Effects of MIFID II on Stock Trade Volumes of Nasdaq Stockholm

IN

DEGREE PROJECT MATHEMATICS, SECOND CYCLE, 30 CREDITS

STOCKHOLM SWEDEN 2019 ,

Effects of MIFID II on Stock Trade Volumes of Nasdaq Stockholm

EVA ELLING

KTH ROYAL INSTITUTE OF TECHNOLOGY

SCHOOL OF ENGINEERING SCIENCES

Effects of MIFID II on Stock Trade Volumes of Nasdaq Stockholm

EVA ELLING

Degree Projects in Mathematical Statistics (30 ECTS credits)

Degree Programme in Applied and Computational Mathematics (120 credits) KTH Royal Institute of Technology year 2019

Supervisor at Skandinaviska Enskilda Banken SEB: Salla Fransén Supervisor at KTH: Anja Janssen

Examiner at KTH: Anja Janssen

TRITA-SCI-GRU 2019:322 MAT-E 2019:79

Royal Institute of Technology

SE-100 44 Stockholm, Sweden

URL: www.kth.se/sci

Abstract

Introducing new financial legislation to financial markets require caution to achieve the intended outcome. This thesis aims to investigate whether or not the newly installed revised Markets in Financial Instruments Directive - the MIFID II regulation - temporally influenced the trading stock volume levels of Nasdaq Stockholm during its introduction to the Swedish stock market.

A first approach of a generalized Negative Binomial model is carried out on aggregated data, followed by an individual Fixed Effects model in an attempt to eliminate omitted variable bias caused by missing unobserved variables for the individual stocks.

The aggregated data is attained by taking the equally weighted average of the trading volume and adjusting for seasonality through Seasonal and Trend decomposition using Loess in combination with a regression model with ARIMA errors to mitigate calendar effects. Due to robustness of the aggregated data, the Negative Binomial model manage to capture significant effects of the regulation on the Small Capital segment, even though clusters of the data show signs of divergent reactions to MIFID II. Since the Fixed Effects model operate on non-aggregated TSCS data and because of the varying effects on each stock the Fixed Effect model fails in its attempt to do the same.

Sammanfattning

När nya finansiella regelverk introduceras på finansmarknaden krävs noggrann aktsamhet för att uppnå de tilltänkta målen. Det här arbetet avhandla huruvida det nyligen implementerade Markets in Financial Instruments Directive - MIFID II - orsakade en tillfällig dipp i handelsvolymerna på Nasdaq Stockholm under dess introduktion på den svenska marknaden. Två strategier behandlas - den första, en Generaliserad Negativ Binomial modell baserad på aggregerade dagliga handelsvolymer och den andra, en Fixed Effects regression baserad på paneldata i ett försök att utesluta modellfel grundade i saknade oberoende variabler. Det aggregerade datat erhålls genom det aritmetiska medelvärde av handelsvolymerna över alla aktier och dessa justeras för äsongmönster genom metoden STL, Seasonal and Trend decomposition using Loess, i kombination med regression med ARIMA-fel. Detta för att reducera års- samt helgeffekter. Tack vare medelvärdets robusthet klarar den Negative Binomial regressionen att fånga upp signifikanta effekter av MIFID II för lågkapitalsegmentet av handelsvolymerna, trots att kluster av dessa påvisar olika effkter av regleringen. Fixed Effects modellen som inte har fördelen av denna robusthet, klarar inte detta på grund av den varierande effekten av MIFID II på de individuella aktierna.

EFFECTS OF MIFID II 1

Effects of MIFID II on Stock Trade Volumes of Nasdaq Stockholm

Eva Elling

Abstract—Introducing new financial legislation to financial markets require caution to achieve the intended outcome. This thesis aims to investigate whether or not the newly installed revised Markets in Financial Instruments Directive- the MIFID II regulation - temporally influenced the trading stock volume levels of Nasdaq Stockholm during its introduction to the Swedish stock market. A first approach of a generalized Negative Binomial model is carried out on aggregated data, followed by an individual Fixed Effects model in an attempt to eliminate omitted variable bias caused by missing unobserved variables for the individual stocks. The aggregated data is attained by taking the equally weighted average of the trading volume and adjusting for seasonality through Seasonal and Trend decomposition using Loess in combination with a regression model with ARIMA errors to mitigate calendar effects. Due to robustness of the aggregated data, the Negative Binomial model manage to capture significant effects of the regulation on the Small Cap. segment, even though clusters of the data show signs of divergent reactions to MIFID II. Since the Fixed Effects model operate on non- aggregated TSCS data and because of the varying effects on each stock the Fixed Effect model fails in its attempt to do the same.

I. I

The stock market composes a progressive, complex dynamical system. The introduction of the regulation MIFID II to the European stock market on January 3rd, 2018, was made in an attempt to strengthen and build upon its predecessor, MIFID (abbreviated Markets in Financial Instruments Directive).

The new regulation is to facilitate greater transparency by its updated requirements for equity and non-equity instruments. In January 2018, the financial regulatory agency and supervisory authority of Europe, the European Securities and Markets Authority (abbreviated ESMA) delayed the implementation of an instance of MIFID II, the double volume cap (abbreviated DVC), due to completeness issues, until March the same year. The purpose of the DVC was to limit the amount of trading under certain equity waivers to ensure the use of such waivers does not harm price formation for equity instruments. The sudden postponement can potentially have stirred the Stockholm stock market during a short period. When investigating the effects of an event such as MIFID II, it is vital to keep in mind the known, or rather suspected, seasonalities and events that could potentially interfere around the time of treatment, in this case when MIFD II was introduced. Such a reoccurring historic pattern, though sometimes debated due to diminishing effect, is the so-called January effect. Previous related work of regulatory causal effects are the early J. Harold Mulherin, 1990, Regulation, Trading Volume and Stock Volatility and the later Cumming et al., 2011, Exchange trading rules and

stock market liquidity and Trebbi and Xiao, 2017, Regulation and Market Liquidity [1] [2] [3]. Mulherin applied the Hardouvelis model and regression of daily turnover on return and absolute return to conclude that increased transaction costs, due the regulation of interest, reduced trading volumes.

Cumming et al. uses difference-in-difference multivariate regression (abbreviated DiD) and states that the predecessor of MIFID II, MIFID, helped to enhance the liquidity of the market. Lastly, in the study of Trebbi and Xiao, three different methods were carried out to assess structural breakpoints in market liquidity. Initially, standard multiple breakpoint testing of liquidity levels are carried out, followed by single breakpoint testing using latent factor models to capture more flexible breakpoints, like changes in trend, factors and serial correlation. The finalising third method is again the DiD method. The MIFID II regulation applies to the whole Nasdaq Stockholm market, and thus a control group is lacking and the DiD-method cannot be used in this case.

On Nasdaq, there are three commonly used main categories of market capitalisation, which is the worth of a company’s outstanding shares. These segments are referred to as Large (LC), Medium (MC) and Small (SC) capitalisation and the effects of MIFID II on each is examined in this paper [4].

Market Segments

LC Companies with a share value over EUR 1 billion.

MC Companies with a share value exceeding EUR 150 million but not more than EUR 1 billion.

SC Companies with a share value up to EUR 150 million.

Further, the stocks of Nasdaq Stockholm can be divided into 11 main market sectors which are used as a categorical variable; Communication Services, Consumer Discretionary, Consumer Staples, Energy, Financials, Health Care, Indus- trials, Information Technology Materials, Real Estate and Utilities.

A. Background

The so-called dark pools are private stock markets where

investors are allowed to trade without exposure until after the

trade has been made. Dark pools first emerged in the 1980s

on the U.S. market, to let large investors swap big volumes

of shares without publicly revealing their intentions during

the search for a buyer or seller, so as not to effect the market

during the trade. Today, dark pools are not only used for

EFFECTS OF MIFID II 2

large trades and they have become a significant part of daily stock trading. To increase transparency on the market, one of the aims of MIFID II was to remedy the use of dark pools for purposes other than large tradings by introducing a double volume cap (abbreviated DVC) for dark pools. Over a rolling 12-month period, just 4% of the total trading in an individual stock can take place through dark pools. Trading of a stock across dark pools is limited to 8% of the total volume. A breach of either of these thresholds means trading in that particular stock is prohibited for the next six months, either from the individual dark pool that breached the regulation or from all dark pools. This leads to the conclusion that volumes traded through dark pools before the implementation of MIFID II, and affected by the new regulation, transferred somewhere else other than the dark pools. Investors can have turned to lit markets, which are the opposite of dark pools, which would mean that markets like Nasdaq Stockholm would have experienced an increase in trading volumes after the regulation was introduced. Another plausible destination is Systematic Internalisers (abbreviated SIs), offered by banks and high-frequency trading companies, that shares many of the features of dark pools. If a company adopts SI status, standards for minimum quote sizes and trade reporting are all eased, and for a small fee it carries out trade for its clients.

Furthermore, the European Securities Markets Authority (abbreviated ESMA) was during the first week of January, 2018, forced to delay the initial implementation of the DVC of the new regulation to March 12. This, due to lack of complete data from exchange operators to calculate effective caps [5]. The abrupt changes can have shaken the market at the time. When MIFID II came into effect, around 45%

of the daily volume of shares traded in Europe took place elsewhere than public exchanges, either through dark pools or via banks [6].

B. Problem Statement

Financial legislation aims to curb an undefined dynamical sys- tem towards a desired outcome. Thereforee it is of importance to evaluate the actual outcome of regulations and identify any unintended side effects. One of the intents behind MIFID II was to reduce the use of dark pools [7]. If that be the case, it is to be expected that liquidity is transferred from dark to lit markets, which would result in a liquidity increase for lit markets such as Nasdaq Stockholm. However, an alternative for dark pools, and lit markets, are SIs. Thus, it is to be expected that liquidity could have been transferred elsewhere.

In addition to this, due to the abrupt changes of the MIFID II’s DVC, parts of the market could have been negatively affected. In other words, a significant group of traders might have been unsure of whether or not they lived up to the new regulation and therefore minimised their trade for a temporary period after MIFID II came in to place, and contributed to the presumed trading volume level drop. Thus, only a fast, short- lived level drop in trading volume after the intervention of the regulation is to be anticipated. Therefore, the hypothesis of interest for this thesis is whether or not there is a level drop

in trade volumes directly after the implementation of MIFID II. As the effect of intervention is potentially (most probably) heterogeneous, the three market capitalisation segments of the said market are explored.

C. Delimitation

This thesis treats whether or not the MIFID II regulation affected the Nasdaq Stockholm trade volumes. To answer the more general questions of how MIFID II affected the full Swedish market requires a more in-depth analysis of where the trade takes place, and how the volumes move between markets. Nasdaq Stockholm is just one of several examples of where trade takes place on the Swedish stock market.

II. D

The dataset of this paper is of daily Nasdaq Stockholm stock data, consisting of trade volume, turnover (trade volume over outstanding shares), closing price (in Swedish SEK), return, outstanding shares, total market capital (in euro), market capitalisation segment and market sector. The data is provided by Skandinaviska Enskilda Banken, SEB. The Time-Series- Cross-Sectional dataset, abbreviated TSCS, consists of 913 stocks that were active on Nasdaq Stockholm between 2009- 12-30 to 2018-12-28, in total around 2300 active trading days of observations. The time period is choosen as to avoid introducing unnecessary errors rooted in the unstable times of the Great recession between 2007 to mid 2009. The TSCS data comprises an unbalanced set. An unbalanced set is in this context a set were there is incomplete data for some stocks. In this case, it is due to the nature of the stock market with stocks entering and exiting during the time interval.

Since trades cease during weekends and public holidays, naturally no measurements are available for these days. The equally weighted average over individual stocks of the three segments (SC, MC, and LC) is calculated for the TSCS data, henceforward referred to as the aggregated data. The existing leap days in the interval are first taken away to not interfere with the seasonal adjustment of the aggregated data since the methods used only handle constant period lengths. Normally, a compromise between maximising sample size and minimising day-to-day fluctuations of volume and return would be to look at weekly data. In this case we are particularly interested in the daily fluctuations since the hypothesis of the thesis is a temporary level drop potentially caused by MIFID II due to the presumed insecurities of the market. The number of trading days on Nasdaq Nordiq is on average

365 · 5

7 3 6 · 5

7 ⇡ 253

for a year of 365 days, where the leap day is dismissed, with

3 weekday holidays and 6 moving holidays. The average

number of trading days of a year in the period 2010-2019

is 251, slightly fewer than on an average year. Therefore

the yearly frequency is assumed to be 251. Note that since

stocks shift market segments from time to time, the number

of stocks in each segment category do not equal the total 931

stocks active during the interval.

EFFECTS OF MIFID II 3

External data are yearly Konsumentprisindex ratio (abbrevi- ated KPI, in English Consumer price index), yearly Produk- tionsvrdeindex ratio (abbreviated PVI, in English Production value index) and STIBOR T/N rate (Stockholm Interbank Offered Rate) [8] [9] [10]. KPI represents the price growth of goods and services consumed by the Swedish public, and therefore yearly KPI ratios capture inflation rate. The yearly PVI ratios capture changes in the private sector production, indicating how well the private sector is doing. The STIBOR rate is a reference rate that shows the average interest rate at which a certain group of large banks in Sweden are willing to lend to one another, without collateral, at different maturities.

A binary treatment variable, MIFID II

2 {0, 1}, represents before and after the MIFID II regulation, where 0 represents before the introduction and 1 the period after. Dummy vari- ables are created for public holidays for days prior and post the holidays based on [11]. The included holidays are New Year’s Eve, Easter, May 1, Ascension day, the National day, Midsummer and Christmas. 7 days pre and 5 days post are used for Easter and Ascension Day [12]. For Christmas and New Year’s 5 days pre Christmas and 2 days pre New Year’s, and 2 days post Christmas and 10 days post New Year’s are used. The extra 5 days after New Year’s Eve are used in an attempt to capture the so-called January Effect of the two first weeks of January. For the rest, two days pre and post are used.

For the Negative Binomial model, an additional set of Fourier- terms are used as dummies to capture annual seasonality.

TABLE I: Aggregated volume 2010-2019

Statistic: mean variance ratio stocks

SC 201141625307.8 31178.96 6451198.37 451 MC 92320 524080795285.26 5676783.58 359 LC 432651 3101597071526.57 7168823 164

III. S

The choice of programming language is R, commonly used for statistical computing [13]. The Negative Binomial model is implemented using the MASS package, and for the fixed effect approach the plm package is used [14], [15]. For the seasonal adjustment of the aggregated data the stlplus package is utilized and also the forecast package for the regression model with ARIMA errors (referred to as RegARIMA) [16], [17].

IV. M

The method of this thesis is divided into two parts, 1) a more heuristic approach of Negative Binomial regression based on the aggregated data and 2) in an effort to avoid omitted- variable biases and aggregated biases rooted in the equal weighted average, a more rigid approach of Fixed Effects modeling based on the TSCS data.

A. Data Processing of the Aggregated Data

Since the data at hand is daily stock trading volumes and the consensus is that this kind of series will exhibit seasonality, there is strong reason to suspect that the time

series also exhibits nonstationarity. This can be due to periodic events like holidays, dividend periods and similar. For the chosen seasonal adjustment weekly trading seasonality, calendar effects and annual trading seasonality is taken into consideration. At first, a heuristic approach of taking the average turnover, for each month of the year in the period between the years 2010-2019, over the turnover for an average month is deployed to examine the overall seasonality.

Especially, to shed some light on the January effect mentioned in the Introduction section. The phenomenon could interfere with the regulation effect since MIFID II was introduced just after New Year’s eve. The results are displayed in Figure 1.

−20.0%

0.0%

20.0%

1 2 3 4 5 6 7 8 9 10 11 12

Month

Impact of month

Segment

Fig. 1: Average monthly impact on turnover within the three segment categories for the period 2010-01-04 - 2018-12-28.

To examine the distribution of the January effect further, the first four weeks of the month are examined as well, following the same logic as the previous approach. The results are displayed in Figure 3. Why the turnover (trade volume over outstanding shares) is examined rather than the trade volumes is because outstanding shares can drastically change due to e.g. new emissions and stock buybacks, which need to be accounted for. Here, it is important to note that taking the average of certain periods can be misleading. In spite of this fact, the method gives an initial, overall picture of the annual trade volume season. An equivalent examination of January is made with volumes from 2016 to 2019, displayed in Figure 2 and Figure 4, since this is the time span used for the modelling process. During this period, the January effect looks more prominent compared to the longer period, and only the SC segment seem to be significantly affected.

1) Seasonal adjustment using STL and RegARIMA

Seasonal and Trend decomposition using Loess, abbrevi-

ated STL, is a well-known and commonly used method for

decomposing time series into trend, seasonal and residual

EFFECTS OF MIFID II 4

−40.0%

−20.0%

0.0%

20.0%

1 2 3 4

Week of January

Impact of January week

Segment LC MC SC

Fig. 2: Average January week impact on turnover within the three segment categories for the period 2010-01-04 - 2018-12-28.

−20.0%

−10.0%

0.0%

10.0%

20.0%

30.0%

1 2 3 4 5 6 7 8 9 10 11 12

Month

Impact of month

Segment LC MC SC

Fig. 3: Average monthly volume change within the three segment categories for the period 2016-01-04 - 2018-12-28.

−40.0%

−20.0%

0.0%

20.0%

1 2 3 4

Week of January

Impact of January week

Segment LC MC SC

Fig. 4: Average January week impact on turnover within the three segment categories for the period 2016-01-04 - 2018-12-28.

components, denoted by T

, S

and R

. For example, the original time series

Y

= T

+ S

+ R

corresponds to the top time series raw, with an example given in Figure 5 for the the SC trade volumes. STL utilises multiple

Date 0100000300000 raw

−2000020004000 seasonal

150002500035000 trend

0100000300000

2010 2012 2014 2016 2018

remainder

Fig. 5: Component of theSC trade volume time series for weekly adjustment with parameters n(s) = 151and n(t) = 303 and the recommended settings of the inner loop, n(i)= 1, and the outer loop, n(o)= 10. Note the different scales of the y-axes. Note also that the weekly seasonality oscillates so much that it in the plot appears as a solid body.

EFFECTS OF MIFID II 5

applications of the non-parametric method of locally weighted regression, abbreviated Loess (which originates in locally estimated scatterplot smoothing), and local least-squares. It is flexible for variation in the seasonal and trend components for different levels of frequency of a time series. In the case of trade volumes this would imply the mentioned weekly and yearly periodicities. First, the six parameters of the method are stated:

n

- The number of observations in each seasonal period.

n

- The window size of the Loess in the low-pass filter.

n

- The window size of the trend smoothing.

n

- The window size of the seasonal smoothing.

n

- The number of passes by the inner loop (usually set to one or two). In other words, how many times to do Loess smoothing for the seasonal and trend components.

n

- The number of passess by the outer loop, thus how many times to use robustness weights.

The parameter settings of the STL are based on eigenvalue and frequency response analyses and aim to avoid the components competing for the same variation patterns in the data. For the last two parameters fine-tuning of how many trading days to include in the trend and seasonality windows is needed. A brief account for the method and its parts is now given below.

Loess

In this part of the section, let y

be the ith observation of a dependent variable, and x

be the ith observation of an independent variable, out of n observations. Then, in the case of trade volumes, y

would represent the true deseasonalised volume and x

the observed volume at time i of a specific stock. The Loess smoothing function of the original volume, ˆ

g(x) , is computed by taking the q values of the set {x

}

closest to x based on the distance measure D

(x). Each of these volumes x

are given a weight,

v

(x) = T

✓ |x

x | D

(x)

◆

where D

(x) is the qth longest distance from x and T (·) the tricube function,

T (u) =

( (1 u

)

, if 0  u < 1

0, otherwise .

Thus, the weights give more influence to volumes close the volume of x. The Loess smoothing function for the seasonal and deseasonalised volume pair (x

, y

) can now be defined as a polynomial of dth order,

ˆ g(x) =

X

v

(x)(y

X

↵

(x)x

)

. (1) Then

ˆ

↵

(x) 2 argmin

↵k(x)2R

ˆ g(x)

yield the final, smoothed function of the ith trade volume

ˆ y

=

X

ˆ

↵

x

. (2)

Thus, the equation is built on the assumption that the relation between the volumes x

and y

can be locally approximated by a polynomial. The recommended order of this polynomial is d = 1 if the underlying pattern of the trade volume is assumed to have gentle curvature and if it is expected to have peaks and valleys the recommended order is d = 2 [18], which in this case is the order to be used. Since the Loess function is defined for all values of x, the STL method can handle missing data

.

For a window size q > n, the distance measure is defined as

D

(x) = q n D

(x)

where D

(x) is the longest distance from volume x to a volume x

. Taking the limit of the Loess function, letting q ! 1, results in v

(x) ! 1 and one ends up with an ordinary least-squared polynomial [18].

STL

The method comprises two nested, recursive loops. The inner loop updates the current state of the seasonal and trend components n

times. The outer loop runs the inner loop, followed by computing the robustness weights, ⇢

, using local least-squares, which are used to scale the Loess weights during the next run of the inner loop to reduce the influence of noise in the trade volumes on the components. The initial values of these weights are set to one, and the outer loop is then run n

times. For the kth pass of the inner loop, suppose a seasonal component S

and trend component T

, where at time position t = 1, .., n, the updates for the next pass are computed taking the following steps [12]:

Step 1: Trend adjustment

The current estimate of the trend is subtracted from the time series, Y

T

= S

+ R

with T

= 0.

Step 2: Preliminary period wise smoothing

The number of subseries, i.e. day of the week, day of the month or day of the year for a daily time series, in each period of the seasonal component is n

. Loess is now applied to each of these subseries for the trend adjusted series Y

T

in Step 1, with an extra n

time position added at the start and end of the subseries interval and q = n

. All values of the subseries are a temporary seasonal series S

, comprising n+2n

values ranging from t = 1 n

to n + n

. Step 3: Smoothing preliminary seasonal component

A low-pass filter consisting of a sequence of two

moving averages with window size n

, followed by

another with window size 3 and a Loess smoother with

d = 1 and q = n

is applied to the smoothed subseries

S

. This results in L

, where t = 1, .., n since

the filter cannot treat the endpoints of the interval,

which is why this was accounted for in Step 2 by

adding n

time positions in each direction of the time

interval. This is done to capture any low-frequency

movements.

EFFECTS OF MIFID II 6

Step 4: Updating seasonal component

To reduce the low-frequency movements in the sea- sonal component the result of the low-pass filter is subtracted, S

= S

L

.

Step 5: Seasonal adjustment

The current estimate of the seasonal component is subtracted from the time series,

Y

S

= T

+ R

. Step 6: Updating trend component

Now the Loess is applied to the seasonal adjusted series Y

S

in Step 5, with q = n

and d = 1, resulting in a new estimate of the trend, T

. The outer loop then proceeds by calculating the robustness weights for the residual

R

= Y

T

S

. The weight at time point t is

⇢

= B

✓ |R

| 6m

◆ ,

where m

is the median of |R

| and B(·) the bisquared function,

B(u) =

( (1 u

)

, if 0  u < 1

0, otherwise .

These weights estimate how much of an outlier the tth volume is, based on |R

|, and will give small weight to heavier outliers and zero to the most extreme. According to Cleveland et al. parameter values of n

= 1 and n

= 10 yield near certain convergence for the decomposition. If prior knowledge of the data indicates no outliers the outer loop can be omitted by setting n

= 0 [18]. Since the stock market is historically sensitive to a variety of influential events, the data are prone to outliers. Thus, the outer loop is used to put less weights on these, to make them less influential.

The drawback of the STL method is that it handles only a single seasonal frequency and cannot handle calendar effects. It is common for a time series to exhibit multiple seasonal frequencies. Then the STL method can be applied sequentially for the different seasonalities starting with the one with highest frequency and continue in descending order. In this paper a weekly seasonal adjustment using STL is carried out on the aggregated data, as done for the weekly adjusted SC trade volume in Figure 5, followed by an attempt to adjust for calendar effects, and annual seasonality, using a regression model with ARIMA errors, abbreviated RegARIMA, in Figure 9.

RegARIMA

To estimate the calendar effect and also annual seasonality, a regression model with ARIMA errors is used. Consider the regression model

y

= ↵ + x x x

+ ✏

. (3) Normally, the errors ✏

, t = 1, ..., T , are assumed to be white noise, but in the case of ARIMA errors they are allowed to be

Date 05000001500000 raw

−1000005000 seasonal

4000080000 trend

05000001500000

2010 2012 2014 2016 2018

remainder

Fig. 6: Components of theMC trade volume time series for weekly adjustment with parameters n(s) = 151and n(t) = 303 and the recommended settings of the inner loop, n(i)= 1, and the outer loop, n(o)= 10. Note the different scales of the y-axes. Note also that the weekly seasonality oscillates so much that it in the plot appears as a solid body.

Date 05000002000000 raw

−4000002000060000 seasonal

300000500000 trend

−5000001000000

2010 2012 2014 2016 2018

remainder

Fig. 7: Components of theLC trade volume time series for weekly adjustment with parameters n(s) = 151and n(t) = 303 and the recommended settings of the inner loop, n(i)= 1, and the outer loop, n(o)= 10. Note the different scales of the y-axes. Note also that the weekly seasonality oscillates so much that it in the plot appears as a solid body.

EFFECTS OF MIFID II 7

autocorrelated. To accomplish this, a non-seasonal ARIMA- model is used to model the errors, which is a combination of an autoregression (abbreviated AR) and a moving average model (abbreviated MA) with a difference dependent variable.

The definition of these models are as follows. An AR-model is a time series model with lagged dependent variables of order p,

✏

= ↵ +

✏

+ · · · +

✏

+ ⇣

, (4) where now ⇣

represent the assumed to be white noise. A MA-model instead uses the lags of this error term of order q,

✏

= ↵ + ⇣

+ ✓

⇣

+ · · · + ✓

⇣

. (5) Combining the two models with a first differenced (abbrevi- ated FD) dependent variable of order d yields the ARIMA- model

(1 1B · · · ^pB^p)

#

AR(p)

(1 B)^d✏t

#

F D(d)

= ↵ + (1 + ✓1B +· · · + ✓^qB^q)⇣t

#

M A(q)

,

where B is the back-shift operator, ↵ = µ(1

· · ·

) and µ =

P

t=1

(1 B)

✏

. The remaining deseasonalised time series is the fitted ARIMA-model, the assigned error component {✏

}

, and is seen in Figure 9, Figure 11 and Figure 13. As independent variables xxx

, dummies of days before and after public Swedish holidays are used and 30 Fourier terms of Equation 6, which is the maximum number of terms recommended by Daniel Ollech [12],

S_t²⁵¹= XD

d

✓

1dsin

✓2⇡dU (t) 251

◆

+ 2dcos

✓2⇡dU (t) 251

◆◆

, (6)

where U(t) is a unit step function indicating each trading day. The former naturally represent the holidays effect and the latter the annual seasonality.

2010 2012 2014 2016 2018

−30000−10000010000200003000040000

Year

Volume

Fig. 8:Calendar effect for the SC weekly adjusted trade volume time series with 30 Fourier-terms and public holiday dummies.

2017 2018 2019

0100000200000300000400000

Date

Volume

Original ARIMA

Fig. 9: TheSC weekly adjusted trade volume time series adjusted for calendar effects. The red dotted line represents the implementa- tion date of MIFID II.

2010 2012 2014 2016 2018

−60000−20000020000400006000080000

Year

Volume

Fig. 10:Calendar effect for the MC weekly adjusted trade volume time series with 30 Fourier-terms and public holiday dummies.

EFFECTS OF MIFID II 8

2017 2018 2019

100000200000300000400000

Date

Volume

Original ARIMA

Fig. 11: The MC weekly adjusted trade volume time series adjusted for calendar effects. The red dotted line represents the implementation date of MIFID II.

2010 2012 2014 2016 2018

−200000−1000000100000

Year

Volume

Fig. 12:Calendar effect for the LC weekly adjusted trade volume time series with 30 Fourier-terms and public holiday dummies.

2017 2018 2019

100000200000300000400000500000

Date

Volume

Original ARIMA

Fig. 13: The LC weekly adjusted trade volume time series adjusted for calendar effects. The red dotted line represent the implementation date of MIFID II.

At this early stage one can by inspection conclude that the residuals of the resulting adjustments of the LC and MC volumes do not show any sign of a trade volume drop around January 3rd, 2018, but for SC the trend clearly does in Figure 5. On the contrary, Figure 6 of the MC volumes shows a slightly positive trend change.

After the final seasonality adjustment, if the resulting series have negatives, its values are level shifted by adding a constant to the series. This, to ensure positive numbers. Then the values are rounded to the nearest integer to again represent count data. The original and the adjusted time series are shown in the period around the introduction date of MIFID II. The mean and variance of the volumes of the adjusted aggregated data is displayed in Table II.

TABLE II: Aggregated volume 2016-2019 Statistic: mean variance ratio no. stocks SC 72444.67 1133115408 15641.11 451 MC 138830.3 1133115408 15641.11 226 LC 258028.1 5087352468 19716.27 164

2) Outliers and Influential Points

A first visual inspection of the aggregated data tells that there is a possibility of a large number of outliers. However, the risk of measurement error is low, and there is a chance that these events will appear again. Thus, no manual data reduction is carried out.

3) Overdispersion

As a first step, the mean and variance of the aggregated

data are calculated and displayed in Table II. It is apparent

from the table that the mean and variance notably differ from

EFFECTS OF MIFID II 9

one another. The variance is higher than the mean, which is evidence pointing towards overdispersion. Overdispersion typically arises because the counts are positively correlated, which indeed is the case of stock volumes, or the mean of the data varies. The presence of overdispersion can affect the quality of estimation and the standard errors of the model parameters are usually underestimated. Significance tests on the independent variables will therefore generally show more significant values than they are, and confidence intervals for the model weights will appear more narrow. Overdispersion is detected by conducting a goodness-of-fit test.

4) Scaling

Since the scale of the volume differ from the other inde- pendent variables, the lagged volume is standardised for more interpretive model weights.

B. Analysis

The causal effect of MIFID II is explored using two coef- ficients in the regressions, MIFID II representing the direct effect of the regulation and Effect decline, representing the decline of the direct MIFID II effect after the introduction.

This can be expressed as

Total MIFID II effect =

MIFID II +

Effect decline, where Effect decline = p t t

, for t > t

and t

is the introduction date of MIFID II. For example, for a negative

= 0.35 and a positive

= 0.05 the total MIFID II effect would look like the function in Figure 14, and would in such a case support the hypothesis of a temporary level drop. Due to the interpretation as count

nov jan mar

−0.35−0.30−0.25−0.20−0.15−0.10−0.050.00

Date

Dependent variable

Fig. 14: Example of the total MIFID II treatment effect.

data and to address the aforementioned overdispersion, a Negative Binomial regression model is initially applied to the

seasonally adjusted time series.

1) The Negative Binomial Regression Model A GLM is based on three components:

•

A stochastic component, specifying the conditional dis- tribution of the response Y

for the ith of n independent observations, given the explanatory variables xxx

.

•

A linear predictor ⌘

= x x x

, were the parameters of the beta vector are unknown.

•

A link function g(·), a one-to-one, continuous and invert- ible transformation for the expected value of the response µ

, for which ⌘

= g(µ

(x x x)) .

The most common link function, the log-link g(·) = log(·) is used in this paper

P (Yi= yi|xxx) = ^yi+✓y_i^{1 1}

✓

✓µi(xxx)

✓µ_i(xxx)+1

◆yi✓

1

✓µ_i(xxx)+1

◆✓ ¹

. (7)

This distribution, as shown above, can be interpreted as a mixture of a Poisson distribution and Gamma-mixed weights [19]. Further, this interpretation gives insight as to why the Negative Binomial is preferred over the Poisson distribution for overdispersed data. Let y

, ..., y

denote n independent, non-negative observations on the response, in this case volume.

These are treated as observations of a random variable Y

, which is assumed to be Poisson distributed with mean

,

Y

|

⇠ P(

). (8)

The

is in turn assumed to be a stochastic Gamma distributed variable

i

|xxx ⇠ (✓µ

(x x x), ✓

), were

> 0, (9) with shape parameter ✓µ

(x x x) and scale parameter ✓

. By marginalising out the probability of

from the joint prob- ability of Y

and

, the well-known probability function of the Negative Binomial distribution can be derived, see above.

Thus,

Y

⇠ N B(✓

, p

(x x x)) (10) has response mean [y

|xxx] = µ

(x x x) and variance V ar[y

|xxx] = µ

(x x x) +

, where p

(x x x) =

and ✓ is the dispersion parameter. Taking the limit of ✓ ! 1 results in a variance equal to the mean, and the Poisson distribution. Thus, the Negative Binomial distribution can be interpreted as a Poisson with an added multiplicative random effect, representing the unobserved heterogeneity in the data.

That is, a high dispersion parameter ✓ is evidence of less overdispersion in the data.

The likelihood function for this model is L

( , ✓) /

Y

(y

+ ✓

) (✓

)

✓ ✓µ

(x x x)

✓µ

(x x x) + 1

◆

✓ 1

✓µ

(x x x) + 1

◆

(11)

where the expected response is µ

(x x x) = e

due to the choice

of link function being the log-link. With the likelihood defined,

the maximum likelihood estimation, abbreviated MLE, of the

dispersion parameter ✓ and the model weights can be derived

by iteration until convergence [20]. The moment estimation,

EFFECTS OF MIFID II 10

where the dispersion parameter is set to zero, is used to obtain an initial estimate for the expected response, which in turn is used to obtain the initial dispersion, ✓

.

Model Assumptions

As touched upon in the beginning of this section, the de- pendent variable is assumed to be independently, and in this case, Negative Binomial distributed. Also the residuals are assumed to be homogeneous and independent, but not normally distributed. Note also that the model do not assume homogeneity of variance and inspection of the raw residuals alone can be misleading.

Model Assessment

The independence assumptions of the dependent variable and the residuals are assessed, though in a relaxed manner, through auto-correlation and partial auto-correlation plots. Further- more, the usage of Pearson residuals is a straightforward and easy way to account for the fact that the observations have different variances [21], which is deployed during the model assessment. The Pearson residuals are derived by scaling the raw residuals with the root-squared variance, and for the Negative Binomial the definition can be written like

R

= y

µ

q µ

+

. (12)

To assess the influence of outliers and leverage points of the regression, the Cook’s distance measure is applied. The definition of the measure is as follows

D

= X

i=1

(ˆ y

y ˆ

)

ks

, (13)

where s is the mean square error and k is the number of variables in the model. Cook’s distance can simply be interpreted as the total changes of the regression when the ith observation is omitted. Lastly, the Akaike Information Criterion (abbreviated AIC) is a goodness-of-fit test and based on the log-likelihood function defined by

AIC = 2 L + 2k, (14)

where L is the log-likelihood of the model and k is the number of independent variables, including the intercept.

By the philosophy of Occam’s razor, the 2k term penalizes larger numbers of independent variables and adjusts for the size and complexity of the model [21]. It is used during the model reduction phase to compare models, with lower values indicating the preferred model.

2) The Individual Fixed Effects model

Due to the complexity of the seasonal adjustment procedure, the previous approach was only feasible for the aggregated data, resulting in two different analyses. In order to address individual effects for each stock, the following alternative analysis is conducted. In this case of individual fixed effects, consider the linear model in Equation 15 for which y

is the observed trading volume of stock i for time t in the TSCS

dataset and xxx

are the independent variables measured for that stock [22],

y

=

+

x x x

+

zzz

+ ✏

. (15) Here, zzz

are the unobserved stock-constant differences, so- called heterogeneities, across the individual stocks i = 1, .., N and

the estimated effect that a change in the independent variable has on the response for a zzz

kept constant. The idiosyncratic error term, denoted ✏

above, varies across stocks and time and [✏

] = 0. By letting ↵

=

+

zzz

the model can be rewritten as

y

= ↵

+

x x x

+ ✏

, (16) where the fixed effects are specified on stock level by including a specific intercept for each stock, here denoted ↵

. The model is equivalent to substituting the zzz

-term in Equation 15 for N 1 dummy variables, see Equation 20,

y

=

+

x x x

+

D

+ · · · +

D

+ ✏

(17) where N is the number of stocks included in the dataset.

Thus, the model rids itself of omitted variable bias caused by missing unobserved variables that change between stocks but are constant across time. Instead of estimating all these dummy variables, which is computationally ineffective, Equation 16 is averaged over the time, resulting in

y

y ¯

= (x x x

x¯ x¯ x ¯

) + (✏

¯ ✏

), (18) where

¯ y

= 1

T X

y

¯ x x x

= 1

T X

x x x

¯

✏

= 1 T

X

✏

.

This transformation is known as demeaning, since it is a mean

subtraction of the response variable using the stock-specific

mean over time. It is also known as within transformation

since the between variation is subtracted and thus leaves only

the within variation. Between variation is the stock difference,

the variation of the stock-specific mean ¯y

over time, and

is deemed contaminated by the heterogeneity of the stocks

[23]. Within variation is the variation over time within the

stocks, the variation of the demeaned left-hand side term in

Equation 18. The fixed effect estimation is finally carried out

using pooled regression by ordinary least squares applied to

the demeaned data. Thus, the method is based on using only

the variation that results in approximately unbiased estimates

of the parameters by excluding the between variation and infer

the causal effect from the within variation alone [22]. In this

case, by comparing each stock’s volumes before and after the

MIFID II regulation was introduced on January the 3rd, 2018.

EFFECTS OF MIFID II 11

Model Assumptions

The Fixed Effects model assumes strict exogeneity [✏

] = 0,

which in turn is assumed to identify the model weight

. This is equivalent to

[✏

|xxx

, ↵

] = 0

for a treatment variable xxx

, where i = 1, ..., N and t = 1, ..., T . Model Assessment

The model fit is measured using the adjusted-R

statistic, R

= 1 SS

SS

, (19)

which is the ratio of the sum of squares for the regression and the total sum of squares, indicating the percentage of variation in the data explained by the model [21]. The Equation 19 of the R

can be scaled to account for the number of observations and the number of model variables,

R

= 1

 (1 R

)(n 1)

(n k 1) . (20)

where n is the number of observation and k is the number of coefficients.

Robust standard errors are utilised to account for the presumed heteroscedasticity of the stocks. Similar as for heteroscedasticity, autocorrelation invalidates standard errors. When both phenomena are present in the data, so-called heteroscedasticity and autocorrelation consistent standard errors (abbreviated HAC) need to be used to not cause misleading statistical inference. These allow for heteroscedasticity and autocorrelated errors within a stock but not correlation across stocks. To accomplish this, the covariance matrix of the -coefficients in the regression is adjusted by using the maximum-likelihood for estimating functions instead of the standard variances of the

’s. For more detail regarding the HAC estimators of the covariance matrix see Zeileis and Achim, 2007 [24]. The residuals are then examined to assess the assumptions of the regression.

More precisely, the residuals’ histogram, to control for normality assumption, and also the total casual effect of MIFID II is plotted with the residuals. Here, relations and consistency of the residuals, or lack thereof, is reviled.

Additionally, the relation between observations and fitted values are plotted.

Note that, although including individual fixed effects elimi- nates the risk of a bias due to omitted factors that vary across stocks but not over time, it is suspected that there are other omitted variables that vary over time and thus cause biases.

TABLE III: Full and Final Regression SC Dependent variable:

Trading volume

Full model w/ MIFID II w/o MIFID II

(1) (2) (3)

Lagged volume 0.119^⇤⇤⇤ 0.120^⇤⇤⇤ 0.129^⇤⇤⇤

(0.009) (0.009) (0.009)

Lagged return 2.508^⇤⇤ 2.601^⇤⇤ 2.010^⇤

(1.189) (1.184) (1.208)

Stibor rate 0.014

(0.231)

KPI 0.133^⇤⇤ 0.133^⇤⇤ 0.110^⇤⇤

(0.054) (0.054) (0.044)

PVI 0.997

(0.993)

Trend 0.001^⇤⇤⇤ 0.001^⇤⇤⇤ 0.001^⇤⇤⇤

(0.0002) (0.0002) (0.0001)

MIFID II 0.334^⇤⇤⇤ 0.326^⇤⇤⇤

(0.065) (0.064)

Effect decline 0.033^⇤⇤⇤ 0.034^⇤⇤⇤

(0.006) (0.005)

Log Shares 0.418^⇤⇤⇤ 0.420^⇤⇤⇤ 0.302^⇤⇤⇤

(0.060) (0.060) (0.058)

Constant 5.277^⇤⇤⇤ 4.201^⇤⇤⇤ 6.156^⇤⇤⇤

(1.499) (1.013) (0.981)

Observations 753 753 753

Log Likelihood -8,503.686 -8,504.183 -8,522.842

✓ 12.410^⇤⇤⇤(0.631)12.394^⇤⇤⇤(0.630)11.810^⇤⇤⇤(0.600) Akaike Inf. Crit. 17,027.370 17,024.370 17,057.690 Note: ^⇤p<0.1;^⇤⇤p<0.05;^⇤⇤⇤p<0.01

V. R

1) The Negative Binomial Model

sep nov jan mar maj

20000400006000080000100000120000

Date

Volume

MIFID II No MIFID II

Fig. 15: Model results for the final SC regression compared to a reduced model without MIFID II variable.

EFFECTS OF MIFID II 12

2016 2017 2018 2019

0510

Date

Residuals

Fig. 16: Model residuals for the final SC regression.

0 20 40 60 80 100

0.00.20.40.60.81.0

Lag

ACF

Fig. 17: Auto-correlation function of the final SC regression residuals.

0 20 40 60 80 100

−0.050.000.050.10

Lag

Partial ACF

Fig. 18:Partial auto-correlation function of the final SC regression residuals.

0.0 0.1 0.2 0.3 0.4

−50510

Leverage

Std. Pearson resid.

glm.nb(volume ~ lagged_volume + lagged_return + kpi + time + mifid + time_a ...

Cook’s distance

1 0.5 0.5 1

2128 2127

2212

Fig. 19:Cook’s distance for the final SC regression.

EFFECTS OF MIFID II 13

TABLE IV: Full and Final MC Regression Dependent variable:

Trading volume

Full model w/ MIFID II w/o MIFID II

(1) (2) (3)

Lagged volume 0.214^⇤⇤⇤ 0.214^⇤⇤⇤ 0.247^⇤⇤⇤

(0.017) (0.017) (0.017)

Lagged return 0.858 (1.254)

Stibor rate 0.910^⇤⇤⇤ 0.935^⇤⇤⇤ 0.670^⇤⇤⇤

(0.218) (0.214) (0.213)

KPI 0.010

(0.050)

PVI 1.569^⇤ 1.513^⇤ 1.150

(0.922) (0.919) (0.845)

Trend 0.001^⇤⇤⇤ 0.001^⇤⇤⇤ 0.0004^⇤⇤⇤

(0.0002) (0.0001) (0.0001)

MIFID II 0.230^⇤⇤⇤ 0.226^⇤⇤⇤

(0.059) (0.055)

Effect decline 0.006 0.006

(0.005) (0.005)

Log Shares 0.706^⇤⇤⇤ 0.711^⇤⇤⇤ 0.636^⇤⇤⇤

(0.073) (0.070) (0.070)

Constant 2.309 2.333 1.753

(1.520) (1.491) (1.416)

Observations 753 753 753

Log Likelihood -8,940.093 -8,940.343 -8,962.545

✓ 14.550^⇤⇤⇤(0.742)14.541^⇤⇤⇤(0.741)13.727^⇤⇤⇤(0.699) Akaike Inf. Crit. 17,900.190 17,896.690 17,937.090 Note: ^⇤p<0.1;^⇤⇤p<0.05;^⇤⇤⇤p<0.01

sep nov jan mar maj

100000200000300000400000

Date

Volume

MIFID II No MIFID II

Fig. 20: Model results for thefinal MC regression compared to a reduced model without MIFID II variable.

2016 2017 2018 2019

−20246810

Date

Residuals

Fig. 21: Modelresiduals for the final MC regression.

0 20 40 60 80 100

0.00.20.40.60.81.0

Lag

ACF

Fig. 22: Auto-correlation function of the final MC regression residuals.

EFFECTS OF MIFID II 14

0 20 40 60 80 100

−0.050.000.05

Lag

Partial ACF

Fig. 23: Partial auto-correlation function of the final MC regres- sion residuals.

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

0510

Leverage

Std. Pearson resid.

glm.nb(volume ~ lagged_volume + stibor + pvi + time + mifid + time_after_mi ...

Cook’s distance

0.5 0.5 1 1946

1545

1757

Fig. 24:Cook’s distance for the final MC regression.

TABLE V: Full and Final Negative Binomial LC Dependent variable:

Trading volume

Full model w/ MIFID II w/o MIFID II

(1) (2) (3)

Lagged volume 0.354^⇤⇤⇤ 0.359^⇤⇤⇤ 0.373^⇤⇤⇤

(0.025) (0.025) (0.025)

Lagged return 0.385 (1.006)

Stibor rate 0.152

(0.212)

KPI 0.058

(0.047)

PVI 0.277

(0.827)

Trend 0.00004

(0.0002)

MIFID II 0.015 0.017

(0.055) (0.046)

Effect decline 0.006 0.007^⇤

(0.004) (0.004)

Log Shares 1.328^⇤⇤⇤ 1.037^⇤⇤⇤ 0.759^⇤⇤⇤

(0.354) (0.209) (0.193)

Constant 12.608^⇤ 7.293^⇤ 1.892

(6.993) (4.046) (3.724)

Observations 753 753 753

Log Likelihood -9,347.740 -9,349.481 -9,354.934

✓ 17.709^⇤⇤⇤(0.904)17.629^⇤⇤⇤(0.900)17.380^⇤⇤⇤(0.887) Akaike Inf. Crit. 18,715.480 18,708.960 18,715.870 Note: ^⇤p<0.1;^⇤⇤p<0.05;^⇤⇤⇤p<0.01

sep nov jan mar maj

100000200000300000400000500000

Date

Volume

MIFID II No MIFID II

Fig. 25: Model results for the final LC regression compared to a reduced model without MIFID II variable.

EFFECTS OF MIFID II 15

2016 2017 2018 2019

−20246

Date

Residuals

Fig. 26: Modelresiduals for the final LC regression.

0 20 40 60 80 100

0.00.20.40.60.81.0

Lag

ACF

Fig. 27: Auto-correlation function of the final MC regression residuals.

0 20 40 60 80 100

−0.10−0.050.000.050.10

Lag

Partial ACF

Fig. 28:Partial auto-correlation function of the final LC regression residuals.

0.00 0.01 0.02 0.03 0.04 0.05 0.06

−4−20246

Leverage

Std. Pearson resid.

glm.nb(volume ~ lagged_volume + time_after_mifid + log(shares)) Cook’s distance

0.5 1514

1515 1624

Fig. 29:Cook’s distance for the final LC regression.

2) The Individual Fixed Effects model

The Fixed Effects model is defined on the form

log(v

) =

x x x

+ log(s

) (21) where v

is the trade volume for stock i and s

outstanding shares for stock i. The Fixed Effects models of SC, MC and LC are displayed in Table VI, Table VII and Table VIII respectively, with dummy variables for public holidays, months of year, days of month and market sector. The dummy variables’ statistics are withdrawn due to space limitations. As can be seen from the tables, the adjusted-R

s are low for SC and MC, indicating the influence of unknown time-varying confounders manifested in the residuals since they are large.

This can also be seen in Figure 30, Figure 33 and Figure 36.