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Review of Economics and Finance, 2023, 21, 1317-1331 1317
Liquidity Classification of Equities Under Stress Using Machine Learning
Models: Evidence from Major World Share Indices
Coskun Tarkocin1,* and Murat Donduran2
1phD Candidate in Economics, Graduate School of Social Sciences, Yildiz Technical University, Istanbul, Turkey.
2Director of Graduate School of Social Sciences, Yildiz Technical University, Istanbul, Turkey.
Abstract: The classification of assets based on their liquidity behaviour under stress is a crucial element of bank li-
quidity stress testing. It is also important to define how financial institutions should fund these assets within the cur-
rent business model whilst avoiding excessive liquidity risk. This study aims to revisit the liquidity coverage ratio
(LCR) assumptions for common equity shares using new data attributes and supervised machine learning models.
This research contributes to the literature by providing fresh insight into which characteristics impact share behav-
iour under liquidity stress. Empirical results suggest sector, share beta, industry, and market capitalisation of the
share are contributing factors which help predict shares’ liquidity behaviour under stress. This study also finds that
the financial, basic materials and energy sectors are more volatile and less liquid under market stress; shares with
lower beta show more liquid characteristics, and higher market cap stocks show more liquid behaviour.
JEL Classification: C10, G01, G21, G33.
Keywords: Liquidity Risk, Equities, Liquidity Coverage Ratio (LCR), Machine Learning Models, Ensemble Model, Random
Undersampling Algorithm, financial stress.
1. INTRODUCTION
Over the last 30 years, regulations and technological ad-
vancements have significantly transformed the banking in-
dustry with instantly available multiple products regulated
by complex rules. Development in academic literature and
practices of risk management did not prevent the financial
crisis of 2007–2008, which was considered one of the worst
economic downturns since the Great Depression of the 1930s
(Bordo, 2010). Major central banks intervened to stop the
collapse of the financial system. Subsequently, the Basel
Committee on Banking Supervision (BCBS) introduced a
new regulatory framework, widely known as the Basel III
rules, to minimise future financial crises. Two new metrics
were also introduced for liquidity risk measurement: the li-
quidity coverage ratio (LCR), and the net stable funding ratio
(NSFR) (BCBS, 2010).
The BCBS integrated the new metrics into the Basel Frame-
work in January 2013. The short-term liquidity metric, LCR,
requires banks to hold enough unencumbered high-quality
liquid assets (HQLA) under idiosyncratic and market-wide
stress to meet net outflows over the following 30 days. LCR
aims to prevent banks from overreliance on short-term fi-
nancing and provides a regular liquidity stress test for banks.
Regulators expect that a bank should survive 30 days using
the stock of the unencumbered HQLA, thereby providing
management and supervisors sufficient time to take correc-
*Address correspondence to this author at the Candidate in Economics,
Graduate School of Social Sciences, Yildiz Technical University, Istanbul,
Turkey, Corresponding Author, E-mail: ctarkocin@hotmail.com
tive actions (BCBS, 2013). The long-term funding metric,
NSFR, requires banks to have funding sources defined as
stable based on their balance sheet structure to increase the
resilience of the banking sector (BCBS, 2014b). Bonner and
Hilbers (2015) assessed the history of the liquidity regulation
until 2013 and found the main reason harmonised liquidity
regulation such as this was not introduced earlier was a lack
of crisis-related supervisory momentum before the 2007–
2008 financial crisis—a crisis mainly driven by liquidity
problems.
In this study, LCR assumptions for common equity shares
1
will be revisited. New data attributes and models will be
employed and the policy implications of these new ap-
proaches will be discussed from both a bank and a regulatory
perspective. Liquidity classification is important for financial
institutions since it will guide how these assets should be
funded within the current business model whilst avoiding
excessive liquidity risk.
This paper contributes to the literature in three aspects. Ex-
isting liquidity metrics were transformed into a binary classi-
fication problem, then supervised machine learning (ML)
models were used to predict the classification of the shares
under stressed conditions. The results and insights gathered
will inform the eligibility criteria of common equity shares
and will provide a more granular approach to understanding
what impacts the behaviour of equities under stress condi-
tions. Additionally, it will open a new research area for fur-
1
Level 2B assets, Equities, Shares and Stocks will be used interchangeably
through this study.
1318 Review of Economics and Finance, 2023, Vol. 21, No. 1 Coskun Tarkocin and Murat Donduran
ther review of the existing Basel Standards with new data
and advanced models. To the best of our knowledge, this is
the first time that a set of supervised machine learning mod-
els, e.g. the ensemble method with random undersampling
algorithm, have been used to further the exploration of li-
quidity stress assumptions embedded in the Basel Standards
and the classification of equities under market-wide stress.
This study is organised as follows: Section 1.2 presents the
literature review, Section 1.3 provides liquidity risk defini-
tions, measurements and regulatory classification details;
Section 1.4 outlines the data selected for this study, and
summarises the handling process along with descriptive sta-
tistics; Section 1.5 explains the methodology of this study,
provides a brief introduction to machine learning models and
explains the selection process for the models used in this
study, whilst Section 1.6 discusses the results of this study,
including any comparisons between results gathered from the
application of different models. Section 1.7 outlines the con-
clusion of the empirical analysis and discusses its policy
implications.
2. LITERATURE REVIEW
This study aims to explore the liquidity characteristics of
shares under stress conditions and its focus will be on market
liquidity risk and its linkage to the classification of liquidity
stress assumptions. The relevant literature is discussed in the
following order: (1) literature relevant to the LCR assump-
tions, (2) literature regarding stock market liquidity and how
to measure it and (3) literature concerning machine learning
applications in liquidity risk management.
The Basel Committee issued guidance on market-based indi-
cators of liquidity to assist supervisors in evaluating the li-
quidity profile of assets. Although each jurisdiction deter-
mines its own HQLA qualifications, common data and tools
help maintain consistency across jurisdictions (BCBS,
2014a). Liquidity standards define HQLA under three cate-
gories: Level 1 assets, Level 2A assets and Level 2B assets.
Level 1 assets are the highest quality assets with 0% haircut;
Level 2A is the next highest quality with a 15% haircut, and
Level 2B the lowest quality with a 50% haircut. Subjective
and objective criteria for asset classification are provided in
the standards at a detailed level (BCBS, 2019).
The assumptions of the LCR were implemented across juris-
dictions with very minor changes and challenges. Yet Ball
(2020) has criticised the assumptions related to retail deposit
outflow, loss of secured funding, and collateral calls under
derivatives contracts (mainly the variation margin compo-
nent) and Level 2B assets. These assumptions were revisited
using publicly available data regarding the 2008 crisis as a
benchmark. A new liquidity stress test was then developed
and applied to six major US banks. Ball argued that, based
on the revised LCR assumptions, all six US banks would fail
within the 30-day liquidity stress period. In the study, all
Level 2B equities were assumed illiquid, yet no data or anal-
ysis were provided to support this assumption—only subjec-
tive expert judgement was used to apply this stress parame-
ter. Furthermore, Ball (2020) also highlighted that there has
been little discussion of specific LCR assumptions by aca-
demic researchers.
A detailed report on HQLA characteristics was compiled by
the European Banking Authority in 2013 (EBA, 2013b). The
report aimed to establish uniform definitions of HQLA char-
acteristics by analysing the wide range in liquidity of the
financial assets traded in the EU between 1 January 2008 and
30 June 2012, then classifying such assets from a liquidity
and credit quality perspective. The report compares and
ranks asset liquidity classes and validates operational and
subjective principles that were defined in the LCR. Several
liquidity measures were calculated for cross-asset analysis in
order to rank them; for instance, when analysing equities
specifically, sector and issuance size were also investigated.
The evidence for the impact of sector attributes on liquidity
is mixed, but it is clear larger issuances have better liquidity
values. Nonetheless, the report concludes that there is insuf-
ficient evidence of market liquidity to classify equities as
“assets of high liquidity and credit quality” (EBA, 2013b, p.
24).
One may argue that the materiality of Level 2B assets is
small in the liquidity asset buffers (LABs) of major banks
using public disclosures in the US. However, as Ball (2020)
argued, material amounts relevant to these assets will be
found in the secured funding lines of the LCR. The reason
for this is, irrelevant of the source of equities in a bank (out-
right holding or received as collateral), as soon as an asset is
posted as collateral it will be encumbered and will not be
shown in the bank’s LAB. Instead, the collateral assets will
be returned once the secured financing transaction (SFT) has
matured.
As discussed above, academic literature regarding LCR as-
sumptions is limited; in contrast, literature about stock mar-
ket liquidity and what types of measures can be used is quite
vast due to better data availability compared to other asset
classes (EBA, 2013b). Jones (2002) provided a comprehen-
sive analysis of the US equity market over 100 years and
reported a general decline in the bid–ask spreads on Dow
Jones stocks, whilst sharp increases were observed during
market stresses. There is noted evidence of liquidity
measures such as spreads and turnover predicting returns one
year in advance; thus, liquidity is an important determinant
of conditional expected returns. Amihud (2002) employed an
illiquidity measure (ILLIQ)
2
and conducted news tests which
showed asset expected returns increasing in illiquidity.
Acharya and Pedersen (2005) built an equilibrium asset pric-
ing model with liquidity risk and used the Amihud measure
as an illiquidity proxy. Brunnermeir and Pedersen (2008)
developed a model to explain empirically documented fea-
tures of market liquidity, including sudden dry-ups, com-
monality across securities, its relation to market volatility, its
sensitivity to “flight to quality”, and co-movement with the
market.
A long list of liquidity metrics
3
can be found in the literature.
Kumar and Misra (2015) classified and organised the litera-
ture and provided a critical review of the frameworks cur-
2
Amihud defines ILLIQ as stock absolute return divided by its daily dollar
volume. This study will follow Amihud’s definition as one of the liquidity
measures to train the machine learning models.
3
In this study the term ‘liquidity metric’ is used interchangeably with ‘li-
quidity proxies’ and ‘illiquidity measures’.
Liquidity Classification of Equities Under Stress Review of Economics and Finance, 2023, Vol. 21, No. 1 1319
rently available for modelling liquidity. They also presented
a summary of the low-frequency liquidity proxies, empirical
studies on liquidity proxies, liquidity determinants and li-
quidity patterns. EBA (2013b) discussed the existing litera-
ture for different asset classes, including equities, and then
divided the literature into two groups of study: the first
which measures liquidity itself, and the second which ex-
plores the asset pricing implications of liquidity.
EBA (2013b) listed 25 liquidity metrics, applicable to stocks
or securities, and examined eight of these to use in uniform
distributions of the assets. Kumar and Misra (2015) listed 18
low-frequency liquidity proxies. Marshall, Nguyen and
Visaltanachoti (2013) used three transaction cost bench-
marks and nine liquidity proxies to investigate which liquidi-
ty proxies measure the actual cost of trading in frontier mar-
kets. They found that Gibbs, Amihud and Amivest proxies
have the highest correlation with the liquidity benchmarks.
Sarr and Lybek (2002) reported nine selected liquidity
measures for equity markets in the US, Mexico, South Ko-
rea, Malaysia and Indonesia, and noted that liquidity
measures may send mixed signals during a crisis. Vayanos
and Wang (2012) surveyed the theoretical and empirical lit-
erature on market liquidity and reported numerous studies of
empirical measures of illiquidity. Fong, Holden and Trzcinka
(2017) investigated the most accurate liquidity proxies using
both low- and high-frequency data, and found that the Ami-
hud measure is one of the best liquidity proxies among the
others. Naes, Skjeltorp and Ødegaard (2011) used four li-
quidity measures to analyse the relation between stock mar-
ket liquidity and the business cycle.
The third part of the literature relevant to this study is the
application of machine learning models to bank risk man-
agement or liquidity risk regulation. A subset of artificial
intelligence, supervised machine learning models are em-
ployed to conduct data experiments in this study. Machine
learning models can be grouped into three main categories:
supervised, unsupervised and reinforcement learning. Super-
vised learning models train data based on a given input and
output. By contrast, unsupervised learning models analyse
data without a given output, and find potential relationships
through clustering data. In reinforcement learning models,
the aim is to maximise the defined reward for the specific
action given (McKinsey&Company, 2021). Further discus-
sion related to the application of machine learning is provid-
ed in the Methodology section.
3. LIQUIDITY RISK DEFINITIONS
There are two types of liquidity risks banks may face in
stress. The first is funding liquidity risk. This is where a
bank does not have sufficient cash or high-quality collateral
to cover liabilities (outflows) as they fall due. Typically, this
type of risk is triggered by an idiosyncratic stress event. By
contrast, the second type of market liquidity risk, is when a
financial asset cannot be sold quickly enough or with a large
enough price impact; this type of risk is more driven by mar-
ket-wide stress. The underlying reason for bank liquidity risk
is the traditional banking model, wherein short-term liabili-
ties are converted into longer-term loans by maturity trans-
formation. The main mitigation for liquidity risk therefore
becomes establishing a stable funding profile, with a second
line of defence provided by having sufficient liquid assets to
act as a buffer (Farag, Harland, & Nixon, 2013).
The two types of liquidity risk are closely related to each
other. For instance, when funding liquidity risk starts to ma-
terialise—which may be for numerous reasons, including
large deposit outflows—a bank may need to monetise its
liquid asset buffer (LAB) to cover outflows under stress.
When a decision is made to monetise non-cash collateral, the
market liquidity of the asset becomes critical. For this rea-
son, historically LABs have been comprised of high liquidity
and credit quality government bonds such as US Treasuries,
UK Gilts and Japanese government debt.
The relationship between market liquidity and funding li-
quidity is not the focus of this study, therefore it will not be
discussed in detail. One of the most cited papers in the litera-
ture, Brunnermeier and Pedersen (2008), provides a model
that links funding liquidity to asset market liquidity. Under
certain conditions, destabilised margins can lead to liquidity
spirals. Brunnermeier and Pedersen also show that when
speculators face capital constraints, they will reduce risky
positions, which later results in a reduction in market liquidi-
ty. In this instance, prices will be driven more by funding
liquidity considerations than movements in fundamentals.
BCBS (2014a) discussed in detail liquidity characteristics,
criteria and metrics as part of guidance provided to the Su-
pervisory Authorities. They defined four main characteris-
tics: asset quality, transparency and standardisation, active
and sizeable market, and liquidity (market liquidity). EBA
(2013a) followed a two-step approach to rank asset classes
and identify explanatory characteristics. The first step was to
identify a common set of liquidity metrics and aggregate
their results. The second step involved testing whether ex-
planatory characteristics could be used to predict liquidity.
Following this EBA (2013a), a detailed report of EBA
(2013b) was constructed and no specific change was pro-
posed regarding shares treatment in the regulation.
3.1. Liquid Asset Buffer Assumptions and Its Importance
in Bank Liquidity Management
Under liquidity stress, banks could face a significant amount
of liabilities leaving such as customers withdrawing deposits
or market participants not rolling over short-term financing
transactions, depending on the characteristics and severity of
the stress event. Banks hold high-quality assets in their LAB
such as cash, government securities and other monetisable
assets to cover these cash outflows. Simply holding cash
assets as a LAB would eliminate the risk associated with
monetisability, time taken to monetise and asset price im-
pact. However, holding only cash assets would not be the
optimal decision since non-cash HQLA may provide higher
returns and natural hedge to banking book positions; it may
also need to be held as part of client activity. Banks with a
large number of reverse repos or financing transactions re-
ceive collaterals which can be used in the LAB, given opera-
tional and other requirements are satisfied.
The LCR Delegated Act (LCR DA) definitions and assump-
tions will be used throughout this study to maintain con-
sistency. In the LCR DA, general requirements (Article 7),
operational requirements (Article 8) and eligibility criteria
1320 Review of Economics and Finance, 2023, Vol. 21, No. 1 Coskun Tarkocin and Murat Donduran
(Chapter 2 Article 10 to Article 17)
4
are defined in detail
(LCR Delegated Act, 2015).
Regulatory rules define which assets can be used in a LAB
and which haircut percentages must be applied, providing
consistency across jurisdictions. Financial institutions may
have a different view from regulators, but differing defini-
tions can be applied only in internal metrics; regulatory met-
rics do not give any flexibility around definitions.
The liquidity classification of assets has three main implica-
tions for a bank. First, the classification affects which assets
and how much of each type of asset can be relied upon for
liquidity stress testing purposes. Second, it affects how assets
will be incentivised or disincentivised as part of the fund
transfer pricing (FTP) framework. Extremely high credit and
liquidity quality assets (e.g. US Treasuries, UK Gilts and
German Government Bonds) can be funded short-term,
whilst long-term lending to clients or illiquid tradable assets
(in some cases short-term assets as well, where franchise risk
consideration is high) will require longer-term funding.
Third, liquidity classification has external pricing implica-
tions. When high-quality collateral is provided as part of
secured financing transactions, the haircut applied will be
lower compared to that of lower quality HQLA or non-
HQLA assets. For these reasons, liquidity classification is an
important part of liquidity risk management. This study will
contribute to this area of study by providing further insight
into what characteristics impact shares’ behaviour under
liquidity stress.
3.2. Regulatory Treatment of the Shares in Liquid Asset
Buffer (LAB)
In this study, the focus will be on the eligibility criteria de-
fined in Article 12(c) of the LCR DA. Fulfilling all require-
ments of these criteria does not mean an unlimited amount of
the assets can be held in the LAB. Caps are applied to each
asset quality class to control the composition of the LAB.
For instance, the LAB can consist of a maximum 15% of the
Level 2B assets (LCR Delegated Act, 2015).
To meet the eligibility requirements of the LCR DA, shares
must:
4
The LCR Delegated Act may be referred to as LCR DA, LCR rules, or
EBA LCR.
Be part of a major stock index;
Be denominated in a member state currency, or can
be counted up to net stress outflow in that currency;
Have a proven record of reliable liquidity source in
normal and stressed liquidity conditions. This re-
quirement can be met if the price drop is less than
40%, or the increase in haircuts is less than 40 per-
centage points during a 30-day period of market
stress.
In addition to the above eligibility criteria, general and oper-
ational requirements must be met for an asset to be deemed
liquid. These requirements are summarised in Table 1.
4. DATA
Individual stocks from the world’s largest stock exchanges
are used in this study and data are sourced from Bloomberg
and Yahoo Finance. Only data from stock exchanges in de-
veloped markets have been analysed to avoid mixing with
developing or frontier markets; the rationale for this is de-
veloped markets are deeper and more active and show high
trading volumes even under stress. Sojka (2019) examined
the dynamics of low-frequency liquidity measures for devel-
oped and emerging markets and evidenced more liquidity
offered on the developed market (Bedowska-Sójka, 2019).
This decision has been made to allow more focus on share-
specific information.
The New York Stock Exchange (NYSE), Nasdaq, Tokyo
Stock Exchange, Shanghai Stock Exchange, Hong Kong
Stock Exchange, NYSE Euronext (Europe), London Stock
Exchange, and Shenzhen Stock Exchange are by far the larg-
est stock exchanges based on market values (Aras, Karaman,
& Kazak, 2020). Data from Shanghai and Shenzhen has not
been included in this study, since based on the annual FTSE
country classification of equity markets study, as of Septem-
ber 2020, Chinese equity markets are not classified as “De-
veloped” but “Secondary Emerging” (FTSE, 2020).
In the second step of data selection, only major indices from
these stock exchanges were selected to investigate the rela-
tionship with the largest stocks listed on the markets. This
selection will also help retain deep and active market charac-
teristics as eliminating criteria. Therefore, this study’s focus
will be on how specific shares can be classified given trans-
Table 1. Summary of LCR DA General and Operational Requirements for Liquid Assets.
General Requirements for Liquid Assets (LCR DA Article 7)
Operational Requirements for Liquid Assets (LCR DA Article 8)
The assets should be unencumbered.
LAB is appropriately diversified all the time.
The assets shall not have been issued by the credit institution itself.
LAB should be readily accessible during 30 days.
Not issued by credit institution itself
LAB is under control of the liquidity function.
The assets shall not be issued by a financial company.
Credit institutions regularly monetise the LAB to test monetisability.
The value of the assets can be determined by easily available market prices.
The Assets can be hedged subject to the conditions in Article 8.
The assets shall be listed on recognised exchange or tradable via outright sale
or via simple repurchase transaction on generally accepted repurchase mar-
kets.
Currency denomination of the LAB is consistent with the currency of net
liquidity outflows.
Liquidity Classification of Equities Under Stress Review of Economics and Finance, 2023, Vol. 21, No. 1 1321
parent pricing, available market depth, predicted price drop
criteria, and Amihud illiquidity measurements.
4.1. Data Transformation and Cleaning
Collecting all shares in the selected major indices initially
left 1100 unique share ISINs. Shares that were not available
in the global financial crisis of 2007–2008 were removed to
leave a list of shares continuously available between January
2007 and June 2019. After removing duplicate shares be-
tween different indices, 882 unique shares remained for
analysis. Mainly Euronex100, Eurostocks50, CAC40,
DAX30 or Nasdaq100 versus SP500 include several shares
from both indices. Variables which are continuously availa-
ble for all remaining shares are kept for the final modelling
training and prediction stage.
In order to test liquidity under stress condition, first we need
to define the most stressful period in the last 12 years. Table
2 shows the Global Financial Crisis Period 1 as the most
stressful event for the global financial markets in this time
period, with an average largest monthly price drop of 50%.
Machine learning models will be applied for this period to
investigate what may define the shares liquidity under this
stressed condition.
Table 2. Monthly Price Drop Across Stress and Historical Peri-
ods.
Period
Largest Monthly Drop
Global Financial Crisis Period 1 (Sep–Nov 08)
−50%
Global Financial Crisis Period 2 (Jan–Mar 09)
−31%
European Debt Crisis (Mar–Nov 11)
−26%
Last 5 Years (Jun 14–Jun 19)
−25%
For each share information in Table 3 sourced, or calculated
to train the models.
5. METHODOLOGY
Mainly due to increased availability of data, computing pow-
er and improved software, the popularity of the machine
learning models has increased in the financial sector (BOE,
2019).
Odom and Sharda (1990) conducted one of the earliest stud-
ies applying machine learning models in bank risk manage-
ment and showed the applicability of the neural network
model for bankruptcy prediction. Chatzis et al. (2018) used
deep and statistical machine learning methods to forecast the
stock market crisis and found that data classification accura-
cy significantly improved with the application of these mod-
els. Balaji et al. (2018) applied deep learning models for
stock price forecasting and generated an accurate forecast of
the direction up to 71.95%.
Leo, Sharma and Maddulety (2019) conducted a literature
review of machine learning models in banking risk manage-
ment and reported many areas in which banking could bene-
fit significantly from their application, including liquidity
risk. Several studies listed for credit, market and operational
risk applications, however, show that the application of ma-
chine learning to liquidity risk management is thus far very
limited. One example of such research is Tavana et al.’s
2018 study, in which the researchers employed Artificial
Neural Network and Bayesian Networks to measure liquidity
risk, demonstrating these models’ applicability and efficien-
cy for bank liquidity risk management. Another example is
Khan et al.’s 2020 study, whereby deep learning models
were used to predict Vietnamese stock market liquidity from
a sample of 220 companies’ daily stock trading data.
(Nosratabadi et al., 2020) conducted a comprehensive review
of advanced machine learning and deep learning methods
applications in economics. According to this recently pub-
lished detailed review, machine learning models are used for
stock price prediction, algorithmic trading, portfolio man-
agement, sentiment analysis, customer behaviour analysis,
Table 3. Monthly Price Drop Across Stress and Historical Periods.
Feature Name
Data Type
Explanation
Features (Input Data)
Sector
Categorical
9 sector, Financial, Basic Materials, Energy, Industrial, Consumer-Cyclical,
Technology, Communications, Consumer-Non-cyclical, Utilities
Industry
Categorical
67 Unique sub industry
Share Beta as of 29Aug 2008
Numerical
Share Beta pre-Lehman Collapse calculated
Log (Median Market Cap)
Numerical
Natural logarithm of the median of market capitalisation of the share during
stress months
Median Market Cap Percentage
Numerical
Median of market capitalisation share divided all shares total median mar-
ket capitalisation (882 shares total)
90-day average trading volume
Numerical
90-day average trading volume calculated for each share (minimum ob-
served during stress period used)
Response Name
Data Type
Explanation
Responses
Cumulative Maximum Price
Drop (CMPD)
Categorical
Numerical value transformed into class label (Liquid/Illiquid)
Amihud Measure (Amh)
Categorical
Same as above
1322 Review of Economics and Finance, 2023, Vol. 21, No. 1 Coskun Tarkocin and Murat Donduran
dynamic credit risk evaluation and bankruptcy prediction,
amongst other uses. Stock price prediction is the most stud-
ied area, followed by marketing including customer behav-
iour analysis, and then corporate bankruptcy (Nosratabadi, et
al., 2020).
To the best of our knowledge, this study will be the first in
the literature to use supervised machine learning models to
understand what characteristics impact the behaviour of eq-
uities under stress conditions. Incorporating the findings of
this study will have cost implications, both from a regulator
and an individual bank perspective. For this reason, any im-
plementation must have controls and monitoring in place,
whilst expert judgement should be applied where required.
5.1. Liquidity Measures
In this study, we will employ two liquidity measures. The
first measure is the criteria defined by the Basel Committee
and other regulators for eliminating shares from inclusion in
a LAB. If a share has more than a 40% price drop in a nor-
mal or stressed condition, it is classified as illiquid. In this
study, cumulative maximum price drop (CMPD) is calculat-
ed for the defined stress period. If a share has more than a
40% drop, it is labelled as illiquid in the empirical analysis to
train the model.
Cumulative Maximum Price Drop (CMPD): Month-
ly log return is calculated and then a minimum of it
is used. The minimum for a negative return will re-
sult in the maximum price drop, since in a stress pe-
riod, equity prices will drop significantly. N is de-
fined as the number of business days used to calcu-
late CMPD.
The second liquidity measure was first proposed by Amihud
(2002) and has since been widely examined in the literature.
This measure has been selected for this study due to its sim-
plicity and prevalence in the literature. Additionally, it does
not require high-frequency data. For Amihud’s measure,
liquidity is defined as a daily absolute return on the trading
volume for each day. Like the CMPD, it will be used to train
models, however one limitation is the need to split what
would be the threshold for illiquidity. It will be assumed the
illiquid portion will be similar to what the CMPD measure
proposes.
The Amihud illiquidity measure (Amihud): The
maximum Amihud measure calculated during the
selected stress period is used to train machine learn-
ing models, as the higher the Amihud measure, the
higher the illiquidity behaviour. In the formula be-
low, N is the same number of business days used in
the CMPD measure (20 business days). Stock i on
day d, is the number of days used. For each day,
the Amihud measure is calculated then an average
is taken for the given period. The measure is also
used with a slight variation to capture behaviour
under stress. Amihud is a widely accepted illiquidi-
ty measure and simply presents the price impact of
dollars traded, as demonstrated below (Amihud,
2002):
MATLAB 2021a version is used for the implementation of
the supervised machine learning models which has eleven
ensemble learning algorithms. For full details see MATLAB
documentation under Ensemble Algorithms (MATLAB,
Ensemble Algorithms, 2019).
The main focus of this study will be on ensemble classifiers
since the underlying data is imbalanced. By combining pre-
dictions from several base estimators, ensemble learning
aims to achieve more robust single estimator (scikit-learn,
2020).
As part of the ensemble models, several boosting methods
can be used; in this study we will show the superiority of the
RUSBoost algorithm which was first introduced by Seiffert
et al. (2008) to reduce class imbalance problems in the data
set. RUSBoost uses random data sampling with boosting,
which, as a result, improves the classification performance of
the training data. Financial stress classification problems
have imbalanced data, wherein one class has fewer members
than others. The RUSBoost algorithm is used for the model-
ling in this study to show its effectiveness for the imbalanced
data. For a comprehensive overview of the RUSBoost algo-
rithm, please refer to Seiffert et al. (2010).
The RUSBoost applies adaptive boosting for multiclass
classification when calibrating weights and constructing
ensembles. MATLAB uses weighted pseudo-loss for N
observation and K classes. Pseudo-loss ( ) is a measure of
classification accuracy (MATLAB, Ensemble Algorithms,
2019).
Each step represented by t; k represents class; N
represents number of observations;
xn is a vector of predictor values for observation n;
yn represents the true class value taking one of the K
values;
ht represents the prediction of the learner for each
step t;
is the confidence of the learner prediction
at step t, class k ranges from zero to one;
represents the observation weights of class k in
step t.
5.2. Performance Evaluation Metrics and Definitions
Confusion Matrix
A confusion matrix was constructed to evaluate the perfor-
mance of the models. Several performance measures were
then calculated from the data presented in the confusion ma-
trix.
The table below (Table 4) summarises the information pre-
sented on the Confusion Matrix.
Liquidity Classification of Equities Under Stress Review of Economics and Finance, 2023, Vol. 21, No. 1 1323
N= Total Number of Data Points= TL+FL+FI+TI, Total
number of data points, or number of unique shares used in
the modelling process.
Formulas for the measures above are outlined above:
6. EMPIRICAL RESULTS
6.1. Implementation of Models and Assumptions
In the MATLAB program (2021a version), a set of classifi-
cation models was used to train machine learning models and
then predict share liquidity classifications. Training the mod-
els first required calculating liquidity measures (responses)
and defining split criteria. For the price drop criteria, the
40% eligibility criteria as defined by LCR DA regulations
was employed as opposed to the Amihud defining threshold,
a limitation of which is that classification assignment is sub-
jective. To split shares based on the Amihud measure, ap-
proximately the same percentage of liquid/illiquid from the
CMPD classification was used.
For each measure, data experiments were performed which
include several distinct models. New functionality in the
2021a version of the MATLAB program automatically
searches for the best-performing algorithm and hyperpa-
rameters if it is optimisable. The results for eight perfor-
mance evaluation metrics are presented in the comparison
tables (Table 9, Table 10). Predicting one specific class (liq-
uid or illiquid) may be more important for an institution or
researcher, however in this study predicting both classes is
assumed to be equally important. For this reason, a model
with a high balanced accuracy, where the gap between sensi-
tivity and specificity is also relatively small, would be pre-
ferred.
6.2. Results using Cumulative Maximum Price Drop
(CMPD) for Model Training
In order to get some initial perspective, a scatter plot of the
results can be a useful tool. In Fig. (1), market capitalisation
(Market Cap) of the share vs share beta is represented. Blue
dots represent shares identified as liquid under stress, with a
CMPD of less than 40% during a stress period. Visual in-
spection of the original observations shows that as market
capitalisation increases, the blue dots intensify, whereas
when share beta is comparatively lower, the top left corner
shows more liquid behaviour.
Table 6 summarises the number of shares falling in each
class using a CMPD condition of 40%. Overall, 61% of the
shares were reported as illiquid. The financial, basic materi-
als and energy sectors showed the highest percentage of il-
liquid shares, whilst the utilities and consumer, non-cyclical
sectors had the most shares classified as a liquid.
Table 7 shows the average log (market cap) across sector and
liquidity classes. For all sectors except financial, the liquid
class has higher average market capitalisation. This intuitive-
ly supports what Fig. (1) shows, and supports the fact that
market cap can be a useful measure for predicting the li-
quidity class of shares.
Table 4. Confusion Matrix.
Share Predicted Class
Share Actual Class
Class
Liquid
Illiquid
Total
Liquid
True Liquid (TL)
False Illiquid (FI)- Type 1 Error
Liq
Illiquid
False Liquid (FL)- Type 2 Error
True Illiquid (TI)
Illiq
Total
Liq*
Illiq*
N
Table 5. Performance Evaluation Metrics.
Measure Name
Formula
Description
Accuracy (Acc)
,
This metric measures how many observations (both liquid and illiquid) were correctly
classified by the model.
Error (Err)
,
This metric provides the misclassification percentage.
Sensitivity (Sens)
,
True Liquid Class Rate. This measures how many shares out of all liquid observa-
tions have a model classified as Liquid.
Specificity (Spec)
,
True Illiquid Class Rate. This measures how many shares out of all illiquid observa-
tions have a model classified as Illiquid.
Balanced Accuracy (BA)
Average of Specificity and Sensitivity measures.
Weighted Balanced Accuracy Liquid
(WBA_L)
Weighted Balance Accuracy, where more weight is assigned to the sensitivity in
liquidity classification, where predicted Liquid shares are assigned more weight.
Weighted Balanced Accuracy Illiquid
(WBA_ILL)
Similar to above, more value is assigned to the predicted Illiquid shares.
1324 Review of Economics and Finance, 2023, Vol. 21, No. 1 Coskun Tarkocin and Murat Donduran
Fig. (1). Original Data Set Market Cap vs Share Beta using Price Drop.
Table 6. Number of Shares in Liquid and Illiquid Class per Sector.
Sector
1_Liquid
2_Illiquid
% Illiquid
Consumer, Cyclical
42
89
68%
Technology
28
37
57%
Financial
36
135
79%
Basic Materials
11
48
81%
Consumer, Non-cyclical
104
62
37%
Industrial
48
99
67%
Communications
28
32
53%
Utilities
35
11
24%
Energy
8
29
78%
Total
340
542
61%
Table 7. Average of Log (Market Cap) per Class Label and the Sector.
Sector
1_Liquid
2_Illiquid
Gap
Gap%
Consumer, Cyclical
0.84
0.82
0.02
2%
Technology
0.99
0.83
0.16
16%
Financial
1.04
1.13
−0.09
−9%
Basic Materials
0.94
0.86
0.08
8%
Consumer, Non-cyclical
1.15
0.66
0.49
42%
Industrial
0.98
0.73
0.25
26%
Communications
1.41
0.87
0.54
38%
Utilities
1.19
1.14
0.05
4%
Energy
2.02
1.32
0.70
35%
All Shares
1.10
0.90
0.20
18%
Liquidity Classification of Equities Under Stress Review of Economics and Finance, 2023, Vol. 21, No. 1 1325
Table 8. Average of Share Beta per Class Label and the Sector.
Sector
1_Liquid
2_Illiquid
Gap
Gap%
Consumer, Cyclical
0.95
1.20
0.25
−26%
Technology
0.87
1.05
-0.18
−21%
Financial
1.14
1.32
-0.18
−16%
Basic Materials
0.95
1.09
-0.14
−15%
Consumer, Non-cyclical
0.66
0.79
-0.13
−19%
Industrial
0.93
1.09
-0.16
−17%
Communications
0.83
0.94
-0.12
−14%
Utilities
0.63
0.74
−0.11
−18%
Energy
0.84
0.91
−0.07
−8%
All Shares
0.83
1.10
−0.28
−34%
Table 9. Comparison of Models
5
.
Model Name Acc Err Sens. Spec. BA WBA_L WBA_ILL AUC
Optimizable Ensemble -Bagged-V6 74.0% 26.0% 57.6% 84.3% 71.0% 64.3% 73.4% 78.0%
Ensemble-Boosted Trees-V6 73.6% 26.4% 60.3% 81.9% 71.1% 65.7% 71.2% 77.0%
Ensemble-Bagged Trees-V6 74.3% 25.7% 60.3% 83.0% 71.7% 66.0% 72.5% 78.0%
Ensemble-RUSBoost-V6 73.2% 26.8% 70.0% 75.3% 72.6% 71.3% 66.8% 78.0%
Ensemble-RUSBoost -V3- PCA 99% 68.5% 31.5% 62.9% 72.0% 67.4% 65.2% 61.8% 74.0%
Ensemble-RUSBoost-V4 73.8% 26.2% 71.8% 75.1% 73.4% 72.6% 67.1% 78.0%
Optimisable Ensemble-V4 75.1% 24.9% 58.2% 85.6% 71.9% 65.1% 75.2% 79.0%
Optimisable Tree 73.2% 26.8% 55.9% 84.1% 70.0% 62.9% 72.7% 74.0%
Logistic Regression 72.6% 27.4% 57.6% 81.9% 69.8% 63.7% 70.5% 77.0%
Optimisable Naïve Bayes 73.8% 26.2% 60.3% 82.3% 71.3% 65.8% 71.7% 78.0%
Optimisable SVM 74.4% 25.6% 55.9% 86.0% 70.9% 63.4% 75.1% 79.0%
Neural Network (Narrow) 70.2% 29.8% 60.6% 76.2% 68.4% 64.5% 65.2% 73.0%
5
Where a model has ‘V6’ next to its name, all six features in Table 1.3 were used. Based on several iterations of the model, if prediction power was not much
impacted by 90-day trading volume and median market cap percentage dropped, then the model name is listed as either just the model name or with ‘V4’ add-
ed, indicating only the first four features were used in the model.
Table 8 shows the average share beta across sector and li-
quidity classes. For all sectors, a higher beta suggests a more
illiquid classification. This makes intuitive sense since high-
er beta means that when there is market-wide stress, a specif-
ic share will have more variance than the market. The con-
sumer, non-cyclical and utilities sectors have the lowest av-
erage share beta across all sectors.
Table 9 presents the performance of 12 models against each
evaluation metric. Each optimisable model ran 30 iterations
of different algorithms and hyperparameters, and the results
for the 12 best-performing models are reported. K-fold cross-
validation (where K=5) was used for all classification mod-
els to prevent overfitting. Without cross-validation, in-
sample accuracy would be very high, but performance for
out-of-sample predictions would suffer.
When using accuracy (or inversely error) or weighted bal-
ance illiquid as a measure, ‘Optimisable Ensemble–V4’
shows the highest predictive power of all models. However,
when the focus is moved to the prediction of each class label,
it performs poorly for liquid class, where sensitivity is only
58.2%. Using the preferred measure of a high balanced accu-
racy and a smaller gap between sensitivity and specificity,
‘Ensemble–RUSBoost–V4’ becomes the best-performing
model, with both classes being correctly predicted more than
70% of the time.
The Confusion Matrix (Fig. 2) for the selected model (En-
semble–RUSBoost) shows a true liquid class rate (sensitivi-
ty) of 71.8% and 75.1% for the true illiquid class rate (speci-
ficity). This high prediction power supports the fact that sec-
tor, industry, market capitalisation and share beta provide
useful information about share liquidity behaviour under
conditions of market liquidity stress.
1326 Review of Economics and Finance, 2023, Vol. 21, No. 1 Coskun Tarkocin and Murat Donduran
6.1. Results Using Amihud Measure for Model Training
To get an initial perspective on the results from the applica-
tion of the Amihud measure for model training, a scatter plot
was produced for market cap and share beta (Fig. 3). Blue
dots represent shares labelled as liquid. High market cap
stocks show more liquidity across different beta calculations.
When market cap reduces, classification first becomes mixed
and then approaches the bottom of the graph as it becomes
illiquid. Since the Amihud measure is price impact per USD
value traded, for big market size stocks, this impact may be
expected to be lower.
When using the Amihud measure, the industrial, basic mate-
rials and technology sectors have the highest percentage of
illiquid shares. The average log (market cap) for shares clas-
sified as liquid is even higher compared to the illiquid class
using the Amihud measure for all sectors. The average share
beta overall is smaller for the liquid shares group, but the
financial, basic materials and energy sectors show the oppo-
site of this. Tables showing details of these results can be
found in the Appendix section.
Table 10 presents the performance of 12 models against each
evaluation metric when the Amihud measure was used to
split shares into class labels. Overall, more models per-
formed well in estimating classification compared to the re-
sults in the CMPD. When using accuracy (or inversely error)
or weighted balance illiquid as a measure, ‘Optimisable En-
semble–V6’ shows the highest predictive power. If Optimis-
Fig. (2). Confusion Matrix- Ensemble Model RUSBoost.
Fig. (3). Original Data Set Market Cap vs Share Beta using Amihud Measure.
Liquidity Classification of Equities Under Stress Review of Economics and Finance, 2023, Vol. 21, No. 1 1327
able Ensemble is run with four variables instead of six (‘Op-
timisable Ensemble–V4’), accuracy suffers only very slight-
ly, therefore fewer variables with less computing and data
usage would be preferable. Models with four variables all
performed reasonably well, except Naïve Bayes, which re-
ported a lower sensitivity measure. Therefore, it can be con-
cluded that several supervised machine learning models pro-
duced a high prediction power (above 80%) for liquidity
classification using the Amihud Measure.
Based on the above empirical results from models trained
using the CMPD or the Amihud measure, it can be conclud-
ed that the predictive performance of the ensemble model
with RUSBoost algorithm using four features/variables is
satisfactory for employment in the liquidity classification
problems. Additionally, producing high prediction from
these measures supports the fact that under stress, liquidity
behaviour of a share is impacted by the sector, industry,
market capitalisation and the share beta. These can be used
to support liquidity classification, which would help to
measure risk sensitivities at the more granular level. Further
work can be done using a wide set of liquidity measures and
different share features to train models.
7. CONCLUSIONS
This paper employed supervised machine learning models to
predict the liquidity classification of common equity shares.
Eight hundred and eighty-two unique shares and market data
from January 2007 to June 2019 were used in the analysis.
The 2007–2008 global financial crisis period following the
Lehman Brothers collapse was identified as the most stress-
ful period, and market liquidity measures and features in this
period were examined closely to provide further insight into
share liquidity behaviour in a market stress environment.
This study showed that the ensemble method with a random
undersampling algorithm (Ensemble – RUSBoost) per-
formed comparatively better using preferred metrics such as
balanced accuracy and a smaller gap between sensitivity and
specificity evaluation metrics. Although this model per-
formed consistently under two liquidity measures used as a
response variable, applying the Amihud measure with other
supervised machine learning models also showed a high pre-
dictive power.
The methodology employed, including transforming liquidi-
ty measures to create a classification problem, distinguishes
this study from existing literature. It has been shown that
supervised machine learning models can be a very useful
tool for banks and regulators to further investigate assump-
tions and initial rules set by the Basel Committee. Another
important contribution made is using sector, share beta, in-
dustry, and market capitalisation information to predict share
liquidity behaviour under stress. Lower beta and higher mar-
ket cap stocks show more liquid behaviour, and some sectors
are more volatile and less liquid than others under market
stress.
The model and framework proposed in this study can be ap-
plied by financial institutions or regulators to achieve a more
granular analysis supported by actual data. This will enable
risk sensitivities to be more accurately distinguished, provid-
ing the right pricing and funding framework for assets ac-
quired.
Although this study addresses the liquidity classification
problem at a more technical level for shares alone, future
research can be done to examine other LCR assumptions.
Insight could also be gained by integrating the liquidity clas-
sification problem into the bank fund transfer pricing mech-
anism and internal stress testing assumptions.
From a policymaking perspective, this study supports the
fact that current eligibility criteria in the LCR DA can be
further examined, and a more granular approach can be used.
This study also shows that machine learning models can be
used by regulators to build more granular and risk sensitive
assumptions for bank stress testing.
DISCLAIMER
The views and opinions expressed in this paper are those of the
authors and they do not necessarily reflect the views of the HSBC
Group or Yildiz Technical University.
Table 10. Comparison of Models.
Model Name Acc Err Sens. Spec. BA WBA_L WBA_ILL AUC
Optimizable Ensemble -Bagged-V6 85.3% 14.7% 78.8% 89.3% 84.0% 81.4% 83.9% 93.0%
Ensemble-Boosted Trees-V6 83.4% 16.6% 78.5% 86.6% 82.5% 80.5% 80.5% 91.0%
Ensemble-Bagged Trees-V6 84.7% 15.3% 78.8% 88.4% 83.6% 81.2% 82.8% 93.0%
Ensemble-RUSBoost-V6 82.9% 17.1% 80.5% 84.3% 82.4% 81.5% 78.3% 91.0%
Ensemble-RUSBoost -V3- PCA 99% 70.0% 30.0% 70.2% 69.8% 70.0% 70.1% 61.9% 78.0%
Ensemble-RUSBoost-V4 82.7% 17.3% 79.6% 84.5% 82.1% 80.9% 78.3% 90.0%
Optimisable Ensemble-V4 84.1% 15.9% 80.5% 86.4% 83.5% 82.0% 80.6% 92.0%
Optimisable Tree 83.6% 16.4% 79.9% 85.8% 82.9% 81.4% 79.9% 84.0%
Logistic Regression 84.0% 16.0% 78.5% 87.5% 83.0% 80.7% 81.6% 88.0%
Optimisable Naïve Bayes 83.0% 17.0% 73.2% 89.1% 81.1% 77.2% 82.9% 91.0%
Optimisable SVM 85.6% 14.4% 80.2% 89.0% 84.6% 82.4% 83.7% 93.0%
Neural Network (Trilayered) 81.6% 18.4% 75.5% 85.5% 80.5% 78.0% 78.7% 84.0%
1328 Review of Economics and Finance, 2023, Vol. 21, No. 1 Coskun Tarkocin and Murat Donduran
APPENDIX
Model Predictions Sector vs Beta
Model Predictions Log (Market Cap) vs Beta
Number of Share per Class Label and Sector
Sector
1_Liquid
2_Illiquid
% Illiquid
Consumer, Cyclical
45
86
66%
Technology
21
44
68%
Financial
65
106
62%
Basic Materials
18
41
69%
Consumer, Non-cyclical
74
92
55%
Industrial
42
105
71%
Communications
29
31
52%
Utilities
24
22
48%
Energy
21
16
43%
Total
339
543
62%
Liquidity Classification of Equities Under Stress Review of Economics and Finance, 2023, Vol. 21, No. 1 1329
Average of Log (Market Cap) Class Label and Sector
Sector
1_Liquid
2_Illiquid
Gap
Gap%
Consumer, Cyclical
1.28
0.59
0.69
54%
Technology
1.40
0.66
0.75
53%
Financial
1.58
0.82
0.77
48%
Basic Materials
1.39
0.65
0.75
54%
Consumer, Non-cyclical
1.44
0.58
0.86
60%
Industrial
1.39
0.58
0.82
59%
Communications
1.59
0.68
0.91
57%
Utilities
1.43
0.89
0.55
38%
Energy
1.94
0.86
1.07
55%
All Shares
1.48
0.67
0.81
55%
Average of Share Beta per Class Label and Sector
Sector
1_Liquid
2_Illiquid
Gap
Gap%
Consumer, Cyclical
1.07
1.14
-0.07
-7%
Technology
0.96
0.98
-0.02
-2%
Financial
1.31
1.27
0.04
3%
Basic Materials
1.16
1.02
0.14
12%
Consumer, Non-cyclical
0.65
0.75
-0.11
-17%
Industrial
0.99
1.06
-0.06
-6%
Communications
0.88
0.90
-0.02
-2%
Utilities
0.65
0.66
-0.01
-1%
Energy
0.93
0.85
0.08
9%
All Shares
0.96
1.02
-0.06
-7%
Model Prediction (Optimisable Ensemble) Log (Market Cap) vs Share Beta
1330 Review of Economics and Finance, 2023, Vol. 21, No. 1 Coskun Tarkocin and Murat Donduran
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Received: May 02, 2023 Revised: May 10, 2023 Accepted: Sep 04, 2023
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