades because it incorporates pull-to-par, for one. The approx I would suggest is [Spot yield - repo*(365/360)]x(dt / (PV01 - dt)), where dt is the length of holding period in years (see Sadr's swaps book), and we use the appropriate term repo rate.

As for roll-down, you pick the appropriate horizon and make the (pretty strong) assumption that the yield curve doesn't change over the horizon. For example to calculate 3mo roll-down on CT2s, which are the .75 2/28/18 with yield of 88 bps. In 3 months the CT2s will roll-down to a note with effective maturity in end of month 11/17. Looking at off-run curve, the .875 11/30/17 are trading at 87 bps, so the approx to 3mo roll-down is 1bp. The flaws with this approx is that we should factor in on-the-run premium of 2y, coupon diff, and date mismatches (term does not match our horizon). Using a well-constructed spline curve that adjusts for OTR premium is a solution.

1M and 3M (or whatever horizon you want to look at) carry roll-down is usually computed by adding the yield carry appox. with the roll-down approx, and is pretty standard. Trying to very cleanly separate each of these components, e.g. to take into acct pull-to-par's affect on both, is trickier (see Tuckman Fixed Income Sec 3rd Ed). Final note on repo - the appropriate term repo rate should be used, and you should factor in bid/offer (long tsys position funds at bid side), which may be wider depending on ctpy and balance sheet constraints (e.g. long tsys position may see bids pulled back behind screens, esp. over quarter-end dates).