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Networth exposure to interest rate risk: An empirical analysis of Indian commercial banks
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European Journal of Operational Research 193 (2009) 581–590 www.elsevier.com/locate/ejor
O.R. Applications
Networth exposure to interest rate risk: An empirical analysis of Indian commercial banks q Asish Saha *, V. Subramanian 1, Sanjay Basu, Alok Kumar Mishra National Institute of Bank Management (NIBM), Pune, India Received 15 April 2006; accepted 14 November 2007 Available online 23 November 2007
Abstract In the Basel II era, management of interest rate risk in the banking book has become significant. In the first study of its kind, we develop a simulation based driver-driven approach to estimate the impact of interest rate volatility on the networth of Indian banks during the period 2002–2004. We derive the interest rates that drive changes in deposit and prime lending rates (PLR). Then we perform Monte Carlo simulation and multiple regressions, on these driver rates, to obtain simulated shocks to deposit rates and PLR. We use these simulated shocks to get the 99% worst EVE loss for the sample banks. These losses are much larger than what the existing literature suggests. This is because, apart from repricing risk, we are the first to find evidence of significant basis risk. Our results have important policy implications both for banks and regulators. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Interest rate risk in banks; Risk management; Simulation; Driver-driven variables
1. Introduction In the wake of a steady rise in the yields of government securities since May 2004, interest rate risk in the trading book has been of great concern to Indian banks and Reserve Bank of India (RBI) alike. The yields on 5 year and 10 year benchmark securities went up from 4.68% to 6.33% and from 5.09% to 6.71% respectively between April 2, 2004 and April 1, 2005. This resulted in huge marked-tomarket (MTM) losses in the investment books of the Indian banks. To deal with the crisis, RBI widened the scope of the held-till-maturity category of securities; it per-
q
We are grateful to our colleague Dr. Arindam Bandyopadhyay for his valuable comments and suggestions. The usual disclaimer applies. * Corresponding author. Tel.: +91 20 2683 3080 87; fax: +91 20 2683 1447. E-mail addresses: [email protected], [email protected] (A. Saha). 1 On leave from NIBM. 0377-2217/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2007.11.038
mitted banks to make a one-time portfolio transfer, up to 25% of their net demand and time liabilities, from MTM (Held for Trading and Available for Sale) to historical cost (Held till Maturity) categories (RBI, 2004). In essence, it shielded them from further MTM losses and capital charges. The purpose of this paper is to show that at least a similar, if not greater, danger lurks in the ‘banking book’ as well. We find that an interest rate hike reduces the present value of bank assets much more than that of outside liabilities. This means that a rate hike depletes a bank’s networth. But, so far, this risk has not evoked knee-jerk responses from Indian banks because (i) the losses are not MTM and (ii) there are no capital charges. Such respite is at best temporary, for two reasons. First, there is empirical evidence of a long-run, negative, correlation between market yields and equity returns of banks (Staikouras, 2003). Secondly, as per Pillar 2 of Basel II (BCBS, 2004a), interest rate risk (IRR) in the banking book should also attract capital charges, if the losses in Economic Value of Equity (EVE) are severe enough.
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Most of our results should be of serious concern to Indian banks. First, we find much higher EVE losses than that reported by the existing literature. Secondly, there is evidence of significant basis risk – asset rate shocks are much stronger than liability rate shocks. In fact, such basis risk is an important reason behind the large EVE losses. Our results are consistent with the recent literature which suggests that basis risk is an important component of IRR for banks, beyond repricing risk which considers Net Interest Income (NII) and EVE losses from equal asset and liability rate shocks only (Wetmore and Brick, 1998; Staikouras, 2006). We report the profile of Basis Risk, from our simulated data, in Table 1. It is clear that as we approach the extremes of the tails (i.e. consider larger rate shocks), the basis risk increases. Our first contribution to the literature is methodological. Most papers focus on scenarios in which market values of assets and liabilities are hit by arbitrary rate shocks. Instead, we begin by selecting the most important rates for the banking book in India. We then investigate what factors ‘drive’ these rate changes and refer to them as ‘driver’ variables. Next, we estimate simulated rate shocks (changes in ‘driven’ variables) from the simulated values of the drivers. We use these rate shocks to hit the present values of banking book assets and liabilities. The EVE impact is calculated as the effect of such shocks on networth. There are three advantages of our ‘driver-driven’ approach. First, it allows us to study the interdependence among several rates prevailing in the Indian market. This has major policy implications for banks, e.g. if banks know how driven rates respond to changes in driver rates, they can use the relationship to choose appropriate strategies. Secondly, we know exactly why a driven rate changes by a certain magnitude, e.g. 1%. This is due to a given change in (underlying) driver rates. Lastly, we do not work with arbitrary rate changes, as is usually the practice, but simulate the shocks from a historical distribution of interest rates. Once we know the EVE impact of simulated rate shocks under normal conditions, we can superimpose stress scenarios. Therefore, our rate shocks are not only rationalizable, but also realistic. Our paper also measures the Value-at-Risk (VaR) for banking book IRR. Most studies (e.g. Maes, 2004; Quemard and Golitin, 2005) analyze the impact of a given rate shock on NII or EVE. Their results are open to the same charges leveled against duration-based measures – they neglect yield curve risk, basis risk and options risk. Instead, Table 1 Profile of basis risk from simulated rates Percentile
99 97.5 95 90
Simulated rate shock (%) Deposit
PLR
3.190 2.803 2.510 2.199
5.1546 4.5780 4.0233 3.5445
Difference in rate shocks (%)
1.9647 1.7747 1.5128 1.3459
in line with suggestions of the Basel Committee (BCBS, 2004b), we use simulated asset and liability rate shocks to find out the 99% worst EVE losses. This is the 99% VaR for the banking book. Finally, we use Rate Sensitive Gap (RSG) reports to arrive at the EVE impact of rate shocks. A recent paper by Patnaik and Shah (2004) uses Structural Liquidity Statements (SLS), to study IRR for Indian banks. Though both reports use time buckets, the SLS is used to gauge the liquidity impact, while the RSG report is used to find out the impact of interest changes on NII or EVE. So, for estimating IRR, the RSG report is more appropriate. To the best of our knowledge, this is the first paper to measure VaR for banking book IRR, from RSG reports. We have also not come across any research that used a driver-driven model to generate rate shocks. Because our shocks are endogenous, we are able to conduct a systematic analysis of IRR as well. From our model, we can pin the blame for our EVE losses on basis risk. This is not possible with standard NII and duration gap analysis. Our paper is organized as follows. In Section 1, we present a literature review of the issues. In Section 2, we discuss our data sources and methodology and state our main results. We conclude, in Section 3, with directions for future research. 2. Literature review We begin this section with a definition of IRR. We then define and describe the different sources of IRR in the banking book. Next, we discuss the pros and cons of the various methods for dealing with such IRR. Then, we sift the existing literature on the measurement and management of IRR in the banking sectors of different countries. In particular, we emphasize on the recommendations of the Basel Committee on Banking Supervision (BCBS). This serves as our point of departure, as we try to highlight how our work is different from the rest, but closer to the suggestions of BCBS. 2.1. Definition and sources of IRR IRR refers to the effect of interest volatility on rate-earning assets and rate-paying liabilities. For a given change in rates (e.g. 1%), IRR also includes the effect of shifts in volume and composition of assets and liabilities. Regulators and commercial banks split IRR into two components, viz. traded IRR and non-traded IRR. Though both refer to the potential adverse effects of market rate movements, the difference lies in the point of impact; ‘traded IRR’ affects MTM values of items in the trading book while ‘non-traded IRR’ covers all assets and liabilities in the banking (accrual) book. There are four main sources of IRR in the banking book. These are: (i) Repricing Risk (ii) Yield Curve Risk (iii) Basis Risk and (iv) Options Risk. Repricing Risk arises from differences in the maturity (fixed-rate) or repricing
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(floating-rate) dates for bank assets, liabilities and off-balance sheet (OBS) items. For instance, a bank funding a 3 year fixed-rate loan with a 6-month fixed deposit is exposed to repricing risk. Since the rate on the fixed deposit is adjusted earlier, an increase in market rates after 6 months reduces the bank’s spread between yields on assets and costs of liabilities. Here, even a parallel shift of the rates can reduce spreads and erode net worth (BCBS, 2004b). Yield Curve Risk refers to the effect of non-parallel shifts of yield curve segments, on assets and liabilities of different maturities. Even if the cumulative (across all time buckets) gap between rate-sensitive assets and liabilities is small, different rate shocks in different buckets could sharply reduce the spread or networth. In this case, the bank’s spread could be immune to a parallel shift of the yield curve (BCBS, 2004b). Basis Risk refers to the impact of an imperfect correlation between indices underlying asset and liability rates, e.g. between LIBOR (governing deposit rates) and PLR (governing loan rates), with otherwise similar repricing frequency. Even if 6-month PLR-linked loans are funded by 6-month LIBOR-linked deposits, there is no guarantee that a 1% change in LIBOR will imply a 1% change in PLR. In other words, if the spread between index rates changes suddenly, earnings and networth might fall (BCBS, 2004b). Options Risk refers to the effect of options embedded in bank assets, liabilities and OBS items. Such options provide the holder the right, but not the obligation, to alter the cash flows of these instruments. For instance, depositors have the right to withdraw their savings, current or term deposits at any point. They are likely to exercise such rights, when market rates rise. This can trigger a sharp decline in cash flows for banks (BCBS, 2004b). 2.2. Effects: IRR management techniques As already discussed, the IRR exposure of a bank affects both its earnings and networth. The focus on earnings is more common than the study of networth. We will discuss both in turn. 2.2.1. Earnings or accounting approach It is a short-term analysis of rate shocks on accrual or reported earnings. It is generally restricted to the accounting cycle and covers only an initial part of the lives of assets and liabilities in the balance sheet. In this approach, assets and liabilities are recorded at historical cost. It is important because outright losses or decline in earnings, from a rate shock, can threaten capital adequacy and undermine market confidence. The main focus of the earnings approach is on the impact of interest rate changes on NII. Banks have traditionally tried to minimize the impact of rate shocks on NII. This reflects the high share of NII in a bank’s earnings. But, gradually, they began to look beyond NII, for three reasons. First, NII can be maneuvered. Secondly, assets and liabilities which reprice beyond the accounting cycle also make opportunity gains or losses
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when rates change. This effect on potential earnings is ignored by NII analysis. Thirdly, even non-interest income and expenses are now being found to be sensitive to rate changes (BCBS, 2004b). So, banks shifted their attention to the economic value approach. 2.2.2. Economic value approach The focus here is on the long-term impact of rate changes on assets and liabilities. It recognizes that rate shocks affect the values of future cash flows as well. The Economic Value of Equity (EVE) is the present value of assets minus present value of liabilities. As EVE is the present value of net expected cash flows, it reflects future earning potential. In the short-run, since it is difficult to judge the effect of internal decisions on market capitalization, many banks analyze the impact of decisions on EVE. The focus of EVE on present values leads naturally to sensitivity analysis along the lines of bonds. Specifically, EVE impact is calculated in terms of leverage adjusted duration gap, where duration is the sensitivity of an asset or liability to a percentage change in rates (Saunders and Cornett, 2006). If assets have higher duration than liabilities, their prices fall more when rates rise. Therefore, banks with high-duration assets and low-duration liabilities (a positive duration gap) are exposed to EVE losses, with a rise in rates. The foregoing discussion brings out a potential conflict between NII and EVE management, since duration is also a proxy for residual time-to-maturity. Since long-duration (long-term) assets might carry much higher rates than short-duration (short-term) liabilities, a bank might try to maximize NII by increasing the duration gap. This could expose its EVE to a rise in rates. Hence, even if the bank management wants to focus on NII, regulators might not allow a sharp decline in EVE, for a given change in rates. They perceive EVE as a proxy for capital adequacy, in market value terms, and might force a bank to adhere to strict NII limits. But, the earnings and economic value approaches cannot estimate yield curve risk, basis risk and options risk. Therefore, banks and regulators conduct static and dynamic simulations, to incorporate yield curve twists, changes in spreads between asset and liability rates or exercise of banking book options (BCBS, 2004b). These simulations can also be used to measure VaR for the banking book. This is an estimate of the worst loss, with a pre-specified probability, and takes into account all kinds of IRR. Therefore, it is a better metric for banking book IRR, than NII or duration. But, as we shall see, the data requirements are also much more. With this overview of IRR management, we move on to the empirical literature, with our focus on the suggestions of BCBS, for measuring and mitigating banking book IRR. 2.3. Attempts to measure IRR Staikouras (2003) presents a literature survey of the research on estimating IRR exposure for banks. In general,
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he observes a statistically significant negative correlation between bank equity returns and changes in market yields. This relationship becomes stronger when surprises in yield changes are introduced. He reports studies by Flannery and James (1984a,b) which show that savings and loan associations (S&L) were thrice as sensitive as banks, between 1976 and 1981. These S&L’s, which ultimately went bankrupt, used short-term deposits to fund long-term home loans. He attributes such interest rate sensitivity of common stock returns primarily to a positive duration gap on the balance sheet. He reports studies by Flannery (1981, 1983) which show that banks try to hedge this gap by altering their balance sheet structures. His observations are supported by an empirical study of interest rate sensitivity of loans in the US banking industry (Purnanandam, 2005). Using a dataset of 8000 banks for the period 1997–2003, he finds that there exists a significant maturity gap in the banking sector. Banks which are larger, have less liquid assets and grow fast, hedge this gap with derivatives. Banks with higher chances of financial distress not only hedge more, but also maintain lower gaps. Further, he shows that derivative non-user banks sharply reduce maturity gaps in response to tight monetary policy. With a rise in the Fed Funds rate, even very large derivative non-user banks sharply cut back their loan volumes. However, derivative users of similar size are found to be immune to such regimes. They do not adjust their loan volumes in response to tighter monetary policies. Those who do not use derivatives have to pursue more conservative on balance sheet asset–liability management policies. Next, we turn to country studies of IRR. English (2002) studies the net interest margins, for a sample of 10 countries, with annual data between 1979 and 2001. He finds that in Australia, Germany, Sweden, UK and the US, assets are more sensitive to long-term rates than liabilities. So, as the yield curve steepens, the NII should rise in these countries. However, apart from Sweden and Germany, there is no statistically significant relationship between the slopes of the yield curves and NII. He concludes that this general absence of statistical significance shows that most countries had been able to limit their exposure to NII. This indicates that banks in these countries were actively hedging their banking book IRR. Maes (2004) studies the effect of interest rate shocks in the Belgian banking sector, between 1993 and 2003. He finds that changes in long and short rates do not affect NII in a statistically significant manner. Secondly, NII of medium and small banks goes up as the yield curve steepens, but no such relationship exists for large banks. However, his market value analysis shows a strong negative correlation of bank assets to long-term rates. While the vulnerability of market value of assets to long-rates exposes the drawbacks of NII analysis, the study is incomplete because it looks only at the asset side of the balance sheet. In case liabilities are as sensitive as assets, banks will be immune to small, parallel shifts of the yield curve.
Quemard and Golitin (2005) estimate IRR in the French banking sector. They conduct a stress test – a rate hike of 300 basis points between 2003 and 2005. While this study shows that both NII and EVE fall with a rise in rates, it also uses an arbitrary shock. There is no reason why a 300 basis point shock is appropriate. Moreover, as in standard duration-based models, the shock does not capture either yield curve or basis risk. It only considers repricing risk. Mahshid and Naji (2004) conduct a qualitative study of IRR in four Swedish savings banks. They also calculate duration gaps, for these banks, from the annual reports of 2002. They observe that these banks have closely matched low-duration assets and liabilities and are exposed to minimal IRR. This risk is managed with interest rate swaps. As in previous studies, the authors consider only repricing risk. The study, which comes the closest in spirit to our own and that of BCBS, was conducted on 42 Indian banks using data from 2002 by Patnaik and Shah (2004). For want of better data, they use structural liquidity statements (SLS) to estimate portfolio duration for banking book assets and liabilities. Owing to lack of data on asset and liability rates, they use the 99% worst rate shock (320 basis points) for 10-year government securities to hit market values of both assets and liabilities. They find that 26 banks suffer EVE losses, 9 banks are unaffected while seven banks make EVE gains from the rate hike. However, their paper has some serious limitations. First, they use SLS, rather than RSG reports, for rate sensitivity analysis. A simple example illustrates their error. At maturity, term deposits are placed in a particular time bucket, net of renewals, in an SLS. Based on behavioural analysis, the rest is slotted in distant buckets. However, in an RSG report, the entire amount is repriced at maturity. This means that duration of term deposits (and hence liabilities) rises when we estimate rate sensitivity from the SLS, rather than the RSG report, because more cashflows are placed in longer buckets. As a result, the EVE impact is distorted. Patnaik and Shah also neglect basis risk. Not only do they neglect the spread between asset and liability rate shocks, but they also ignore the spread between changes in G-sec rates and the asset (or liability) rates, in various buckets. Their implicit assumption that a percentage change in the risk-free (G-sec) rate also implies a percentage change in all asset (or liability) rates might not be correct. In sum, by considering basis risk, we move closer to BCBS (2004b), which suggests that all material IRR in the banking book should be assessed. By using three years of data, we are also able to report short-term trends in EVE. The regulator can use such trends to identify those banks for which EVE losses consistently exceed 20% of the sum of Tier-1 and Tier-2 capital. It can ask them to maintain capital for IRR in the banking book (BCBS, 2004a,b). With this background, we move on to a detailed discussion of our empirical study.
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3. Data and empirical analysis In this section, our final aim was to estimate the size of the deposit rate and PLR shocks and use them for EVE analysis. These rates (driven variables) might be governed by various factors (driver variables). We began with equality tests, to eliminate those factors which follow the same distribution and are highly correlated with others (i.e. are virtually identical). We then examined whether the remaining time series is stationary or not, in order to avoid spurious regressions. This allowed us to prepare a tentative list of driver variables. To pare it down, we conducted Granger causality tests with appropriate lags. This gives us the final list of driver variables. Our last step was to use this list for simulating deposit rate and PLR shocks in three stages. First, we found out the distributions of the driver variables. Secondly, we conducted an OLS regression to estimate the strength of the relationship between the driver and driven variables. Finally, using the distributions of the driver variables and the OLS regression coefficients, we simulated 1000 deposit rate and PLR shocks. Using these values, we found out the EVE impact in rupees and as a proportion of Market Value of Assets, for the banks in our sample. 3.1. Interest rate data We considered weekly data on 45 different interest rate series in the Indian financial market, between 16th November 2001 and 30th January 2004, using 116 observations collected from various sources (see Appendix). 3.2. Rate sensitive gap data For this study, we wrote to all the public sector commercial banks in India for three years of data on RSG statements which depict the banks’ exposure to repricing risk over time. We received RSG statements in the format prescribed by the RBI for three years from nine banks and for less than three years from two banks. This data is a banklevel aggregate and does not distinguish between credit risk free and credit risky assets. In view of limited data availability in our markets, we used a single discount rate each for assets and liabilities. However, credit spread was incorporated into the asset rate. 3.3. Analysis and results 3.3.1. Equality tests Among the 45 different interest rate series, we took a sub-group of zero-coupon rates, from 1 to 25 years, to represent treasury yields. It is well known that some zero rates are highly correlated with others. We wanted to eliminate all those zeroes which follow the same distribution (whether normal or non-normal) and are highly correlated. In effect, these are identical (same mean/median, variance and high correlation) series and including all of them
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would have distorted our regression analysis later. So, we tried to pick out the unique zeroes. From a preliminary analysis of the data, we found that none of the above series follow a normal distribution and there is a high correlation between the movements of the zero coupon rates. In view of this, we used the mean and median equality tests (at 5% level of significance) to arrive at the unique zeroes, which represent the treasury yields. We constructed a correlation matrix for all the 25 series of zero-coupon rates. Fifteen variables were excluded from the study, for the two reasons as follows: [(a)] Correlation between the variables at least equal to 0.99, and [(b)] Mean and median equality tests at 5% significance level. From this set, ZER1, ZER2, ZER4, ZER6, ZER9, ZER12, ZER15, ZER18, ZER21 and ZER25 were found to be unique and included for further analysis. 3.3.2. Unit root tests As already explained, we want to estimate deposit rate and PLR, by regressing them on a set of driver variables. However, in regressions involving time series data, there is a possibility that standard ‘t’ tests could incorrectly portray a relationship as statistically significant (i.e. show that b is statistically significant and R2 is high), when in fact no relationship exists between the variables. In such cases, estimation and forecasting are no longer meaningful. This problem of ‘spurious regression’ (Johnston and DiNardo, 1997) occurs if the variables are non-stationary. Therefore, before we drew up a list of potential driver variables for deposit rate and PLR shocks, the data series (remaining after equality tests) were subjected to unit root tests, to find out which of them are stationary and also the level at which they are stationary. For the unit root tests, we used augmented Dickey–Fuller (ADF) tests, of the concerned variables, both at trend and intercept levels. On the basis of the above test, we found the following variables to be stationary at their level and at their first difference (see Table 2). 3.3.3. Granger causality tests After preparing a list of potential driver variables, which are stationary, we narrowed it down to include only those variables which ‘Granger cause’ deposit rate and PLR. The definition of Granger causality says that (i) the cause y occurs before the effect x and (ii) the causal series contains special information about the series being caused, that is not available in any other series (Granger, 1980, 1988). In our case, this means that, if regressions better explain current deposit rate and PLR, after including lagged values of a potential driver variable xt j, then xt j Granger causes current deposit rate and PLR. To find out driver variables for deposit rate and PLR, we used the Granger Causality test with a lag of 2 weeks.
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Table 2 Stationarity of variables
Table 4 Driver and driven variables at Lag-2a
Variables stationary at their level
Variables stationary at their first difference
PLRa CALLBa CALLa REPOa WPIa 14DTBa 91DTBa 182DTBa 364DTBa ZER4a ZER6a ZER12a MIBID14Da MIBOR14Da MIBIDONa MIBORONa
CRRa BRATEa DEPOa ZER1a ZER2a ZER9a ZER15a ZER18a ZER21a ZER25a MIBID1Ma MIBOR1Ma MIBID3Ma MIBOR3Ma
a
Depo PLR
a
Level of significance is 5%.
The lag selection is crucial because our driver variables might not affect the driven ones with any other lag, e.g. of 1 or 3 weeks. The results might change dramatically if lag selection is not correct. In our paper, it is based on the Akaike Information Criterion (AIC), Final Prediction Error (FPE) criterion, Sequential Modified LR Test Statistic, Schwarz Information Criterion (SC) and Hannan– Quinn Information Criterion (HQ). The results are reported in Table 3: From the Granger Causality tests, we found ‘unidirectional causality’ between 204 pairs and ‘bidirectional causality’ between 59 pairs. Since we focus on Deposit Rates and PLR as driven variables, we report the following relevant driver variables in Table 4. In words, this means that 1. dbrate (change in bank rate) Granger causes ddepo (change in deposit rate). 2. repo (repo rate) Granger causes plr (prime lending rate). 3. 91 dtb (91 day t-bill rate) Granger causes plr (prime lending rate). 4. 182 dtb (182 day t-bill rate) Granger causes plr (prime lending rate). 5. 364 dtb (364 day t-bill rate) Granger causes plr (prime lending rate).
Driver Variables
Driven Variables
F-Stats
P -Value
dbrate repo 91 dtb 182 dtb 364 dtb
ddepo plr plr plr plr
6.68737 31.0271 11.3047 9.67697 13.0074
0.00183 2.20E 11 3.50E 05 0.00014 8.60E 06
Level of significance is 1%.
3.3.4. Impulse response function In order to find out the sensitivity of the driven variables for a one standard deviation shock to driver variables, we constructed the Impulse Response Functions. At Lag 2, the results of the impulse response are reported in Figs. 1–5. In Fig. 1, the response of ddepo due to one standard deviation shock in dbrate is plotted. From the figure we see that a normalized random one standard deviation shock to dbrate in the Vector Autoregression (VAR) system produces fluctuations in ddepo for up to 7 weeks (periods) ahead. Thereafter, the responses decay towards zero. In Fig. 2, a one standard deviation shock in repo leads to fluctuations in plr for up to 6 weeks, which then normalizes. In Fig. 3, a one standard deviation shock in 91 dtb produces fluctuations in plr for up to 7 weeks, which thereafter decay towards zero. Similarly, one standard deviation shocks to 182 dtb and 364 dtb (Figs. 4 and 5) produce fluctuations in plr for up to 5 and 12 weeks respectively, before decaying towards zero.
Fig. 1. Response of DDEPO to Cholesky One S. D. DBRATE Innovation.
Table 3 Lag length criterion Lag
LogL
LR
FPE
0 1 2
4236.629 8033.09 9655.052
NA 5509.907 1492.780*
4.91E 70 4.12E 92 3.53E 96*
AIC 74.4536 125.718 138.4965*
SC 73.7295 103.2718* 94.3273
HQ 74.1598 116.61 120.5731*
Note: * indicates lag order selected by the concerned criterion. LR: sequential modified LR test statistic (each test at 5% significance level), FPE: Final prediction error, AIC: Akaike information criterion, SC: Schwarz information criterion, HQ: Hannan–Quinn information criterion.
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Fig. 5. Response of PLR to 364DTB.
Fig. 2. Response of PLR to REPO.
driver variables. Next, using the distributions of the driver variables, the regression coefficients and the correlation matrix between pairs of driver variables, we simulated 1000 values of deposit rates and PLR. Finally, we subtracted the original (current) deposit rate and PLR from the simulated rates and found 1000 simulated values of changes in deposit rates and PLR. We used these simulated first differences as shocks to bank assets and liabilities in our EVE analysis. Step 1: Distribution followed by the driver variables To simulate the driven variables through driver variables, we needed to find out the distributions of the driver variables. We used the BestFit2 software (of Palisade Corporation) to identify the appropriate distributions followed by the driver variables. The chi-square goodness of fit test was used to select the most suitable distribution for each driver variable. The results of the fitted distributions of the driver variables are as follows (see Table 5). Step 2: Regression to specify the functional relationship In order to carry out Monte Carlo simulation of the driven variables (deposit rate and PLR), we needed the functional relationship between the driver and the driven variables. For this we carried out a regression analysis. The results are presented below (see Table 6). Step 3: Simulation of the driven variables Using the distributions of the driver variables obtained in Step 1, the regression coefficients found in Step 2 and the following correlation matrix between each pair
Fig. 3. Response of PLR to 91DTB.
Fig. 4. Response of PLR to 182DTB.
3.3.5. Monte Carlo simulation and EVE impact Having found the causal or driver variables for deposit rates and PLR, we moved on to Monte Carlo Simulation. We began by estimating the distributions of the driver variables. Then, we regressed deposit rates and PLR on their
2
BestFit is a Windows based software (of Palisade Corporation) which finds the distribution that best fits input data. It goes through the following steps when finding the best fit for the input data: (i) For input sample data, parameters are estimated using maximum-likelihood estimators. For density and cumulative data, the method of least squares is used to minimise the distance between the input curve points and the theoretical function; (ii) fitted distributions are ranked using one or more goodnessof-fit statistics, including chi-square, Anderson–Darling, and Komolgorov–Smirnov.
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Table 5 Distributions of driver variables Sr. No.
Driver variables
Distribution
1 2 3 4 5
Dbrate Repo 91 dtb 182 dtb 364 dtb
Extreme Value Triangular Normal Normal Logistic
Table 6 Regressions Dependent variable
Independent variable C
Coefficient
C
Repo
91dtb Plr 182dtb
364dtb
DW
0.002471
2.103758
0.239699
1.885652
0.028 (0.008) [3.231]
Ddepo Dbrate
R2
0.137 (0.261) [0.524] 9.251 (0.394) [23.469] 0.320 (0.215) [1.487] 0.022 (0.370) [ 0.060] 0.521 (0.364) [ 1.428] 0.568 (0.422) [1.345]
Table 8 Duration gap Bank
Note: Terms within first brackets ( ) show standard errors and terms within third brackets [ ] show t-statistics.
Table 7 Correlation matrix
Repo 91 dtb 182 dtb 364 dtb
Income Money Market and Derivatives Association – FIMMDA) using Best Fit and simulated 1000 values of the spread using @Risk. These values were added to the simulated PLR to obtain the discount rates for all assets.Finally, we subtracted the original (current) values of the deposit rate and PLR from their simulated values (including spread over PLR) to obtain 1000 simulated values of first differences in deposit rate and PLR. These rate shocks were given to assets and liabilities in our EVE analysis. Step 5: Computation of change in EVE at the 99% confidence level We used the Rate Sensitive Gap Statements of 11 Indian banks to compute their Economic Value of Equity (EVE) for each year. Each of the 1000 simulated values of the driven variables, as computed in Step 3, was used to shock the base interest rate each year, to compute the change in EVE. The 99th percentile of the change in EVE was chosen as the unexpected loss in EVE for each bank. The duration gap profile of the banks, indicating the potential exposure to interest rate shock, is as follows (see Tables 8,9).
Repo
91 dtb
182 dtb
364 dtb
1 0.94795 0.944798 0.954531
1 0.983869 0.986886
1 0.987587
1
of driver variables, we simulated 1000 values of each driven variable. A regression coefficient converts the simulated value of a driver variable into a simulated value of its driven variable. For all our simulations, we used @Risk3 (At-Risk), a standard simulation software from Palisade Corporation (see Table 7). Step 4: Simulation of Spread over PLR To add the credit spread to PLR, we identified the distribution of the spread over PLR (collected from Fixed 3 @Risk is a Windows based software (of Palisade Corporation) for Monte Carlo Simulation, that supports a number of statistical distributions. Correlation among input distributions can be defined to incorporate the dependence structure among them.
Bank-1 Bank-2 Bank-3 Bank-4 Bank-5 Bank-6 Bank-7 Bank-8 Bank-9 Bank-10 Bank-11
Year 2002
2003
2004
0.557 0.534 0.738 1.614 0.825 0.645 0.170 0.430 0.863 n.a n.a
0.838 0.897 0.530 1.124 1.016 0.971 0.107 0.976 0.830 n.a n.a
0.858 0.979 1.409 1.322 1.001 0.951 0.611 0.915 n.a. 0.952 0.245
Table 9 EVE impact (Rs. crores) Bank
Bank-1 Bank-2 Bank-3 Bank-4 Bank-5 Bank-6 Bank-7 Bank-8 Bank-9 Bank-10 Bank-11
Year 2002
2003
2004
792.561 1079.272 1048.482 779.012 626.989 1104.471 800.733 840.766 3341.196 n.a n.a
1132.148 1326.537 1057.504 702.482 771.384 1713.132 948.405 769.969 3737.161 n.a n.a
1183.627 1475.475 2150.607 900.455 753.784 1790.278 1536.979 958.689 n.a. 1136.770 1905.577
(Rs. 1 crore = Rs. 10 million = USD 0.222 million).
A. Saha et al. / European Journal of Operational Research 193 (2009) 581–590 Table 10 EVE impact as percent of MVRSA Bank
Bank-1 Bank-2 Bank-3 Bank-4 Bank-5 Bank-6 Bank-7 Bank-8 Bank-9 Bank-10 Bank-11
Appendix 1. Data definition and sources
Year 2002 5.195 8.298 5.668 9.471 6.188 5.978 3.195 5.430 6.476 n.a. n.a.
589
2003 6.345 9.284 5.337 7.481 7.288 7.394 3.694 4.382 6.266 n.a. n.a.
2004 6.076 9.153 8.509 8.376 6.878 7.046 4.874 4.441 n.a. 6.577 3.866
In order to make the EVE profile independent of size and hence comparable, we divided the EVE of each bank by its Market Value of Rate Sensitive Asset (MVRSA) for each year. The results are as follows (see Table 10). It is clear that our EVE losses (as a proportion of MVRSA) are much higher than those in Patnaik and Shah (2004). For instance, their lowest loss is 1.1%, while ours is 3.195% (Table 10, Bank 7, year 2002). Their highest loss is 4.4%, ours is 9.471% (Table 10, Bank 2, year 2002). We attribute this to basis risk – our analysis suggests that asset rate shocks are much stronger than liability rate shocks. Moreover, almost all banks (except bank 8) have positive duration gaps. Therefore, asset values fall much more than liability values. 4. Conclusions Banking book IRR has not been studied in detail, especially in developing countries. As banks in these countries gear up to meet the deadlines for implementation of Basel II, they must pay close attention to the duration mismatches in their accrual books and the consequent threat to EVE. In one of the first studies on estimating banking book IRR in a developing country like India, apart from repricing risk, we find evidence of significant basis risk between PLR and deposit rate shocks. This leads to very large EVE losses for our sample banks. Being oblivious to such EVE reduction would lead to serious erosion of capital and future earnings. This implies that pursuit of myopic, NII based, ALM policies by Indian banks would distort product pricing and hence the balance sheet structure over time. The results of the study have regulatory policy implications as well. Interest rate volatility, in developing counties like India, has made Asset–Liability Management extremely challenging. The task becomes all the more difficult with the advent of international best practices, under the rubric of Basel II. To get a complete picture of vulnerability of Indian banks to interest rate fluctuations, we plan to incorporate yield curve risk and options risk in our future work.
Variables CRR
Definition
Cash Reserve Ratio BRATE Bank rate set by RBI PLR Prime Lending Rate DEPO Deposit rate CALLB Call Borrowing CALL Call Lending REPO Average of Repo rates WPI Wholsale Price Index 14DTB Yield on 14 day tbill 91DTB Yield on 91 day tbill 182DTB Yield on 182 day t-bill 364DTB Yield on 364 day t-bill MIBID14D 14-day Mumbai Inter-bank Bid rate (MIBID) MIBOR14D 14-Day Mumbai Inter-bank Offer rate (MIBOR) MIBID1M 1 month MIBID MIBOR1M 1 month MIBOR MIBID3M 3 month MIBID MIBOR3M 3 month MIBOR MIBIDON Overnight MIBID MIBORON Overnight MIBOR ZER1-25 Zero coupon yield for 1–25 year maturity
Source RBI Weekly Statistical Supplement (WSS) RBI WSS RBI WSS RBI RBI RBI RBI
WSS WSS WSS WSS
RBI WSS RBI WSS RBI WSS RBI WSS RBI WSS National Stock Exchange (NSE) website NSE website
NSE NSE NSE NSE NSE
website website website website website
NSE website Computed based on parameters provided in NSE website
References Basel Committee on Banking Supervision (BCBS), 2004a. Basel II: International Convergence of Capital Measurement and Capital Standards: A Revised Framework, June 2004. Basel Committee on Banking Supervision (BCBS), 2004b. Principles for the Management and Supervision of Interest Rate Risk, July 2004. English, W., 2002. Interest rate risk and bank net interest margins. BIS Quarterly Review (December), 67–82. Flannery, M., 1981. Market interest rates and commercial bank profitability: An empirical investigation. Journal of Finance 36, 1085–1101. Flannery, M., 1983. Interest rates and bank profitability: Additional evidence. Journal of Money, Credit and Banking 15, 355–362.
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Flannery, M., James, C., 1984a. The effect of interest rate changes on the common stock returns of financial institutions. Journal of Finance 39, 1141–1153. Flannery, M., James, C., 1984b. Market evidence on the effective maturity of bank assets and liabilities. Journal of Money, Credit and Banking 16, 435–445. Granger, C., 1980. Testing for causality: A personal viewpoint. Journal of Economic Dynamics and Control 2, 329–352. Granger, C., 1988. Some recent developments in a concept of causality. Journal of Econometrics 39, 199–211. Johnston, J., DiNardo, J., 1997. Econometric Methods, fourth ed. McGraw-Hill, Singapore. Maes, K., June 2004. Interest Rate Risk in the Belgian Banking Sector. Financial Stability Review, National Bank of Belgium, pp. 157–179. Mahshid, D., Naji, M., 2004. Managing Interest Rate Risk: A Case Study of Four Swedish Savings Banks. School of Economics and Commercial Law. Goteborg University. Patnaik, I., Shah, A., 2004. Interest Rate Volatility and Risk in Indian Banking. IMF Working Paper No. WP/04/17. International Monetary Fund, January.
Purnanandam, A., 2005. Interest Rate Risk Management at Commercial Banks: An Empirical Investigation, May 2005. Available from:. Quemard, J., Golitin, V., 2005. Interest Rate Risk in the French Banking System. Financial Stability Review, Banque de France. June 2005, pp. 81–94. Reserve Bank of India (RBI), 2004. Prudential Norms on Classification of Investment Portfolio of Banks. DBOD. No. BP.BC.37/21.04.141/ 2004-05, September 2, 2004. Saunders, A., Cornett, M.M., 2006. Financial Institutions Management: A Risk Management Approach. McGraw Hill, New York. Staikouras, S., 2003. The interest rate risk exposure of financial intermediaries: A review of the theory and empirical evidence. Financial Markets, Institutions and Instruments 12, 257–289. Staikouras, S., 2006. Financial intermediaries and interest rate risk: II. Financial Markets, Institutions and Instruments 15, 225–272. Wetmore, J., Brick, J., 1998. The basis risk component of commercial bank stock returns. Journal of Economics and Business 50, 67–76.
European Journal of Operational Research 193 (2009) 581–590 www.elsevier.com/locate/ejor
O.R. Applications
Networth exposure to interest rate risk: An empirical analysis of Indian commercial banks q Asish Saha *, V. Subramanian 1, Sanjay Basu, Alok Kumar Mishra National Institute of Bank Management (NIBM), Pune, India Received 15 April 2006; accepted 14 November 2007 Available online 23 November 2007
Abstract In the Basel II era, management of interest rate risk in the banking book has become significant. In the first study of its kind, we develop a simulation based driver-driven approach to estimate the impact of interest rate volatility on the networth of Indian banks during the period 2002–2004. We derive the interest rates that drive changes in deposit and prime lending rates (PLR). Then we perform Monte Carlo simulation and multiple regressions, on these driver rates, to obtain simulated shocks to deposit rates and PLR. We use these simulated shocks to get the 99% worst EVE loss for the sample banks. These losses are much larger than what the existing literature suggests. This is because, apart from repricing risk, we are the first to find evidence of significant basis risk. Our results have important policy implications both for banks and regulators. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Interest rate risk in banks; Risk management; Simulation; Driver-driven variables
1. Introduction In the wake of a steady rise in the yields of government securities since May 2004, interest rate risk in the trading book has been of great concern to Indian banks and Reserve Bank of India (RBI) alike. The yields on 5 year and 10 year benchmark securities went up from 4.68% to 6.33% and from 5.09% to 6.71% respectively between April 2, 2004 and April 1, 2005. This resulted in huge marked-tomarket (MTM) losses in the investment books of the Indian banks. To deal with the crisis, RBI widened the scope of the held-till-maturity category of securities; it per-
q
We are grateful to our colleague Dr. Arindam Bandyopadhyay for his valuable comments and suggestions. The usual disclaimer applies. * Corresponding author. Tel.: +91 20 2683 3080 87; fax: +91 20 2683 1447. E-mail addresses: [email protected], [email protected] (A. Saha). 1 On leave from NIBM. 0377-2217/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2007.11.038
mitted banks to make a one-time portfolio transfer, up to 25% of their net demand and time liabilities, from MTM (Held for Trading and Available for Sale) to historical cost (Held till Maturity) categories (RBI, 2004). In essence, it shielded them from further MTM losses and capital charges. The purpose of this paper is to show that at least a similar, if not greater, danger lurks in the ‘banking book’ as well. We find that an interest rate hike reduces the present value of bank assets much more than that of outside liabilities. This means that a rate hike depletes a bank’s networth. But, so far, this risk has not evoked knee-jerk responses from Indian banks because (i) the losses are not MTM and (ii) there are no capital charges. Such respite is at best temporary, for two reasons. First, there is empirical evidence of a long-run, negative, correlation between market yields and equity returns of banks (Staikouras, 2003). Secondly, as per Pillar 2 of Basel II (BCBS, 2004a), interest rate risk (IRR) in the banking book should also attract capital charges, if the losses in Economic Value of Equity (EVE) are severe enough.
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Most of our results should be of serious concern to Indian banks. First, we find much higher EVE losses than that reported by the existing literature. Secondly, there is evidence of significant basis risk – asset rate shocks are much stronger than liability rate shocks. In fact, such basis risk is an important reason behind the large EVE losses. Our results are consistent with the recent literature which suggests that basis risk is an important component of IRR for banks, beyond repricing risk which considers Net Interest Income (NII) and EVE losses from equal asset and liability rate shocks only (Wetmore and Brick, 1998; Staikouras, 2006). We report the profile of Basis Risk, from our simulated data, in Table 1. It is clear that as we approach the extremes of the tails (i.e. consider larger rate shocks), the basis risk increases. Our first contribution to the literature is methodological. Most papers focus on scenarios in which market values of assets and liabilities are hit by arbitrary rate shocks. Instead, we begin by selecting the most important rates for the banking book in India. We then investigate what factors ‘drive’ these rate changes and refer to them as ‘driver’ variables. Next, we estimate simulated rate shocks (changes in ‘driven’ variables) from the simulated values of the drivers. We use these rate shocks to hit the present values of banking book assets and liabilities. The EVE impact is calculated as the effect of such shocks on networth. There are three advantages of our ‘driver-driven’ approach. First, it allows us to study the interdependence among several rates prevailing in the Indian market. This has major policy implications for banks, e.g. if banks know how driven rates respond to changes in driver rates, they can use the relationship to choose appropriate strategies. Secondly, we know exactly why a driven rate changes by a certain magnitude, e.g. 1%. This is due to a given change in (underlying) driver rates. Lastly, we do not work with arbitrary rate changes, as is usually the practice, but simulate the shocks from a historical distribution of interest rates. Once we know the EVE impact of simulated rate shocks under normal conditions, we can superimpose stress scenarios. Therefore, our rate shocks are not only rationalizable, but also realistic. Our paper also measures the Value-at-Risk (VaR) for banking book IRR. Most studies (e.g. Maes, 2004; Quemard and Golitin, 2005) analyze the impact of a given rate shock on NII or EVE. Their results are open to the same charges leveled against duration-based measures – they neglect yield curve risk, basis risk and options risk. Instead, Table 1 Profile of basis risk from simulated rates Percentile
99 97.5 95 90
Simulated rate shock (%) Deposit
PLR
3.190 2.803 2.510 2.199
5.1546 4.5780 4.0233 3.5445
Difference in rate shocks (%)
1.9647 1.7747 1.5128 1.3459
in line with suggestions of the Basel Committee (BCBS, 2004b), we use simulated asset and liability rate shocks to find out the 99% worst EVE losses. This is the 99% VaR for the banking book. Finally, we use Rate Sensitive Gap (RSG) reports to arrive at the EVE impact of rate shocks. A recent paper by Patnaik and Shah (2004) uses Structural Liquidity Statements (SLS), to study IRR for Indian banks. Though both reports use time buckets, the SLS is used to gauge the liquidity impact, while the RSG report is used to find out the impact of interest changes on NII or EVE. So, for estimating IRR, the RSG report is more appropriate. To the best of our knowledge, this is the first paper to measure VaR for banking book IRR, from RSG reports. We have also not come across any research that used a driver-driven model to generate rate shocks. Because our shocks are endogenous, we are able to conduct a systematic analysis of IRR as well. From our model, we can pin the blame for our EVE losses on basis risk. This is not possible with standard NII and duration gap analysis. Our paper is organized as follows. In Section 1, we present a literature review of the issues. In Section 2, we discuss our data sources and methodology and state our main results. We conclude, in Section 3, with directions for future research. 2. Literature review We begin this section with a definition of IRR. We then define and describe the different sources of IRR in the banking book. Next, we discuss the pros and cons of the various methods for dealing with such IRR. Then, we sift the existing literature on the measurement and management of IRR in the banking sectors of different countries. In particular, we emphasize on the recommendations of the Basel Committee on Banking Supervision (BCBS). This serves as our point of departure, as we try to highlight how our work is different from the rest, but closer to the suggestions of BCBS. 2.1. Definition and sources of IRR IRR refers to the effect of interest volatility on rate-earning assets and rate-paying liabilities. For a given change in rates (e.g. 1%), IRR also includes the effect of shifts in volume and composition of assets and liabilities. Regulators and commercial banks split IRR into two components, viz. traded IRR and non-traded IRR. Though both refer to the potential adverse effects of market rate movements, the difference lies in the point of impact; ‘traded IRR’ affects MTM values of items in the trading book while ‘non-traded IRR’ covers all assets and liabilities in the banking (accrual) book. There are four main sources of IRR in the banking book. These are: (i) Repricing Risk (ii) Yield Curve Risk (iii) Basis Risk and (iv) Options Risk. Repricing Risk arises from differences in the maturity (fixed-rate) or repricing
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(floating-rate) dates for bank assets, liabilities and off-balance sheet (OBS) items. For instance, a bank funding a 3 year fixed-rate loan with a 6-month fixed deposit is exposed to repricing risk. Since the rate on the fixed deposit is adjusted earlier, an increase in market rates after 6 months reduces the bank’s spread between yields on assets and costs of liabilities. Here, even a parallel shift of the rates can reduce spreads and erode net worth (BCBS, 2004b). Yield Curve Risk refers to the effect of non-parallel shifts of yield curve segments, on assets and liabilities of different maturities. Even if the cumulative (across all time buckets) gap between rate-sensitive assets and liabilities is small, different rate shocks in different buckets could sharply reduce the spread or networth. In this case, the bank’s spread could be immune to a parallel shift of the yield curve (BCBS, 2004b). Basis Risk refers to the impact of an imperfect correlation between indices underlying asset and liability rates, e.g. between LIBOR (governing deposit rates) and PLR (governing loan rates), with otherwise similar repricing frequency. Even if 6-month PLR-linked loans are funded by 6-month LIBOR-linked deposits, there is no guarantee that a 1% change in LIBOR will imply a 1% change in PLR. In other words, if the spread between index rates changes suddenly, earnings and networth might fall (BCBS, 2004b). Options Risk refers to the effect of options embedded in bank assets, liabilities and OBS items. Such options provide the holder the right, but not the obligation, to alter the cash flows of these instruments. For instance, depositors have the right to withdraw their savings, current or term deposits at any point. They are likely to exercise such rights, when market rates rise. This can trigger a sharp decline in cash flows for banks (BCBS, 2004b). 2.2. Effects: IRR management techniques As already discussed, the IRR exposure of a bank affects both its earnings and networth. The focus on earnings is more common than the study of networth. We will discuss both in turn. 2.2.1. Earnings or accounting approach It is a short-term analysis of rate shocks on accrual or reported earnings. It is generally restricted to the accounting cycle and covers only an initial part of the lives of assets and liabilities in the balance sheet. In this approach, assets and liabilities are recorded at historical cost. It is important because outright losses or decline in earnings, from a rate shock, can threaten capital adequacy and undermine market confidence. The main focus of the earnings approach is on the impact of interest rate changes on NII. Banks have traditionally tried to minimize the impact of rate shocks on NII. This reflects the high share of NII in a bank’s earnings. But, gradually, they began to look beyond NII, for three reasons. First, NII can be maneuvered. Secondly, assets and liabilities which reprice beyond the accounting cycle also make opportunity gains or losses
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when rates change. This effect on potential earnings is ignored by NII analysis. Thirdly, even non-interest income and expenses are now being found to be sensitive to rate changes (BCBS, 2004b). So, banks shifted their attention to the economic value approach. 2.2.2. Economic value approach The focus here is on the long-term impact of rate changes on assets and liabilities. It recognizes that rate shocks affect the values of future cash flows as well. The Economic Value of Equity (EVE) is the present value of assets minus present value of liabilities. As EVE is the present value of net expected cash flows, it reflects future earning potential. In the short-run, since it is difficult to judge the effect of internal decisions on market capitalization, many banks analyze the impact of decisions on EVE. The focus of EVE on present values leads naturally to sensitivity analysis along the lines of bonds. Specifically, EVE impact is calculated in terms of leverage adjusted duration gap, where duration is the sensitivity of an asset or liability to a percentage change in rates (Saunders and Cornett, 2006). If assets have higher duration than liabilities, their prices fall more when rates rise. Therefore, banks with high-duration assets and low-duration liabilities (a positive duration gap) are exposed to EVE losses, with a rise in rates. The foregoing discussion brings out a potential conflict between NII and EVE management, since duration is also a proxy for residual time-to-maturity. Since long-duration (long-term) assets might carry much higher rates than short-duration (short-term) liabilities, a bank might try to maximize NII by increasing the duration gap. This could expose its EVE to a rise in rates. Hence, even if the bank management wants to focus on NII, regulators might not allow a sharp decline in EVE, for a given change in rates. They perceive EVE as a proxy for capital adequacy, in market value terms, and might force a bank to adhere to strict NII limits. But, the earnings and economic value approaches cannot estimate yield curve risk, basis risk and options risk. Therefore, banks and regulators conduct static and dynamic simulations, to incorporate yield curve twists, changes in spreads between asset and liability rates or exercise of banking book options (BCBS, 2004b). These simulations can also be used to measure VaR for the banking book. This is an estimate of the worst loss, with a pre-specified probability, and takes into account all kinds of IRR. Therefore, it is a better metric for banking book IRR, than NII or duration. But, as we shall see, the data requirements are also much more. With this overview of IRR management, we move on to the empirical literature, with our focus on the suggestions of BCBS, for measuring and mitigating banking book IRR. 2.3. Attempts to measure IRR Staikouras (2003) presents a literature survey of the research on estimating IRR exposure for banks. In general,
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he observes a statistically significant negative correlation between bank equity returns and changes in market yields. This relationship becomes stronger when surprises in yield changes are introduced. He reports studies by Flannery and James (1984a,b) which show that savings and loan associations (S&L) were thrice as sensitive as banks, between 1976 and 1981. These S&L’s, which ultimately went bankrupt, used short-term deposits to fund long-term home loans. He attributes such interest rate sensitivity of common stock returns primarily to a positive duration gap on the balance sheet. He reports studies by Flannery (1981, 1983) which show that banks try to hedge this gap by altering their balance sheet structures. His observations are supported by an empirical study of interest rate sensitivity of loans in the US banking industry (Purnanandam, 2005). Using a dataset of 8000 banks for the period 1997–2003, he finds that there exists a significant maturity gap in the banking sector. Banks which are larger, have less liquid assets and grow fast, hedge this gap with derivatives. Banks with higher chances of financial distress not only hedge more, but also maintain lower gaps. Further, he shows that derivative non-user banks sharply reduce maturity gaps in response to tight monetary policy. With a rise in the Fed Funds rate, even very large derivative non-user banks sharply cut back their loan volumes. However, derivative users of similar size are found to be immune to such regimes. They do not adjust their loan volumes in response to tighter monetary policies. Those who do not use derivatives have to pursue more conservative on balance sheet asset–liability management policies. Next, we turn to country studies of IRR. English (2002) studies the net interest margins, for a sample of 10 countries, with annual data between 1979 and 2001. He finds that in Australia, Germany, Sweden, UK and the US, assets are more sensitive to long-term rates than liabilities. So, as the yield curve steepens, the NII should rise in these countries. However, apart from Sweden and Germany, there is no statistically significant relationship between the slopes of the yield curves and NII. He concludes that this general absence of statistical significance shows that most countries had been able to limit their exposure to NII. This indicates that banks in these countries were actively hedging their banking book IRR. Maes (2004) studies the effect of interest rate shocks in the Belgian banking sector, between 1993 and 2003. He finds that changes in long and short rates do not affect NII in a statistically significant manner. Secondly, NII of medium and small banks goes up as the yield curve steepens, but no such relationship exists for large banks. However, his market value analysis shows a strong negative correlation of bank assets to long-term rates. While the vulnerability of market value of assets to long-rates exposes the drawbacks of NII analysis, the study is incomplete because it looks only at the asset side of the balance sheet. In case liabilities are as sensitive as assets, banks will be immune to small, parallel shifts of the yield curve.
Quemard and Golitin (2005) estimate IRR in the French banking sector. They conduct a stress test – a rate hike of 300 basis points between 2003 and 2005. While this study shows that both NII and EVE fall with a rise in rates, it also uses an arbitrary shock. There is no reason why a 300 basis point shock is appropriate. Moreover, as in standard duration-based models, the shock does not capture either yield curve or basis risk. It only considers repricing risk. Mahshid and Naji (2004) conduct a qualitative study of IRR in four Swedish savings banks. They also calculate duration gaps, for these banks, from the annual reports of 2002. They observe that these banks have closely matched low-duration assets and liabilities and are exposed to minimal IRR. This risk is managed with interest rate swaps. As in previous studies, the authors consider only repricing risk. The study, which comes the closest in spirit to our own and that of BCBS, was conducted on 42 Indian banks using data from 2002 by Patnaik and Shah (2004). For want of better data, they use structural liquidity statements (SLS) to estimate portfolio duration for banking book assets and liabilities. Owing to lack of data on asset and liability rates, they use the 99% worst rate shock (320 basis points) for 10-year government securities to hit market values of both assets and liabilities. They find that 26 banks suffer EVE losses, 9 banks are unaffected while seven banks make EVE gains from the rate hike. However, their paper has some serious limitations. First, they use SLS, rather than RSG reports, for rate sensitivity analysis. A simple example illustrates their error. At maturity, term deposits are placed in a particular time bucket, net of renewals, in an SLS. Based on behavioural analysis, the rest is slotted in distant buckets. However, in an RSG report, the entire amount is repriced at maturity. This means that duration of term deposits (and hence liabilities) rises when we estimate rate sensitivity from the SLS, rather than the RSG report, because more cashflows are placed in longer buckets. As a result, the EVE impact is distorted. Patnaik and Shah also neglect basis risk. Not only do they neglect the spread between asset and liability rate shocks, but they also ignore the spread between changes in G-sec rates and the asset (or liability) rates, in various buckets. Their implicit assumption that a percentage change in the risk-free (G-sec) rate also implies a percentage change in all asset (or liability) rates might not be correct. In sum, by considering basis risk, we move closer to BCBS (2004b), which suggests that all material IRR in the banking book should be assessed. By using three years of data, we are also able to report short-term trends in EVE. The regulator can use such trends to identify those banks for which EVE losses consistently exceed 20% of the sum of Tier-1 and Tier-2 capital. It can ask them to maintain capital for IRR in the banking book (BCBS, 2004a,b). With this background, we move on to a detailed discussion of our empirical study.
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3. Data and empirical analysis In this section, our final aim was to estimate the size of the deposit rate and PLR shocks and use them for EVE analysis. These rates (driven variables) might be governed by various factors (driver variables). We began with equality tests, to eliminate those factors which follow the same distribution and are highly correlated with others (i.e. are virtually identical). We then examined whether the remaining time series is stationary or not, in order to avoid spurious regressions. This allowed us to prepare a tentative list of driver variables. To pare it down, we conducted Granger causality tests with appropriate lags. This gives us the final list of driver variables. Our last step was to use this list for simulating deposit rate and PLR shocks in three stages. First, we found out the distributions of the driver variables. Secondly, we conducted an OLS regression to estimate the strength of the relationship between the driver and driven variables. Finally, using the distributions of the driver variables and the OLS regression coefficients, we simulated 1000 deposit rate and PLR shocks. Using these values, we found out the EVE impact in rupees and as a proportion of Market Value of Assets, for the banks in our sample. 3.1. Interest rate data We considered weekly data on 45 different interest rate series in the Indian financial market, between 16th November 2001 and 30th January 2004, using 116 observations collected from various sources (see Appendix). 3.2. Rate sensitive gap data For this study, we wrote to all the public sector commercial banks in India for three years of data on RSG statements which depict the banks’ exposure to repricing risk over time. We received RSG statements in the format prescribed by the RBI for three years from nine banks and for less than three years from two banks. This data is a banklevel aggregate and does not distinguish between credit risk free and credit risky assets. In view of limited data availability in our markets, we used a single discount rate each for assets and liabilities. However, credit spread was incorporated into the asset rate. 3.3. Analysis and results 3.3.1. Equality tests Among the 45 different interest rate series, we took a sub-group of zero-coupon rates, from 1 to 25 years, to represent treasury yields. It is well known that some zero rates are highly correlated with others. We wanted to eliminate all those zeroes which follow the same distribution (whether normal or non-normal) and are highly correlated. In effect, these are identical (same mean/median, variance and high correlation) series and including all of them
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would have distorted our regression analysis later. So, we tried to pick out the unique zeroes. From a preliminary analysis of the data, we found that none of the above series follow a normal distribution and there is a high correlation between the movements of the zero coupon rates. In view of this, we used the mean and median equality tests (at 5% level of significance) to arrive at the unique zeroes, which represent the treasury yields. We constructed a correlation matrix for all the 25 series of zero-coupon rates. Fifteen variables were excluded from the study, for the two reasons as follows: [(a)] Correlation between the variables at least equal to 0.99, and [(b)] Mean and median equality tests at 5% significance level. From this set, ZER1, ZER2, ZER4, ZER6, ZER9, ZER12, ZER15, ZER18, ZER21 and ZER25 were found to be unique and included for further analysis. 3.3.2. Unit root tests As already explained, we want to estimate deposit rate and PLR, by regressing them on a set of driver variables. However, in regressions involving time series data, there is a possibility that standard ‘t’ tests could incorrectly portray a relationship as statistically significant (i.e. show that b is statistically significant and R2 is high), when in fact no relationship exists between the variables. In such cases, estimation and forecasting are no longer meaningful. This problem of ‘spurious regression’ (Johnston and DiNardo, 1997) occurs if the variables are non-stationary. Therefore, before we drew up a list of potential driver variables for deposit rate and PLR shocks, the data series (remaining after equality tests) were subjected to unit root tests, to find out which of them are stationary and also the level at which they are stationary. For the unit root tests, we used augmented Dickey–Fuller (ADF) tests, of the concerned variables, both at trend and intercept levels. On the basis of the above test, we found the following variables to be stationary at their level and at their first difference (see Table 2). 3.3.3. Granger causality tests After preparing a list of potential driver variables, which are stationary, we narrowed it down to include only those variables which ‘Granger cause’ deposit rate and PLR. The definition of Granger causality says that (i) the cause y occurs before the effect x and (ii) the causal series contains special information about the series being caused, that is not available in any other series (Granger, 1980, 1988). In our case, this means that, if regressions better explain current deposit rate and PLR, after including lagged values of a potential driver variable xt j, then xt j Granger causes current deposit rate and PLR. To find out driver variables for deposit rate and PLR, we used the Granger Causality test with a lag of 2 weeks.
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Table 2 Stationarity of variables
Table 4 Driver and driven variables at Lag-2a
Variables stationary at their level
Variables stationary at their first difference
PLRa CALLBa CALLa REPOa WPIa 14DTBa 91DTBa 182DTBa 364DTBa ZER4a ZER6a ZER12a MIBID14Da MIBOR14Da MIBIDONa MIBORONa
CRRa BRATEa DEPOa ZER1a ZER2a ZER9a ZER15a ZER18a ZER21a ZER25a MIBID1Ma MIBOR1Ma MIBID3Ma MIBOR3Ma
a
Depo PLR
a
Level of significance is 5%.
The lag selection is crucial because our driver variables might not affect the driven ones with any other lag, e.g. of 1 or 3 weeks. The results might change dramatically if lag selection is not correct. In our paper, it is based on the Akaike Information Criterion (AIC), Final Prediction Error (FPE) criterion, Sequential Modified LR Test Statistic, Schwarz Information Criterion (SC) and Hannan– Quinn Information Criterion (HQ). The results are reported in Table 3: From the Granger Causality tests, we found ‘unidirectional causality’ between 204 pairs and ‘bidirectional causality’ between 59 pairs. Since we focus on Deposit Rates and PLR as driven variables, we report the following relevant driver variables in Table 4. In words, this means that 1. dbrate (change in bank rate) Granger causes ddepo (change in deposit rate). 2. repo (repo rate) Granger causes plr (prime lending rate). 3. 91 dtb (91 day t-bill rate) Granger causes plr (prime lending rate). 4. 182 dtb (182 day t-bill rate) Granger causes plr (prime lending rate). 5. 364 dtb (364 day t-bill rate) Granger causes plr (prime lending rate).
Driver Variables
Driven Variables
F-Stats
P -Value
dbrate repo 91 dtb 182 dtb 364 dtb
ddepo plr plr plr plr
6.68737 31.0271 11.3047 9.67697 13.0074
0.00183 2.20E 11 3.50E 05 0.00014 8.60E 06
Level of significance is 1%.
3.3.4. Impulse response function In order to find out the sensitivity of the driven variables for a one standard deviation shock to driver variables, we constructed the Impulse Response Functions. At Lag 2, the results of the impulse response are reported in Figs. 1–5. In Fig. 1, the response of ddepo due to one standard deviation shock in dbrate is plotted. From the figure we see that a normalized random one standard deviation shock to dbrate in the Vector Autoregression (VAR) system produces fluctuations in ddepo for up to 7 weeks (periods) ahead. Thereafter, the responses decay towards zero. In Fig. 2, a one standard deviation shock in repo leads to fluctuations in plr for up to 6 weeks, which then normalizes. In Fig. 3, a one standard deviation shock in 91 dtb produces fluctuations in plr for up to 7 weeks, which thereafter decay towards zero. Similarly, one standard deviation shocks to 182 dtb and 364 dtb (Figs. 4 and 5) produce fluctuations in plr for up to 5 and 12 weeks respectively, before decaying towards zero.
Fig. 1. Response of DDEPO to Cholesky One S. D. DBRATE Innovation.
Table 3 Lag length criterion Lag
LogL
LR
FPE
0 1 2
4236.629 8033.09 9655.052
NA 5509.907 1492.780*
4.91E 70 4.12E 92 3.53E 96*
AIC 74.4536 125.718 138.4965*
SC 73.7295 103.2718* 94.3273
HQ 74.1598 116.61 120.5731*
Note: * indicates lag order selected by the concerned criterion. LR: sequential modified LR test statistic (each test at 5% significance level), FPE: Final prediction error, AIC: Akaike information criterion, SC: Schwarz information criterion, HQ: Hannan–Quinn information criterion.
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Fig. 5. Response of PLR to 364DTB.
Fig. 2. Response of PLR to REPO.
driver variables. Next, using the distributions of the driver variables, the regression coefficients and the correlation matrix between pairs of driver variables, we simulated 1000 values of deposit rates and PLR. Finally, we subtracted the original (current) deposit rate and PLR from the simulated rates and found 1000 simulated values of changes in deposit rates and PLR. We used these simulated first differences as shocks to bank assets and liabilities in our EVE analysis. Step 1: Distribution followed by the driver variables To simulate the driven variables through driver variables, we needed to find out the distributions of the driver variables. We used the BestFit2 software (of Palisade Corporation) to identify the appropriate distributions followed by the driver variables. The chi-square goodness of fit test was used to select the most suitable distribution for each driver variable. The results of the fitted distributions of the driver variables are as follows (see Table 5). Step 2: Regression to specify the functional relationship In order to carry out Monte Carlo simulation of the driven variables (deposit rate and PLR), we needed the functional relationship between the driver and the driven variables. For this we carried out a regression analysis. The results are presented below (see Table 6). Step 3: Simulation of the driven variables Using the distributions of the driver variables obtained in Step 1, the regression coefficients found in Step 2 and the following correlation matrix between each pair
Fig. 3. Response of PLR to 91DTB.
Fig. 4. Response of PLR to 182DTB.
3.3.5. Monte Carlo simulation and EVE impact Having found the causal or driver variables for deposit rates and PLR, we moved on to Monte Carlo Simulation. We began by estimating the distributions of the driver variables. Then, we regressed deposit rates and PLR on their
2
BestFit is a Windows based software (of Palisade Corporation) which finds the distribution that best fits input data. It goes through the following steps when finding the best fit for the input data: (i) For input sample data, parameters are estimated using maximum-likelihood estimators. For density and cumulative data, the method of least squares is used to minimise the distance between the input curve points and the theoretical function; (ii) fitted distributions are ranked using one or more goodnessof-fit statistics, including chi-square, Anderson–Darling, and Komolgorov–Smirnov.
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Table 5 Distributions of driver variables Sr. No.
Driver variables
Distribution
1 2 3 4 5
Dbrate Repo 91 dtb 182 dtb 364 dtb
Extreme Value Triangular Normal Normal Logistic
Table 6 Regressions Dependent variable
Independent variable C
Coefficient
C
Repo
91dtb Plr 182dtb
364dtb
DW
0.002471
2.103758
0.239699
1.885652
0.028 (0.008) [3.231]
Ddepo Dbrate
R2
0.137 (0.261) [0.524] 9.251 (0.394) [23.469] 0.320 (0.215) [1.487] 0.022 (0.370) [ 0.060] 0.521 (0.364) [ 1.428] 0.568 (0.422) [1.345]
Table 8 Duration gap Bank
Note: Terms within first brackets ( ) show standard errors and terms within third brackets [ ] show t-statistics.
Table 7 Correlation matrix
Repo 91 dtb 182 dtb 364 dtb
Income Money Market and Derivatives Association – FIMMDA) using Best Fit and simulated 1000 values of the spread using @Risk. These values were added to the simulated PLR to obtain the discount rates for all assets.Finally, we subtracted the original (current) values of the deposit rate and PLR from their simulated values (including spread over PLR) to obtain 1000 simulated values of first differences in deposit rate and PLR. These rate shocks were given to assets and liabilities in our EVE analysis. Step 5: Computation of change in EVE at the 99% confidence level We used the Rate Sensitive Gap Statements of 11 Indian banks to compute their Economic Value of Equity (EVE) for each year. Each of the 1000 simulated values of the driven variables, as computed in Step 3, was used to shock the base interest rate each year, to compute the change in EVE. The 99th percentile of the change in EVE was chosen as the unexpected loss in EVE for each bank. The duration gap profile of the banks, indicating the potential exposure to interest rate shock, is as follows (see Tables 8,9).
Repo
91 dtb
182 dtb
364 dtb
1 0.94795 0.944798 0.954531
1 0.983869 0.986886
1 0.987587
1
of driver variables, we simulated 1000 values of each driven variable. A regression coefficient converts the simulated value of a driver variable into a simulated value of its driven variable. For all our simulations, we used @Risk3 (At-Risk), a standard simulation software from Palisade Corporation (see Table 7). Step 4: Simulation of Spread over PLR To add the credit spread to PLR, we identified the distribution of the spread over PLR (collected from Fixed 3 @Risk is a Windows based software (of Palisade Corporation) for Monte Carlo Simulation, that supports a number of statistical distributions. Correlation among input distributions can be defined to incorporate the dependence structure among them.
Bank-1 Bank-2 Bank-3 Bank-4 Bank-5 Bank-6 Bank-7 Bank-8 Bank-9 Bank-10 Bank-11
Year 2002
2003
2004
0.557 0.534 0.738 1.614 0.825 0.645 0.170 0.430 0.863 n.a n.a
0.838 0.897 0.530 1.124 1.016 0.971 0.107 0.976 0.830 n.a n.a
0.858 0.979 1.409 1.322 1.001 0.951 0.611 0.915 n.a. 0.952 0.245
Table 9 EVE impact (Rs. crores) Bank
Bank-1 Bank-2 Bank-3 Bank-4 Bank-5 Bank-6 Bank-7 Bank-8 Bank-9 Bank-10 Bank-11
Year 2002
2003
2004
792.561 1079.272 1048.482 779.012 626.989 1104.471 800.733 840.766 3341.196 n.a n.a
1132.148 1326.537 1057.504 702.482 771.384 1713.132 948.405 769.969 3737.161 n.a n.a
1183.627 1475.475 2150.607 900.455 753.784 1790.278 1536.979 958.689 n.a. 1136.770 1905.577
(Rs. 1 crore = Rs. 10 million = USD 0.222 million).
A. Saha et al. / European Journal of Operational Research 193 (2009) 581–590 Table 10 EVE impact as percent of MVRSA Bank
Bank-1 Bank-2 Bank-3 Bank-4 Bank-5 Bank-6 Bank-7 Bank-8 Bank-9 Bank-10 Bank-11
Appendix 1. Data definition and sources
Year 2002 5.195 8.298 5.668 9.471 6.188 5.978 3.195 5.430 6.476 n.a. n.a.
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2003 6.345 9.284 5.337 7.481 7.288 7.394 3.694 4.382 6.266 n.a. n.a.
2004 6.076 9.153 8.509 8.376 6.878 7.046 4.874 4.441 n.a. 6.577 3.866
In order to make the EVE profile independent of size and hence comparable, we divided the EVE of each bank by its Market Value of Rate Sensitive Asset (MVRSA) for each year. The results are as follows (see Table 10). It is clear that our EVE losses (as a proportion of MVRSA) are much higher than those in Patnaik and Shah (2004). For instance, their lowest loss is 1.1%, while ours is 3.195% (Table 10, Bank 7, year 2002). Their highest loss is 4.4%, ours is 9.471% (Table 10, Bank 2, year 2002). We attribute this to basis risk – our analysis suggests that asset rate shocks are much stronger than liability rate shocks. Moreover, almost all banks (except bank 8) have positive duration gaps. Therefore, asset values fall much more than liability values. 4. Conclusions Banking book IRR has not been studied in detail, especially in developing countries. As banks in these countries gear up to meet the deadlines for implementation of Basel II, they must pay close attention to the duration mismatches in their accrual books and the consequent threat to EVE. In one of the first studies on estimating banking book IRR in a developing country like India, apart from repricing risk, we find evidence of significant basis risk between PLR and deposit rate shocks. This leads to very large EVE losses for our sample banks. Being oblivious to such EVE reduction would lead to serious erosion of capital and future earnings. This implies that pursuit of myopic, NII based, ALM policies by Indian banks would distort product pricing and hence the balance sheet structure over time. The results of the study have regulatory policy implications as well. Interest rate volatility, in developing counties like India, has made Asset–Liability Management extremely challenging. The task becomes all the more difficult with the advent of international best practices, under the rubric of Basel II. To get a complete picture of vulnerability of Indian banks to interest rate fluctuations, we plan to incorporate yield curve risk and options risk in our future work.
Variables CRR
Definition
Cash Reserve Ratio BRATE Bank rate set by RBI PLR Prime Lending Rate DEPO Deposit rate CALLB Call Borrowing CALL Call Lending REPO Average of Repo rates WPI Wholsale Price Index 14DTB Yield on 14 day tbill 91DTB Yield on 91 day tbill 182DTB Yield on 182 day t-bill 364DTB Yield on 364 day t-bill MIBID14D 14-day Mumbai Inter-bank Bid rate (MIBID) MIBOR14D 14-Day Mumbai Inter-bank Offer rate (MIBOR) MIBID1M 1 month MIBID MIBOR1M 1 month MIBOR MIBID3M 3 month MIBID MIBOR3M 3 month MIBOR MIBIDON Overnight MIBID MIBORON Overnight MIBOR ZER1-25 Zero coupon yield for 1–25 year maturity
Source RBI Weekly Statistical Supplement (WSS) RBI WSS RBI WSS RBI RBI RBI RBI
WSS WSS WSS WSS
RBI WSS RBI WSS RBI WSS RBI WSS RBI WSS National Stock Exchange (NSE) website NSE website
NSE NSE NSE NSE NSE
website website website website website
NSE website Computed based on parameters provided in NSE website
References Basel Committee on Banking Supervision (BCBS), 2004a. Basel II: International Convergence of Capital Measurement and Capital Standards: A Revised Framework, June 2004. Basel Committee on Banking Supervision (BCBS), 2004b. Principles for the Management and Supervision of Interest Rate Risk, July 2004. English, W., 2002. Interest rate risk and bank net interest margins. BIS Quarterly Review (December), 67–82. Flannery, M., 1981. Market interest rates and commercial bank profitability: An empirical investigation. Journal of Finance 36, 1085–1101. Flannery, M., 1983. Interest rates and bank profitability: Additional evidence. Journal of Money, Credit and Banking 15, 355–362.
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Flannery, M., James, C., 1984a. The effect of interest rate changes on the common stock returns of financial institutions. Journal of Finance 39, 1141–1153. Flannery, M., James, C., 1984b. Market evidence on the effective maturity of bank assets and liabilities. Journal of Money, Credit and Banking 16, 435–445. Granger, C., 1980. Testing for causality: A personal viewpoint. Journal of Economic Dynamics and Control 2, 329–352. Granger, C., 1988. Some recent developments in a concept of causality. Journal of Econometrics 39, 199–211. Johnston, J., DiNardo, J., 1997. Econometric Methods, fourth ed. McGraw-Hill, Singapore. Maes, K., June 2004. Interest Rate Risk in the Belgian Banking Sector. Financial Stability Review, National Bank of Belgium, pp. 157–179. Mahshid, D., Naji, M., 2004. Managing Interest Rate Risk: A Case Study of Four Swedish Savings Banks. School of Economics and Commercial Law. Goteborg University. Patnaik, I., Shah, A., 2004. Interest Rate Volatility and Risk in Indian Banking. IMF Working Paper No. WP/04/17. International Monetary Fund, January.
Purnanandam, A., 2005. Interest Rate Risk Management at Commercial Banks: An Empirical Investigation, May 2005. Available from: