a garch analysis of dark-pool trades - philippe de peretti, oren j. tapiero .december, 15 2013

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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

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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

Agenda • Dark – Pools

• Regulatory Concerns

• Academic response

• Incentives & Risks

• Objectives & Data

• Methodology

• Results & Discussion

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

Dark-pool trading

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

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.

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.

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).

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 Æ Zhu (2011) indicates that while

price discovery is improved by the presence of a dark-pool, liquidity is reduced in public exchanges.

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”.

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.”

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 Æ 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

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.

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

20130102

9:30:00.2 D 250 27.25

20130102

9:30:00.3 K 100 27.27

20130102

9:30:00.4 P 200 27.28

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)

VtD =PSD QS

D

PS QS

NtD =

TNtD

TNt

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

Objectives & Data

Objectives & Data

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 htht = 0 + 1 t

2 + ht 1 + Xt

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.

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:

dtf ×( )lndtf rt+1( )

dtg ×( )lndtg rt+1( )

out-of-sample one-step-ahead density forecasts

log-scores evaluated at the outcome rt+1.

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.

lndtf rt+1( ){ }t=int( T )T 1

& lndtg rt+1( ){ }t=int( T )T 1

Methodology • Weighthed Likelihood Ratio (WLR) test statistics:

• Under the null:

tn =WLR T ,n

n

tn ~ N(0,1)tn > 0 Æ f() over g() tn < 0 Æ g() over f()

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+1st

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.

Results & Discussion • Seven competing models:

Results & Discussion • Weighted Likelihood Ratio tests :

Results & Discussion • Weighted Likelihood Ratio tests :

Results & Discussion • Weighted Likelihood Ratio tests :

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.

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 Æ evidence of a martingale price process.

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.

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.

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