A GARCH analysis of dark-pool trades - Philippe de Peretti, Oren J. Tapiero .December, 15 2013. CFE 2013

1. A GARCH analysis of
dark-pool trades
SYstemic Risk TOmography:
Signals, Measurements, Transmission Channels, and
Policy Interventions
Philippe de Peretti
Centre d’Economie de la Sorbonne Université Paris 1 Panthéon-Sorbonne and SYRTO
Oren J. Tapiero
Centre d’Economie de la Sorbonne Université Paris 1 Panthéon-Sorbonne and LabEx-ReFi
CFE 2013, London – 14-16 December 2013

2. Agenda
• Dark – Pools
• Regulatory Concerns
• Academic response
• Incentives & Risks
• Objectives & Data
• Methodology
• Results & Discussion

3. Dark-pool trading
• Today, in the U.S.A and elsewhere (E.U., Canada,
Australia) trading is fragmented. i.e.: a stock can
be traded in different public exchanges, ECN’s
and dark-pools.
• Dark-pools allows to trade without publicly
announcing trading orders.
• Mid-quote pricing

4. Dark-pool trading

5. Dark-pool trading
Trading in dark-pools has increased in tandem
with high frequency trading activity.

6. Regulatory concerns
• Trading activity in dark-pools (also known as dark
liquidity) may impair the price discovery process.
(Mary Schapiro and James Brigagliano, SEC)
• NY Times: an impairment of the price discovery
process would eventually drive ordinary
investors away from the markets.
• A potential venue for price manipulations. For
example, a trader may push up the price on the
public exchange (by issuing multiple buy orders)
while simultaneously selling in the dark-pool.

7. Regulatory concerns
• Canada, for example, heavily regulates this
activity by allowing these kinds of trades only if
there is a significant price improvement relative
to executions on public exchanges.
• Australia regulators have recently proposed to
impose a minimum threshold for orders in dark-
pools.

8. Academic Response
• Kratz et Al. (2011) overrules the possibility of price
manipulations.
• Buti et al. (2011) indicate dark-pool trading activity is
higher on days with high share volume, low intraday
volatility and high depth. Hence, overall market quality
improves.
• O’Hara and Ye (2011) find that market fragmentation (in
general) does not impair overall market quality.
Moreover they find that while short-term volatility has
increased, price dynamics has become closer to the
random walk (implying greater market efficiency).

9. Academic Response
• Ye (2011) indicate that introducing a dark-pool does
negatively affect price discovery on the public
exchange while improving overall liquidity.
• Weaver (2011) also finds a negative relationship
between increased dark-pool activity and market
quality (i.e.: price discovery) by indicating the
positive effect it has on the measures of bid-ask
spread.
• On the other hand Zhu (2011) indicates that while
price discovery is improved by the presence of a
dark-pool, liquidity is reduced in public exchanges.

10. Academic Response
• Ready (2012) analyzes volume in dark-pools to finds that
lower stock spreads (in dollars term) coincide with reduced
dark-pool activity.
• Nimalendran and Ray (2011) mitigate the “price discovery
impairment” argument by indicating the possibility that
informed traders may also trade in dark-pools and therefore
“spilling” information into the quotes that are seen in public
exchanges.
• Nevertheless, two years later, the same authors (using
propriety data) find increased quoted spreads on public
exchanges following dark-pool transactions (Nimalendran and
Ray, 2013). Moreover, they find that “informed traders” may
be concurrently trading in the “light” and in the “dark”.

11. Incentives & Risks
• Not obliged to make their intentions public.
• This implies that an institutional investor is able to execute large
orders with fewer trades and without significantly affecting
market impact risk.
• Combined with mid-quote pricing, overall transaction costs paid
by the institutional investor decreases.
• Avoid trading against an informed order-flow (Zhu, 2011).
• Dark-pool activity may reflect institutional investors’ distrust of
public exchanges due to high frequency trading activity.
“Provided this is true and provided institutional investors are able
to detect high frequency trading activity, trading in dark-pools
may coincide with the latter trading activity. Hence, the study of
dark-pools may (perhaps indirectly) relate to the high frequency
trading activity.”

12. Incentives & Risks
• Dark-pools do not guarantee trading execution. In other
words, traders face an execution risk.
• This may imply that in moments of high intraday price volatility,
the investor will prefer to trade in public exchanges.
• Trade highly liquid stocks where it is likely to find a seller or a
buyer.
• Information leakage risk The pool may leak the information
or front – running the order.
• Example (The Economist): “…a dark-pool operator receiving a
pension fund’s order to sell one million MSFT shares might
reasonably expect to profit by shorting MSFT”.
• KEY WORDS: Trust, Liquidity and Volatility

13. Objectives & Data
• Objectives:
• The aim of this research is to implement the
GARCH analysis framework to a microstructure
problem.
• Understand linear and non-linear effects of
dark-pool trading on the return and volatility
process.
• Determine the informational content of “dark-
trades” volume and number of transactions.

14. Objectives & Data
• Data:
• We use data on MSFT, on a millisecond timestamp and provided by
the Trades and Quotes (TAQ) database.
• We aggregate the date into 5 minutes time-interval.
• In the “EX” column of the the TAQ trade file, the letter D indicates all
trades reported by the Financial Industry Regulatory Authority
(FINRA), which oversees trades executed in other Trade Reporting
Facilities (TRF) including dark-pools.
• this variable has been used as a proxy for dark-pool trading in
Boni et al. (2011) and Weaver (2011).
DATE TIME EX SIZE PRICE
2013010
2
9:30:00.2 D 250 27.25
2013010
2
9:30:00.3 K 100 27.27
2013010
2
9:30:00.4 P 200 27.28

15. Objectives & Data
• Data:
• Log-returns are computed at 5 minutes interval.
• Two proxies for dark trading:
• proportion of volume traded in the dark (VD)
• proportion of dark-trades (ND)
Vt
D
=
PS
D
QS
D
PS QS
Nt
D
=
TNt
D
TNt

16. Objectives & Data
Time evolution V of N and (5-minute time interval)

17. Objectives & Data

18. Objectives & Data

19. Methodology
• The AR(1)-GARCHX(1,1)-GED equation:
• Where:
• ρ, α, α0, α1, and β are parameters to be estimated.
• α0>0,α1>0, β>0 and α1+β<1
• φ is a (1×k) vector of parameters associated with the (k×n) matrix
of exogenous variables Xt.
• εt∼L(.)
• To capture excess kurtosis in intraday returns, define L. as the
Generalized Error Distribution (GED) law with ν degrees of
freedom (Nelson, 1991).
rt = rt 1 + + t ht
ht = 0 + 1 t
2
+ ht 1 + Xt

20. Methodology
• We focus on the predictive accuracy of competing AR(1)-
GARCHX(1,1)-GED models, each one differing by the variables
included in the matrix Xt. Especially, we focus on pairwise
comparisons based on the accuracy of out-of-sample one-
step-ahead density forecasts.
• Features:
• Comparison takes place over the full distribution (Enables, for
instance, to analyze tail effects of dark-trades).
• The competing models are allowed to be only an approximation
of the true underlying data generating process.
• Designed to deal with heterogeneous data.
• For two nested models, the suggested approach allows to analyze
the marginal influence of a given exogenous explanatory variable
in terms of predictive content.

21. Methodology
• Amisano and Giacomini (2007):
• Define Zt=(rt,Xt')' and let Ft=σ(Z1,Z2,…,Zt) be the information set at
time t.
• Two competing AR(1)-GARCHX(1,1)-GED models, to be ranked:
• ft(Z1,Z2,…,Zt-m+1: φ1)
• gt(Z1,Z2,…,Zt-m+1: φ2)
• Let:
Point forecasts
-or-
Density forecasts
Analyze:
dt
f
×( )
lndt
f
rt+1( )
dt
g
×( )
lndt
g
rt+1( )
out-of-sample one-step-ahead density forecasts
log-scores evaluated at the outcome rt+1.

22. Methodology
• Amisano and Giacomini (2007) suggest a test based on a loss
function that uses these logarithmic scoring rules.
• Define λ∈(maxm,p,(T-1)/T)
• Using a rolling scheme, one can estimate the two models on the time
period 1:t=int(λT). Then, produce density forecasts and re-estimate
the model on 1:t=intλT+1.
• This procedures is repeatedly carried on, yielding two sets of n log-
scores:
• we allow the models to capture structural changes in the parameters
as well as in the kurtosis of the returns.
lndt
f
rt+1( ){ }t=int( T )
T 1
& lndt
g
rt+1( ){ }t=int( T )
T 1

23. Methodology
• Weighthed Likelihood Ratio (WLR) test statistics:
• Under the null:
tn =
WLR T,n
n
tn ~ N(0,1)
tn > 0 f() over g()
tn < 0 g() over f()

24. Methodology
• The weighting function w(.)
• The weighting function w(.) is used to set to highlight a particular
region of the density forecast.
• If w(.) is uniform, i.e. taking the value of 1 whatever rt+1
st is (case
0), then the test highlights the entire distribution.
• Four other definitions of w(.) are of interest for any variable y
with zero mean and unit variance:
1. Center of the distribution: w(y)=ϕ(y)
2. Tails of distribution: w(y)=1-ϕ(y)/ϕ(0)
3. Right tail of distribution: w(y)=Φ(y)
4. Left tail of distribution: w(y)=1-Φ(y)
• ϕ is the standard normal density function.
• Φ is the cumulative standard normal distribution function.

25. Results & Discussion
• Seven competing models:

26. Results & Discussion
• Weighted Likelihood Ratio tests :

27. Results & Discussion
• Weighted Likelihood Ratio tests :

28. Results & Discussion
• Weighted Likelihood Ratio tests :

29. Results & Discussion
• Summary:
i. The information contribution of dark trading:
• V and N do not provide the same information regarding returns one-
step-ahead forecast.
• Using V as an explanatory variable:
• does not significantly improve the forecasting performances over the simple
AR(1)-GARCH (1,1) model when only the center of the distribution is considered
(table 4).
• However, returns important information about right and left tails (Table 5).
• Using N as an explanatory variable:
• improve forecasts for both the center of the distribution and for the tails
• V and N yields significant information about the likelihood of extreme
intraday movements in the price of traded shares.

30. Results & Discussion
• Summary:
ii. Proportion of dark volume vs. proportion of dark trades:
• Models that include either V or N, significantly over perform the AR(1)-
GARCH(1,1)-GED model (benchmark)
• The proportion of dark-trades (N) seem to provide superior information
regarding the one-step-ahead density.
iii. Linear vs. non-linear effects
• the proportion of dark trades (N) provides superior information
while considering non-linear relationships with returns.
iv. Past vs. contemporaneous effects
• The model M4 performs best.
• No past effect of V evidence of a martingale price process.

31. Conclusion
• The results indicate that number of dark trades
within a predetermined time-interval provides
more information regarding the (one-step-
ahead) point and density forecast of returns.
• Though we do not discuss the issue of price
discovery, it is obvious that dark trading has a
role in the price discovery process.

32. Conclusion
• Dark trading may provide valuable information to regulators
and market participants alike.
• For regulators: dark trading maybe provide information over the
effects of high - frequency trading, provided that dark trading
activity coincides with the latter activity. Therefore:
• It is important to empirically determine how trading in the dark
coincides with high frequency trading. Determining this relationship
may provide an important piece of information for regulators in the
activity of overseeing financial markets.
• For market participants: dark-trading seems to be well integrated
in current trading activity.
• Traders on public exchanges react to dark trading once it is exposed
to the public.

33. This project has received funding from the European Union’s
Seventh Framework Programme for research, technological
development and demonstration under grant agreement n° 320270
www.syrtoproject.eu