Liquidity Mismatch Index and Bank Performance

The relationship between liquidity and bank performance in finance literature remains an unresolved empirical issue. The main objective of this article was to investigate the relationship between liquidity mismatch index (LMI) initially developed by Brunnermeier, Gorton and Krishnamurthy (2012) and further developed by Bai, Krishnamurthy, and Weymuller (2018) and South African bank performance empirically. Different from other prior studies, the study undertook to determine the relationship employing the liquidity measure that integrates both market liquidity and funding liquidity within a context of asset liability mismatches. The unit of analysis was a panel of 12 South African banks over the period 2008–2018. Specifically, two liquidity measures – the bank liquidity mismatch index (BLMI) and the aggregate liquidity mismatch index (ALMI) were regressed against bank performance matrices. The newly developed liquidity measures are based on portfolio management theory and they account for the significance of liquidity spirals. Results revealed that, bank performance is negatively and significantly related with BLMI. While the bank performance is positively related to ALMI, the relationship is not significant. Also, the nature of relationship is dependent on the measure of profitability employed.


Introduction
Liquidity is the centrepiece in the performance of banks. In the theoretical model by Diamond and Dybvig (1983), banks performance is primarily derived from the difference between the returns from illiquid bank assets and the cost of liquid bank liabilities. Therefore, bank liquidity should be analysed from the asset standpoint and liability view point. International Monetary Fund (2011) assent that liquidity should be viewed from two realities, namely market liquidity and funding liquidity. Also, Brunnermeier, Gorton and Krishnamurthy (2012) argue that liquidity should be viewed from the perspective of the overall banking system which comprise of the bank assets, bank liabilities and the liquidity of the general market.
This article empirically tests the relationship between bank performance and the modified liquidity mismatch indices. Specifically, Bai, Krishnamurthy and Weymuller's (2018) liquidity mismatch index was further developed to come up with two liquidity measures, the bank liquidity mismatch index (BLMI) and the aggregate liquidity mismatch index (ALMI). The modified liquidity measures were then regressed against the bank performance measures including, return on assets (ROA), net interest income (NIM) and return on equity (ROE). This investigation is premised on the hypothesis that bank performance is influenced by its level of liquidity as measured by BLMI and the ALMI.
The linkage between net interest margin and liquidity is assumed to be positive. Empirical studies by Pradhan and Shrestha (2016) found a significant negative relationship bank performance and liquidity as their results show that return on assets and return on equity deteriorated with the improvement in bank liquidity. However, Maudos and Solí s (2009) though they found a negative relationship between market liquidity and net interest margin the relationship is not significant.
While it is generally agreed that there is a negative relationship between liquidity and bank profitability there is counter evidence which shows the need to consider the trade-off between resilience to liquidity shocks and cost of holding less profitable liquid assets. The latter is assumed to impact on the bank's ability to take advantage of opportunities arising in the market which may result in increase in revenue, capital or ability to extend capital credit (Bordeleau & Graham, 2010). Banks on the asset side hold low yielding securities such as treasury bills and highly rated short-term corporate bonds in order to minimise a scramble for liquidity when credit use increases in time when money is constricted (Holmstrom & Tirole, 1998). This is confirmed by Maudos and De Guevara (2004) who find a positive and significant relationship between market liquidity risk and net interest income. Thus, in essence, a liquid bank is encouraged to have a smaller portion of its assets in long-term loans and a greater proportion of its assets in short-term securities that can be quickly liquidated into cash that can then be loaned out. Nevertherless, other scholars argue that a highly liquid bank might mean lack of profitable projects to invest the money. Bai et al. (2018) empirically tested the LMI using American banks focusing on the performance of the bank as measured by enhancement of shareholder capital (changes in bank's share price). They find that as the aggregate liquidity conditions worsen, a firm with a inferior LMI should be more negatively affected. In this article bank performance is measured in terms of net interest margin (NIM), return on assets (ROA), return on equity (ROE) and economic value added (EVA).
Due to the strong persistent behaviour of bank performance, the estimation model is specified as a dynamic panel model which includes a one period lag of the bank performance. The models were estimated employing the Arellano and Bover (1995) two-step system generalised method of moments (GMM) with forward orthogonal deviations instead of differencing. Fixed effects model was also estimated specifically for robustness checking. assets as they think they have greater chance to borrow from the central bank. Bank performance was also found to be negatively related to NPL meaning that, the higher the NPL the higher the bank cost and therefore the lower the bank's profitability. Therefore, it is recommended that banks should diligently manage their loan book.
The liquidity dynamics in the banking sector underscored bank performance especially during and after the global financial crisis of 2007-2009. Thus far, the impact of bank liquidity risk on bank performance has been studied scantly in both emerging and developed markets, and such studies were done using standard liquidity measures. Amongst the known empirical studies on liquidity phenomenon, liquidity was explored within the segments of market liquidity and funding liquidity; yet, these two are profoundly interconnected. Liquidity standard measures also failed to grasp the banking sector important characteristic of liquidity spirals (Bai et al., 2018;Berger & Bouwman, 2009). Despite the introduction of theoretically baseless Basel III liquidity measures, there are still some shortcomings as both the standard and Basel III liquidity measures are not comprehensive enough, cannot be aggregated and therefore cannot be used as part of DSGE models (Brunnermeier et al., 2013).
However, there is a plethora of studies (see Oberholzer & Van der Westhuizen, 2004;Okeahalam, 2006;Erasmus, 2014) on bank performance and efficiency in South Africa. However, very few studies (e.g. Marozva, 2015;Visser & Van Vuuren, 2014) investigated the pertinent issue of bank liquidity in South Africa. Visser and Van Vuuren (2014) built liquidity stress testing model but did not examine the main determinants of liquidity risk. Whilst Marozva (2015) investigated liquidity under two dimensions of asset liquidity and funding liquidity, the analysis was not done within the context of asset liability mismatches. The conversional liquidity measures were interrogated and empirically tested. Moreover, their models were not tested within a context of other liquidity stress testing measures like the LMI.
It is against this background that this article aimed at testing the effect of BLMI and the ALMI on bank performance empirically. These new liquidity measures capture both the funding liquidity risk and the market liquidity risk within the context of asset liability mismatches. Furthermore, they address the pertinent issue of liquidity spirals. The IMF (2011) argues that the Basel III liquidity measures fail to address the additional risk of simultaneous shortfalls that arise from the nexus of various financial institutions across the universe of financial markets. Therefore, they recommend the development of a macro-prudential liquidity measure that captures the liquidity spirals, which can be used to mitigate systemic liquidity risks. A study by Brunnermeier (2008) laid the foundation to the understanding of systemic risk and liquidity spillover effects. Then Brunnermeier (2012) gave one basis for modelling the key response indicator of the spillover effects, the liquidity mismatch index (LMI).
The LIM by  laid the background for the LMI by Bai et al. (2018) and the modified liquidity mismatch indices by Marozva (2017;2020). The BLMI and the ALMI are better measures of liquidity as they account for the systemic risk. The BMLI and the ALMI are useful in the context of macro-prudential, as the measures placate three fundamentals. These are: (i) the BLMI can be aggregated to give ALMI, and the aggregated LMI can capture the liquidity condition of the whole banking sector quantitatively, (ii) BLMI is seful at bank level as it points out the institution that is more susceptible to liquidity shocks, and (iii) they account for time variation as liquidity conditions vary through time.
This article examines the empirical relationship between the modified liquid mismatch indices and bank performance by means of a strongly balanced sample using annual data (2008-2018) from 12 South African banks. Most studies investigated this phenomenon using the traditional liquidity measures and conversion and standard bank performance measures, ROE, ROA and NIM. Over and above these standard measures the Economic value Added (EVA) is also employed as a performance measure. EVA is tested because it is considered a financial performance yardstick, an investment decision tool and a performance measure that shows the absolute amount of shareholder value created (Owusu-Antwi, Mensah, Crabbe & Antwi, 2014). According to Bhasin (2017), EVA links economic, accounting and shareholder returns, this makes it a superior performance measure. data were employed. Since the approach was both longitudinal and cross-sectional, the study therefore conducted a panel study using pooled time series and cross-sectional data on selected South African banks.
From a country population of 18 locally registered banks in South Africa a sample of 12 banks was selected for this study. These banks constituted 99% of the assets of all South African registered banks by the time of analysis. These banks were included in this study because of the availability of bank-specific data on the variables under investigation for the study period running from 2008 to 2018. Six small banks were excluded from the analysis because data on non-performing loans and bank profitability was inaccessible for the period of study. The study primarily used annual data. However, some monthly data was used to compute annual averages for the modified liquidity mismatch indices (MLMI). The list of South Africa registered banks are presented in Table 1 with their corresponding asset bases.  (2017) The article tests the effects of BLMI and the ALMI on bank performance. These two liquidity measures were part of the independent variables. , , (2017).

Liquidity Mismatch Index (LMI)
The LMI measures the mismatch between the market liquidity of assets and the funding liquidity of liabilities (Bai et al., 2018). This measure incorporates both the asset side and the liability side . Therefore, the BLMI for an entity i at a given time t is the net of the asset and liability liquidity, calculated as, where assets ( are key components that are computed (Bai et al., 2018). The liquidity weight on the asset side should ideally represent the market liquidity, which is defined by Holden, Jacobsen, and Subrahmanyam (2014) as the ability of an institution to trade a significant portion of a security at a low cost in a short time. Like Bai et al. (2018) the asset weights assigned ranges from 0 to 1 depending on the asset class, and these vary over time. Using the data from the banks' balance sheets, the computed asset liquidity weight is set at to represent cash and cash equivalent and to represent mainly the non-current goodwill and intangible assets. The other assets were assigned weights between 0 and 1. Deviating from Krishnamurthy, Bai & Weymuller (2016) and Bai et al. (2018) the weights were computed using Danyliv, Bland and Nicholass's (2014) liquidity index (LIX). The liquidity index takes into account both the price range and volume traded.
Using the selected bank stock prices over the period under investigation, the asset liquidity weights were computed as follows: The calculated weight is adjusted by which is the coefficient allocated to the assets depending on the level of liquidity. The asset weights took the weights between 0 and 1, implying that assets liquidity weights for these assets were set to . ISSN 1923-4023 E-ISSN 1923-4031

Liability-Side Liquidity Weights
Liability-side liquidity is synonymous with funding liquidity, which is defined by Drehmann and Nikolaou (2009) as the ability of the organisation to settle its obligations as they fall due. The weights of liability-side liquidity is based on computation proposed by  in which they model access to liquidity as following a Poisson process (Meeker, Hahn & Escobar, 2017). There is a probability θ that represents the ability of an institution to raise capital in any given day. Then, the BLMI is based on the expected liquidity outflow going forward. This leads to the following function: , which measures the probability that the firm is unable to access free liquidity by date s, where s = 1 corresponds to one day and s = 30 to corresponds to thirty days. The probability is decreasing in s at a decay rate governed by the parameter θ. The asymptotic liquidity weight is modulated by transforming the funding liquidity factor that captures variation in θ, and the resulting function is as follows:  is the asymptotic liquidity weight and t FL is the state-dependent funding factor and ' k L  controls the exposure of the debt entity. To capture to feedback between BLMI and liquidity stress, the endogenous funding liquidity factor is computed as follows: where  represent a weighting parameter that weighs down the scale of aggregate BLMI to a similar level of spread between the treasury bills rate and the South African benchmark overnight rate (SABOR). Nagel (2014) argues that SABOR accurately measures the time variation of a money market instrument. In this study, the liability weights were captured through the adjustment of the state-dependent funding factor and produced equation 2.5.
[ ] (2.5) where is the coefficient allocated to the liability depending on the level of liquidity. When substituting for liquidity sensitivity weights and aggregate bank level LMI and then linearising the exponential term, the closed-form solution for the aggregate liquidity mismatch index (ALMI) was as follows: The ALMI can be used as barometer for market wide liquidity condition and this measure satisfies all the conditions the satisfies a good measure of bank liquidity as argued in Section 1. Table 3 presents the dependent and control variables.

Econometric Model Specification
As a preliminary to the detailed empirical analysis, the study presents the descriptive statistical analysis of all the variables under investigation. The data used in this sample of South African Banks was readily available from published financial statements and BA900 forms filed by banks to the central bank. Since all the banks were in South Africa, policy difference between countries was not a problem. The panel data analysis approach was employed primarily using the generalised method of moments (GMM) model. This approach meant that the study could account for whether there were bank-specific variations or time-specific variations. The fixed effects model (FEM) is presented for robustness and hence no details analysis is provided for it. Neither are the pre-diagnostic statistics discussed for this model.

The Generalised Method of Moments (GMM)
GMM estimation was formalized by Hansen (1982). The method is widely used method of estimation for economics and finance models. Distribution of the data does not matter when using this method, what is required is the specified moments obtained from an underlying model. However, challenges are faced when the dependent variable is persistent that is a lagged dependent variable is part of the regressors, particularly when N is greater than T (Nickell, 1981). Bank performance is persistent hence need to employ the Dynamic GMM approach.
Also, the challenge of a dynamic model is that coefficients may also be biased if the regressors are correlated with the lagged dependent variable to some degree. This challenge through employing Arellano and Bond's (1991) differenced GMM model where all the regressors are differenced. The differenced GMM was augment by Arellano and Bover (1995) and Blundell and Bond (1998) system GMM estimator which includes lagged levels as well as lagged differences. ISSN 1923-4023 E-ISSN 1923-4031 The system GMM estimator assumes that first differences of instrumental variables are uncorrelated with the fixed effects. It allows the introduction of more instruments and can substantially improve efficiency. Roodman (2006), among others, argues that both difference and system GMM estimators are more appropriate for a short panel that is when N>T; were independent variables are not strictly exogenous; were there is fixed individual effects; heteroskedasticity and autocorrelation among the subjects being analysed. Since the sample in this paper shares many of these features, this study employs the system GMM model to assess the determinants of South Africa bank profitability.
The optimal lag length was determined using the moment selection criteria and downward testing procedures developed by Andrews and Lu (2001). In this paper the optimal lag length was found to be one year as per Hansen test statistic. The exogenous variables, the lagged dependent variable and the difference of the lagged dependent variable were used as instruments. Given the limited number of banks under consideration meant only two lags could be tested if the instruments were not to exceed the number of subjects (banks). Employing the system GMM approach, the estimation models are expressed in equations 1 to 8. Where

represents the bank liquidity mismatch index for bank i in time t, is the aggregate liquidity mismatch index for the market in time t, represents the economic value added for bank i in time t, represents the return on assets for bank i in time t, measures the return on equity for bank i in time t, is the interest margin for bank i in time t, is the non performing loan for bank i in time t, is the capital ratio for bank i in time t, is an auto-regression coefficient,
is coefficient which represents the sensitivity of independent variables, is a disturbance term which is independent across banks. The fixed effects model is also estimated to allow comparison of results, and as a robustness check. The results from the estimation are discussed in the following section.

Empirical Results and Discussion
The research techniques were used to test the nexus between bank performance and liquidity in the presence of control variables which included NPL and CR. The study carried out the data analysis and presents the empirical results here and discusses them. This Section begins with presentation and brief discussion of descriptive statistics in Sub-section 4.1. An analysis of correlations and presentation of cross-sectional dependence results is done in Sub-section 4.2 and 4.3 respectively. Lastly, the presentation and discussion of the results from the main models is done in Sub-section 4.4.

Descriptive Statistics
In this section, the summary statistics of the variables used in the estimations for the entire sample of the banks were considered. Three bank performance measures of ROE, ROA and NIM were used in this article as dependent  ISSN 1923-4023 E-ISSN 1923-4031 variables. There are two liquidity measures and two control variables that were used. The descriptive statistics for all the variables are presented in Table 4.  Table 5 contains the cross-correlation analysis between the four performance measures, two liquidity measures and two control variables. The two liquidity measures of BLMI and ALMI have a negative correlation with EVA, the relationship is significant at the 1% level. The cross-correlation between liquidity and other performance measures indicates a negative relationship and the relationship is not significant. Therefore, the a priori expectation is that a negative relationship should hold. As expected, the performance measures exhibit a very strong and significant cross-correlation with each other. Non-performing loans contrary to expectation is positively correlated to all performance measures. Lastly, we observe a positive and significant cross-correlation between bank capital ratio and two performance measures, NIM and ROA. Where: (*), (**) and (***) indicate 10%, 5% and 1% significance level, respectively.

Econometric Model Estimation Results, Discussion and Analysis
Due to the strong persistent nature of bank performance, the estimation models were specified as a dynamic panel model which includes a lag of the dependent variable. Therefore, before running the models, the test for cross sectional dependence was done as part of initial diagnostic tests.   Table 6 confirm the notion that cross-sectional dependence is not a problem with micro panels as we fail to reject the null hypothesis of cross-sectional inter-dependence. The empirical results for the relationship between bank performance and bank liquidity (BLMI) are presented in Table 7. The post estimation diagnostic statistics for the main model i.e. GMM are shown in Table 8.   Table 7 The BLMI is intended to measure the exposure of a bank to a liquidity spirals and contagion effects. If the BLMI can capture these dimensions, it is expected that it will affect bank performance as the BLMI varies with time and across market-wide liquidity events. According to Bai et al. (2018), banks with low BLMI are to perform worse under a negative liquidity shock and bank performance improves when there is a positive liquidity shock.
The results of this study reveal a significant impact of BLMI on performance as measured by ROA, ROE and NIM. The relationship is negative implying that as the bank liquidity condition improved its performance deteriorated. This is in line with the hypothesis that liquidity represent and opportunity cost, holding huge volume of liquid assets crowds out more profitable loan portfolio. Therefore, hoarding liquidity is costly, and may only generates benefits in crises periods. Also, an increase in deposits (more liquid liabilities) other things being equal will help the banks to increase their profitability as demand deposits are cheaper. These results are line with Al-Jafari and Alchami (2014) and Marozva (2017) who finds that banks tend to be more profitability measured by return on asset (ROA) when they have lower scaled liquidity. Berger and Bouwman (2012) argue that, banking sector actively build liquidity buffers at the expense of building performance.
The results showed that bank profitability (ROA and NIM) is negatively affected by an increase in NPLs. An increase in non-performing means more bad debts written off thereby pushing up the cost of banks. This increase in the impairment of loans ultimately affected the performance of the banks. However, capital ratio is negatively related with bank performance measures (ROA ROE and EVA) but the relationship is not significant. The net interest margin is positively related to capital ratio and also the relationship is insignificant. Finally bank performance was found to be persistent as the lagged performance measures were found to be positive and significant.   Table 9 Models 5 to 8 were employed to investigate the nexus between the broad market liquidity as measured by ALMI and bank performance. The empirical results are presented in Table 9. The aggregate liquidity mismatch index is used as the barometer to measure the market wide liquidity condition. It is expected that banks perform better or worse when the market is awash with money. Bank performance will depend on the bank portfolio and liquidity position, if the bank is illiquid it performs better as it funds its profitable illiquid loans cheaply. When the bank is more liquid it implies it will invest its liquid assets in short term or long-term investments at a lower interest. Our results confirm the former notion as the relationship was found to be positive but not significant (where ROA, ROE and EVA were used as performance measures). There is a negative relationship between net interest margin and aggregate liquidity.
The results here confirm the results in Table 6 that bank performance is persistent, bank performance is negatively related to NPL and CR. Among other determinants of bank performance, NPLs play a central role because a significant part of banks' revenue accumulates from loans from which interest is derived (Kolapo, Ayeni, & Oke, 2012). Our results are consistent with those by Williams (2007) which showed a negative association between credit risk and bank performance. Also, Fungáčová and Poghosyan (2011) find a negative relationship between credit risk and net interest margin. The negative relationship could emanate from the banks' failure to appropriately price credit risk.
The negative and significant linear relationship between EVA and capital ratio indicate that increase in capital has a negative influence on bank's profitability. This is contrary to the results by Arias (2011) and Yilmaz (2013), who finds that, an improvement in bank capital ratio is associated with a reduction in costly external borrowing and consequently increasing bank performance.

Conclusion and Policy Implications
Thus far, the determinants of bank performance have been studied widely. However, the effects of bank liquidity on bank performance have been studied scantly in both emerging and developed markets, and such studies were done using standard liquidity measures. Amongst the known empirical studies on liquidity phenomenon, liquidity was explored within the segments of market liquidity and funding liquidity; yet, these two are profoundly interconnected (Marozva, 2017). Liquidity standard measures also failed to grasp the banking sector important characteristic of liquidity spirals (Berger and Bouwman, 2009). Therefore, main aim of this article was to investigate the nexus between bank performance and bank liquidity (as measured by BLMI and ALMI).
Using a panel of 12 banks over a period of 11 years and GMM as the primary method used in the analysis, several interesting deductions from the results were exposed. First, there is a negative relationship between BLMI and bank performance (ROA, ROE and NIM), and the association is both statistically and economically significant. The observation that bank liquidity mismatch index is has a negative effect on bank performance is in line with the liquidity preference theory, where highly liquid assets tend to generate less returns. Banks are encouraged to monitor closely the banks liquidity developments because BLMI measure was found to negatively affect bank performance. Despite findings in this article, liquidity is highly desired during crisis as Bai et al. (2018) argue that banks with high LMI tend to perform better during crisis. When banks forecast and deterioration in market liquidity they should hold 2 Step System GMM 2 Step System GMM 2 Step System GMM 2 Step System GMM more liquid assets and more long-term liabilities. However, there is a positive relationship between ALMI and bank performance, but the relationship is insignificant.
Second, bank performance is significantly negatively related to both capital ratio and credit risk as measured by non-performing loans. The higher the NPL the higher the bank cost and therefore the lower the bank's profitability. Banks should diligently manage their loan book. They should carry out thorough credit checking before they extend any credit. Capital ratio significantly affects bank profitability in a negative way this is contrary to theory and other empirical studies findings. I appear as if banks tend to practise reckless lending when they are well capitalised and therefore suffer significant impairment losses. Third, the bank performance was found to be persistent as all the previous period profitability measures were positively and significantly related to current period bank performance. Finally, the nature and strength of relationship between bank performance and liquidity is dependent on the type of performance measure under consideration.
The limitations of the current study emanate from the measures of performance used. ROA, ROE and EVA do not directly impact shareholder wealth. Also, the study was country specific over a period that included the global financial crisis of 2007-2009. However, the period of analysis was not split between crisis and stable period. Therefore, stock returns or share price should be used instead to supplement performance measurements. Future studies should test the nexus between bank liquidity and bank stock returns as it is established that bank liquidity is critical in the performance of the bank. The performance of the bank is directly linked to enhancement of shareholder's wealth hence need to investigate the impact of BLMI on bank stock returns. Since countries may be structurally different a cross country analysis may be required. Finally future studies should look at the nexus under distinct economic periods that is during the global financial crisis and /or during pandemic periods for example COVID-19 period.