Beyond the Z‐score: A novel measure of bank stability for effective policymaking

• Published date: 01 November 2023
• Author: Rachita Gulati
• Date: 01 November 2023
• DOI: http://doi.org/10.1002/pa.2866

RESEARCH ARTICLE

Beyond the Z-score: A novel measure of bank stability for

effective policymaking

Rachita Gulati

Department of Humanities and Social

Sciences, Indian Institute of Technology

Roorkee, Roorkee, India

Correspondence

Rachita Gulati, Department of Humanities and

Social Sciences, Indian Institute of Technology

Roorkee, Roorkee, Uttarakhand, India.

Email: rachita.gulati@hs.iitr.ac.in

Funding information

Indian Council of Social Science Research,

Grant/Award Number: IMPRESS/

P344/2018-19

This article looks beyond Z-score and proposes a novel methodological framework to

build an all-encompassing indicator of bank stability for individual banks using the

optimisation-based ‘benefit-of-the-doubt (BoD)’approach. Unlike other available

approaches, this approach is totally data-driven and generates endogenous weights

to aggregate sub-indicators of bank stability and dimensions. Further, the final out-

comes are not limited to a scalar measure of bank stability. The unique optimal

weights offer valuable policy-relevant insights and highlight the most precarious

areas of stability, which demand the immediate attention of the bank's management

and the industry regulators for both micro-and macro-level policymaking. Using the

data of Indian public sector banks operating in the year 2018, the study illustrates

the proposed framework to obtain a holistic indicator of bank stability, defined on

14 ratio sub-indicators and 5 broad dimensions (soundness, asset quality, profitabil-

ity, management efficiency, and liquidity) of bank stability.

KEYWORDS

bank stability indicator, benefit-of-the-doubt model, composite index, data envelopment

analysis, Indian banks, policy weights

1|INTRODUCTION

Since the 2007–2009 global financial crisis (GFC), the issue of bank

stability has attracted considerable attention from bank supervisors

and regulators. This is because a stable banking system enables banks

to perform their financial intermediation function effectively and gives

businesses the assurance they need to raise and deploy capital confi-

dently. Instability in the bank system, on the other hand, entails enor-

mous economic costs, increases unemployment, heightens the risk of

financial disruptions, and precipitates a significant slowdown in eco-

nomic growth. Interestingly, bank stability is difficult to quantify

empirically since its measurement has been fraught with a great deal

of complexity. In the extant literature on the subject, there is a dis-

agreement on the appropriate method to compute a measure of bank

stability. The empirical literature reveals that bank stability is typically

proxied by a risk index and that the Z-score, a highly simplified mea-

sure of insolvency risk, frequently serves as a surrogate for bank sta-

bility (see, e.g., Al-Shboul et al., 2020; Bai & Elyasiani, 2013;

ˇ

Cihák

et al., 2021; Demyanyk & Hasan, 2010; Djebali & Zaghdoudi, 2020;

Fiordelisi & Mare, 2014; Kabir & Worthington, 2017; Schaeck &

ˇ

Cihák, 2014; Phan et al., 2022; among others). In its simplistic form, Z-

score is computed as a ratio of ROA plus equity-to-asset ratio to the

standard deviation of ROA and thus quantifies bank solvency risk by

comparing buffers (capitalisation and asset returns) with risk (volatility

of asset returns). A higher Z-score indicates a reduced likelihood of

insolvency and suggests a higher level of bank stability. Despite the

widespread usage of the Z-score as an indicator of bank stability,

there are numerous downsides that render it an inadequate measure.

One of the prominent downsides of the Z-score is that it reflects

just bank insolvency risk and overlooks other types of risk that banks

face, including credit risk, market risk, and operational risk

(Huljak, 2015; Shaddady & Moore, 2019). As a result, the Z-score is

never regarded as an adequate measure of bank stability. Therefore,

bank experts and regulators also dismiss this metric as an all-

encompassing indicator of bank stability. A further downside is that it

is essentially a backward-looking measure (Hafeez et al., 2022), and its

value is sensitive to the yearly window length (3, 4, or 5 years) used to

calculate the standard deviation of ROA. Lapteacru (2016) raised the

Received: 23 January 2022 Revised: 28 January 2023 Accepted: 28 April 2023

DOI: 10.1002/pa.2866

J Public Affairs. 2023;23:e2866. wileyonlinelibrary.com/journal/pa © 2023 John Wiley & Sons Ltd. 1of18

https://doi.org/10.1002/pa.2866

issue of inconsistency of traditional accounting-based Z-score as an

indicator of the probability of default or the banking system stability,

particularly when the entire computation process of Z-score and its

variants is based on the unrealistic assumption that ROA is a random

variable with a normal distribution. The author proved the inconsis-

tency of a traditional Z-score using Monte Carlo simulations. It has

been inferred that since, in practice, the distributions of ROA are

rather skewed (especially left-skewed for the banking institutions con-

fronting a financial crisis) and exhibit an excess of kurtosis, the Z-score

loses its utility as a reliable indicator of the probability of default/

bankruptcy.

Against this concise background, the present study looks beyond

the Z-score and proposes a holistic indicator of bank stability, free of

any restrictive and unrealistic assumption such as the normality in the

distribution of bank's returns. In fact, the proposed indicator of bank

stability is fully non-parametric in nature and based on the “benefit-

of-the-doubt”(BoD) approach, which has gained immense popularity

as a potent methodological tool for constructing composite indicators.

Cherchye et al. (2004,2007) developed the first BoD model by

expanding the work of Melyn and Moesen (1991). At the core of this

approach, the endogenous weights of the sub-indicators are gener-

ated using a data envelopment analysis (DEA)-type model with a

dummy input equal to 1 (Mariano et al., 2015), and then these weights

are aggregated to build a composite indicator. Thus, a typical BoD

model tantamounts to a DEA model in a “pure output setting”. In light

of this, the focus of a BoD model is only on “achievements”

(i.e., outputs) without considering the input side (Lavigne et al., 2019).

For the construction of an index, the BoD approach offers some key

advantages, which make it a rational and optimum choice. First, being

a non-parametric approach, it is independent of a priori statistical

assumptions as associated with traditional measures of bank stability,

and is appropriate to aggregate the unit-invariant data. Second, it

works superbly well with small samples (Puyenbroeck, 2018; Rogge &

Puyenbroeck, 2007), such as those used in the illustrated example of

this article. Third, it assigns each composite indicator a single numeri-

cal score (so-called stability performance index). This facilitates the

researcher to rank and group the sampled banks easily on the differ-

ent dimensions of bank stability. Fourth, it permits a differentiated

and benevolent weighting scheme, providing endogenous (that is,

determined by the model rather than predetermined) and flexible

weights for sub-indicators that vary across sample units (Greco

et al., 2019; Zhou et al., 2007). Therefore, the weighting scheme gen-

erated through a BoD model cannot only assist the researcher in line-

arly aggregating ratio sub-indicators in an objective manner but also

guide him to formulate relevant and appropriate policy directions for

less stable or underperforming banks (Nardo et al., 2008). In sum, the

BoD approach provides policymakers with an endogenously derived

weighting scheme for determining the relative importance of distinct

sub-indicators and getting much-needed diagnostic information for

effective policymaking.

In the current study, we develop a two-step BoD-based aggrega-

tion framework to calculate the bank stability indicator. In particular,

we employ the constrained BoD model, which generates bank-specific

endogenously derived weights for underlined sub-indicators (in the

first step) and dimensions (in the second step). The optimal weighting

scheme generated through the BoD approach provides a clear picture

of a bank's preferences for each ratio sub-indicator and dimension.

Using a dataset of 21 Indian public sector banks operating in the year

2018, an illustrative example presents the step-by-step procedure to

construct a bank stability indicator using 14 ratio sub-indicators that

cover five different aspects of stability, namely ‘soundness’,‘asset

quality’,‘management efficiency’,‘profitability’, and ‘liquidity’. The

choice of sub-indicators and dimensions is based on the IMF's finan-

cial soundness indicators for deposit-taking institutions. It is notewor-

thy here that this research uses data from Indian public sector banks

just for demonstration; however, the framework completely is flexible

and adaptable to data from any nation's banking institution. The exhi-

bition provides the detailed diagnostic information required for

improving the stability performance of individual banks in diverse

areas ranging from risk management to earnings management. Such

diagnostic and policy-related information cannot be extracted from

the alternative weighting schemes, including the popular Principal

Component Analysis (PCA). Considering this, the BoD estimated opti-

mal policy weights for a sampled bank from our proposed framework

will give a clear indication of the most threatening areas of stability

that require the immediate intervention of the bank's management

and the industry regulators for micro-and macro-level policy analyses.

This article adds value to the extant literature on measuring bank

stability since this is perhaps the first methodological and empirical

effort to use the BoD approach for constructing a composite indicator

of bank stability for individual banks, which can be used as a mecha-

nism of signalling bank fragility and distress. The values of the BoD-

based composite indicator range between 0 and 1 and indicate the

relative levels of bank stability. These values can be used for bench-

marking, classification, ranking, and effective policymaking purposes.

There are no such contributions in the literature that give a holistic

framework for the building of a frontier-based indicator of bank stabil-

ity, to our knowledge. Thereby, we confidently feel that this article

significantly enriches the strand of literature, which focuses on the

construction of a bank stability indicator. As noted above, the pro-

posed bank stability indicator using the data of Indian public sector

banks incorporates 14 ratio sub-indicators that encompass five critical

dimensions of stability, and therefore, shed more light on the prob-

lematic areas needing the attention of managers and regulators. Three

significant points of reporting such a granular analysis draw attention

here. First, the construction of the frontier-based bank stability indica-

tor is based on a computationally less cumbersome algorithm to get

bank-specific weights for stability sub-indicators and distinct dimen-

sions. Second, the aggregation of sub-indicators and dimensions

requires only data-driven endogenously determined weights rather

than weights based on any subjective judgement. Third, our approach

is readily adaptable to the context of any banking system by merely

altering the number of available sub-indicators and dimensions of

bank stability.

The remainder of the article is organised as follows. The next

section briefly discusses the relevant empirical literature on the

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