Dealer Trading
at the Fix
Central Bank Workshop on the
Microstructure of Financial Markets
Banque de France
September 29, 2016
Carol Osler, Brandeis University
Alasdair Turnbull, Clarkson University
Scandal and Intrigue
• June 13, 2013: Bloomberg: There’s market
manipulation at London 4 pm fix
• Dealers conspire in small forex “chat rooms”
• Invitation only: “The Cartel” “A-Team”
• Sharing confidential info on client orders
• Collusive trading strategies
• “Banging the close”
Scandal and Intrigue
• Within 2 years ….
•
•
•
•
•
•
30+ forex dealers let go
$11.6 bn paid by major banks
5 banks plead guilty to felony charges
1 dealer arrested in England
Class-action lawsuit filed, U.S.
Regulators release tantalizing chat details
“Let’s double-team them”
“Hopefuly …we can team whack it”
“Is he gonna protect us like we protect each other
against our own branches?”
“Don’t want other numpty's in mkt to know”
• Up next: Criminal suits against individual traders?
“London 4pm Fix”?
• Foreign exchange market never closes, so …. no closing prices
• But benchmark prices still needed
• 1993: WM Co + Reuter established hourly “Fixes“
• Median traded price over 60 seconds centered on a the hour
• Most influential: 4pm London time
• 3:45 cutoff for “fill-at-fix” orders
• Dealers commit to trade quantity with customer @ Fix price
• Especially used by funds trying to avoid tracking error
• Funds indexed to a MSCI index (which are benchmarked to the fix)
• Bespoke structured products benchmarked to fix
• Many other fixes investigated, striking similarities
• Forex “ECB Fix” 2:15 C.E.T.
Gold
• Interest-rate derivatives
Treasury securities
Silver
Platinum
Striking Price Dynamics @ Fix
•
•
•
•
High volatility
Partial retracements
Convex price path
Consistent for all major currencies vs. USD
Basis Points
•
20
15
20
5
0
-5
-10
-15
-20
3pm
>75th percentile end-month
End-month avg
Mid-month avg
Mid-month avg
End-month avg
>75th percentile end-month
3:30
4:00
4:30
5:00
Chart from Evans (2015)
Many Mysteries
• Fix price dynamics
• “Not well accounted for in existing microstructure models”
• Melvin and Prins, 2011
• “A challenge to [existing] theories of trading behavior”
• Evans, 2015
• Mysteries are a problem: Regulators want to tame fix-price
dynamics but don’t have framework for thinking about it
• Major reforms @ London Fix since 2015
• But: Price dynamics qualitatively unchanged
• According to market participants
A Model of Fix Trading
• Identifies strategic dealer behaviors at fix
• Everything listed in original Bloomberg piece plus
• Front-running (or equivalent)
• Free ride on other dealers
• Explains fix price dynamics: Strategic behavior can account for
• Some of the volatility, all of the retracements
• Implies higher convexity under collusion
• Preliminary empirical test
• Does convexity rise after 2007, when collusion began?
• Discussion
• Should price dynamics survive in an efficient market? Yes
• Why do price dynamics seem unchanged despite 2015 reforms?
• Non-dealers
Model Basics
Dealer d begins with
desired inventory
Receives customer
fix orders, Fd
P0
Dealer d buys
D1d from other
dealers at P1
P1
Dealer d sells
Fd to customers
at fix price PF
P2P=2 PF
Dealer d buys
D2d from other
dealers at P2
3:45
P3
Dealer d trades Xd,
excess inventory,
with other
dealers at P3
4:00
• Risk-neutral dealer d competes with N < identical fix dealers
• Interdealer price responds to order flow
Pt+1-Pt = (Net Fix Purchasest + et)
•  reflects atomistic fringe of non-fix dealers
• et = Forces orthogonal to fix trading = News, etc.
2
• et  i.i.d., E{et} = 0,  e > 0
Dealer d
ends
with
desired
inventory
Outline of Model Analysis
• Baseline model
• Dealers trade independently
• Uncorrelated fix orders
• Correlated fix orders
• Dealers share info on customer orders
• Dealers collude
• Add more realism
• Endogenous price impact
• Risk aversion
Uncorrelated Fix Orders
• Suppose customer wants to buy $90 million @ Fix, initial price P0
•
•
•
•
•
•
By 4:00 dealer must buy $90 million to sell to customer, so maybe …..
Period 1: Dealer buys $30 = D1 , price rises to P1 (in expectation)
Period 2: Dealer buys $60 = D2; price rises to P2 (in expectation)
Dealer conveys $90 to customer at PF= P2
Period 3: No more fix trading, price stays at PF = P2 (in expectation)
Profits = (PF  P1)*$30 = (P2  P1)D1
Anticipated Exchange Rate Path
P 2 = PF
P3
P1
P0
3:45 pm
4:00 pm
Maximizing Fix Profits
• With uncorrelated fix orders, profits maximized if D1 = D2
• In example: Dealer buys $45 million in both periods
• Implies linear price path pre-fix
Anticipated Exchange Rate Path
P2 = PF
P3
P1
P0
3:45 pm
4:00 pm
Excess Trading
• How much to trade in total? What if dealer buys an extra $20?
• Period 1, Period 2: Buys $55 (> $45) each period. Price rises farther than before
• Period 3: Dealer liquidates extra $20, price falls
• Dealer takes loss in period 3: (P2  P1)*$55 + (P3 P2)*$20
+
• But extra rise in P2 can more-than-compensate
• To maximize profits: Excess trading  Xd = (1/3)Fd
•
P 2 = PF
•
•
P3
P1
P0
3:45 pm
4:00 pm
(= $30)
D1d = (2/3)Fd
(= $60)
D2d = (2/3)Fd
(= $60)
Excess Trading & Front-running
• Did dealers trade in excess? Yes. CFTC conversation transcript:
• Bank U Trader: 4:03 p.m.:
by 100
haha i sold a lot up there and over sold
• Front-running: Dealer trading for own account in advance of
known customer trade
• Customer gets worse prices due to dealer trading for own account
• Usually illegal
• Front-running not illegal in forex, though considered unethical
• U.K. Non-investment products code
• Signed by all major foreign exchange banks in 2011
• In “[t]he handling of customer orders …. caution should be taken so that
customers’ interests are not exploited when financial intermediaries trade
for their own accounts. …”
Correlated Fix Orders
• Fix orders reflect economy-wide forces, so correlated
• Rising wealth
• Recent equity / bond returns around world
• Fd =  + d
•
•
•
•
 = Common order shock across dealers
d = Idiosyncratic shock, dealer d
2
2


Standard assumptions:  , d , i.i.d.,  ,  , mutually uncorrelated
2
Positive correlation of orders across dealers, r
0r 

1
2
2
   
Correlated Orders: Free Riding
• Continue with Fd =$90 > 0


• Dealer d expects other dealers to buy, too: Ed  Fn  = rN Fd
N 
• Incentive to free ride by trading more in period 1
Profits = (P2  P1)D1d
• Equilibrium with correlated orders, independent trading
• Trading concentrated in period 1
• Concave price path
Independent
Trading, Correlated
Fix Orders
3:45 pm
4:00 pm
,
,
Correlated Orders: Free Riding
• Equilibrium with correlated orders, independent trading, N > 0
(2  rN )(1  rN )
Fd  1 Fd
2
(2  rN )  (1  rN )
2
 1 1
3
(2  rN )

Fd   2 Fd
2
(2  rN )  (1  rN )
2
0  2 
3
(1  rN )
X d   D3d 
Fd  xFd
2
(2  rN )  (1  rN )
1
0 x
3
D1d 
D2 d
Correlated Orders:
Information Sharing
• Dealers regularly shared information about their fix orders
•
•
•
•
Bank W Trader:
Bank R Trader:
Bank U Trader:
Bank U Trader:
3:36:13 pm:
3:36:26 pm:
3:38:26 pm:
3:38:29 pm:
im seller 170 gbp atmofix
we sellers of 40
lhs in cable at the fix
good amount
Correlated Orders:
Information Sharing
• Information sharing: Give true info on fix orders
• Equilibrium trading with information sharing
 (1  N )( 2  N ) 
 F   1 F
D1d  
2
 (2  N )  (1  N ) 
2
 1  1
3


(1  N ) 2
 F  Fd   2 F
D 2 d  Fd  
2
 (2  N )  (1  N ) 
0  s 
X d   D3d


1 N
 F  F
 
2
 (2  N )  (1  N ) 
2
3
1
0 
3
Correlated Orders:
Information Sharing
• Equilibrium: Trading more concentrated in period 1 than
independent trading, more concave price path
• Profits fall
• Less excess trading
Independent
Trading, Correlated
Fix Orders
Information
Sharing
3:45 pm
4:00 pm
With Many Dealers: Collusion
• Chat group often had 1 dealer control all trading
• “Ammo”: Dealers with same-side fix orders added theirs to the
controlling dealer’s total
• Netting: Dealers with opposite-side fix orders netted out
• Transcripts show: Dealers went beyond information sharing
• Bank W Trader 1: 3:25:07 pm:
• Bank W Trader 1: 3:28:02 pm:
im seller 130 cable that it
hopefuly a few more get same way and
we can team whack it
• Bank W Trader 1: 3:43:52 pm:
• Bank W Trader 1: 3:44:15 pm:
right ive taken him out
so shud have got rid of main buyer for u
Collusion
• Profit-maximizing collusive strategy
• Same as one dealer operating with uncorrelated orders
• Period 1: D1d = (2/3) Fd
• Period 2: D1d = (2/3) Fd
• Period 3: Xd = (1/3) Fd
Collusion
Info Sharing
P3
P0
3:45 pm
Independent
Trading, Correlated
Fix Orders
P2 = PF
4:00 pm
Why Collude?
• Why give one dealer control over market-wide net fix orders?
• Why not just share information about fix orders?
• Collusion shuts down free riding, maximizes dealer profits
• So:
E0     F2 x





E0  Collude  E0  Indep  E0  InfoShare

Banging the Close
• “Concentrating orders in the moments before and during the
60-second window” (Vaughan, Finch, and Choudhury, 2013)
• Happened in forex, according to chat-room transcripts
• Formally:
D
N 1
2,n
D
N 1
2,n
1
• Model so far does not predict banging the close
• It emerges immediately with more realism
Greater Realism: 2 Extensions
1. Endogenous price impact:   Qte , e > 0
• Reasoning
• Standard in execution algorithms for limit-order markets
• Split a large trade into many small transactions, spread out over time
• Liquidity replenishes between each transaction
• By symmetry: Maximize price impact by trading a lot, “walk up the book”
• Implies: Price impact is rising in amount per period
Greater Realism: 2 Extensions
1. Endogenous price impact:   Qte , e > 0
2. Risk aversion

Max E d   Var ( d )
2
• Dealers face multiple risks
• Non-fix trading, et
• Other dealers orders and trading
Banging the Close
• In both model extensions, trading shifts from period 1 to period 2
• With collusion there’s clearly banging the close — D2 > D1
Collusive Price Paths (in expectation)
Baseline model
Extended model
P 2 = PF
Risk Aversion
Endog. 
P 2 = PF
P3
P3
P0
P0
3:45 pm
4:00 pm
3:45 pm
4:00 pm
Banging the Close & Convexity
• In both model extensions, trading shifts from period 1 to period 2
• Information sharing & independent trading:
• Banging the close if N small
DImpact
D2/D1 With Endogenous Price
2/D1 Under Risk Aversion
3
5
e=2
e=1
e=0.5
e=0
2
4
Moderate Risk Aversion
3
DLate
2/D
1
High Risk Aversion
Early
> 1  Banging the Close
Risk Neutral
1
0
0
0
20
40 0
N
602
80
4
100
6
N
8
10
Price Dynamics @ Fix
• Model captures 3 key features of price dynamics
1.
Higher volatility than normal
* High fix orders
* Excess trading
2.
Partial retracements
after the fix
* Excess trading/front-running
3.
Convexity of pre-fix price path
* Banging the close
D
N 1
2,n
D
N 1
1, n
1
 ( P2  P1 ) ( P1  P0 )  1
* Whenever competition is limited
* Under endogenous price impact or risk aversion
A Model of Fix Trading
• Identifies strategic dealer behaviors
•
•
•
•
•

Proprietary trading
Free riding
Share confidential customer order information
Bang the close
Collude
• Explains fix price dynamics

• Volatility, retracements, convexity
• Empirical test: Does convexity rise after 2007?
• Discussion
• Should price dynamics survive in an efficient market?
• Why do price dynamics seem unchanged despite 2015 reforms?
Empirical Test
• Model implies: Convexity higher under collusion
• Dealing banks plead guilty to collusion beginning around 2007-2008
Average Price Path: GBP/USD
Month-end dates
100.15
100.10
100.05
100.00
1996-2007
2008-2013
99.95
15:30
15:45
16:00
16:15
Measuring Convexity
• Ratio of areas
• Shaded Area ( |||) / Triangle ABC
Measuring Convexity
100.14
100.12
100.10
B
Actual Path
100.08
Linear Path
100.06
100.04
100.02
A
C
100.00
3:45
3:50
3:55
4:00
Testing Convexity
• Bootstrap test
• Data: Reuters Dealing tick data, 4 major currencies, 1996-2013
• Null hypothesis: Convexity the same 1996-2007 and 2008-2013
• Use 1996 – 2007 one-minute mid-quote returns to represent the null
• Simulate distribution of convexity in average month-end fix paths
• Sample with replacement from original 1-minute mid-quote returns
Testing Convexity
• Results: Consistent with higher convexity during 2008-2013
Convexity
2008-2013
Marginal
significance
GBP
EUR
JPY
CHF
0.304**
0.193***
0.224**
0.185**
0.038
0.000
0.012
0.026
1. Is This an Efficient Market?
• Should these price dynamics be competed away? No
• Participants are STRATEGIC COMPLEMENTS
• They reinforce the optimality of each other’s strategies
• (They’re not strategic substitutes)
• The more the dealers create volatility, the more funds trade @ fix
• The more big dealers create volatility, the more small dealers avoid risk
• By passing on their fix orders to the big dealers
• The more big dealers control the fix orders, the more they front-run
and create excess volatility
Fix Dynamics Seem Unchanged
Despite Reforms: Why?
• Market concern: Volatility still high, retracements still strong
• 2014-2015 Reforms eliminated strategic dealer behavior
• Dealers trade fix orders via automated algorithms, spread trades out
• Model implies: It could be strategic behavior by non-dealers
• Under information sharing, dealers have signal of upcoming trend
• Signal = Average net fix order
• All dealers take identical prop. positions in period 1, then liquidate
• TODAY: Non-dealers have signal of upcoming trend
• Signal = Initial trend after 3:45, correlated with dealers’ net fix order
• Rationally take speculative position immediately, then liquidate
• Algorithm now available for sale to helps non-dealers do exactly this
Summary
• London fix: “A challenge to
theories of trading behavior”
• Model of rational fix trading captures those dynamics
• Key implications
• Excess trading will arise regardless of competition, bringing
• Excess volatility before the fix
• Retracements after fix
• Collusion is profitable because it shuts down free riding among dealers
• Banging the close and a strictly convex pre-fix price path arise
• When competition is limited or dealers collude
• Persisting volatility and retracements since reforms may reflect strategic
trading by non-dealers