The focus of developments in the Islamic financial services industry is Islamic banking. Islamic banking shares a common platform with conventional banks in the overwhelming majority of countries, meaning that Islamic financial services face similar risks with different impacts (Archer & Karim, 2019). These different impacts are also evident in their respective balance sheets (Chattha, 2013)(Chattha et al., 2020). The activities of Islamic banks are exposed to various risks, such as credit risk, counterparty risk, equity investment risk, market risk, rate of return (ROR) risk and liquidity risk ((Board, 2005);(Chattha, 2013)(Archer & Karim, 2019). A major adverse effect of such risks is reduced market value of equity (Bierwag & Kaufman, 1992)(Bierwag et al., 2000)(Entrop et al., 2009)(Chattha & Alhabshi, 2018).

ROR risk is similar to interest rate risk in Islamic financial institutions (Chattha et al., 2020). It is also sometimes referred to as “benchmark rate risk” (Chattha & Alhabshi, 2018) and very much has the potential to affect the net worth of Islamic financial institutions along with their off-balance sheet positions, if those positions are not properly managed ((Archer & Karim, 2019); (Chattha et al., 2020)). The Islamic Financial Services Board (IFSB) has stressed guarding against the pitfalls of ROR risk in pillar II using the duration gap approach.

Duration, introduced by (Macaulay, 1938), is the most common measure of risk management and was used by (Hicks, 1939) to assess sensitivity against yield curve movements. (Hicks, 1939) work extended the application of duration into estimation of interest rate risk (Radermacher & Recht, 2020). Moreover, (Fisher & Weil, 1971) extended the duration for portfolio immunization, and (Ho, 1992) led duration for non-parallel shifts of yield curve by introducing duration based on some key rates. (Bierwag et al., 1978) identified an important consideration in the development of duration models, i.e., that the choice of weights in a duration model is arbitrary and is dependent on the use of those weights.

It has been established, over the period, that Islamic bank balance sheets are structurally different from those of conventional banks (Chattha et al., 2020). This requires them to develop their own risk management models and other measures to tackle their risk exposures ((Shah et al., 2021);(Shah et al., 2021)). However, research over the period of time reveals that most of the research in the Islamic context is primarily based on applying conventional tools of financial risk modeling and management in the Islamic context. Application of the concept of duration in Islamic banks has also received similar treatment (Chattha & Bacha, 2010);Chattha & Alhabshi, 2017;(Chattha & Alhabshi, 2018)(Chattha et al., 2020). Addressing the issue, (Shah et al., 2020) proposed a Shariah-compliant duration model that requires comprehensive testing.

The purpose of this study is to test the above model from (Shah et al., 2020) following the theme of implementing the durations models under the theory of Macaulay’s duration (Shah et al., 2020). This study firstly develops a framework for testing a financial model and then proceeds by developing a methodology for testing the Shariah-compliant duration model. It collects maturity wise data relating to return bearing assets and liabilities of Islamic banks from Pakistan. The model of (Shah et al., 2020) has been tested by developing an alternative duration model excluding the principal amounts from the Shariah-compliant duration model. The purpose is to examine the effect of changes in returns on earnings assets and returns paid on return bearing liabilities on the maturity gap risk management of Islamic banks in the short run and long run. This research uses multiple regression analysis, Johansen co-integration, the error correction model, vector error correction model and threshold vector error correction model.

Literature on Islamic Banks

Discussions regarding the impact of changes in monetary policy on financial institutions have revealed that Islamic banks respond to monetary policy in a way which is similar to that seen with large conventional banks (Zaheer et al., 2012). A study on 128 banks found that privately owned Islamic banks provide more protection to their shareholders' equity as compared to state-owned banks (Daher et al., 2015). A study on volatility and persistence in Islamic and conventional banks reported that Islamic banks are more resilient toward uncertainties, but that resilience varies according to the model of Islamic financial system which a country has adopted (Fakhfekh et al., 2016). The results of (Beltrame et al., 2016) suggest a highly negative correlation between interest rates and returns of Islamic banks.

(Sadiq et al., 2017) found that Islamic banks in Pakistan are less cost efficient due to excess liquidity, inadequate support and competition from conventional banks. Another study, addressing the financial sector of Pakistan using the DEA technique, revealed that Pakistan’s insurance sector is more technically efficient than its banking sector (Shah & Masood, 2017). Additionally, the Islamic financial sector has performed better in the allocation of resources than its conventional counterparts (Shah & Masood, 2017). (Hamza & Saadaoui, 2018), in their work on Islamic banks, reported that interest rate changes negatively affect the financing of Islamic banks. Although the results in performance analysis of Islamic and conventional banks are similar, discussions on the usage of credit risk transfer techniques have revealed that the implementations of credit risk management techniques are not similar in both contexts; rather, there exist Shariah compliance constraints in the case of Islamic banks (Saeed & Ayub, 2017).

The impact of credit and liquidity risk has been analyzed by a few research studies, with the findings revealing no relation between the two and recommending different treatment (Trad et al., 2017)(Ghenimi et al., 2017). Research over the period of time found that, although size and capital expansion positively affect profitability, they negatively affect liquidity. Similar results have also been reported by (Shafiullah & Shamsuddin, 2018) who, after addressing the topic of risk management, found that Islamic banks possess higher liquidity risk but lower insolvency and credit risks compared to conventional banks. Additionally, they discussed the issue of operational risk, reporting that it declines with an increase in the numbers and qualifications of members of the Shariah supervisory board. The relationship between sukuk and conventional bonds has been analyzed in terms of factors that affect correlations between the two. The results suggest that money market liquidity, stock market liquidity and credit information are the factors affecting volatility in emerging and developing markets, almost similarly (Bhuiyan, 2017). (Nawaz & Farzana, 2018) analyzed management of investment risks in Islamic and conventional banks, finding that both types of banks use similar risk management practices for management of their investments.

Another study, which conducted performance analysis regarding the banking sector, revealed that the profitability of banks is affected similarly in the cases of Islamic and conventional banks in response to changes in interest rates (Ahmed et al., 2018). (Chattha & Alhabshi, 2018) reported that Islamic banks respond similarly to changes in interest rates because they use benchmark rates of interest similar to those employed by their conventional counterparts.

(Chattha & Alhabshi, 2018) and (Chattha et al., 2020) observed that Islamic banks have longer durations as compared to their conventional parts. These longer durations create a paradox, since longer duration means higher risk and higher risk should lead to higher profitability. Contrary to this risk-return principle, a comparison of the results suggests that Islamic banks are less profitable as compared to conventional banks ((Chattha & Alhabshi, 2018); (Chattha et al., 2020)). This conventional Islamic bank risk-return paradox requires investigation. The impact of variations in capital adequacy has also been examined in the case of Islamic and conventional banks, revealing that highly capitalized banks react positively to changes in capital adequacy ratio while the relation reverses in cases of low capitalized banks. The study did not report any difference between Islamic and conventional banks (Narmeen et al., 2018).

Shariah Review of Duration Models:

(Shah et al., 2021) reviewed the following duration models and regarded them as non-Shariah-compliant.

Having reviewed the literature on Islamic banks and various duration models developed and tested so far, the objective in this research is to further test the Shariah-compliant duration model of (Shah et al., 2020), which was tested by (Shah et al., 2021)

This research uses the methodology from (Shah et al., 2021) for testing Shariah-compliant duration models. Following (Shah et al., 2021), this research employs data relating to financial assets and liabilities of various maturity ladders as reported in various financial statements of Islamic banks in Indonesia and Pakistan for the period spanning 2009–2019. Maturities are calculated using guidance from (Stohs & Mauer, 1996). According to them, maturities of less than 1 year are taken as actual periods, whereas maturities ranging above 1 to 2 years are taken as 1.5 years, 2 to 3 years are taken as 2.5 years, 3 to 4 years are taken as 3.5 years, and 4 to 5 years are taken as 4.5 years. However, for the last category, which is primarily over 5 years or 10 years, the maturities are calculated on the assumption that every following year has the same proportion of assets or liabilities as the one immediately preceding until 100% of the values are allocated.

Descriptive statistics used for the data consist of Mean, Variance, Skewness and Kurtosis. Skewness has been measured by the third moment from mean divided by second moment to the ½ power. Kurtosis is the square root of the fourth moment from mean divided by the second moment. The descriptive statistic has been used to confirm the observations of (Bildersee, 1975), (Gultekin & Rogalski, 1984), (Chen, 2014), (Weber, 2017) and (Y. et al., 2017) that returns are skewed leptokurtically. The research also calculates t-statistics to ensure that the hypotheses equal zero. This has been achieved by calculating the product of ’s to the square root of years in the sample period and taking its ratio to the standard deviation of yearly estimates. Lastly, the average of R2 and the standard deviation of R2 have been presented after adjusting for degrees of freedom. These are meant to measure the dependency between risk and return.

The procedure for testing a financial model has also been explained by (Shah et al., 2021). Their framework for testing the duration model has been given hereunder:

According to them, return's relationship with duration can be expressed using the following function:

(1)

where R i,t is the net return, margin b 1 is estimated coefficient, and DUR i,t is duration.

(Gultekin & Rogalski, 1984) provided three hypotheses to be tested on duration models using multiple regression analysis; these hypotheses were amended for use in the Shariah context by (Shah et al., 2021), as below:

All three hypotheses have been tested using the function below:

In the above function, is the net return margin on earning assets, $\hat{\gamma}t$ are average estimated coefficients, $DK{(r-1)(0-1)(t-1)}$ is the duration of the th assets calculated using return and benchmark rates of the previous period, is the square of duration to check linearity, and lastly, is the factor used to check whether duration normalizes reversed present values.

The duration of earning assets has been tested by regressing the independent variables on returns earned on earning assets.

Similarly, the duration of liabilities has been tested using the below function:

To examine the relationship, this research assesses two models of Shariah-compliant duration from (Shah et al., 2020). The model of (Shah et al., 2020) to be tested in this research for earning assets is:

And for return bearing liabilities is:

This methodology complies with earlier works from (Lanstein & Sharpe, 1978), as well as various subsequent studies, such as those from (Lettau & Wachter, 2007), (Chen, 2014),(Weber, 2018) and (Shah et al., 2021).

For the purpose of this research, the changes in returns of Islamic banks have been calculated in line with (Shah et al., 2020), as below:

Where:

∆ = Change

NI = Net income

D_EA = Duration of earning assets

D_RBL = Duration of risk bearing liabilities EA = Earning Assets

RBL = Return Bearing Liabilities

∆ROR_EA = Change in rate of return on assets

∆IBOR = Change in interbank offered rates

∆ROR_RBL = Change in rate of return on liabilities

∆IBAR = Change in industry average rates of return on liabilities

However, besides testing the duration of assets and liabilities, this study also tests the duration gap of Islamic banks. The duration gap has been calculated in line with (Shah et al., 2020), as below:

Duration Gap = Duration of Earning Assets – Duration of

Return Bearing liabilities (7)

The regression function to be used for testing the duration gap shall take the following form:

Explanation: indicates that the level of rates of return is not significant between maturity brackets. In the second column, the level is negative and insignificant, confirming the observation of (Chattha et al., 2020) that Islamic banks have higher duration and lower profitability. Non-zero serial correlation of indicates the interrelationship between the rates of returns. Serial correlation close to zero values of indicates durations are not interrelated. The significant p-values of and show reliability of results.

Explanation: has largely remained between 20 and 30, indicating no big difference in rates of return between maturity brackets. Values of and indicate no significant linear relationship between returns on assets and duration. Exhibits negative signs to show negativity and significance, illustrating a non-linear relationship between duration and returns over 1-year maturity brackets. Serial correlation values of indicate an interrelationship between the rates of returns. However, there is serial correlation and durations are not interrelated.

Explanation: indicates no big difference of rates of return between over 1 year maturity brackets. Exhibit positive signs to show a positive relationship with returns, illustrating that rates of return and benchmark rates significantly affect the long-term relationship between returns and duration.

Explanation: indicates no big difference of rates of return between maturity brackets, particularly over 1 year. It shows that the relationship between returns and duration is not linear. It also illustrates that rates of return and benchmark rates significantly affect the long-term relationship between returns and duration. Serial correlation values are close to zero, which shows that durations are not interrelated.

Explanation: indicates that level of rates of return is heterogeneous between various liabilities brackets. Values in the second column indicate no significant linear relationship between return bearing liabilities and duration. Non-zero serial correlation values indicate an interrelationship between the rates of returns. Close to zero serial correlation values show that durations are not interrelated.

Explanation: values are significant from 6 months to 3 years. This shows that the relationship of return duration is not linear. Serial correlation values of are non-zero, indicating an interrelationship between the rates of returns. However, serial correlation values of and are close to zero, which shows that durations are not interrelated.

Explanation: exhibit positive signs, showing that rates of return and benchmark rates significantly affect the long-term relationship between returns and duration. Serial correlation values of are non-zero, indicating an interrelationship between the rates of returns. However, serial correlation values of and are close to zero, which shows that durations are not interrelated.

Explanation: shows that the relationship between return and duration is not linear. It also exhibits positive signs, showing that rates of return and benchmark rates significantly affect the long-term relationship between returns and duration. Serial correlation values of are non-zero, indicating an interrelationship between the rates of returns. However, the serial correlation values of and are close to zero, which shows that durations are not interrelated.

Explanation: indicates that above 1-year rates of returns are very close between maturity brackets. This confirms the observation of Chattha et al. (2020) that Islamic banks have higher duration and lower profitability. The non-zero serial correlation of indicates interrelationship between rates of returns. The serial correlation values of are close to zero, which shows that durations are not interrelated.

Explanation: Values of and negate linear relationship and show a negative long-run non-linear relationship between duration and returns. Close to zero, the serial correlation values of and show that durations are not interrelated.

Explanation: show that rates of return and benchmark rates significantly affect the long-term relationship between returns and duration. The serial correlation values of are non-zero, indicating an interrelationship between the rates of returns. However, the serial correlation values of are close to zero, showing that durations are not interrelated.

Explanation: and negate linear relationship and shows that the relationship between return and duration is not linear. It also indicates that rates of return and relevant benchmarks affect the relationship between net income and duration of Islamic banks. The serial correlation values of and are close to zero, which shows that durations are not interrelated.

The descriptive statistics results in Table 2 to Table 7 confirm (Bildersee, 1975), (Gultekin & Rogalski, 1984), (Chen, 2014), (Weber, 2017) and (Y. et al., 2017) notion of skewed and leptokurtic distribution. Besides, various tests have been performed to determine the implications of duration measures. The tests have been performed using maturity-wise data from Islamic banks relating to their return bearing assets and liabilities. The results yielded by testing the duration models on earning assets, return bearing liabilities and duration of Islamic banks have been reported hereunder. The results have been presented in four different versions of return-duration regression equations that have been incorporated at the top of each respective table. Table 11, Table 15 and Table 19 are based on regression equations incorporating all the respective variables. However, in the remaining tables (Table 8, to Table 19, excluding Table 11, Table 15 and Table 19), one or more of the variables have been omitted.

For each of the holding periods using the model expressed at the top of Table 8, to Table 19, there are coefficients for each of the maturity brackets as regression coefficient estimate and respective first order autocorrelation. The table also shows p-values calculated on the basis of the t-statistics of this testing procedure—a procedure which corresponds to the testing mechanism forwarded by Fama and MacBeth (1973). The p-values have been calculated across return on earning assets and duration of earning assets relationships of the entire Indonesian Islamic banking sector, which has aided in obtaining period by period estimated along with the confidence intervals of significance tests. In the final columns of Table 8, to Table 19, R2 and S (R2) have been presented; these are coefficients of determination and its standard deviation.

The descriptive statistics inTable 2 to Table 7 regarding duration of assets and liabilities show that the data have skewed and leptokurtic distributions. The results of the duration functions after they were incorporated into a multiple regression function have been reported in Table 8, to Table 19. Table 7 toTable 11 relate to duration of earning assets, while Table 12 to Table 15 relate to duration of return bearing liabilities, and Tables 16 to Table 19 relate to duration of Islamic banks in Indonesia, which is calculated as the duration gap.

To test the hypotheses, multiple regression has been used for duration for assets and liabilities in four different combinations that have been reproduced at the top of each of the tables, although Table 8, and Table 12are based on full equations. The tables produce regression coefficients in columns 1 to 4, autocorrelations in columns 6 to 10, and p-values in columns 11 to 14, while the last two columns report means and standard deviations of the coefficient of determination.

The results in Table 8,Table 12 and 16 mean that the linearity hypothesis cannot be accepted for either duration of earning assets or return bearing liabilities. Table 7,Table 13 and Table 17 lead us to the finding that the long-term relationship between duration and returns is quadratic, i.e., upward sloping. Table 8, Table 14 and 18 lead us to the finding that rates of return, interbank offered rates, principal sum and maturities are complete determinants of the relationship between duration and returns, thereby meaning that our second hypothesis is accepted. Table 9, 15 and 19 lead us to the finding that the factor reversed present values does have a relationship with duration in the original state. This can be confirmed through undertaking a combined analysis of Table 9 andTable 10, 1Table 14 and Table 15, and 18 andTable 19, which shows that, by including the reversed present value factor in the regression function, neither the linear relationship nor the non-linear relationship is affected. These results confirm the findings of (Bildersee, 1975), (Gultekin & Rogalski, 1984), (Chen, 2014), (Weber, 2017) and (Y. et al., 2017).

This research employs the duration models testing procedures from (Gultekin & Rogalski, 1984), as amended by (Shah et al., 2021), using multiple regressions to test Shariahcompliant duration models. However, the results of this research although do not conform to all of the previous results of (Gultekin & Rogalski, 1984) but conform to the results of (Shah et al., 2021). The results of first hypothesis conform to (Gultekin & Rogalski, 1984) & (Shah et al., 2021) that duration of assets and liabilities do not have linear relationship. In case of second and third hypotheses the results although conform to (Shah et al., 2021) but do not conform to (Gultekin & Rogalski, 1984). This is because rate of return earned on earning assets and interbank offered rates are significant factors for determining duration of earning assets whereas rate of return return paid on return bearing liabilities and interbank average rates of deposit are significant factors in case of duration on return bearing liabilities. This research confirms the works of (Shah et al., 2020),(Shah et al., 2020) and subsequently of (Shah et al., 2021). This research further confirms the nature and behavior of earning assets and return bearing liabilities of two distinct Islamic countries due to existence of a common feature of Shariah compliance. Furthermore, it answers the observation of (Chattha & Alhabshi, 2018) and (Chattha et al., 2020) that Islamic banks have longer durations with low profitability. This is because Islamic banks have earning assets of longer maturity at similar rates of returns; and on the liabilities they have to offer higher rates of return for liabilities of similar maturities when compared to conventional banks. This makes them bear more risk due to longer duration gap at lower profitability.

Limitations & Future Research Directions

The study mainly focuses duration of earning assets and return bearing liabilities and their relationship with earnings of Islamic banks. Furthermore, as the study is only conducted on Islamic banks of Indonesia, therefore a larger sample and testing in various other banks operating in non-Muslim countries is also recommended to validate the model.

Lastly, The study only deals with assets and liabilities that have maturities alongwith return characteristics. As Islamic banks have various assets and liabilities that do not have returns and maturities therefore a study encompassing such assets and liabilities will yield more comprehensive results regarding duration of a Islamic banking organization. The study also severely suffers from availability of data. As most of the Islamic banks do not have long histories, along with difference in year of commencement of business therefore the length of data is not enough and is unbalanced. The models proposed in this study therefore require continuous testing over the period to better analyze the respective models. This research has been conducted only on such full-fledged Islamic banks that have been involved in business similar to conventional banks. Therefore a study on all Islamic financial institutions that deal with earning assets and return bearing liabilities such as takaful companies, Islamic mutual funds and Islamic microfinance institutions may further be used to validate the model.