Tuesday, July 9, 2013

Converting UST Market Volume to Interest Rate Risk

A question from a subscriber about Market Volume, and my response:
Govt - can you explain this: "12mm/bp traded over last 30 minutes". I know you are referring to volume, but beyond that, I can't figure out what it means! Also, it would be helpful (at least in the early stages until we catch on) to get some explanation for the meaning you are taking from the volume figures that you cite. They must be important to you, or you wouldn't be tweeting them. Is it high volume or low volume - and how is that volume figure supporting or invalidating your working hypothesis?
--my response-- (this is a little long..but you'll learn something)

 US Treasuries all share certain characteristics 
-they all pay their coupons semi annually
-they all accrue interest on the same Actual/Actual DayCount Schedule
-they all have their own maturity date
-the formula to calculate price --> yield...and yield --> price is the same for all UST securities (the only variable is coupon and maturity date)

So, we can do some simple bond math on them...and apply it the same way.

Now, all US treasuries have a market price...and each market price is equivalent to a specific yield. For example, today (July 9) the current 10yr notes bid price of 92-07 = a yield of 2.653%

There is a formula to calculate a yield from a bond, given its price.  There is a similar formula to calculate a bond price, given its yield (these are inter-changeable).

We can change the yield on any UST security by 1 basis point, and we can then calculate the new price (so back to our 10yr example 92-07 = 2.653%...today). If we change the yield to 2.643% (1bp lower)...we can then calculate the equivalent price...which would be approximately 92-095 (2 5/8 ticks higher in price for 1bp lower in yield). This is the sensitivity of the 10yr note price (2 5/8 ticks) for a 1 basis point change in yield of the 10yr note (from 2.653% to 2.643%).

If we do the same exercise for the other securities on the curve, we will find different price sensitivities to a 1 basis point change in yield:

2yr    5/8 of a tick
5yr     1+ ticks
10yr   2 5/8 ticks
30yr   5 1/4 ticks

--Update --> including treasury futures

ZF (FV)    1 5/8 ticks
ZN (TY)   2 1/2 ticks
ZB (US)   4 3/4 ticks
UB (UL)  7 1/2 ticks

These are the changes in price for these securities for a 1 basis point change in each of their respective yields. This value is referred to as PV01...or...the "price value of 1 basis point" change in yield for the security.

Why do we care about this?
Because the 1st assumption in bond trading is that all securities move in lock step on a YIELD basis. Meaning..when the market rallies....it rallies in yield...and all securities rally or selloff in the same amount of yield. (of course we know this is not true...and we deal with that later...but it is a 1st level assumption which allows us to speak about bonds with different maturities in a apples to apples comparison)

So, imagine you are long 1mm 10yr notes...and you decide you do not want any outright exposure or market risk, to a change in the level of interest rates.

You have a couple choices:

1) you could sell your 1mm 10yr notes making you flat
2) you could sell another instrument (perhaps a 30yr bond), as a hedge against your 10yr notes

In option #2...how do you decide how many 30yr bonds to sell, to hedge your position in 1mm 10yr notes?

The answer comes from their PV01. You will notice that the 30yr PV01 (5 1/4 ticks) is DOUBLE the PV01 of the 10yr note (2 5/8 ticks). This means that the 30yr bond price will move DOUBLE the amount that the 10yr note price moves assuming parallel yield changes...(for ex...all UST yields increase by 4 basis points).

So...if the 10yr note sells off by 4 bps (remember, price down = yield up)...
the price change will be 4 * 2 5/8 = 10+ (10 and 1/2) ticks.

If the 30yr bond sells of by 4 basis points...its price will change by 4 * 5 1/4 =21 ticks.

In order for the P&L of the hedged position to be = 0 in this scenario (parallel yield change)...we would need to sell 0.5mm 30yr bonds to hedge our long 1mm 10yr notes position.

Or in other words..the hedge ratio = 10yr PV01 / 30yr PV01....or (2 5/8) / (5 1/4) = 0.5

We now know that 1mm 10yr notes are equivalent in a parallel yield move to 0.5mm 30yr bonds. The P&L of the 2 positions will be equal and offsetting.

I hope you are still with me...cuz we are just about done...

The actual dollar value of 1mm 10yr notes = $312.5/tick * 10yr PV01 (2 5/8 ticks) = $820.
This is referred to as DV01.  The only difference between DV01 and PV01 is multiplication

DV01  = PV01 (ticks) * $312.5 / tick / 1mm

This mean that when the 10yr note moves 1bp...a position of 1mm will move (in P&L) $820. A position of 2mm would move (in P&L) 2 * $820 = $1640

If we do the same exercise for the 30yr bond...we find that 1mm 30yr bonds PV01 of 5 1/4 ticks * $312.5/tick = $1640

So, 1mm 30yr bonds are equivalent to 2mm 10yr notes (in P&L exposure assuming a parallel move in yields).  

Back to quoting Market Volume 

When we count the volume traded in the mkt...we first count each security on its own (10mm 10yr notes trade....then 7mm 30yr bonds trade, etc...).

However...if we want to add the volume together (in this example 10 + 7 = 17)...we can't...because it wouldn't be an apples to apples comparison in terms of P&L exposure. While saying that 17mm US Treasuries just traded is technically accurate...it does not give us a meaningful description of how much INTEREST RATE RISK just traded.

In order to get an apples to apples comparison..we need to convert each securities VOLUME into DV01 (dollar value of a 1bp move in yields). We do this by multiplying each securities VOLUME * PV01 = DV01

When i quote 17mm/bp traded in the last 30min..i am saying that the total DV01 traded = (the sum*product of the Volume * PV01 for all US Treasuries that have traded in the market in the specified time interval).

If i wanted, i could then convert that DV01 into an equivalent amount of 10yr notes.
17mm/bp = $17,000,000 (total DV01 traded) / $840 (DV01 of 1mm 10yr notes) = 20,238 million = 20.238 billion 10yr notes.

These are equivalent statements. 

By aggregating the DV01 traded of all the securities together...i'm not telling you what the composition of the market volume was. Perhaps all the volume came from trading 5yr notes...perhaps it was all 10yr futures (ZN)?? In that case, would it make sense to quote market volume in terms of 10yr notes? (while equivalent is technically accurate...it can be misleading)

This is why i tend to quote DV01 traded (17mm/bp)...rather than 10yr note equivalents traded (20bln 10yr equivalents) (even though they are interchangeable)

In other words...when we are counting total market volume, we tend to not care what the structure or composition of the volume is (how much 30yr...how much 10yr...how much 2yr...etc..)...we just want 1 number..which makes it easy to grasp quickly what the "status"of the market is.

Now, of course its also valuable to know where the volume is coming from (how much DV01 from each instrument) when the curve steepens or flattens...or in other words...what is the composition of the volume trading in the market (how much 30yr...how much 10yr...how much 2yr...etc..) compared to the change in yields of the various instruments.

So in 1 sense...we don't care about composition..and in another sense...we do care.

When we just want to know how much volume has traded...we don't care so much...but when we want to understand the movement in the curve (when it steepens or flattens)...then we do care about the composition of the market volume....but that is a different type of question.

That is the end of today's lesson - are there any questions?


  1. Hello - Thank you so much for the explanation!!!!

    Would you be kind enough to give the price/yield formula, I'm still confused to to calculate one from the other...

  2. great post! I met a Govt Bond Trader last year at a BB. I wish I were trading with such inight.

  3. "If i wanted, i could then convert that DV01 into an equivalent amount of 10yr notes.
    17mm/bp = $17,000,000 (total DV01 traded) / $840 (DV01 of 1mm 10yr notes) = 20,238 million = 20.238 billion 10yr notes."

    Where does the $840 come from? In the previous example, the DV01 = $820.