54
New York University Courant Institute of Mathematical Sciences Robert Almgren Interest Rate Futures Market Microstructure Dec 9, 2010 Thu, Dec 9, 2010
New York UniversityCourant Institute of Mathematical Sciences
Robert Almgren
Interest Rate Futures
Market MicrostructureDec 9, 2010
Thu, Dec 9, 2010
QB = Algorithmic Execution
2
10:20 10:30 10:40 10:50
122−11+
122−12
122−12+
122−13
122−13+
122−14
122−14+
122−15
122−15+
122−16
122−16+
EDT time on Wed 28 Jul 2010
2000 lots
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SELL 179 ZNU0
14:47:50 UTC14:17:51 UTC
Exec 122−14.54
TWAP 122−14.18Strike 122−14.24
●
Bid−ask"Micro" priceMarket tradesFillsLimit orders
pex = 122−14.54pAP = 122−14.24cAP = −00−00.31 = −$9.59
pTWAP = 122−14.18cTWAP = −00−00.36 = −$11.16
Our limit orders
Our fills
(Sept 2010 10-yr Treasury)
Produced by QB from CME and internal data
Thu, Dec 9, 2010
3
Algorithmic Execution + TCA (Example 2)(Dec 2010 5-yr Treasury)
Cointegration signal
Produced by QB from CME and internal data
Thu, Dec 9, 2010
Quantitative Brokers
Algo execution and cost measurementNo prop trading or market making
Interest rate products, starting with futuresEquities already well servedCurrently live with futures on CME
Value add is microstructure expertise
4
Thu, Dec 9, 2010
1. The products
2. Pro rata matching algorithms
3. Treasury roll
4. LDB data set
5
Thu, Dec 9, 2010
1. Interest rate futures productsChicago Mercantile Exchange (CME)
US Treasury futuresEurodollar futuresFed Funds
London International Financial Futures (LIFFE)Euribor, Euroswiss, Euroyen, etcShort SterlingGilt
EurexBund, Bobl, Schatz
6
Thu, Dec 9, 2010
Futures are not securities
Regulated by CFTC not SEC (US)primary purpose is information dissemination
Defined and owned by exchangesno fragmentation (many attempts)exchanges have much more central rolemicrostructure is much more important
Almost all trading is now electronicvery good market data
7
Thu, Dec 9, 2010
CME US Treasury futures
8
Min deliv Max deliv ADV (`000)
2-yr note 1.9 yr 2 yr 342
3-yr note 2.9 yr 3 yr 0
5-yr note 4.2 yr 5.3 yr 741
10-yr note 6.6 yr 10 yr 1468
Bond (30 yr) 15 yr 25 yr 469
Ultra bond 25 yr -- 92
Short position has choice of security and dateconversion factor to approximate 6% yield
Cheapest-to-deliver (CTD) embedded option
Thu, Dec 9, 2010
Treasury futures trading
Quarterly expirations (Mar, Jun, Sep, Dec)front month is only liquid one (Roll event)
Price quotes relative to par, with 32ndse.g. 118-15+ = $118 + 15.5/32
Tick size 1/4, 1/2, or 1 32ndNotional $100k: 1/32 = $31.25(brokerage commissions ~$1-2)
9
Thu, Dec 9, 2010
CME Eurodollar futures
Eurodollar = dollar deposit outside US (1956)“Euro” = “foreign”
Eurodollar futures on CME since 1981first cash-settled futures contract
Forward bet on changes in LIBOR rate9950 = 99.50 = LIBOR at 1.50%/yr
Delivery amt is 3-month interest on $1MM9950 → 9951 (1 bp) = $25 gainTick size is 1/2 bp = $12.50
10
Thu, Dec 9, 2010
Inherently multidimensional
Quarterly expirations to 10 yrs (+ serials)40 contracts, 10-15 activeAll are short-term rates: very correlated
Spread contractsCalendar spreads: +1 Jun, -1 DecButterflies: +1 Jun, -2 Sep, +1 DecTreasury inter-commodity: +8 5-yr, -5 10-yr
Additional modeling featuresimplied liquiditycointegration
11
Thu, Dec 9, 2010
2. Pro rata matching
How market orders are matched to limitAlgorithm fixed by exchange
to attract more volumeto attract correct mix of participantsetc
12
Thu, Dec 9, 2010
First-in first-out (FIFO) order matching
13
1 2 3 4 5 6 7Best bid price
Resting limit buy ordersof different sizes
Time of order submission
Incoming market sell order
Earliest limit orderfilled completely first
Remaining quantityin time order
Thu, Dec 9, 2010
Pro rata order matching
14
1 2 3 4 5 6 7Best bid price
Incoming volume dividedamong all resting orders
at best price
Incoming market sell order
Thu, Dec 9, 2010
Reasons for pro rata matching:Historical tradition from pit tradingEncourage submission of large limit ordersAllow late entrants to participate
Characteristic of interest rate futures marketsEurodollar, Euribor, Treasury calendar spreadsShort sterling
“Arms race” to oversize limit orderslimited only by risk of overfillingJonathan Field & Jeremy Large 2008
15
Thu, Dec 9, 2010
16
1
10
100
1000
0% 20% 40% 60% 80% 100%
Proportion of the time that the spread exceeds the price tick size
Av
erag
e in
sid
e d
epth
/ a
ver
age
trad
e si
ze
SS
EU
ED
NKTNTB
TN2TN5
Figure 1: A chart plotting the 40 observed futures markets. Those markets of greatest
interest to us are labeled. One observation fell below the x-axis, at coordinates (94%,0.7).
Of these 100 electronic limit order books, 40 had on average more than 10 updates per
minute. Since our interest is in fairly liquid markets, we select these for closer analysis.3
The retained set of 40 markets comprises six currency futures, nine government bond
futures, three short-term interest rate futures (STIRs), twenty stock index futures from
12 countries (including ‘E-mini’ products), and two commodity futures.
Based on a simple criterion regarding deviation from median daily prices, outliers in
our data were censored.4
Each market was observed continuously between an appropriate
fixed start and end time of day, so as to include more than 90 per cent of official opening
hours on its primary floor exchange. Table 1 documents our observation start and end
times for eight markets of particular interest.
Figure 1 plots the 40 retained futures markets along two central dimension for this
study. On the vertical axis it shows the average of the mean depth at the best bid and
the mean depth at the best ask, when divided by the average trade size: in brief, the
3The busiest market in this subsample had on average 484 updates per minute.4Applied to cases where prices were greater than 25% away from the daily mid. Instances of crossed
markets, where the price of the best bid exceeded the best ask, were also excluded.
5
“Pro-Rata Matching and One-Tick Futures Markets,”preprint 2007-08, Jonathan Field (Man Investments) and
Jeremy Large (Oxford-Man Institute and Man Investments)Short Sterling (Euronext)
Eurodollar
2-year Treasury5-year Treasury
3010-yr
Euribor
Nikkei stock index
Interest rate futures typically have pro rata matching, large resting liquidity, and large tick size
Optimal strategy is to oversize
Thu, Dec 9, 2010
CME Eurodollar pro rata
1. First order at new level is filled firstwhen filled, no new order
2. Remaining volume is allocated pro ratavolumes rounded down to integral trade size0-lots and 1-lots rounded down to zero
3. Remaining volume is allocated FIFO
17
Thu, Dec 9, 2010
18
7
1. Orders placed during the “pre-opening” or at the indicative opening price (IOP) will be matched on
a price and time priority basis. Note that implied orders are not taken into consideration, as
they are only active during the continuous trading session.
2. Priority is assigned to an order that betters the market, i.e. a new buy order at 36 betters a 35 bid.
Only one order per side of the market (buy side and sell side) can have this TOP order priority.
There will be situations where a TOP order doesn’t exist for one or both sides of the market (for
example, an order betters the market, but is then canceled). There will never be a situation that
results in two orders on the same side of the market having TOP order status.
3. Only outright orders can be TOP orders, however the TOP orders of underlying orders that are
creating implied orders will be taken into consideration during the matching process so as not to
violate the TOP order rule in any market.
4. TOP orders are matched first, regardless of size.
5. After a TOP order is filled, Pro Rata Allocation is applied to the remainder of the resting orders at
the applicable price levels until the incoming order is filled.
6. The Pro Rata algorithm allocates fills based upon each resting order’s percentage representation
of total volume at a given price level. For example, an order that makes up 30% of the total
volume resting at a price will receive approximately 30% of all executions that occur at that price.
Approximate fill percentages may occur because allocated decimal quantities are always rounded
down (i.e. a 10-lot order that receives an allocation of 7.89- lots will be rounded down to 7-lots).
7. The Pro Rata algorithm will only allocate to resting orders that will receive 2 or more contracts.
8. After percentage allocation, all remaining contracts not previously allocated due to rounding
considerations are allocated to the remaining orders on a FIFO basis.
! Outright orders will have priority over implied orders and will be allocated the remaining
quantity according to their timestamps.
! Implied orders will be then allocated by maturity, with the earliest expiration receiving the allocation
before the later expiring contracts. If spread contracts have the same expiration (i.e., CONTRACT A-
CONTRACT B and CONTRACT A-CONTRACT C), then the quantity will be allocated to the earliest
maturing contracts making up that spread (i.e., the CONTRACT A-CONTRACT B will get the allocation
before the CONTRACT A-CONTRACT C because the CONTRACT B expires before the CONTRACT
C).
Example: Pro Rata Allocation Matching
Note: For this example, any of the orders involved could be either outright or implied. As timestamp is
not taken into account, the outcome is the same.
Orders in the market:
Order No. Bid Qty Bid Price Offer Price Offer Qty Order No.
INCOMING 250 9711 9711 200 1 (Top Order)
9711 25 2
9711 50 3
9711 10 4
Thu, Dec 9, 2010
Consequences of pro rata matching
Massive oversizing of limit orders“arms race” in competition for liquiditylimited only by risk tolerance
Incentive for marketable limit ordersbecome new TOP order
Rapid variations on limit order sizeno penalty for cancellation and resubmission
19
Thu, Dec 9, 2010
Eurodollar market data
20
Dec 2011 Eurodollar
10:00 10:10 10:20 10:30 10:40 10:50 11:00 11:10 11:20 11:30
9944½
9945
9945½
9946
9946½
9947
CDT time on Mon 01 Nov 2010
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●
Produced by Quantitative Brokers from CME Market Data
Thu, Dec 9, 2010
Variations in quote size
21
10:20 10:25 10:30 10:35 10:40 10:45 10:50 10:55 11:00 11:05 11:10
CDT time on Mon 01 Nov 2010
Bid
size
(tho
usan
ds)
0
5
10
15
20
25
30GEZ1 Bid = 9945 Vlm = 201
10:20 10:25 10:30 10:35 10:40 10:45 10:50 10:55 11:00 11:05 11:10
CDT time on Mon 01 Nov 2010
Ask
size
(tho
usan
ds)
0
5
10
15
20
25
30 GEZ1 Ask = 9945½ Vlm = 1531
Dec 2011 Eurodollar
Produced by Quantitative Brokers from CME Market Data
Thu, Dec 9, 2010
22
100x decreaseinto credit crisis
Rebound
200 lots
Avg Posted Liquidity: Eurodollar FuturesBi
d si
ze +
offe
r size
(tho
usan
ds)
Apr 07 Oct 07 Apr 08 Oct 08 Apr 09 Oct 09 Apr 10 Oct 10
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● Eurodollar outrights 5−day moving exponential average
Produced by Quantitative Brokers from CME Market Data
Thu, Dec 9, 2010
Average Trade Size: Eurodollars
23
Individualtrade prints(allocations)
Aggregate multiple legsof match events
(size of aggressive order)
10x decreaseinto credit crisis
rebound
Produced by Quantitative Brokers from CME Market Data
Oversize by factorsof 100 or more
Aver
age
trade
size
Apr 07 Oct 07 Apr 08 Oct 08 Apr 09 Oct 09 Apr 10 Oct 10
5
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Aggressive ordersEurodollar outrights 5−day moving exponential average
Thu, Dec 9, 2010
Trade volumes vary much less
24
Trad
ed v
olum
e (M
M)
2005 2006 2007 2008 2009 2010
0
0.5
1
1.5
2
2.5
3
3.5
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Electronic (10−day moving avg)Floor (5−day moving avg) Eurodollars
Produced by Quantitative Brokers from CME Market Data
Thu, Dec 9, 2010
25
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Jan 08 Apr 08 Jul 08 Oct 08 Jan 09 Apr 09 Jul 09 Oct 09 Jan 10 Apr 10 Jul 10 Oct 10 Jan 11
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1
2
5
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2−year10−year5−year30−yearUltra 5−day moving exponential average
Produced by Quantitative Brokers from CME Market Data
Thu, Dec 9, 2010
26
4x decreaseinto credit crisis
2x rebound
Average Trade Size: TreasuriesAv
erag
e tra
de s
ize
Jan 08 Apr 08 Jul 08 Oct 08 Jan 09 Apr 09 Jul 09 Oct 09 Jan 10 Apr 10 Jul 10 Oct 10
5
10
20
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10−year2−year5−year30−yearUltra 5−day moving exponential average
Produced by Quantitative Brokers from CME Market Data
Thu, Dec 9, 2010
Trade volume: Treasuries
27
Trad
ed v
olum
e (M
M)
2005 2006 2007 2008 2009 2010
0
1
2
3
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Electronic (10−day moving avg)Floor
Peaks are roll events
Produced by Quantitative Brokers from CME Market Data
Thu, Dec 9, 2010
How much pro rata, how much FIFO?
Jianhong Wang, NYU MMF 2010Depends on limit order size distribution
uniform order size: more FIFO volumelarge and small orders: more pro rata
28
Thu, Dec 9, 2010
LIFFE IR matching (pre July 2010)
Pro-rata, weighted by sequence numberOptimal strategy is to split limit order:
one large order, plusmany small 1-lot orders
If all traders are symmetric size,optimal size is golden ratioKarel Janeček and Martin Kabrhel (RSJ Invest)“Matching algorithms of international exchanges”preprint Dec 2007
29
Thu, Dec 9, 2010
LIFFE Euribor “time pro rata”
1. First order at new level is filled firstwhen filled, no new order
2. Remaining volume is allocatedby pro rata weighted by preceding volumevolumes rounded down to integral trade size0-lots rounded up to one
3. Remaining volume is allocated
30
Purposeencourage small tradersreduce transient quotes
Thu, Dec 9, 2010
2. Treasury roll event
Who trades with whom?Role of market makers
31
Thu, Dec 9, 2010
Futures open interest
32
A B
Open interest = 0
Open interest = 1
Open interest = 0
time
A buys B sells
A sells B buys
long 1 short 1
Thu, Dec 9, 2010
Roll
33
A B
long 1 Dec short 1 Dec
Dec-Mar calendar spread
long 1 Mar short 1 Mar
Open interest
Dec Mar
1 0
0 1
sell buy
If position holder trades with position holder, then1 spread prints for each 1 change in open interest
Thu, Dec 9, 2010
Roll 2: via market maker
34
A B
long 1 Dec short 1 Dec
Dec-Mar calendar spread
long 1 Mar short 1 Mar
sell buy
MM
Dec-Mar calendar spread
sell buy
flat
flat
If position holders trade with intermediaries, then2 spreads print for each 1 change in open interest
Thu, Dec 9, 2010
Transfer of open interest
35
Business days relative to first intention date
Ope
n in
tere
st (M
M)
−10 −5 0 5 10
0
0.5
1
1.5● ● ● ● ● ●
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OutgoingIncomingTotalCumulative spread volume
ZN
Cumulative tradedvolume of spread
Open interest ofold and new
front month contract
Ratio ofspread volume
to open interestmeasures efficiency
Ratio near 1:open interest moves
via direct trades
Ratio near 2:open interest movesvia intermediaries
ZN: Average across 10 rolls March 2008 to June 2010
Produced by Quantitative Brokers from CME Market Data
Thu, Dec 9, 2010
Historical evolution of volume ratio
36
Contract date
Cum
ulat
ive v
olum
e ra
tio
Mar 2008 Jun 2008 Sep 2008 Dec 2008 Mar 2009 Jun 2009 Sep 2009 Dec 2009 Mar 2010 Jun 2010
0.0
0.5
1.0
1.5
2.0
2.5
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●
ZB
Values near 1: good
What happened to 30-yearin June 2009?
Produced by Quantitative Brokers from CME Market Data
Thu, Dec 9, 2010
4. LDB data set
How to measure market impact of trades?
37
Signed order size
Price change
BuySell
Regression lineslope = impact model
Thu, Dec 9, 2010
What is a buy or a sell?
38
Thu, Dec 9, 2010
What is a buy or a sell?1. Public market data:
trade at ask = buy, at bid = sellliquidity demanders try to act like providers
38
Thu, Dec 9, 2010
What is a buy or a sell?1. Public market data:
trade at ask = buy, at bid = sellliquidity demanders try to act like providers
38
2. Broker data set:market impact of our client populationdependent on details of data setimpossible for external analysts to replicate
Thu, Dec 9, 2010
What is a buy or a sell?1. Public market data:
trade at ask = buy, at bid = sellliquidity demanders try to act like providers
38
2. Broker data set:market impact of our client populationdependent on details of data setimpossible for external analysts to replicate
3. CME LDB:market participants labelled by typeestimate temporary and permanent impact
Thu, Dec 9, 2010
Customer Trade Indicator (CTI) code
1. Exchange local trading for own accountmarket maker
2. Member firm trading for own accountbank proprietary trading desk
3. Local trading for other’s account(almost no volume -- merge with CTI 1)
4. External firmliquidity demander
39
Thu, Dec 9, 2010
CME Liquidity Data Bank (LDB)
For Treasury outrights since Jan 2009
40
Thu, Dec 9, 2010
CME Liquidity Data Bank (LDB)
For Treasury outrights since Jan 2009
40
For each 15-minute interval
Thu, Dec 9, 2010
CME Liquidity Data Bank (LDB)
For Treasury outrights since Jan 2009
40
For each 15-minute interval
For each trade price level
Thu, Dec 9, 2010
CME Liquidity Data Bank (LDB)
For Treasury outrights since Jan 2009
40
For each 15-minute interval
For each trade price level
→Buy and sell volume for each CTI category
Thu, Dec 9, 2010
CTI example
41
−6 −4 −2 0 2 4 6
126−03+
126−04
126−04+
126−05
126−05+
126−06
126−06+
126−07
Volume (thousands)
BuySell
ZNZ0: Mon 01 Nov 2010, 10:00 to 10:15 CTI 1CTI 2CTI 3CTI 4
Averagebuy prices
Averagesell prices
Dec 2010 10-year TreasuryNov 1, 2010, 10:00 to 10:15 Chicago
Produced by Quantitative Brokers from CME LDB Data
Thu, Dec 9, 2010
Market data
42
10:00 10:01 10:02 10:03 10:04 10:05 10:06 10:07 10:08 10:09 10:10 10:11 10:12 10:13 10:14 10:15
126−03+
126−04
126−04+
126−05
126−05+
126−06
126−06+
126−07
CDT time on Mon 01 Nov 2010
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Dec 2010 10-year TreasuryNov 1, 2010, 10:00 to 10:15 Chicago
Produced by Quantitative Brokers from CME Market Data
Thu, Dec 9, 2010
Average price difference -- 15 min
43
Jan 2009 Apr 2009 Jul 2009 Oct 2009 Jan 2010 Apr 2010 Jul 2010 Oct 2010 Jan 2011
−0.15
−0.10
−0.05
0.00
0.05
0.10
0.15
0.20
Sell
pric
e −
buy
pric
e (3
2nds
)
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124●
CTI 1+3CTI 2CTI 4
10 −day avg
Average sell price across 15 min- average buy price across 15 min
0.25/32 = 1/2 bid-ask spread“haircut” paid by
liquidity demandersto suppliers
Produced by Quantitative Brokers from CME LDB Data
Thu, Dec 9, 2010
Average price difference -- daily
44
Jan 2009 Apr 2009 Jul 2009 Oct 2009 Jan 2010 Apr 2010 Jul 2010 Oct 2010 Jan 2011
−0.4
−0.2
0.0
0.2
Sell
pric
e −
buy
pric
e (3
2nds
)
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CTI 1+3CTI 2CTI 4
10 −day avg
Average sell price across 1 day- average buy price across 1 day
0.5/32 = bid-ask spread
Produced by Quantitative Brokers from CME LDB Data
Thu, Dec 9, 2010
Market impact estimates
45
Pric
e ch
ange
(32n
ds)
−15 −10 −5 0 5 10 15
−10
−50
510
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ZNZ0 CTI 1+3
Mon 2010−11−01 to Tue 2010−11−30
−0.226 32nds/1000
Pric
e ch
ange
(32n
ds)
−15 −10 −5 0 5 10 15
−10
−50
510
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ZNZ0 CTI 2
Mon 2010−11−01 to Tue 2010−11−30
−0.0221 32nds/1000Pr
ice
chan
ge (3
2nds
)
−15 −10 −5 0 5 10 15−1
0−5
05
10
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ZNZ0 CTI 4
Mon 2010−11−01 to Tue 2010−11−30
0.249 32nds/1000
Pric
e ch
ange
(32n
ds)
−5 0 5
−10
010
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ZNH9 CTI 1+3
Mon 2009−02−02 to Fri 2009−02−27
−1.11 32nds/1000Pr
ice
chan
ge (3
2nds
)
−5 0 5−1
00
10
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ZNH9 CTI 2
Mon 2009−02−02 to Fri 2009−02−27
0.484 32nds/1000
Pric
e ch
ange
(32n
ds)
−5 0 5
−10
010
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ZNH9 CTI 4
Mon 2009−02−02 to Fri 2009−02−27
0.629 32nds/1000
Feb 2009
Nov 2010
Net trade volume (thousands)
Price change(32nds)
0.629
0.249-0.0221
0.484-1.11
-0.226
Produced by Quantitative Brokers from CME LDB and market data
Thu, Dec 9, 2010
Correlation in order flow
46
Primary flow isCTI 4 ↔ CTI 2
v1
v2
v4
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Produced by Quantitative Brokers from CME LDB Data
Thu, Dec 9, 2010
Conclusions
47
1.Market details are important
2. Futures have different and interesting properties
3.Can get insight into market properties
Thu, Dec 9, 2010
Disclaimer
This document contains examples of hypothetical performance. Hypothetical performance results have many inherent limitations, some of which are described below. No representation is being made that any account will or is likely to achieve profits or losses similar to those shown. In fact, there are frequently sharp differences between hypothetical performance results and the actual results subsequently achieved by any particular trading program. One of the limitations of hypothetical performance results is that they are generally prepared with the benefit of hindsight. In addition, hypothetical trading does not involve financial risk, and no hypothetical trading record can completely account for the impact of financial risk in actual trading. For example, the ability to withstand losses or to adhere to a particular trading program in spite of trading losses are material points which can also adversely affect actual trading results. There are numerous other factors related to the markets in general or to the implementation of any specific trading program which cannot be fully accounted for in the preparation of hypothetical performance results and all of which can adversely affect actual trading results.The reader is advised that futures are speculative products and the risk of loss can be substantial. Futures spreads are not necessarily less risky than short or long futures positions. Consequently, only risk capital should be used to trade futures. The information contained herein is based on sources that we believe to be reliable, but we do not represent that it is accurate or complete. Nothing contained herein should be considered as an offer to sell or a solicitation of an offer to buy any financial instruments discussed herein. All references to prices and yields are subject to change without notice. Past performance/profits are not necessarily indicative of future results. Any opinions expressed herein are solely those of the author. As such, they may differ in material respects from those of, or expressed or published by or on behalf of, Quantitative Brokers or its officers, directors, employees or affiliates. Quantitative Brokers, LLC, 2010.
48
Thu, Dec 9, 2010
