“Bank solvency: The role of credit and liquidity risks, regulatory capital and economic stability”

Banking stability is essential to any economy due to its many functions, including in- termediation, payment facilitation, and credit creation. Thus, the stability of the banking industry is one of the critical ingredients in economic growth. This paper analyzes how bank capital, credit and liquidity requirements impact bank solvency, using ten major banks controlling 90% of the UK market share in 2009–2018. The GMM model indicates a strong association between credit and liquidity risks. That is, when banks finance a risky or distressed project, this will lead to an increase in non-performing loans (NPL), which reduces bank liquidity. Poor liquidity profile of a bank may restrict its ability to act as a financial intermediary. In addition, the findings indicate that efficiency, asset quality, and economic growth have a significant positive effect on the solvency of banks. The results also show that the regulatory capital (Tier1) has a positive significant influence on bank solvency. Further, the results indicate that during the economic boom, banks tend to increase their regulatory capital. Therefore, there is a need to ensure that during the “good time”, banks can accumulate enough capital that is genuinely capable of absorbing negative shock. Also, it is important for banks to ensure that they are efficient but also have a robust credit appraisal system to reduce NPL. This paper also demonstrates the implications of increased capital requirements. That is, increased capital requirements ensure not only banks are liquid but also solvent, which allows them to provide financial intermediation.


INTRODUCTION
Banks are the most regulated firms because of the various risks they face and the role they play in the economy. Regulation range consists of many aspects, including minimum capital requirements, liquidity level, investment activities and financial and non-financial disclosures. The underpinning objective of regulation is to ensure that banks not only engage in risky activities, but also ensure that banks are solvent and sustainable. The objective of this paper is to analyze how liquidity and credit risk, efficiency, economic freedom, and regulatory capital affect bank solvency.
Following the 2009 financial crisis, significant reforms were implemented that led to Basel III, which requires banks to have a minimum common equity of 4.5% and capital conservation buffer of 2.5% of risk weighted assets. In addition, banks are required to have sufficient high-quality liquid assets (HQLA) that can withstand a 30-day liquidity stressed scenario. This is commonly called a liquidity coverage ratio that came into force in 2016. From 2016, banks were required to have a minimum LCR of 70%, and 100% from 2019. This liquidity requirements enhance the ability of banks to withstand financial and economic Therefore, there is a trade-off between the benefits of financial stability and the costs of lower liquidity creation to the economy. This paper extends the literature by examining how economic growth and the regulatory capital interplay between liquidity and credit risks. In addition, this paper assesses the impact of efficiency using the cost-income ratio (CIR) on solvency. In addition, unlike the previous study, the effect of economic freedom on banking is considered.
Using 10 largest banks in the UK (HSBC, Barclays, Natwest, Lloyds, Nationwide, RBS, Halifax, Santander, Bank of Scotland and Cooperative) that control 90% of the market share, the results show that there is a positive correlation between solvency and GDP growth. This implies that during economic growth, most of banks will be solvent. The results also indicate a cyclical nature of regulatory capital. That is, banks increase the regulatory capital as the economy grows. Also, a 1% increase in profitability leads to a 0.02% reduction in credit risk compared to 0.023 % liquidity risk. The results also indicate that a 1% increase in the total regulatory capital leads to a 2.35% and 0.006% reduction in credit and liquidity risk, respectively. This is in line with Salachas et al. (2017) who noted that less capitalized banks engage in risky activities. In addition, a 1% growth in GDP leads to an 8% improvement in solvency level. In other words, economic downturn exacerbates bank insolvency because there will be an increase in NPLs, which in turn will worsen the liquidity position of banks.

LITERATURE REVIEW AND HYPOTHESES DEVELOPMENT
The solvency of a bank mirrors its capability to perform the intermediation function. The risk of insolvency emanates from liquidity, credit, and market risk. Gualandri et al. (2009) define a bank's liquidity as its monetary obligations on demand, in the form of deposits in current accounts and credit lines. This indicates the im-portance of the bank's ability to meet its financial obligation, both short-term and long-term. Kim  The net stable funding ratio (NSFR) requires that available stable funding (i.e., equity and liability financing expected to remain stable over a oneyear time horizon) be at least equal to the matching assets (i.e., illiquid assets that cannot be easily turned into cash over the following 12 months).
Berger and Bouwman (2009) argued that regulatory capital has two effects. First, through the "financial fragility structure" in which higher capital requirement may result in less monitoring, leading to less liquidity creation. Second, higher capital requirements may lead to "crowding-out of deposits" and reduce liquidity creation (Gorton & Winton, 2000). The study noted that customer deposits are more effective liquidity hedges compared to equity.
Also, Berger et al. (2012) analyzed the effects of regulatory interventions and capital support on bank risk-taking and liquidity creation. They noted that both types of actions are generally associated with statistically significant reductions in risk-taking and liquidity creation in the short and long run. A recent study by Nguyen and Nghiem (2015) analyzed the nexus between default risk, regulatory capital, and bank efficiency in 40 banks. The results indicated that those banks with high capital levels were efficient and had fewer insolvency risks. Existing literature also indicates that increased capital requirements increase a bank's risk (Lee & Hsieh, 2013). This view implies that a bank's lending capacity will be reduced or weakened. Indeed, evidence from the recent study (Sum, 2016) has shown that in the short run, increased capital requirements may constrain bank activities, reduce deposit funding, increase the costs of lending and limit credit expansion. Also, in terms of entry barriers, higher capital requirements will restrict entry, which may reduce competition. Limiting credit creation will lead to lower credit risk, but also this will lead to low-er profitability. This is because the main business of banks is to offer credit. Indeed, Mendes and Abreu (2003) and Valverde and Fernández (2007) noted a positive relationship between credit risk and profitability. Using bank capital as a channel, it is safe to state that highly capitalized firms, in the long run, will be profitable and, in turn, will have a well-documented credit policy that will reduce both liquidity and credit risks. Therefore: H2: Profitability affects both credit and liquidity risks and solvency.
Economic growth (GDP) is one of the determinants of bank profitability (Athanasoglou et al., 2008). Other studies have noted that GDP growth controls for cyclical output effects (Flamini et al., 2009). Therefore, GDP can significantly affect the supply, demand, and repayment of loans and deposits. For instance, during the economic boom, the need for loans will increase, positively impacting profitability (all other factors held constant). On the flip side, poor economic growth or recession will lead to an increase in non-performing loans, affecting the liquidity and profitability of the banks. Therefore: H3: GDP growth affects credit and liquidity risks.
Although regulation is essential, especially when there is market failure, excessive control also may be seen as a threat to the efficient functioning of the banking industry (Beach & Kane, 2008

Data sources
Using BankScope and Fitchconnect, the study extracted a set of reported annual series for a period for bank-specific data. The study used 10 largest banks in the UK (HSBC, Barclays, Natwest, Lloyds, Nationwide, RBS, Halifax, Santander, Bank of Scotland, and Cooperative) that control 90% of the entire market share. Time series data from 2009 to 2018 were used to avoid the overlap of 2008 financial crisis. For economic growth (gross domestic product), the growth rate was extracted from the World Bank database and economic freedom from the Heritage Foundation for economic growth (gross domestic product).

Definition of variables
In line with Laeven and Levine (2009), to measure bank solvency, the study uses the Z-score (ZROA) that indicates the number of standard deviations that the bank's ROAA must fall below its expected value before equity is entirely exhausted. Following Ghenimi et al. (2017), a higher Z-score is interpreted as a decrease in bank insolvency risk, ZROA is formulated as follows: where u -average performance of a bank's assets (ROA); ROA is the return on assets, and the standard deviation of the σ ROA calculated moving averages over eight periods; k -equity as a percentage of total assets; σ -standard deviation of ROA as a proxy for return volatility.
Regulatory capital requirement is measured using Tier 1 capital. Tier 1 capital is calculated based on risk-weighted assets. In addition, each asset in a bank is classified according to the probability of default, as shown in Table A2 (Appendix). Further, to assess the impact of efficiency on profitability, the cost-to-income ratio (CIR) is used; this ratio measures the bank's overhead or running costs as a percentage of the income generated before provisions.

Econometric modeling
This section evaluates the impact of bank capital regulation, efficiency, credit risk, liquidity risk, and economic growth on bank stability in the UK. After testing for the stationarity of the data, the model is plugged in the form: Note: Sol (Solvency-ratio); CIR (Cost income ratio); CUST_DEPS_TOTAL_FUND (Customer deposit to total funds ratio); EF (Economic Freedom); EQUITY_TA (Equity to Total Assets ratio); GDPG (Gross domestic product growth); GROWTH_LOAN (Growth of loans); IMPAIRMENTLOANS_GROSS_EQ (Impairment of gross loans to equity ratio; LIQUID_ASSETS_TOTAL_AS (Liquid assets to total assets ratio); LOANS_DEPOSIT (Loans to total deposit ratio); ROE (Return on Equity); Tier 1 (Tier 1 Capital requirement); TOTAL_REG_CAP (Total Regulatory Capital). where Sol i,t is the solvency of a bank; Prof i,t-1 is the profitability measured by ROA; REG i,t-1 is the regulatory capital; Credrisk i,t-1 is the credit risk measured by the probability of asset default; liqrisk i,t-1 is the liquidity risk; EFF i,t-1 is the efficiency of a bank expressed as a total expense as a ratio of total income; ECON t is the economic growth measured by gross domestic product growth, and Assetqual i,t-1 is the quality of the asset measured by the percentage of impaired gross loans to equity, and β 8 EFt stands for Economic Freedom expressed through the Fraser index from Heritage.
In running the regression, it is ensured that the classical linear assumptions are met. For instance, the assumption var(μt) = σ2 < ∞ is tested that the error variance is constant. If the errors do not constant variance, they are said to be heteroscedastic. However, there is no solid evidence to suggest heteroscedasticity using the Breusch-Pagan-Godfrey test, as shown in Table 2. Both F and scaled explained SS p values are considerably more than 0.05. In addition, cov(μi,μj) = 0 for i ≠ j is tested, which is the zero covariance between the error terms over time. In other words, the errors are uncorrelated with one another. Table 3 shows that the null hypothesis of autocorrelation can be rejected.
Running the above equation (4) as shown in Table  4, both F and the fitted value indicate that the model is expressed appropriately. To deal with endogeneity issue, this study lags the bank variables by one year as suggested by Lindquist (2004). In addition, to address heteroskedasticity of errors, the generalized method of moments (GMM) is used with economic growth and economic freedom as the instrumental variables as it is considered more efficient than two-stage least squares (2SLS) regression. This is in line with Hall's (2005) recommendations. Finally, the fixed effect model (Table A3 Appendix) is also used to assess the results robustly. Table 5 reports summary statistics of the key variables used in the analysis. Within the sample, the profitability indicator measured by ROE suggests that, on average, the profitability is 1.19%, with the highest and lowest being 15.17% and -13.59%, respectively. The indicator of solvency ratio was measured by a log Z-score. The results indicate that, on average, the Z score is 4.56. The maximum solvency ratio is 6.95 and the minimum 1.50. The results show a negative relationship between CIR and solvency level. However, the results indicate a positive correlation between solvency and GDP growth, taking into account the solvency level and economic status. This implies that most banks will be solvent during the economic growth but begs if they will withstand during the dry spell.

RESULTS
In terms of capital adequacy, the results indicate an average of 11.95 and 16.04 for Tier 1 and total regulatory capital, respectively. Table 5 shows that banks tend to increase the regulatory capital during the economic boom or growth. This implies the cyclical nature of the regulatory capital. Therefore, banks need to build a buffer capital sufficient to absorb any shock during the economic downturn.
Examining the efficiency of the banks, on average, the cost-income ratio is 62.5%. The standard deviation is very significant, i.e., 12.008, indicating a considerable variation in efficiency across banks in the UK. The Pearson correlation suggests a positive association between GDP growth and CIR. This suggests that during economic growth, banks lose their financial discipline, especially on bonuses. Analyzing the total funds for the banks, the results indicate that 67.8% comes from the customers' deposits. As one would expect, there is a positive association between GDP growth and customer deposits to total funds. Loans form a significant part of a bank's earnings. Table 5 indicates that on average, grant of loans increased by 7.5%, compared to 32% impairment of loans within the same period of study 2005 to 2017.
When analyzing the relationship between solvency and other variables, Table 6 shows a negative correlation between the cost-income ratio and solvency. That is, efficiency enhances the solvency of a bank. In other words, inefficiency impairs the long-term stability of banks. Similarly, unsustainable growth in loans reduces the stability of the banks. Table 6 also shows that the more profitable the bank is, the more stable or solvent it is. In addition, the results point out the need for banks to be more capitalized to enhance the solvency level. Finally, in terms of liquidity measured by liquid assets to total assets and growth in a customer's deposit, the more liquid the bank is, the more solvent it is likely to be.

The association between credit risk and liquidity risk using GMM
Before running any regression, the stability of data was tested, i.e., the presence of a unit root. As shown in Table A1 (Appendix), all series except ROE are stable, i.e., there is no strong evidence of a unit root. Therefore, with ROE as a possible remedy, the data are lagged. Table 7 presents the results estimated by employing the GMM technique. Credit risk is proxied by the ratio of impairment of loans gross to total equity ratio, and liquidity (inverse of liquidity risk) is proxied by the ratio of liquid to total assets. The results indicate that the ratio of liquid assets to total assets significantly positively influences credit risk. Unlike Ghenimi et al. (2017), credit risk positively influences liquidity risks. This implies the when a bank has so much of the NPL, it will face liquidity challenges. Note: Sol (Solvency ratio); CIR (Cost income ratio); CUST_DEPS_TOTAL_FUND (Customer deposit to total funds ratio); EF (Economic Freedom); EQUITY_TA (Equity to Total Assets ratio); GDPG (Gross domestic product growth); GROWTH_LOAN (Growth of loans); IMPAIRMENTLOANS_GROSS_EQ (Impairment of gross loans to equity ratio); LIQUID_ASSETS_TOTAL_AS (Liquid assets to total assets ratio); LOANS_DEPOSIT (Loans to total deposit ratio); ROE (Return on Equity); Tier 1 (Tier 1 Capital requirement); TOTAL_REG_CAP (Total Regulatory Capital).   Note: Sol (Solvency ratio); CIR (Cost income ratio); CUST_DEPS_TOTAL_FUND (Customer deposit to total funds ratio); EF (Economic freedom); EQUITY_TA (Equity to total assets ratio); GDPG (Gross domestic product growth); GROWTH_LOAN (Growth of loans); IMPAIRMENTLOANS_GROSS_EQ (Impairment of gross loans to equity ratio); LIQUID_ASSETS_TOTAL_AS (Liquid assets to total assets ratio); LOANS_DEPOSIT (Loans to total deposit ratio); ROE (Return on equity); Tier 1 (Tier 1 capital requirement); TOTAL_REG_CAP (Total regulatory capital).
The results also show that the efficiency of a bank (CIR) significantly influences liquidity risk. That is, the higher the cost-income ratio, the higher the liquidity risk. In other words, inefficiency increases both liquidity and credit risks.
Further, the results indicate the need to increase funding as a ratio of customer deposit. The higher the customer deposit to total funding, the more credit and liquidity risk tends to decrease. This is probably because the likelihood of bank run is low when there is an increase in customer deposits. The growth of loans is significant in influencing both credit (negatively) and liquidity (positively) risk. This implies that if there is uncontrolled granting of loans, the credit risk will be magnified. This was noticeable in the 2007-2008 global financial crisis when there was "free" credit because of low-interest rates that encouraged mortgage lending. Also, during the period preceding the global financial crisis, many US banks bundled the mortgages into mortgage-backed securities with loose underwriting criteria.
The profitability of banks is essential in inversely influencing credit and liquidity risks. However, in terms of the magnitude, a 1% increase in profitability will lead to a 0.02% reduction in liquidity risk, compared to 2.6% credit risk. Similarly, the results demonstrate the importance of regulatory  ); CUST_DEPS_TOTAL_FUND (Customer deposit to total funds ratio); EF (Economic freedom); EQUITY_TA (Equity to total assets ratio); GDPG (Gross domestic product growth); GROWTH_LOAN (Growth of loans); IMPAIRMENTLOANS_ GROSS_EQ (Impairment of gross loans to equity ratio); LIQUID_ASSETS_TOTAL_AS (Liquid assets to total assets ratio); LOANS_ DEPOSIT (Loans to total deposit ratio); ROE (Return on equity); Tier 1 (Tier 1 capital requirement); TOTAL_REG_CAP (Total regulatory capital).
capital as it inversely influences both credit and liquidity risks. The results also indicate that a 1% increase in the total regulatory capital leads to a 2.35% and 0.006% reduction in credit and liquidity risk. This shows the motivation why banks tend to have higher capital requirements than the minimum requirement. Table 8 indicates that the banks' efficiency is significant in influencing the solvency level of a bank. In addition, the analysis suggests the need for increased savings from customers. That is, the more customer deposits are, the more solvent it is likely to be. This implies that banks with good and diversified customer deposits are likely to reduce the risk of solvency. This enhances financial stability, which is the core of any regulatory regime.
Like Baselga-Pascual et al. (2015) noted that capital, earnings, and efficiency are inversely related to banking risk, while loan-to-assets are positively correlated; the results indicate that ROE significantly influences a bank's solvency level. This implies that capital, earnings, and efficiency have a negative impact on banking failure. This suggests that highly profitable banks are less likely to become insolvent.
Similarly, an increase in regulatory capital (both Tier 1 and total regulatory) is paramount in determining a bank's solvency. This underscores the importance of Basel III that requires banks to maintain higher levels of capital, with minimum common equity holdings at banks increasing from 2% to 7% of risk-weighted assets. Therefore, this study fails to reject Hypothesis 1. That is, increased regulatory capital reduces the likelihood of insolvency of a bank. The main objective of the regulatory capital is to increase the loss absorption capacity. That is, increased regulatory capital enhances bank stability and resilience. Also, higher capital requirements reduce credit and liquidity risks. This is in line with Acharya et al. (2016) and Barth and Seckinger (2018), who noted that increased regulatory capital restricts risk appetite. Basell III requires banks to classify their assets according to the probability of defaults so that a prudent credit appraisal policy will mitigate haphazard lending. Indeed, the lack of a clear credit appraisal policy will lead to irresponsible lending, which was prevalent before the 2009 global finan-cial crisis. As a result, bankers were more motivated to the commission or bonuses without regard to the payment capability. However, it is essential to note that responsible lending is not only aimed at only the bankers but all market participants, including borrowers.
In addition, as shown in Table 7 and Table 8, profitability reduces credit and liquidity risks and significantly reduces the insolvency in banking.
In other words, profitable banks reduce credit and liquidity risks and increase a bank's solvency. Therefore, this study fails to reject Hypothesis 2.
Post the global financial crisis, there has been an emphasis on capital requirements and bank financial performance and liquidity (Vickers Report, 2011). This is not surprising, given that recent studies consider profitability as a macro-prudential indicator (Adusei, 2015). This is because profitable banks are able to safeguard themselves in an economic or financial downturn. In other words, profitable banks are able to build a buffer of earning, which will improve the liquidity level and hence lower liquidity risks.
In terms of the impact of economic growth on liquidity, past empirical results have been mixed. For example, Bunda and Desquilbet (2008) and Moussa (2015) stated that GDP has a positive impact on bank liquidity, while Aspachs et al. (2005) and Chen and Phuong (2014) indicated a negative influence of GDP on bank liquidity. However, this study has shown a positive association between GDP growth and liquid assets to total assets. In addition, the growth of the economy has a positive impact on the solvency of banks. In terms of significance, GDP growth is significant at 1% in influencing the solvency level of banks. The results indicate that a 1% increase in GDP leads to an 8% improvement in solvency level. Therefore, the study fails to reject Hypothesis 3. That is, during the economic boom, there will be reduced credit and liquidity risks and improved profitability of a bank. This is because economic booms do lead to job creation and, to some extent, improved earnings. With job security and earnings, loan defaults are likely to be low. As borrowers will be honoring their obligation, this will improve banks' liquidity level. However, it is noted that economic freedom has a positive and significant impact on credit risks and negatively affects the banks' sol-vency level. This drums the need for regulations.
Indeed, past studies have demonstrated a positive association between investors protection and capital growth (Houston et al., 2010). This suggests that the government needs to improve macroeconomic policies, which can be the driving force behind economic growth. This helps reduce the risk of banking failure.

CONCLUSION
Recent years have demonstrated the critical role that banks play and, therefore, the need to determine how the banks' stability is influenced by the degree of economic growth, a sound regulatory framework, and internal factors. The stability of banks affects the financial intermediation role they play. By extension, to play the financial intermediation role, banks must be profitable. Assessing what influences the solvency of banks, the results indicate that the more profitable the bank is, the more solvent it would be. However, profitability is impacted by various risks, including credit and liquidity risks. Provision of credit is one of the bank's functions and hence the importance of being liquid enough. Therefore, it calls for a careful balance of credit and liquidity. This paper studies the effect of liquidity and credit risks on banking solvency using a panel dataset of the UK's ten major banks from 2009 to 2018. The ten banks control a combined market share of more than 90% of the UK banking asset base. The results indicate ; CUST_DEPS_TOTAL_FUND (Customer deposit to total funds ratio); EF (Economic freedom); EQUITY_TA (Equity to total assets ratio); GDPG (Gross domestic product growth); GROWTH_LOAN (Growth of loans); IMPAIRMENTLOANS_GROSS_EQ (Impairment of gross loans to equity ratio); LIQUID_ ASSETS_TOTAL_AS (Liquid assets to total assets ratio); LOANS_DEPOSIT (Loans to total deposit ratio); ROE (Return on equity); Tier 1 (Tier 1 capital requirement); TOTAL_REG_CAP (Total regulatory capital).
that both credit and liquidity risk are significant in influencing the solvency of banks. The ratio of liquid assets to total assets significantly influences both credit risk and liquidity risk. The level of liquidity is essential as it affects the well-functioning of an institution. While it is necessary to ensure that banks do not hold too much liquid assets, it is crucial to ensure that they are sufficiently liquid enough to meet liquidity obligations. From 2019, banks are required to have a minimum liquidity coverage ratio of 100%. Liquidity requirements are to ensure banks have sufficient assets to mitigate liquidity disruptions due to changing economic climate. Illiquidity in banks will trigger a bank run, and this will have a ripple effect on the economy.
Additionally, the liquidity of a bank is influenced by how efficient the bank is. That is, the higher the cost-income ratio, the higher the liquidity risk. Tier 1 and total regulatory capital appear to have a detrimental impact on bank profitability and a tendency to reduce the risk of bankruptcy. In the case of greater economic growth, the results indicate that it positively affects solvency in banking. In addition, there is a negative association between economic freedom and banking solvency. However, it is noted that economic freedom has a significant positive influence on liquidity and credit risk.
The findings have several interesting policy implications that provide several recommendations for bank managers and bank supervisors. First, the financial crisis has shown that bank failures driven by credit risk in their portfolios can cause a freeze of the liquidity market. Second, the results indicate that during the economic boom, banks tend to increase their regulatory capital. Therefore, there is a need to ensure that during the "good time", banks can accumulate sufficient capital that is genuinely capable of absorbing negative shock during the economic downturn. Second, the results imply that a bank's joint liquidity management and credit risks could substantially increase banking stability. Finally, the results support recent regulatory efforts mainly by the new Basel III framework, which put more emphasis on capital conservation buffer, designed to enforce corrective action when a bank's capital ratio deteriorates, and a countercyclical buffer to require banks to hold more capital in good times to prepare for the inevitable rainy days ahead. Note: Sol (Solvency ratio); CIR (Cost income ratio); CUST_DEPS_TOTAL_FUND (Customer deposit to total funds ratio); EF (Economic Freedom); EQUITY_TA (Equity to Total Assets ratio); GDPG (Gross domestic product growth); GROWTH_LOAN (Growth of loans); IMPAIRMENTLOANS_GROSS_EQ (Impairment of gross loans to equity ratio); LIQUID_ASSETS_TOTAL_AS (Liquid assets to total assets ratio); LOANS_DEPOSIT (Loans to total deposit ratio); ROE (Return on Equity); Tier 1 (Tier 1 Capital requirement); TOTAL_REG_CAP (Total Regulatory Capital). ; CUST_DEPS_TOTAL_FUND (Customer deposit to total funds ratio); EF (Economic Freedom); EQUITY_TA (Equity to total assets ratio); GDPG (Gross domestic product growth); GROWTH_LOAN (Growth of loans); IMPAIRMENTLOANS_GROSS_EQ (Impairment of gross loans to equity ratio); LIQUID_ASSETS_TOTAL_AS (Liquid assets to total assets ratio); LOANS_DEPOSIT (Loans to total deposit ratio); ROE (Return on equity); Tier 1 (Tier 1 Capital requirement); TOTAL_REG_CAP (Total regulatory capital); Sol (Solvency ratio).