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Time-varying bank risk: Forward-looking z-score
Bilal Hafeez
a, Xiping Li
b, M. Humayun Kabira, David TripeaThis version: October 2020
Abstract
While the standard measure of the z-score has been widely used to evaluate bank insolvency risk, it has been criticized as a backward-looking measure. This paper proposes a forward-looking method to construct the time-varying z-score, by incorporating analyst forecasts. Using a sample of the U.S. banks listed in S&P1500, we find that the forward-looking z-score is able to predict the fluctuation of the standard z-score one quarter ahead of time. We provide evidence that the forward- looking z-score is able to provide predictive signals of banks’ future profitability and non-performing loan ratio. The forward-looking z-score is also significantly associated with market-based risk measures. Overall, our findings suggest that the forward- looking z-score overcomes the shortcoming of the standard z-score, and that it is effective at capturing banks’ future risk and performance.
Keywords:
Bank risk, Z-score, Forward-looking, Predictive ability JEL codes: G21,
a School of Economics and Finance, Massey University, Palmerston North, New Zealand
b Xiamen National Accounting Institute, Xiamen, China
Corresponding author. E-mail address: [email protected]
Address: School of Economics and Finance, Massey University (Manawatu Campus), Private Bag 11-222, Palmerston North, 4442, New Zealand
Phone: +64 6 356 9099 Ext. 85628
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1. Introduction
Since the Global Financial Crisis (GFC), both regulatory authorities and commercial banks have revived attention to the importance of banks’ risk, and the ways in which risk is measured. The recent COVID-19 further imposes concerns regarding uncertainties about banks’ future risk and performance. Built on work by Roy (1952) and subsequently developed by Boyd and Graham (1986), Hannan and Hanweck (1988), and Boyd, Graham, and Hewitt (1993), the z-score is a well-established indicator of bank insolvency risk among academic. The z-score measure is advantageous in its relative simplicity of computation and the fact that it can be computed using accounting information only.
The basic principle of the z-score measure is to relate a bank’s capital level to variability in its returns, so that one can know how much variability in returns can be absorbed by capital without the bank becoming insolvent. A higher value of the z- score means lower bank risk. However, both the simplicity of the z-score and its reliance on accounting data lead to potential challenges of the standard z-score (Lepetit & Strobel, 2015; Bouvatier, Lepetit, Rehault, & Strobel, 2018). Importantly, the standard z-score has been criticized by its backward-looking characteristics. This mostly arises from the use of accounting data, which is usually considered as a record of past events. Hence, there are rising concerns that the standard z-score is unable to capture the movement of banks’ future risk.
Despite of above criticism, we argue in this paper that the z-score measure is still relevant in evaluating banking stability1, and the z-score measure is an important complement of market-based risk measures. Consequently, this paper intends to make contributions to the construction of time-varying z-score by introducing a
1 Examples of recent papers that use the z-score measure include Khan, Scheule, & Wu (2017), Tsionas
& Mamatzakis (2017), Caiazza, Gotugno, Fiordelisi, & Stefanelli (2018), and Pino & Sharma (2018).
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forward-looking z-score measure that incorporates analyst forecasts in the computation.
Analysts play a prominent role in today’s financial markets, and they interpret and disseminate information through providing earnings forecasts and stock recommendations (Alford & Berger, 1999; Barber, Lehavy, McNichols, & Trueman, 2001; Loh & Mian, 2006). Analyst forecasting accuracy has improved over time (Brown, 1997; Tan, Wang, & Welker, 2011). Although analyst forecasts are relatively less studied in banks (Hong, Huseynov, Sardarli, & Zhang, 2020), analyst forecasts have been widely used by investors and non-financial corporations (e.g. Barber, Lehavy, &
Trueman, 2010; Laih, Lai, & Li, 2015). In this paper, we make use of analyst forecasts on banks’ earnings and financial positions, which allows us to incorporate forward- looking elements into the construction of the time-varying z-score.
We exploit the forward-looking z-score based on a sample of the U.S. banks listed in S&P1500 for the period 2002Q1-2020Q1. With the quarterly accounting data available for the U.S. banks, this provides us with a wide scope of observations to explore the construction of the time-varying forward-looking z-score. Our empirical results show that the forward-looking z-score is able to predict the movement of the standard z- score one quarter ahead of time. We find that the forward-looking z-score is positively associated with banks’ future profitability (proxied by ROA and ROE), and negatively associated with banks’ future non-performing loan (NPL) ratios. An implication from these results is that by examining the forward-looking z-score in the current period, it provides us with early prediction of banks’ profitability or NPL ratio for the following quarter. The predictive ability of the forward-looking z-score is not affected by the dispersion of analyst forecasts. The forward-looking z-score is also significantly associated with market-based risk measures.
Overall, this paper makes an important contribution to the construction of the time- varying z-score. The forward-looking z-score incorporates analyst forecasts of earnings
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and financial positions into the computation of the z-score, which overcomes the shortcoming of accounting data being backward-looking. The forward-looking z-score shows significant predictive ability of banks’ future risk and performance, which is expected to provide early warning signals of banks’ insolvency to policymakers, commercial banks, and investors.
The rest of this paper is organised as follows. Section 2 describes the construction of the forward-looking z-score, and discusses the data sources. Section 3 reports core results. Section 4 reports robustness checks. Section 5 concludes the paper.
2. Forward-looking z-score and relevant data 2.1 Construction of forward-looking z-score
The standard z-score measure defines the situation in which a bank’s capital is insufficient to offset its losses (Hannan and Hanweck, 1988; Boyd et al., 1993).
Mathematically, z-score is computed as ROA plus capital-asset ratio (CAR) divided by the standard deviation of ROA.
𝑍 − 𝑠𝑐𝑜𝑟𝑒 = 𝑅𝑂𝐴+ 𝐶𝐴𝑅
𝜎(𝑅𝑂𝐴) Equation 1
According to Bouvatier et al. (2018), the best computation of the standard z-score is to use current values of capital-asset ratio, combined with moving mean and standard deviation of ROA. Following this suggestion, we compute the standard z-score using an 8-quarter moving window.
To construct the forward-looking z-score, we also use an 8-quarter forward-looking moving window. The forward-looking moving window consists of actual values of the z-score elements (i.e. total assets, capital, and net income) for the previous 7 quarters (including current quarter), and the forecasted values of relevant elements (i.e. total assets, capital, and net income) provided in the current quarter. It is notable that these
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forecasted values are analysts’ estimation for banks’ earnings and financial position for the next quarter. Hence, the forward-looking z-score is computed by moving mean and standard deviation of ROA over an 8-quarter forward-looking moving window, and combines these with forecasted capital-asset ratio of the 8th quarter. The calculation of the forward-looking z-score is presented in Equation 2. In this way, the forward-looking z-score not only captures the time-varying bank risk, but also incorporates financial forecasts.
𝐹𝑧_𝑠𝑐𝑜𝑟𝑒𝑖,𝑡 =
∑𝑇 𝑅𝑂𝐴𝑖,1−𝑇 𝑛=1 +𝑅𝑂𝐴𝑖,𝑡̂
𝑇+1 + 𝐶𝐴𝑅̂𝑖,𝑡
𝜎(𝑅𝑂𝐴𝑖,1−𝑇,…, 𝑅𝑂𝐴𝑖,𝑡, 𝑅𝑂𝐴̂ )𝑖,𝑡 Equation 2
where 𝐹𝑧_𝑠𝑐𝑜𝑟𝑒𝑖,𝑡 is the forward-looking z-score for bank i at time t (t being the current period). ∑𝑇 𝑅𝑂𝐴𝑖,1−𝑇
𝑛=1 is the sum of the ROA during the previous T quarters (including current quarter) and T equals to 7 for the 8-quarter forward-looking moving window. 𝑅𝑂𝐴̂𝑖,𝑡 is analysts’ forecasts of ROA for bank i at time t. 𝐶𝐴𝑅̂𝑖,𝑡 is analysts’
forecasts of capital-asset ratio for bank i at time t. The denominator 𝜎(𝑅𝑂𝐴𝑖,1−𝑇, … , 𝑅𝑂𝐴𝑖,𝑡, 𝑅𝑂𝐴̂ )𝑖,𝑡 represents the standard deviation of ROA including the set of ROA for bank i at time [1-T, t] and 𝑅𝑂𝐴̂𝑖,𝑡.
To better interpret the meaning of the forward-looking z-score, we create a proxy by comparing the standard z-score and the forward-looking z-score. We propose a dummy variable that takes the value one if the forward-looking z-score is less than the standard z-score in the same quarter, and zero otherwise. As a higher value of z-score means a lower bank insolvency risk, we interpret this proxy as a “downward signal”.
It is expected that bank i would have higher insolvency risk during the next quarter if the downward signal takes the value one. In other words, the downward signal captures the trends of bank insolvency risk during the next quarter.
Moreover, it is notable that analyst forecasts play an essential role in the construction of the forward-looking z-score, while the forecasts from different analysts for each
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individual bank might vary2. Hence, we propose an “analyst consensus” proxy, which measures the dispersion of estimated ROA. The analyst consensus is calculated by the coefficient of variation of ROA, as shown in Equation 3.
𝐶𝑜𝑛𝑠𝑒𝑛𝑠𝑢𝑠𝑖,𝑡 =𝜎(𝑅𝑂𝐴̂ )𝑖,𝑡
𝑅𝑂𝐴̂𝑖,𝑡 Equation 3
where 𝜎(𝑅𝑂𝐴̂)𝑖,𝑡 and 𝑅𝑂𝐴̂𝑖,𝑡 represent the standard deviation and mean of ROA reported by different analyst for bank i at time t, respectively.
In order to test the effectiveness of the forward-looking z-score in capturing bank insolvency risk, we employ a set of empirical tests, with relevant discussions in the next section. A series of bank-level control variables are included in the regression equation. A summary of key variables is provided in Table 1.
Table 1 Variable description
This table lists the variables used in the empirical analysis, together with the description of their calculation procedure.
Variables Symbol Description
Standard z-score Sz_score The sum of moving mean of ROA over an 8- quarter moving window and current value of capital-asset ratio as the numerator, and combined with standard deviation of ROA over an 8-quarter moving window as the denominator
Forward-looking z-score Fz_score The sum of moving mean of ROA over an 8- quarter forward-looking moving window and forecasted capital-asset ratio as the
numerator, and combined with standard deviation of ROA over an 8-quarter forward- looking moving window as the denominator Downward signal Signal A dummy variable that take the value one if the forward-looking z-score is less than the standard z-score in the same quarter, and zero otherwise
2 In this study, the sample banks on average receive 11 analyst followings in each quarter. Please refer to the descriptive statistics in Table 2 for more information.
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No. of analyst followings # Analyst Number of analyst followings a bank receive in each quarter
Analyst consensus Consensus The dispersion of forecasted ROA provided in analyst followings; Calculated by the coefficient of variation of forecasted ROA Return on assets ROA Net income to total assets
Return on equity ROE Net income to total equity
Non-performing loan ratio NPL Non-performing loans to total loans Total risk TR Annualized standard deviation of a bank’s
stock return
Total market-adjusted risk TMR Annualized standard deviation of a bank’s stock return in excess of S&P1500
Bank size Size Natural logarithm of total assets
Income diversification Diversification The share of non-interest income in total operating income
Bank leverage Leverage The share of bank total assets to total equity Cost-to-Income ratio Cost-Income The ratio of non-interest costs to total non-
interest incomes
2.2 Sample descriptions and data sources
The sample consists of all the U.S. banks listed in S&P1500. This includes a total of 109 banks. To construct the standard z-score and forward-looking z-score, we collect data from different datasets. We collect banks’ quarterly accounting data from COMPUSTAT. Relevant accounting data includes total assets, capital, net income, total operating income, non-interest income, non-interest cost, and NPL ratio. Analyst following provides one-year guide for banks’ assets, capital, and net income, and relevant information is obtained from the Datastream Institutional Brokers Estimate System (I/B/E/S) dataset. Banks’ stock prices and market price index are collected from Datastream. Our sample covers the period from 2002Q1 to 2020Q1. Table 2 presents descriptive statistics for the time-varying standard z-score, forward-looking z-score, and other variables used in our empirical investigation.
Table 2 Descriptive statistics
The table provides descriptive statistics for the time-varying standard z-score, forward-looking z-score, and other variables used in our empirical investigation. The variable definitions are provided in Table 1. All continuous variables are winsorized at 1st and 99th percent.
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Variables N Mean Std.dev. Min p25 p50 p75 Max
Sz_score 5935 83.5 76.12 1.44 29.79 60.38 112.78 369.33 Fz_score 5964 90.56 81.79 1.08 32.74 67.28 121.95 415.24
Signal 5984 0.44 0.5 0 0 0 1 1
ROA 5983 0.97 0.69 -2.49 0.78 1.04 1.33 2.72
ROE 5983 9.18 7.33 -27.31 6.84 9.52 12.66 30.74
NPL 5956 0.95 1.09 0.02 0.3 0.56 1.11 5.84
TR 5796 0.30 0.19 0.12 0.19 0.24 0.32 1.20
TMR 5796 0.24 0.16 0.09 0.16 0.2 0.26 1.05
# Analyst 5223 11.02 8 1 5 8 14 38
Consensus 5604 0.12 2.34 -42.33 0.03 0.05 0.09 137.5
Size 5984 9.49 1.48 5.92 8.54 9.18 10.09 14.52
Diversification 5984 0.22 0.13 -0.01 0.13 0.21 0.3 0.58
Leverage 5983 9.56 2.30 4.85 7.94 9.3 10.81 19.08
Cost-Income 5984 3.03 2.42 -1.51 1.72 2.35 3.42 15.46
As shown in Table 2, the average value of the forward-looking z-score is higher than the standard z-score. An interpretation is that the forward-looking z-score reflects an overall improvement of banking stability over the sample period. This is also reflected by the mean and median values of the downward signal. The downward signal has a mean value of 0.44, which means that 44% (56%) of the observations take the value one (zero). This reflects an overall reduction in insolvency risk.
Table 3 reports the Pearson correlation matrix among variables. The forward-looking z-score is positively correlated with the standard z-score. This provides evidence that the forward-looking z-score would be a reliable proxy for bank insolvency risk. The correlations among other variables are normally low except for a few cases.
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Table 3 Correlation matrix
This table provides correlation matrix among key variables. The variable definitions are provided in Table 1. All continuous variables are winsorized at 1st and 99th percent.
Variables 1 2 3 4 5 6 7 8 9 10 11
1 Sz_score 1.00
2 Fz_score 0.93 1.00
3 Consensus -0.03 -0.03 1.00
4 Size 0.03 0.03 0.00 1.00
5 Cost-Income -0.01 -0.02 -0.02 -0.26 1.00
6 Diversification -0.07 -0.07 -0.01 0.45 -0.58 1.00
7 NPL -0.31 -0.30 0.03 -0.08 0.08 -0.03 1.00
8 ROA 0.25 0.26 -0.06 0.01 -0.19 0.10 -0.49 1.00
9 ROE 0.20 0.21 -0.06 0.00 -0.22 0.14 -0.49 0.93 1.00
10 TR -0.30 -0.30 0.06 -0.07 0.04 -0.08 0.44 -0.48 -0.44 1.00
11 TMR -0.31 -0.32 0.06 -0.13 0.08 -0.11 0.47 -0.52 -0.47 0.96 1.00
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3. Empirical results
3.1 Time-varying trends of forward-looking z-score and standard z-score.
We first show the time-varying trends of the forward-looking z-score and standard z- score. For the sake of clear presentation, we construct an aggregate forward-looking z-score and an aggregate standard z-score, which serve as a proxy for the banking market stability (Ijtsma, Spierdijk, & Shaffer, 2017; Li, Tripe, Malone, & Smith, 2020).
Figure 1 plots the time-varying aggregate z-scores for the sample banks.
Figure 1 Trends of aggregate forward-looking z-score and aggregate standard z-score This figure plots the time series of the aggregate forward-looking z-score and the aggregate standard z-score for the sample banks.
Importantly, the figure shows that the aggregate forward-looking z-score generally leads the movement of the aggregate standard z-score throughout the sample period.
Specifically, the aggregate forward-looking z-score move upwards (or downwards) before the increase (or decrease) of the aggregate standard z-score. The association is statistically significant at 5% level (t-statistics = 2.322, p-value = 0.02). The shape of the two lines become more identical post the GFC, which is consistent with improved forecast accuracy (Tan et al., 2011). (We can add the COVID-19 case here, based on data availability)
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To ensure the predictive ability of the forward-looking z-score, we compare the time- varying values of the forward-looking z-score and the standard z-score, by running a regression of the standard z-score for bank i at time t on the downward signal proxy3 for bank i at time t, together with a set of bank-level control variables. The regression model is shown in the following equation.
𝑆𝑧_𝑠𝑐𝑜𝑟𝑒𝑖,𝑡= 𝛽0+ 𝛽1𝑆𝑖𝑔𝑛𝑎𝑙𝑖,𝑡−1+ ∑ 𝛽𝑘 𝑘𝑋𝑖,𝑡−1+ 𝜀𝑖,𝑡 Equation 4
where 𝑆𝑧_𝑠𝑐𝑜𝑟𝑒𝑖,𝑡 is the actual value of the standard z-score for bank i at time t.
𝑆𝑖𝑔𝑎𝑙𝑖,𝑡−1 represents the downward signal for bank i at time t-1. A series of control variables (𝑋𝑖,𝑡−1) are included in the regression equation, including bank size (Size), income diversification (Diversification), bank leverage (Leverage), cost-to-income ratio (Cost-Income) and analyst consensus (Consensus), as provided in Table 1. We control for bank and year fixed effects, and cluster standard errors at bank level.
Table 4 reports relevant results. We start the analysis by the regression without control variables (Column (1)). Columns (2) and (3) report results with various control variables. To separate the effect of analyst consensus, we add this variable separately into the regression, as reported in Column (3).
Table 4 Downward signal and standard z-score
This table reports the results of Equation 3 for the association between the downward signal and the standard z-score. The dependent variable is the standard z-score at time t, and the explanatory variable is the downward signal at time t-1. The control variables include bank size (Size), income diversification (Diversification), bank leverage (Leverage), cost-to-income ratio (Cost-Income) and analyst consensus (Consensus). The variable definitions are provided in Table 1. Robust standard errors are provided below in the parentheses and are clustered at bank level. All continuous variables are winsorized at 1st and 99th percent. ***, **, and * represent statistical significance at 1%, 5% and 10% levels, respectively.
(1) (2) (3)
Variables Sz_score Sz_score Sz_score
Signalt-1 -12.4930*** -12.5736*** -12.6515***
(2.2204) (2.2066) (2.2180)
3 To avoid the multicollinearity problem, we do not use the forward-looking z-score directly in this regression.
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Sizet-1 6.8237 4.9247
(5.8320) (6.4505)
Diversificationt-1 -12.5807 -3.7911
(30.1193) (29.9572)
Leveraget-1 -1.1562* -1.3006**
(0.6824) (0.6483)
Cost-Incomet-1 0.0068 -0.0554
(1.0855) (1.0634)
Consensust-1 -18.5398***
(4.0851)
Constant 58.5703*** 5.7317 42.4459
(9.0374) (51.8607) (58.6617)
Observations 5,938 5,932 5,460
R-squared 0.4081 0.4095 0.4254
Bank FE Yes Yes Yes
Year FE Yes Yes Yes
Robust standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1
As shown in Table 4, the downward signal is negatively related to the standard z-score in the following quarter, statistically significant at 1% level. To be more specific, as defined in Table 1, the downward signal takes the value one if the forward-looking z- score is less than the standard z-score, which predicts an increased insolvency risk during the next quarter. The significantly negative sign means that a higher value of the downward signal at time t-1 is associated with a lower value of the standard z- score at time t, reflecting higher insolvency risk. This confirms our finding in Figure 1 that the forward-looking z-score would be able to predict the movement of the standard z-score one quarter ahead of time.
The negative association is strongly held after controlling for bank-level variables, as reported in Columns (2) and (3). The negative estimate of the coefficient of analyst consensus indicates that the dispersion of the analyst forecasts is negatively related to banks’ insolvency risk, while the dispersion does not affect the predictive ability of the forward-looking z-score.
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3.2 Predictive ability of the forward-looking z-score
We explore whether the forward-looking z-score provides predictive signals of banks’
future profitability (proxied by ROA or ROE) and asset quality (proxied by NPL ratio).
We run regressions of the actual values of ROA (or ROE, or NPL ratio) for bank i at time t on the forward-looking z-score for bank i at time t-14.
𝑅𝑂𝐴𝑖,𝑡 = 𝛽0+ 𝛽1𝐹𝑧_𝑠𝑐𝑜𝑟𝑒𝑖,𝑡−1+ ∑ 𝛽𝑘 𝑘𝑋𝑖,𝑡−1+ 𝜀𝑖,𝑡 Equation 5 𝑅𝑂𝐸𝑖,𝑡 = 𝛽0+ 𝛽1𝐹𝑧_𝑠𝑐𝑜𝑟𝑒𝑖,𝑡−1+ ∑ 𝛽𝑘 𝑘𝑋𝑖,𝑡−1+ 𝜀𝑖,𝑡 Equation 6 𝑁𝑃𝐿𝑖,𝑡 = 𝛽0+ 𝛽1𝐹𝑧_𝑠𝑐𝑜𝑟𝑒𝑖,𝑡−1+ ∑ 𝛽𝑘 𝑘𝑋𝑖,𝑡−1+ 𝜀𝑖,𝑡 Equation 7
where 𝑅𝑂𝐴𝑖,𝑡 (or 𝑅𝑂𝐸𝑖,𝑡, or 𝑁𝑃𝐿𝑖,𝑡) represents the actual value of ROA (or ROE, or NPL ratio respectively) for bank i at time t. 𝐹𝑧_𝑠𝑐𝑜𝑟𝑒𝑖,𝑡−1 represents the downward for bank i at time t-1. The same series of control variables (𝑋𝑖,𝑡) are included, as in Equation 4. We control for bank and year fixed effects, and cluster standard errors at bank level. Table 5 reports relevant results.
Table 5 Forward-looking z-score and banks’ future performance
This table reports the results of Equations 4-6 for the link between the forward-looking z-score and banks’ future performance. The dependent variables in Columns (1)-(3) are the actual value of ROA, ROE and NPL ratio respectively for bank i at time t. The explanatory variable is the forward-looking z-score for bank i at time t-1. The control variables include bank size (Size), income diversification (Diversification), bank leverage (Leverage), cost-to-income ratio (Cost- Income) and analyst consensus (Consensus). The variable definitions are provided in Table 1.
Robust standard errors are provided below in the parentheses and are clustered at bank level.
All continuous variables are winsorized at 1st and 99th percent. ***, **, and * represent statistical significance at 1%, 5% and 10% levels, respectively.
(1) (2) (3)
Variables ROA ROE NPL
Fz_scoret-1 0.0004** 0.0039*** -0.0013***
(0.0001) (0.0015) (0.0003)
Sizet-1 -0.0100 -0.7137 0.0056
(0.0513) (0.5856) (0.0928) Diversificationt-1 0.5191* 6.6246** -0.0469
4 We use the downward signal as the explanatory variable in robustness checks.
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(0.2811) (2.9437) (0.3835)
Leveraget-1 -0.0151** -0.1206* 0.0152
(0.0065) (0.0625) (0.0131) Cost-Incomet-1 -0.0220* 0.5653*** -0.0123
(0.0124) (0.1379) (0.0296)
Consensust-1 0.1601** 1.9499** -0.1495
(0.0802) (0.8312) (0.1277)
Constant 1.5284*** 12.9109** 0.8007
(0.5126) (5.9609) (0.9498)
Observations 5,433 5,433 5,418
R-squared 0.4108 0.4255 0.6619
Firm FE Yes Yes Yes
Year FE Yes Yes Yes
Robust standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1
As reported in Columns (1) and (2), the forward-looking z-score is positively related to banks’ ROA or ROE in the following quarter, statistically significant at 5% level or above.
This means that a higher value of the forward-looking z-score, as an indicator of decreased insolvency risk in the next quarter, is significantly associated with an improvement in banks’ profitability during the next quarter. This provides direct evidence that the forward-looking at time t-1 provides an early signal of the banks’
profitability at time t.
In another aspect, the forward-looking z-score is negatively related to banks’ NPL ratio in the following quarter, statistically significant at 5% level. This means that a bank’s ratio is expected to decrease during the next quarter with a higher value of the forward-looking z-score in this quarter. In other words, the forward-looking z-score is able to provide an early prediction of the bank’s NPLs in the next quarter.
The analyst consensus is statistically and positively related to banks’ future ROA or ROE, as reported in Columns (1) and (2). But the dispersion of analyst forecasts does not affect the predictive ability of the forward-looking z-score.
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3.3 Forward-looking z-score and market-based measures
We further examine the association between the forward-looking z-score, as a typical accounting-based risk measure, and market-based risk measures. Two market-based risk measures are used, namely total risk and total market-adjusted risk. Total risk is computed by the annualized standard deviation of a bank’s stock return. Total market- adjusted risk is computed by the annualized standard deviation of a bank’s stock return in excess of S&P1500. We examine the link between forward-looking z-score and market risks using the following equations.
𝑇𝑅𝑖,𝑡 = 𝛽0+ 𝛽1𝐹𝑧_𝑠𝑐𝑜𝑟𝑒𝑖,𝑡−1+ ∑ 𝛽𝑘 𝑘𝑋𝑖,𝑡−1+ 𝜀𝑖,𝑡 Equation 8 𝑇𝑀𝑅𝑖,𝑡 = 𝛽0+ 𝛽1𝐹𝑧_𝑠𝑐𝑜𝑟𝑒𝑖,𝑡−1+ ∑ 𝛽𝑘 𝑘𝑋𝑖,𝑡−1+ 𝜀𝑖,𝑡 Equation 9
where 𝑇𝑅𝑖,𝑡 and 𝑇𝑀𝑅𝑖,𝑡 represents total risk and total market-adjusted risk respectively for bank i at time t. 𝐹𝑧_𝑠𝑐𝑜𝑟𝑒𝑖,𝑡−1 represents the forward-looking z-score for bank i at time t-1. The series of control variables (𝑋𝑖,𝑡−1) are included, as in Equation 4. We control for bank and year fixed effects, and cluster standard errors at bank level.
Table 6 provides relevant results.
Table 6 Forward-looking z-score and market-based risk measures
This table provides the results of Equations 7-8 for the comparison between the forward- looking z-score and market-based risk measures. The dependent variables are total risk and total market-adjusted risk for bank i at time t, respectively. The explanatory variable is the forward-looking z-score for bank i at time t-1. The control variables include bank size (Size), income diversification (Diversification), bank leverage (Leverage), cost-to-income ratio (Cost- Income) and analyst consensus (Consensus). The variable definitions are provided in Table 1.
Robust standard errors are provided below in the parentheses and are clustered at bank level.
All continuous variables are winsorized at 1st and 99th percent. ***, **, and * represent statistical significance at 1%, 5% and 10% levels, respectively.
(1) (2)
Variables TR TMR
Fz_score -0.0132*** -0.0131***
(0.00260) (0.00260)
Size 1.364 2.058**
(0.970) (1.001)
Diversification -18.39*** -23.93***
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(3.880) (4.096)
Leverage -0.0248 -0.0422
(0.151) (0.154)
Cost-Income 0.744*** 0.725***
(0.197) (0.215)
Consensus -2.094 -1.535
(1.519) (1.660)
Constant 3.021 2.932
(9.662) (9.821)
Observations 5,333 5,333
R-squared 0.602 0.618
Bank FE Yes Yes
Year FE Yes Yes
Robust standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1 Note: The estimates of all the coefficients are multiplied by 100 in this table.
As reported in Table 6, the forward-looking z-score is negatively related to the market- based measures, statistically significant at 1% level. A higher value of the forward- looking z-score, which predicts a reduction in banks’ insolvency risk, is negatively related to total risk or total market-adjusted risk in the next quarter. As market-based measures usually reflect forward-looking information, the significant association between the forward-looking z-score and market-based risk measures supports our argument that forward-looking z-score provides reliable prediction of a bank’s future risk.
4. Robustness checks
We conduct several robustness tests. Firstly, there is no consensus on a moving window used to compute the time-varying z-score. Prior studies usually employ 3- to 5-year moving windows. As the first robustness test, we check whether the selection of moving windows would make a difference in the predictive ability of the forward- looking z-score. We use 4-quarter, 12-quarter, and 16-quarter moving windows respectively in the computation of the time-varying z-score (including the standard z- score and forward-looking z-score). Relevant results are reported in Table 7.
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Table 7 Downward signal and standard z-score, various moving windows
This table provides robustness results of Equation 3 for the association between the downward signal and standard z-score. We use 4-quarter, 12-quarter, or 16-quarter moving windows to calculate the elements of the time-varying z-scores, as reported in different columns. The dependent variable is the standard z-score at time t, and the explanatory variable is the downward signal at time t-1. The control variables include bank size (Size), income diversification (Diversification), bank leverage (Leverage), cost-to-income ratio (Cost- Income) and analyst consensus (Consensus). The variable definitions are provided in Table 1.
Robust standard errors are provided below in the parentheses and are clustered at bank level.
All continuous variables are winsorized at 1st and 99th percent. ***, **, and * represent statistical significance at 1%, 5% and 10% levels, respectively.
(1) (2) (3)
Variables Sz_score_4 Sz_score_12 Sz_score_16 Signalt-1 -28.9742*** -4.6385*** -4.6893***
(3.6840) (1.5324) (1.2579)
Sizet-1 5.3759 5.7487 8.7612*
(10.6728) (5.5871) (4.8884) Diversificationt-1 -38.8964 6.7987 9.7657
(35.6527) (26.1867) (25.6484)
Leveraget-1 -2.6992** -0.6929* -0.4236
(1.1042) (0.4162) (0.3754)
Cost-Incomet-1 -2.0168 -0.4410 -0.7851
(1.7800) (0.8888) (0.8122) Consensust-1 -21.0147*** -11.0793*** -6.9471***
(7.8031) (2.6253) (1.9657)
Constant 165.9956* 5.4656 -20.5741
(98.2072) (51.1429) (45.3218)
Observations 5,460 5,390 5,262
R-squared 0.3152 0.4852 0.5266
Bank FE Yes Yes Yes
Year FE Yes Yes Yes
Robust standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1
It is obvious that with different moving windows, the downward signal at time t-1 is always significantly and negatively correlated with the standard z-score at time t. This confirms our main findings that the forward-looking z-score leads the movement of the standard z-score.
Secondly, instead of using the forward-looking z-score directly, we use the downward signal as the explanation variable to check the predictive ability of the forward-looking
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z-score. We re-estimate Equations 4-8. Relevant results are reported in Tables 8 and 9, respectively.
To interpret these results, it is important to remember that the downward signal takes the value one when the forward-looking z-score predicts increased insolvency risk.
Hence, in Columns (1) and (2) of Table 8, the significantly negative correlation between the downward signal and ROA (or ROE) indicates an improvement of banks’
profitability in the following quarter if the downward signal (i.e. the forward-looking z-score) predicts a decrease in bank risk. On the contrary, the positive correlation with the NPL ratio means that the banks’ NPL ratio is likely to increase in the next quarter if the downward signal predicts an increase in bank risk.
Table 9 also shows a significant correlation between the downward signal and the market-based risk measures. This confirms our argument that the forward-looking z- score provides forward-looking estimates of bank insolvency risk.
Table 8 Downward signal and banks’ future performance
This table reports the robustness results of Equations 4-6. The dependent variables in Columns (1)-(3) are the actual value of ROA, ROE and NPL ratio respectively for bank i at time t. The explanatory variable is the downward signal for bank i at time t-1. The control variables include bank size (Size), income diversification (Diversification), bank leverage (Leverage), cost-to-income ratio (Cost-Income) and analyst consensus (Consensus). The variable definitions are provided in Table 1. Robust standard errors are provided below in the parentheses and are clustered at bank level. All continuous variables are winsorized at 1st and 99th percent. ***, **, and * represent statistical significance at 1%, 5% and 10% levels, respectively.
(1) (2) (3)
Variables ROA ROE NPL
Signalt-1 -0.0485*** -0.5270*** 0.0745***
(0.0156) (0.1606) (0.0258)
Sizet-1 -0.0094 -0.7014 0.0006
(0.0517) (0.5960) (0.0936)
Diversificationt-1 0.4729 6.1352** -0.0264
(0.2869) (2.8869) (0.3933)
Leveraget-1 -0.0158** -0.1281** 0.0177
(0.0066) (0.0634) (0.0134)
Cost-Incomet-1 -0.0245* 0.5349*** -0.0090
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(0.0127) (0.1440) (0.0305)
Consensust-1 0.1297* 1.6035** -0.0781
(0.0757) (0.7835) (0.1133)
Constant 1.6156*** 13.8278** 0.6571
(0.5196) (6.1308) (0.9605)
Observations 5,460 5,460 5,445
R-squared 0.4100 0.4238 0.6571
Bank FE Yes Yes Yes
Year FE Yes Yes Yes
Robust standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1 Table 9 Downward signal and market-based risk measures
This table provides the robustness results of Equations 7-8 for the comparison between the forward-looking z-score and market-based risk measures. The dependent variables are total risk and total market-adjusted risk for bank i at time t, respectively. The explanatory variable is the forward-looking z-score for bank i at time t-1. The control variables include bank size (Size), income diversification (Diversification), bank leverage (Leverage), cost-to-income ratio (Cost-Income) and analyst consensus (Consensus). The variable definitions are provided in Table 1. Robust standard errors are provided below in the parentheses and are clustered at bank level. All continuous variables are winsorized at 1st and 99th percent. ***, **, and * represent statistical significance at 1%, 5% and 10% levels, respectively.
(1) (2)
Variables TR TMR
Signal 0.0078** 0.0044
(0.0038) (0.0042)
Size 0.0131 0.0201**
(0.0097) (0.0099)
Diversification -0.1832*** -0.2385***
(0.0385) (0.0407)
Leverage -0.0000 -0.0002
(0.0015) (0.0016)
Cost-Income 0.0079*** 0.0077***
(0.0020) (0.0021)
Consensus -0.0128 -0.0067
(0.0140) (0.0155)
Constant 0.0152 0.0146
(0.0961) (0.0977)
Observations 5,359 5,359
R-squared 0.6004 0.6169
Bank FE Yes Yes
Year FE Yes Yes
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Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
5. Conclusions
In this study, we propose a forward-looking method to construct the time-varying z- score. The forward-looking z-score incorporates analyst forecasts of banks’ earnings and financial position in the computation of the time-varying z-score. Using a sample of the U.S. banks listed in S&P1500 covering the period 2002Q1-2020Q1, we provide evidence that the forward-looking is able to predict the movement of the standard z- score one quarter ahead of time. We also find evidence that the forward-looking z- score is able to provide early predictive signals of banks’ future profitability or NPL ratio. The forward-looking z-score is also significantly associated with market-based risk measures.
Overall, this paper makes an important contribution to the construction of the time- varying z-score. The use of financial analysts and forecasts in the computation of z- score overcomes the shortcomings of accounting data being backward-looking. The predictive ability of the forward-looking z-score provides important implications for policymakers, commercial banks, and investors.
References
Alford, A. W., & Berger, P.G. (1999). A simulation equations analysis of forecast accuracy, analyst following and trade volume. Journal of Accounting, Auditing, &
Finance, 14(3), 219-240.
Barber, B. M., Lehavy, R., McNichols, M., & Trueman, B. (2001). Can investors’ profit from the prophets? Security analyst recommendations and stock returns. The Journal of Finance, 56(2), 531-563.
Barber, B. M., Lehavy, R., & Trueman, B. (2010). Ratings changes, ratings levels, and the predictive value of analysts’ recommendations. Financial Management, 39(2), 533-553.
Bouvatier, V., Lepetit, L., Rehault, P-N., & Strobel, F. (2018). Bank insolvency risk and z-score measures: Caveats and best practice. Working paper.
Boyd, J. H., and Graham, S. L. (1986). Risk, regulation, and bank holding company expansion into nonbanking. Quarterly Review (Spring), 2-17.
22
Boyd, J. H., and Graham, S. L. (1988). The profitability and risk effects of allowing bank holding companies to merge with other financial firms: A simulation study.
Quarterly Review (Spring), 3-20.
Brown, L. D. (1997). Analyst forecasting errors: Additional evidence. Financial Analysts Journal, 53(6), 81-88.
Caiazza, S., Gotugno, M., Fiordelisi, F., & Stefanelli, V. (2018). The spillover effect of enforcement actions on bank risk-taking. Journal of Banking & Finance, 91, 146- 159.
Hannan, T. H., and Hanweck, G. A. (1988). Bank insolvency risk and the market for large certificates of deposit. Journal of Money, Credit and Banking, 20(2), 203- 211.
Hong, Y., Huseynov, F., Sardarli, S., & Zhang, W. (2020). Bank earnings management and analyst coverage: Evidence from loan loss provisions. Review of Quantitative Finance and Accounting, 55, 29-54.
Ijtsma, P., Spierdijk, L., & Shaffer, S. (2017). The concentration-stability controversy in banking: New evidence from the EU-25. Journal of Financial Stability, 39, 273-284.
Khan, M. S., Scheule, H., & Wu, E. (2017). Funding liquidity and bank risk taking. Journal of Banking and Finance, 82, 203-2016.
Laih, Y-W., Lai, H-N., & Li, C-A. (2015). Analyst valuation and corporate value discovery.
International Review of Economics and Finance, 35, 235-248.
Lepetit, L., & Strobel, F. (2015). Bank insolvency risk and Z-score measures: a refinement. Finance Research Letters, 13, 214-224.
Li, X., Tripe, D., Malone, C., & Smith, D. (2020). Measuring systemic risk contribution:
The Leave-one-out z-score method. Finance Research Letters, 36.
Loh, R. K., & Mian, G. M. (2006). Do accurate earnings forecasts facilitate superior investment recommendations? Journal of Financial Economics, 80, 455-483.
Pino, G., & Sharma, S. C. (2019). On the contagion effect in the US banking sector.
Journal of Money, Credit and Banking, 51(1), 261-280.
Roy, A. D. (1952). Safety first and the holding of assets. Econometrica, 20(3), 431-449.
Tan, H., Wang, S., & Welker, M. (2011). Analyst following and forecast accuracy after mandated IFRS adoptions. Journal of Accounting Research, 49(5), 1307-1357.
Tsionas, E. G., & Mamatzakis, E. C. (2017). Adjustment costs in the technical efficiency:
An application to global banking. European Journal of Operational Research, 256(2), 640-649.
