The impact of bank size and funding risk on bank stability

Figures & data

Table 1. Major rural bank credit products

Loan type	Description
Microfinance loans	These loans are provided to groups of individuals to finance small and micro income generating activities. For some banks, the group is the borrower. For others, each member of the group is a borrower. In both cases, the group is jointly liable for the loan. The size of a microfinance loan ranges between GH¢ 50^a and GH¢ 1,000; however, most loans are between GH¢ 100 and GH¢ 500. The term of a microfinance loan is four to six months, and the interest rate ranges between 30 and 36%
Susu loans	These loans are provided to individuals following a three-month susu deposit. The size and term of susu loans are similar to those of microfinance loans, but susu loans are provided to individuals whereas microfinance loans are group loans
Salary loans	These loans provided to salaried individuals, are secured by the individual’s salary, which is paid through the bank. The bank automatically deducts the loan repayment installment from the salary payments
	Salary loans are used for consumption and investment, as well as social purposes. The size of the loan is determined by the salary of the borrower. The maximum term of a salary loan is 48 months, and the interest rate ranges between 30 and 33%
Commercial loans	These loans are provided to companies and individual entrepreneurs for working capital or fixed capital. The maximum loan size is GH¢ 100,000, the maximum term is 36 months, and the interest rate ranges between 28 and 35%

^a US$1 = GH¢ 4.

Source: Nair and Fissha (2010).

Table 2. The legal, regulatory and tax framework of RCBs

Licensing requirements	Minimum paid-up capital of GH¢ 150,000^a
	Ownership of shares by residents
	Operation within a radius of about 25 miles
Prudential requirements	Minimum paid-up capital of GH¢ 150,000
	Capital adequacy ratio of 10%
	Liquidity reserve ratio of 43%
	Exposure limits of 25% for secured loans, 10% for unsecured loans, and 2% for loans to members of board of directors
Tax requirements	Corporate income tax rate of 8%
	Value-added tax of 15%
	National Health Insurance Scheme tax of 2.5%

^a US$1 = GH¢ 4.

Source: Nair and Fissha (2010).

Table 3. Variables, definitions, notations and expected signs

Variable	Definition	Notation	Expected sign	Source
Dependent variable
Bank stability risk	Z-score made up of ROA, capitalization ratio and standard deviation of ROA	Z-score		ARB Apex Bank
	Risk-adjusted return on assets	RAROA		ARB Apex Bank
	Risk adjusted equity to assets ratio	RAEA		ARB Apex Bank
Independent variables
Bank size	Natural logarithm of total Assets	BSIZE	?	ARB Apex Bank
Bank size	Natural logarithm of bank deposits	DEPO	?	ARB Apex Bank
Funding risk	Z-score defined as deposits to assets ratio plus equity to assets ratio divided by the standard deviation of deposits to assets ratio	FUNDRISK	+	ARB Apex Bank
Control variables
Liquidity risk	Cash and due from balances held at other depository institutions to total assets	LRISK	−	ARB Apex Bank
Credit risk	Total loans divided by total Assets	CRISK	−	ARB Apex Bank
Diversification	Total short-term and long-term securities divided by total assets	DIV	+	ARB Apex Bank
Profitability	Return on equity and return on assets	ROE, ROA	+	ARB Apex Bank
Inflation	Quarterly inflation rate	INFL	?	Bank of Ghana
Financial development or structure	Growth in private sector credit	FINDEV	?	Bank of Ghana
Economic growth	Quarterly GDP at current prices	GDP	?	Ghana Statistical Service

Source: Adusei (2015).

Table 4. Descriptive statistics

Statistic	Z-score	RAROA	RAEA	BSIZE	DIV	ROE (%)	ROA (%)	LRISK	CRISK	FUNDRISK	INFL	FINDEV	GDP	DEPO
Mean	2.29	1.55	0.03	15.62	0.29	85.43	2.26	16.38	45.12	1.64	11.75	27.41	9.36	15.32
Maximum	69.41	4.95	0.22	18.85	0.86	4,721.77	69.41	2,664.5	4,973.99	6.44	9.47	27.59	10.19	17.75
Minimum	−26.97	−2.76	0.00	12.56	0.00	−663.84	−26.97	−1.66	0.00	0.09	20.7	51.44	8.49	11.76
Std. Dev.	2.85	1.20	0.02	0.93	0.14	141.66	2.85	56.87	142.97	0.73	8.4	9.7	0.60	0.95
Observations	2,200	2,200	2,200	2,200	2,200	2,200	2,200	2,200	2,200	2,200	2,200	2,200	2,200	2,200

Notes: Z-score is bank stability Z-score, RAROA is risk-adjusted return on assets, RAEA is risk-adjusted equity to assets ratio, BSIZE is bank size, DIV is diversification, ROE is return on equity, LRISK is liquidity risk, CRISK is credit risk, FUNDRISK is funding risk, INFL is inflation, FINDEV is financial development, GDP is gross domestic product, and DEPO is deposits.

Source: Adusei (2015).

Table 5. Pearson correlation matrix

	BSIZE	DEPO	LRISK	CRISK	FUNDRISK	DIV	ROE	ROA	FINDEV	INFL	GDP
BSIZE	1
DEPO	0.98^a	1
LRISK	−0.20	−0.15	1
CRISK	0.15	0.17	−0.15	1
FUNDRISK	−0.13	−0.05	0.15	0.09	1
DIV	0.03	0.06	0.07	−0.43	0.18	1
ROE	0.46	0.45	−0.08	0.06	−0.27	0.08	1
ROA	0.17	0.16	−0.04	0.07	0.11	0.12	0.80^b	1
FINDEV	0.14	0.14	0.02	0.02	−0.08	−0.13	0.14	0.10	1
INFL	−0.24	−0.26	0.08	0.02	0.01	−0.03	−0.04	−0.01	0.23	1
GDP	0.43	0.42	−0.12	0.02	−0.09	−0.08	0.17	0.12	0.39	−0.50	1

Notes: BSIZE is bank size, DEPO is deposits, LRISK is liquidity risk, CRISK is credit risk, FUNDRISK is funding risk, DIV is diversification, ROE is return on equity, ROA is return on assets, INFL is inflation, FINDEV is financial development, and GDP is Gross domestic product.

^a The correlation between BSIZE (natural logarithm of total assets) and DEPO (natural logarithm of total deposits) is high. Thus, the two do not enter one model.

^b The correlation between ROE and ROA is high. Thus, the two do not enter one model.

Source: Adusei (2015).

Table 6. Regression results. Dependent variable: Z-score

Variable	Full model (2009Q1–2013Q4)			2009Q1–2011Q2			2011Q3–2013Q4
	Coefficient	t-Value	p-Value	Coefficient	t-Value	p-Value	Coefficient	t-Value	p-Value
BSIZE (−1)	0.2931	4.0392	0.0001^***	0.5358	3.8714	0.0001^***	0.3774	3.1218	0.0019^***
LRISK (−1)	0.0151	0.5794	0.5624	−0.0225	−0.5129	0.6082	0.0172	0.4683	0.6397
CRISK (−1)	−0.0412	−0.9598	0.3373	−0.0448	−0.5881	0.5566	−0.0034	−0.0433	0.9855
FUNDRISK (−1)	0.7298	9.3826	0.0000^***	0.3734	2.6598	0.0080^***	0.7971	5.4869	0.0000^***
DIV (−1)	0.0247	0.7719	0.4403	−0.0057	−0.0780	0.9378	−0.0131	−0.3224	0.7472
ROE (−1)	0.4464	23.0080	0.0000^***	0.3207	9.7913	0.0000^***	0.3518	12.7647	0.0000^***
Constant	−5.8320	−4.9059	0.0000^***	−8.7637	−3.9111	0.0001^***	−7.0478	−3.4386	0.0006^***
	R^2 = 0.71; N = 1,899			R^2 = 0.75; N = 871			R^2 = 0.74; N = 1,028
	Durbin–Watson stat = 1.8			Durbin–Watson stat = 2			Durbin–Watson stat = 1.8
	F-statistic = 32.35^***			F-statistic = 18.52^***			F-statistic = 20.61^***
	Wald test: χ^2(7) = 6,360.77^***			Wald test: χ^2(7) = 2,162.97^***			Wald test: χ^2(7) = 4,589.9^***
	Hausman test: χ^2(6) = 64.79^***
	Likelihood ratio (χ^2) = 1,994.48^***

Notes: Z-score is bank stability Z-score, BSIZE (−1) is lagged bank size, LRISK is lagged liquidity risk, CRISK (−1) is lagged credit risk, FUNDRISK (−1) is lagged funding risk, DIV (−1) is lagged diversification and ROE (−1) is lagged return on equity.

^*** Significance at 1% level.

^** Significance at 5% level.

Source: Adusei (2015).

Table 7. Panel regression results. Dependent variable: RAROA

Variable	Full model (2009Q1–2013Q4)			2009Q1–2011Q2			2011Q3–2013Q4
	Coefficient	t-Value	p-Value	Coefficient	t-Value	p-Value	Coefficient	t-Value	p-Value
BSIZE (−1)	0.2780	3.7693	0.0002^***	0.5247	3.6432	0.0003^***	0.2384	1.9762	0.0484^**
LRISK (−1)	0.0201	0.7579	0.4486	−0.0036	−0.0787	0.9373	0.0147	0.4055	0.6852
CRISK (−1)	−0.0436	−0.9988	0.3180	−0.0634	−0.8000	0.4239	0.0212	0.2760	0.7826
FUNDRISK (−1)	0.6689	8.4550	0.0000^***	0.2568	1.7510	0.0804	0.5527	3.7839	0.0002^***
DIV (−1)	0.0230	0.7073	0.4794	−0.0260	−0.3394	0.7344	0.0077	0.1903	0.8491
ROE (−1)	0.4373	22.0700	0.0000^***	0.2872	8.3478	0.0000^***	0.3488	12.8001	0.0000^***
Constant	−5.9573	−4.9274	0.0000^***	−8.8179	−3.7807	0.0002	−5.2031	−2.5457	0.0111^***
	R^2 = 0.72; N = 1,896			R^2 = 0.73; N = 869			R^2 = 0.78; N = 1,027
	Durbin–Watson stat = 1.9			Durbin–Watson stat = 2.06			Durbin–Watson stat = 1.9
	F-statistic = 34.40^***			F-statistic = 16.30^***			F-statistic = 26.48^***
	Wald test: χ^2(7) = 1,683.27^***			Wald test: χ^2(7) = 405.46^***			Wald test: χ^2(7) = 1,248.68^***
	Hausman test: χ^2(6) = 25.67^***
	Likelihood ratio (χ^2) = 2,172.32^***

Notes: RAROA is risk-adjusted return on assets, BSIZE (−1) is lagged bank size, LRISK is lagged liquidity risk, CRISK (−1) is lagged credit risk, FUNDRISK (−1) is lagged funding risk, DIV (−1) is lagged diversification and ROE (−1) is lagged return on equity.

^*** Significance at 1% level.

^** Significance at 5% level.

Source: Adusei (2015).

Table 8. Regression results. Dependent variable: RAEA

Variable	Full model (2009Q1–2013Q4)			2009Q1–2011Q2			2011Q3–2013Q4
	Coefficient	t-Value	p-Value	Coefficient	t-Value	p-Value	Coefficient	t-Value	p-Value
BSIZE (−1)	0.2891	6.9192	0.0000^***	0.2471	3.3282	0.0009^***	0.3956	6.0263	0.0000^***
LRISK (−1)	−0.0170	−1.1302	0.2585	−0.0570	−2.4109	0.0161	0.0319	1.6161	0.1064
CRISK (−1)	−0.0450	−2.0277	0.0427^**	0.0082	0.1995	0.8419	0.0167	0.3979	0.6908
FUNDRISK (−1)	1.3223	33.9867	0.0000^***	0.8625	13.0207	0.0000^***	0.9589	12.9687	0.0000^***
DIV (−1)	−0.0373	−2.0501	0.0405^**	−0.0512	−1.2802	0.2009	−0.0041	−0.1870	0.8517
ROA (−1)	0.0010	0.0110	0.9248	−0.0002	−0.0131	0.9896	−0.0166	−1.1253	0.2608
Constant	−8.3570	−12.236	0.0000^***	−7.4893	−6.2610	0.0000^***	−10.3482	−9.2984	0.0000^***
	R^2 = 0.83; N = 1,947			R^2 = 0.86; N = 898			R^2 = 0.88; N = 1,049
	Durbin–Watson stat = 1.7			Durbin–Watson stat = 1.8			Durbin–Watson stat = 1.8
	F-statistic = 68.44^***			F-statistic = 39.82^***			F-statistic = 53.09^***
	Wald test: χ^2(7) = 452,660.5^***			Wald test: χ^2(7) = 221,948.4^***			Wald test: χ^2(7) = 333,371.8^***
	Hausman test: χ^2(6) = 36.51^***
	Likelihood ratio (χ^2) = 3,337.58^***

Notes: RAEA is risk-adjusted equity to assets ratio, BSIZE (−1) is lagged bank size, LRISK is lagged liquidity risk, CRISK (−1) is lagged credit risk, FUNDRISK (−1) is lagged funding risk, DIV (−1) is lagged diversification and ROA (−1) is lagged return on assets.

^*** Significance at 1% level.

^** Significance at 5% level.

Source: Adusei (2015).

Table 9. Results of robustness analysis with inflation, financial development and GDP as additional control variables

	Dependent variables
	Z-score			RAROA			RAEA
Variables	Coefficient	t-Value	p-Value	Coefficient	t-Value	p-Value	Coefficient	t-Value	p-Value
Constant	−4.7175	−7.6657	0.0000^***	−6.8283	−9.8071	0.0000^***	−5.1067	−13.1573	0.0000^***
BSIZE (−1)	0.0109	0.3275	0.7433	0.1618	3.7554	0.0002^***	0.1011	3.4623	0.0005^***
LRISK (−1)	0.0215	0.6064	0.5443	0.0472	1.2659	0.2057	−0.0225	−1.5102	0.1312
CRISK (−1)	0.0414	0.7944	0.4270	0.1549	2.7181	0.0066^***	−0.0605	−2.4991	0.0125^***
FUNDRISK (−1)	0.3722	5.8295	0.0000^***	0.2541	3.3042	0.0010^***	1.2093	33.3338	0.0000^***
DIV (−1)	0.0040	0.1119	0.9109	−0.0283	−0.6964	0.4863	−0.0394	−2.2271	0.0261^**
ROE (−1)	0.2652	13.5270	0.0000^***	0.2134	10.2689	0.0000^***
INFL (−1)	0.6851	9.0116	0.0000^***	0.6848	8.8177	0.0000^***	0.1538	5.0661	0.0000^***
FINDEV (−1)	−0.0959	−2.5335	0.0114^***	−0.0970	−2.5146	0.0120^***	−0.0414	−2.7687	0.0057^***
ROA (−1)							−0.0067	−0.8068	0.4199
GDP	0.2686	5.9559	0.0000^***	0.167021	3.436372	0.0006^***	−0.0897	−3.8239	0.0001^***
	R^2 = 0.13; N = 1,899			R^2 = 0.12; N = 1,896			R^2 = 0.43; N = 1,947
	Durbin–Watson stat = 1.9			Durbin–Watson stat = 1.9			Durbin–Watson stat = 1.6
	F-statistic = 32.02^***			F-statistic = 27.55^***			F-statistic = 162.67^***
	Wald test: χ^2(10) = 1,095.963^***			Wald test: χ^2(10) = 242.981^***			Wald test: χ^2(10) = 8,283.080^***

Notes: Z-score is bank stability Z-score, RAROA is risk-adjusted return on assets, RAEA is risk-adjusted equity-to-asset ratio, BSIZE (−1) is lagged bank size, LRISK is lagged liquidity risk, CRISK (−1) is lagged credit risk, FUNDRISK (−1) is lagged funding risk, DIV (−1) is lagged diversification and ROE (−1) is lagged return on equity.

^*** Significance at 1% level.

^** Significance at 5% level.

Source: Adusei (2015).

Table 10. Regression results with deposits (DEPO) as proxy for bank size without macroeconomic variables

Variable	Dependent variables
	Z-score			RAROA			RAEA
	Coefficient	t-Value	p-Value	Coefficient	t-Value	p-Value	Coefficient	t-Value	p-Value
DEPO (−1)	0.1269	1.8415	0.0657^*	0.1144	1.6339	0.1025^*	0.0031	0.0778	0.9380
LRISK (−1)	0.0076	0.2870	0.7741	0.0131	0.4900	0.6242	−0.0193	−1.2600	0.2078
CRISK (−1)	−0.0645	−1.5122	0.1307	−0.0659	−1.5201	0.1287	−0.0750	−3.0395	0.0024^***
FUNDRISK (−1)	0.6373	8.6515	0.0000^***	0.5798	7.7437	0.0000^***	1.2036	32.8820	0.0000^***
DIV (−1)	0.0148	0.4497	0.6530	0.0142	0.4266	0.6697	−0.0344	−1.8126	0.0701^*
ROE (−1)	0.4452	22.8106	0.0000^***	0.4362	21.8946	0.0000^***	–	–	–
ROA (−1)							0.0016	0.1413	0.8876
Constant	−3.0538	−2.8195	0.0049^***	−3.2276	−2.9321	0.0034^***	−4.1296	−6.5740	0.0000^***
	R^2 = 0.71; N = 1,899			R^2 = 0.72; N = 1,896			R^2 = 0.87; N = 1,947
	Durbin–Watson stat = 1.8			Durbin–Watson stat = 1.9			Durbin–Watson stat = 1.8
	F-statistic = 32.02^***			F-statistic = 34.09^***			F-statistic = 90.95^***
	Wald test: χ^2(7) = 6,301.814^***			Wald test: χ^2(7) = 1,660.89^***			Wald test: χ^2(7) = 440,969.7^***
	Hausman test: χ^2(6) = 76.683^***			Hausman test: χ^2(6) = 28.46^***			Hausman test: χ^2(6) = 80.35^***
	Likelihood ratio (χ^2) = 1,972.67 ^***			Likelihood ratio (χ^2) = 2,164.92 ^***			Likelihood ratio (χ^2) = 3,230.43 ^***

Notes: Z-score is bank stability Z-score, RAROA is risk-adjusted return on assets, RAEA is risk-adjusted equity-to-asset ratio, BSIZE (−1) is lagged bank size, LRISK is lagged liquidity risk, CRISK (−1) is lagged credit risk, FUNDRISK (−1) is lagged funding risk, DIV (−1) is lagged diversification and ROE (−1) is lagged return on equity.

^*** Significance at 1% level.

^* Significance at 10% level.

Source: Adusei (2015).

Table 11. Regression results with deposits as proxy for bank size including macroeconomic variables as control variables

Variables	Dependent variables
	Z-score			RAROA			RAEA
	Coefficient	t-Value	p-Value	Coefficient	t-Value	p-Value	Coefficient	t-Value	p-Value
Constant	−4.2656	−7.2099	0.0000^***	−6.2654	−9.3327	0.0000^***	−3.5036	−9.5829	0.0000^***
DEPO (−1)	−0.0360	−1.1601	0.2461	0.1151	2.7560	0.0059^***	−0.0452	−1.5956	0.1107
LRISK (−1)	0.0189	0.5352	0.5926	0.0390	1.0461	0.2956	−0.0213	−1.4037	0.1606
CRISK (−1)	0.0489	0.9452	0.3447	0.1504	2.6289	0.0086^***	−0.0678	−2.7845	0.0054^***
FUNDRISK (−1)	0.3802	6.1285	0.0000^***	0.2265	2.9611	0.0031^***	1.1498	32.8000	0.0000^***
DIV (−1)	0.0152	0.4240	0.6716	−0.0348	−0.8478	0.3967	−0.0333	−1.8299	0.0674^*
ROE (−1)	0.2769	14.2012	0.0000^***	0.2180	10.4797	0.0000^***
INFL (−1)	0.6753	8.8563	0.0000^***	0.6836	8.7618	0.0000^***	0.1226	3.9534	0.0001^***
FINDEV (−1)	−0.0953	−2.5150	0.0120^***	−0.0988	−2.5574	0.0106^***	−0.0379	−2.5017	0.0124^***
ROA (−1)							−0.0053	−0.6344	0.5259
GDP	0.2939	6.5754	0.0000^***	0.1919	3.9618	0.0001^***	−0.0056	−0.2380	0.8119
	R^2 = 0.14; N = 1,899			R^2 = 0.11; N = 1,896			R^2 = 0.43; N = 1,947
	Durbin–Watson stat = 1.9			Durbin–Watson stat = 1.9			Durbin–Watson stat = 1.6
	F-statistic = 33.00^***			F-statistic = 26.75^***			F-statistic = 160.60^***
	Wald test: χ^2(10) = 1,187.70^***			Wald test: χ^2(10) = 316.98^***			Wald test: χ^2(10) = 8,492.70^***

Notes: Z-score is bank stability Z-score, RAROA is risk-adjusted return on assets, RAEA is risk-adjusted equity-to-asset ratio, BSIZE (−1) is lagged bank size, LRISK is lagged liquidity risk, CRISK (−1) is lagged credit risk, FUNDRISK (−1) is lagged funding risk, DIV (−1) is lagged diversification and ROE (−1) is lagged return on equity.

^*** Significance at 1% level.

^** Significance at 5% level.

^* Significance at 10% level.

Source: Adusei (2015).

Nair, A., & Fissha, A. (2010). Rural banking: The case of rural and community banks in Ghana (Agriculture and Rural Development Discussion Paper 48). Washington, DC: The World Bank.

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Adusei, M. (2015). Bank profitability: Insights from the rural banking industry in Ghana. Cogent Economics & Finance, 3, 1078270.

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