Demand Deposits: Valuation and Interest Rate Risk Management

YANG LU KEVIN VISVANATHAR

Master of Science Thesis Stockholm, Sweden 2015

Avistakonton: Värdering och Ränteriskhantering

YANG LU KEVIN VISVANATHAR

Examensarbete Stockholm, Sverige 2015 Avistakonton: V¨arderingoch R¨anteriskhantering

Yang Lu Kevin Visvanathar

Examensarbete INDEK 2015:29 KTH Industrial Engineering and Management Industrial Management SE-100 44 STOCKHOLM Demand Deposits: Valuation and Interest Rate Risk Management

Yang Lu Kevin Visvanathar

Master of Science Thesis INDEK 2015:29 KTH Industrial Engineering and Management Industrial Management SE-100 44 STOCKHOLM Sammanfattning

Till f¨oljdav finanskrisen 2008 har regulatoriska myndigheter inf¨ortmer strikta regelverk f¨or att fr¨amjaen sund finansiell riskhantering hos banker. Trots avistakontons ¨okade betydelse f¨orbanker har inga regulatoriska riktlinjer introducerats f¨orhur den associerade r¨anterisken ska hanteras ur ett riskperspektiv. Avistakonton ¨arf¨orknippademed tv˚afaktorer som f¨orsv˚ararutv¨arderingenav dess r¨anterisk med traditionella r¨anteriskmetoder: de saknar en f¨orutbest¨amdl¨optidoch avistar¨antan kan ¨andrasn¨ars˚abanken ¨onskar. Med h¨ansyn till detta gap fokuserar denna studie p˚aatt empiriskt analysera tv˚amodelleringsramverk f¨oratt v¨arderaoch m¨atar¨anterisken hos avistakonton: Economic Value Model Framework (EVM) and Replicating Portfolio Model Framework (RPM). Analysen genomf¨orsgenom att initialt ta fram modeller f¨orhur avistar¨antan och volymen p˚aavistakonton utvecklas ¨over tid med hj¨alp av ett modernt och unikt dataset fr˚anen av Sveriges st¨orstakommersiella banker. Studiens resultat indikerar att modellerna f¨oravistar¨antan och avistavolymen inte f¨orb¨attras n¨armakroekonomiska variabler ¨arinkluderade. Detta ¨ari kontrast till vad tidigare studier har f¨oreslagit.Vidare visar studiens resultat att det modellerna skiljer sig n¨aravistakontona ¨arsegmenterade p˚aen mer granul¨arniv˚a.Slutligen p˚avisarresultatet att EVM producerar r¨anteriskestimat som ¨armindre k¨ansligaf¨orantanganden ¨anRPM.

Nyckelord: avistakonton, r¨anterisk, marknadsr¨anta, stokastisk simulering, nuv¨arde,rep- likerande portf¨olj,sparkonto, transaktionskonto

i Abstract

In the aftermath of the financial crisis of 2008, regulatory authorities have implemented stricter policies to ensure more prudent risk management practices among banks. Despite the growing importance of demand deposits for banks, no policies for how to adequately account for the inherent interest rate risk have been introduced. Demand deposits are as- sociated with two sources of uncertainties which make it difficult to assess its risks using standardized models: they lack a predetermined maturity and the deposit rate may be changed at the bank’s discretion. In light of this gap, this study aims to empirically in- vestigate the modeling of the valuation and interest rate risk of demand deposits with two different frameworks: the Economic Value Model Framework (EVM) and the Replicating Portfolio Model Framework (RPM). To analyze the two frameworks, models for the demand deposit rate and demand deposit volume are developed using a comprehensive and novel dataset provided by one the biggest commercial banks in Sweden. The findings indicate that including macroeconomic variables in the modeling of the deposit rate and deposit volume do not improve the modeling accuracy. This is in contrast to what has been suggested by previous studies. The findings also indicate that there are modeling differences between demand deposit categories. Finally, the EVM is found to produce interest rate risks with less variability compared to the RPM.

Keywords: demand deposits, interest rate risk, market interest rate, stochastic simulation, economic value, replicating portfolio, savings account, transaction account

ii Acknowledgement

We would like to express our gratitude for all the received support during this thesis. First, we would like to thank Max Loxbo and Carl L¨onnbark for the introduction of this topic and their continuous support throughout this process. Furthermore, we would also like to thank our supervisor Gustav Martinsson at the Royal Institute of Technology for his invaulable advice and support. Finally, we would like to express our gratiude to our families and friends for their constant support.

Stockholm, May 2015 Yang Lu & Kevin Visvanathar

iii Contents

List of Figures vi

List of Tables vii

List of Definitions viii

1 Introduction 1 1.1 Background ...... 1 1.1.1 Current Practices ...... 3 1.2 Problem Discussion ...... 4 1.3 Purpose and Research Questions ...... 5 1.4 Delimitations ...... 5 1.5 Contributions ...... 6 1.6 Disposition ...... 6

2 Literature Review 7 2.1 Market Competition and Implications for Demand Deposits ...... 7 2.2 Economic Value Model Framework (EVM) ...... 8 2.3 Replicating Portfolio Model Framework (RPM) ...... 10

3 Theoretical Framework 12 3.1 Market Interest Rate Models ...... 12 3.2 Economic Value Model Framework (EVM) ...... 13 3.2.1 SARIMAX ...... 14 3.2.2 Box-Jenkins Model Fitting ...... 16 3.2.3 Interest Rate Risk ...... 18 3.3 Replicating Portfolio Model Framework (RPM) ...... 19 3.3.1 Interest Rate Risk ...... 20

4 Methodology 21 4.1 General Method ...... 22 4.1.1 Demand Deposit Categorization ...... 23 4.2 Market Interest Rate Model ...... 23 4.3 Economic Value Model Framework (EVM) ...... 24 4.3.1 Deposit Rate Model ...... 25 4.3.2 Deposit Volume Model ...... 25 4.3.3 Interest Rate Risk ...... 26 4.4 Replicating Portfolio Model Framework (RPM) ...... 27

iv 4.4.1 Interest Rate Risk ...... 28 4.5 Limitations ...... 29 4.6 Reliability and Validity ...... 29

5 Data 31 5.1 Deposit Volumes ...... 31 5.2 Deposit Rates ...... 32 5.3 Macroeconomic Variables ...... 33 5.3.1 Unemployment Rate ...... 33 5.3.2 Gross Domestic Product ...... 34 5.3.3 Monetary Aggregate ...... 34 5.3.4 Market Concentration ...... 35 5.4 Market Interest Rate Securities ...... 35

6 Results and Analysis 37 6.1 Market Interest Rate Model ...... 37 6.2 Economic Value Model Framework (EVM) ...... 38 6.2.1 Deposit Rate Model ...... 39 6.2.2 Deposit Volume Model ...... 43 6.2.3 Interest Rate Risk ...... 50 6.3 Replicating Portfolio Model Framework ...... 52 6.3.1 Portfolio Construction ...... 53 6.3.2 Interest Rate Risk ...... 56

7 Discussion 58 7.1 Model differences: Account and Client Categories ...... 58 7.2 Interest Rate Risk Comparison of EVM and RPM ...... 60 7.3 Sustainability ...... 63

8 Conclusion 64

References 66

Appendix 69 Appendix A - Complementing Data ...... 69 Appendix B - Model Parameter Diagnostics ...... 73 Appendix C - Model Residual Correlation Plots ...... 75

v List of Figures 4.1 Methodology Flow Chart ...... 21 5.1 Deposit Volume Data ...... 32 5.2 Deposit Rate Data ...... 33 5.3 Market Interest Rate Securities Data ...... 36 6.1 Modeled STIBOR 1-Month ...... 38 6.2 Modeled Deposit Rates: Aggregate ...... 41 6.3 Modeled Deposit Rate: Categorized ...... 41 6.4 Modeled Deposit Volume: SA Aggregate ...... 46 6.5 Modeled Deposit Volume: TA Aggregate ...... 46 6.6 Modeled Deposit Volume: SA Private ...... 47 6.7 Modeled Deposit Volume: SA Corporate ...... 47 6.8 Modeled Deposit Volume: TA Private ...... 48 6.9 Modeled Deposit Volume: TA Corporate ...... 48 A.1 Deposit Volume Data: SA Private ...... 69 A.2 Deposit Volume Data: SA Corporate ...... 69 A.3 Deposit Volume Data: TA Private ...... 70 A.4 Deposit Volume Data: TA Corporate ...... 70 A.5 Unemployment Data ...... 71 A.6 Gross Domestic Product Data ...... 71 A.7 Monetary Aggregate Data ...... 72 A.8 The market Concentration Data ...... 72 C.9 Deposit Volume ACF and PACF: SA Aggregate ...... 75 C.10 Deposit Volume ACF and PACF: TA Aggregate ...... 75 C.11 Deposit Volume ACF and PACF: SA Private ...... 76 C.12 Deposit Volume ACF and PACF: SA Corporate ...... 76 C.13 Deposit Volume ACF and PACF: TA Private ...... 77 C.14 Deposit Volume ACF and PACF: TA Corporate ...... 77 C.15 Deposit Rate ACF and PACF: SA Aggregate ...... 78 C.16 Deposit Rate ACF and PACF: TA Aggregate ...... 78 C.17 Deposit Rate ACF and PACF: SA Private ...... 79 C.18 Deposit Rate ACF and PACF: SA Corporate ...... 79 C.19 Deposit Rate ACF and PACF: TA Private ...... 80 C.20 Deposit Rate ACF and PACF: TA Corporate ...... 80

vi List of Tables 6.1 Fitted Market Interest Rate Model ...... 37 6.2 Fitted Deposit Rate Models ...... 40 6.3 Evaluation of Deposit Rate Models ...... 42 6.4 Fitted Deposit Volume Models ...... 44 6.5 Evaluation of Deposit Volume Models ...... 50 6.6 Interest Rate Risk for EVM ...... 51 6.7 Portfolio Constructions - Aggregate Level ...... 54 6.8 Portfolio Constructions - Saving Accounts ...... 55 6.9 Portfolio Constructions - Transaction Accounts ...... 56 6.10 Interest Rate Risk for the RPM ...... 57 B.1 Deposit Rate Model Combinations ...... 73 B.2 Deposit Volume Model Combinations ...... 74

vii List of Definitions

Corporate Accounts - Accounts held by firms and used for business related purposes.

Demand Deposits - Deposits that may be withdrawn at any given point in time and the offered deposit rate may be changed at the bank’s discretion.

Deposit Liability - The net deposit liability banks’ owe customers. Defined as the current deposited capital less the expected present value of future rents.

Deposit Rate - The rate customers earn from depositing capital in demand deposits ac- counts.

Deposit Volume - The total amount of capital deposited in demand deposits accounts.

EVM - Economic Value Model Framework. A framework used for valuing and measuring the interest rate risk in demand deposits.

HHI - Herfindahl-Hirschman Index. A commonly used measure for estimating the market concentration.

IRE - Interest Rate Elasticity. A measure of the interest rate risk which is used in the EVM.

M0 - A measure of the monetary aggregate in an economy. Defined as the total amount of physical cash and coins.

Private Accounts - Accounts held by individuals for personal use.

Deposit Rent - The net cash flow banks receive from investing deposited capital in a short term market security less the deposit rate paid.

RPM - Replicating Portfolio Model Framework. A framework used for valuing and mea- suring the interest rate risk in demand deposits.

SA - Saving Accounts. Accounts that enable parties to save money for a prolonged period to high interest rate.

STIBOR - Stockholm Interbank Offered Rate, which is the average rate banks at the Swedish Market are willing to lend to each other without demanding collateral.

TA - Transaction Accounts. Typically used for everyday banking needs.

viii 1 Introduction

This section serves to introduce the reader to this study. First, a background of the problem area is presented followed by a deeper discussion of the problem and its relevance. The purpose and aim of the study is then presented, which is broken down into two research questions. Next, the delimitations and contributions of the thesis are discussed. The section is concluded with a brief synopsis of the disposition for the remainder of the paper.

The purpose of this study is to empirically evaluate the modeling of the valuation and in- terest rate risk in demand deposits. Two sets of frameworks are investigated: the Economic Value Model Framework (EVM) and the Replicating Portfolio Model Framework (RPM). Demand deposits, such as savings accounts and transaction accounts, do not have a prede- termined maturity and the offered deposit rate may be changed at the bank’s discretion. These intrinsic properties make demand deposits difficult to model and quantify the asso- ciated risks. This topic is of interest since the absence of a generally accepted model has prompted regulatory authorities to recommend a conservative approach for managing the inherent risk in demand deposits, which is suboptimal for banks. This study constructs and analyzes models for valuing and estimating the interest rate risk in demand deposits using a unique, comprehensive and novel dataset provided by one the biggest commercial banks in Sweden.

1.1 Background

One of the primary functions for commercial banks is enabling people and firms to save capital while also providing access to financial markets (Swedish National Bank, 2014). This allows parties to save capital for future needs and provides opportunities to borrow capital for immediate investment needs. Banks1 are able to generate profits from the spread in the interest rate earned from outstanding loans and the deposit rate paid to customers for depositing capital, as the deposit rates paid are typically below the market interest rate.

To finance the outstanding loans, banks have two main sources of short-term funding avail- able: capital deposited by its customers and issued securities such as bonds. Traditionally, transforming issued securities to provide lending have been a more expensive alternative than transforming deposited capital. While deposits typically are a source of cheaper fund- ing, they also expose banks to risks as deposits and loans mature at different points in time.

1The word “banks” refers to commercial banks unless otherwise stated.

1 Banks normally control the risks through Asset and Liability Management (ALM). Deposits are typically seen among banks’ liabilities while outstanding loans are regarded as assets. ALM oversees the process of effectively managing risks arising due to mismatches between assets and liabilities, while also finding the optimal allocation mix of assets and liabilities for funding the institution’s operations and maximizing profits.

For Sweden’s four biggest commercial banks, the net interest rate income, generated by their assets and liabilities constitutes on average 61% of their total income.2 The transformation of deposited funds into loans is of importance because 54% of Swedish banks’ liabilities are represented by deposits from customers and 63% of the banks’ assets are loans (Statistics Sweden (SCB), 2014).

There are two main risk categories associated with demand deposits: liquidity risk and in- terest rate risk. This paper focuses on the interest rate risk which reflects banks’ sensitivity to changes in interest rates (Swedish Supervisory Financial Authority (SFSA), 2014). It is defined as the risk that an investment’s value will change as a result of changes in interest rates. Usually, this is reflected in the fact that the interest rates used to calculate an invest- ment’s present value changes, thus affecting the present value. With demand deposits, the interest rate risk is also manifested in the fact that changing interest rates could also affect customer behavior. For example, increasing market interest rates might lead to customers withdrawing money and seeking more profitable alternatives elsewhere. In contrast, the liquidity risk is the risk that a bank might not have enough capital to appease withdrawals caused by other factors than interest rate changes.

Due to the unique uncertainties in future deposit rates and volumes3, it is notoriously difficult to value demand deposits and quantify the associated risks. There is no generally accepted method as of yet, despite a range of sophisticated methods being suggested in previous studies. This could potentially be due to the fact that this area has not been regulated until very recently, resulting in banks sticking to simpler (and to some degree inadequate) methods rather than dedicating enough resources to understand and implement the more sophisticated ones.

2Computed as an unweighted average of the net interest rate income’s share of the total income in 2014 for Sweden’s biggest four banks: Nordea (72%), SEB (42%), Handelsbanken (71%) and Swedbank (58%). The numbers in the parentheses are the corresponding share for respective bank. All relevant figures are provided in the income statement in each bank’s annual report for the fiscal year 2014. 3Volume refers to the monetary value, also known as balance.

2 1.1.1 Current Practices

The Basel II accord issued by the Basel Committee on Banking Supervision (BCBS) under- lines the importance of modeling deposit rates and volumes in order to accurately report interest rate risk in the banking book4. The absence of a generally accepted valuation and interest rate risk model for demand deposits prompted BCBS (2004) to review contempo- rary practices among banks. BCBS (2004) identified three methods banks typically use: gap analysis, duration based methods and simulation techniques.

The simplest method, gap analysis, uses a maturity schedule to distribute the interest rate sensitive assets to pre-determined “time bands” (BCBS, 2004). A “time band” is an estimation of the time the demand deposit will remain at the bank. The interest rate risk exposure is evaluated by subtracting the interest rate sensitive liabilities from corresponding asset for each “time band”. This produces a “gap” informing of the expected change in net interest income from an interest rate movement (BCBS, 2004). For instance, a negative gap, i.e. when the liabilities exceed the assets, implies that an increase in market interest rate may have a negative effect on banks’ net interest income. Moreover, as all assets in a given “time band” are assumed to mature simultaneously, this method neglects variations in characteristics for the assets within a “time band” (BCBS, 2004). Furthermore, gap analysis does not consider differences in the spread between market interest rates and deposit rates that might occur due to market interest rates movements and its affect on customer behavior (BCBS, 2004).

An alternative approach used in conjunction with “time bands” are duration based methods (BCBS, 2004). Duration is a measure of the sensitivity of the value of an asset to changes in market interest rates. This class of methods assign a sensitivity weight to each “time band” that is determined by estimating the duration of the assets and liabilities for respective “time-band”. Duration based methods are prevalent among Japanese banks (Bank of Japan (BOJ), 2014). Like gap analysis, this approach suffers from the arbitrary construction of the “time bands” (BCBS, 2004; BOJ, 2014).

To address the shortcomings of the previous approaches, some banks use simulation tech- niques (BCBS, 2004). This approach estimates the interest rate risk on simulated future scenarios regarding the development of demand deposits. It is considered more complex as it typically requires a model for the dynamics of the deposit volume, deposit rate, and market interest rate (BCBS, 2004). Due to the complexity, banks prefer to use a combination of gap analysis and duration based approaches as described above (BCBS, 2004).

4The banking book is an accounting term that refers to assets on a bank’s balance sheet that are expected to be held to maturity.

3 The two most prevalent models in previous studies are the economic value model framework, henceforth EVM (Hutchison and Pennacchi, 1996; Jarrow and van Deventer, 1998; Nystr¨om, 2008) and the replicating portfolio model framework, henceforth RPM (Kalkbrener and Willing, 2004; Maes and Timmermans, 2005). Both frameworks are based on simulation techniques. The aim of the EVM is to estimate the net present value of the cash flows that a bank receives from investing the demand deposits at a market interest rate minus the deposit rate paid for the deposits (Hutchison and Pennacchi, 1996; Jarrow and van Deventer, 1998). The economic value is usually seen as the sum of the present value of these expected net cash flows (BCBS, 2004). Interest rate risk is typically estimated by examining how changes in market interest rates affect the economic value (Hutchison and Pennacchi, 1996; O’Brien, 2000). In contrast, the RPM aims to estimate the margin banks may earn by investing the demand deposits in a replicating portfolio consisting of market interest rate securites with finite maturities (Kalkbrener and Willing, 2004). The interest rate risk is typically measured by analyzing the duration of the replicating portfolio (Kalkbrener and Willing, 2004; Maes and Timmermans, 2005). There exists a need for empirical evaluation of both frameworks since previous studies mainly focus on the theoretical aspects.

1.2 Problem Discussion

In recent years, demand deposits have become an increasingly important part of banks’ ALM. Constituting a substantial share of banks’ funding source, it is necessary to understand the intrinsic properties of demand deposits. Since the future volumes and deposit rates of demand deposits are unknown, correctly incorporating demand deposits into ALM and capital and funding planning poses a significant challenge as it requires a clear understanding of the underlying risks.

In the wake of the 2008 financial crisis, supervisory authorities have increased the monitoring of banks’ management regarding demand deposits. The continued absence of a generally accepted model for estimating the value and maturity of demand deposits have contributed to the SFSA adopting a conservative approach, recommending the repricing date5 to be set at zero years for all demand deposits (SFSA, 2014). Although demand deposits may be withdrawn at the customers’ discretion, a substantial part of the demand deposit volume can usually be found relatively stable over time as seen in historical data, which banks refer to as core deposits (Kalkbrener and Willing, 2004). Thus, setting the repricing date to zero years may result in banks missing out on the potentially higher returns typically associated with investments in long maturity securities. On the other hand, setting a repricing date

5The repricing date is the date at which an asset or liability is revalued. For instance, a repricing date of zero years implies that the value of an asset is reestimated continuously.

4 too distant into the future implies that the banks can tie up their capital in investments with longer maturities. These uncertainties may result in increased maturity mismatches between assets and liabilities (Goldstein and Pauzner, 2005; Dermine, 2015). By postponing the repricing date into a distant future, banks may not be able to meet unpredictable future withdrawals from demand deposits. This in turn increases banks’ exposure towards panic- based bank runs, i.e. bank runs occurring when all depositors withdraw simultaneously believing the bank will fail.

It can also be misleading to view demand deposits as one unified category, as both savings accounts and transaction accounts count as demand deposits but have different purposes and dynamics such as deposit rates. Since the pressures from regulatory authorities are relatively new, there has not been a need to properly model the behavior of demand deposits until recently. There is thus a knowledge gap in this area, both in theory and in practice, considering its importance for financial institutions.

1.3 Purpose and Research Questions

The purpose of this study is to empirically evaluate the modeling of the valuation and interest rate risk in demand deposits. The goal of this study is to examine the following:

♦ How can demand deposit rates, volumes, and interest rate risk be modeled?

The foundation of this study is composed of the two sets of frameworks: the Economic Value Model (EVM) and the Replicating Portfolio Model (RPM). Furthermore, given that demand deposits come in different shapes, the following research questions are formulated to assist in reaching the goal of this study:

♦ RQ1: How does the modeling of demand deposit rates and volumes differ between account and client categories?

♦ RQ2: How do the interest rate risk estimations from the EVM compare to those of the RPM?

1.4 Delimitations

A number of delimitations is required for the implementation of this thesis. First, this study is solely focusing on the Swedish demand deposits market. Thus, the analysis is subject to

5 the Swedish regulatory setting which may not necessarily extend to other jurisdictions. This study does not investigate the effect of different regulatory settings on the demand deposits market. Second, the lack of a generally accepted framework for valuing demand deposits and its corresponding interest rate risk has resulted in the development of several different frameworks by both practitioners and academics. The scope of this study is delimited to only focus on investigating the two most prevalent frameworks in the academic literature.

1.5 Contributions

This study is of interest both from a practical and theoretical perspective. The practical contribution of this study are modeling frameworks for valuing and assessing the interest rate risk in demand deposits based on the latest research. Thus, it complements and im- proves banks’ current risk management practices, particularly for Swedish banks. From a theoretical perspective, the contribution is threefold: first, this study provides an update of an arguably outdated research field using a novel and comprehensive dataset. Secondly, this study extends existing body of knowledge by considering macroeconomic factors in extended time series models for the deposit rate and volume. Finally, the separation of demand deposits into client categories provides additional unique insights.

1.6 Disposition

The remainder of this study is structured as follows: Section 2 reviews the relevant literature regarding the modeling of demand deposits. Section 3 presents the theoretical framework that this study is based upon, including an extensive description of the EVM and the RPM. Section 4 presents the methodology and discusses its limitations, validity and reliability. Section 5 describes the examined data. This entails a detailed review of the dataset regarding the demand deposit rates and volumes that are provided by the case bank. Section 6 presents and analyzes the obtained results. Section 7 discusses the findings with respect to each research question. This section is concluded with a discussion regarding the implications of the findings from a sustainability perspective. Section 8 concludes this study by summarizing the results in the context of the main goal of this study, with additional suggestions for future research.

6 2 Literature Review

This paper contributes to the existing literature regarding the valuation and interest rate risk management of demand deposits. In general, the literature on this topic is relatively scarce and somewhat outdated (Hutchison and Pennacchi, 1996; Jarrow and van Deventer, 1998; O’Brien, 2000; Frauendorfer and Sch¨urle, 2003). This paper extends the existing literature by empirically analyzing the two most prominently discussed frameworks, the EVM and the RPM, using a comprehensive and novel dataset. The outline for the remainder of the section is as follows: next, a review of past studies examining how market competition affects the demand deposit market is presented. This is followed by a review of the EVM and the RPM for managing the interest rate risk in demand deposits.

2.1 Market Competition and Implications for Demand Deposits

In order to develop models that are able to capture the dynamics of demand deposits adequately, it is important to understand how banks’ demand deposit products are affected by the competitive environment. Neumark and Sharpe (1992) are among the first to study how banks’ offered deposit rates are affected by market concentration. The authors find banks in concentrated markets to be more rigid in increasing deposit rates, i.e. showing delayed reactions to rising market interest rates, while being more responsive with lowering deposit rates in response to declining market interest rates (Neumark and Sharpe, 1992). This behavior can be seen as banks exercising market power, allowing banks to maximize the spread between offered deposit rates and market interest rates which in turn improves their profits. This sort of imperfect competition is attributed to the fact that customers, i.e. the depositors, face search and switching costs, hindering them from moving their money to other banks (Neumark and Sharpe, 1992).

Rosen (2007) extends Neumark and Sharpe’s (1992) research by also analyzing how the market size structure of a local market, the presence of multimarket banks, and the bank’s size affect the offered deposit rates. Market size structure of a local market is defined as the distribution of market shares of banks of different sizes (Rosen, 2007). Rosen’s (2007) findings support Neumark and Sharpe’s (1992) conclusion of banks taking advantage of customers’ information disadvantage when setting the deposit rate. The author also provide evidence of banks competing more intensely against other banks of a similar size and that large banks generally tend to offer lower deposit rates than small banks (Rosen, 2007). Lastly, Rosen (2007) finds the market size structure of a local market and the bank size to have a larger effect on banks’ offered deposit rates than the market concentration at a local

7 market level. This is also supported by Hannan and Prager (2006) who find the offered deposit rates for multi-market banks to depend more on the market concentration at a state market level than at a local market level.

Overall, past studies are in unison of market competition having a significant effect on banks’ offered deposit rates. Though all the above reviewed studies focus on the American market, Swedish banks are also likely to consider the competitive environment when determining the deposit rate. The evidence of a significant relationship between market competition and deposit rates (Neumark and Sharpe, 1992; Hannan and Prager, 2006; Rosen, 2007) may be necessary to account for in modeling the deposit rate.

2.2 Economic Value Model Framework (EVM)

This section reviews the literature regarding the EVM for valuing demand deposits and estimating the associated interest rate risk. Past studies primarily focus on the theoretical development of interest rate risk management for demand deposits (Hutchison and Pennac- chi, 1996; Jarrow and van Deventer, 1998; Nystr¨om,2008).

In their seminal paper, Hutchison and Pennacchi (1996) develop an analytical valuation framework for demand deposits under an equilibrium-based approach. The framework con- sists of a model for the market interest rate, deposit volume, deposit rate, and interest rate risk respectively.6 The market interest rate is assumed to be the only source of risk (Hutchison and Pennacchi, 1996). The deposit volume is assumed to be dependent on the deposit rate, market interest rate and other exogenous factors affecting the volume such as macroeconomic factors (Hutchison and Pennacchi, 1996). Analogously, the deposit rate is suggested to be a function of market interest rate and other exogenous factors (Hutchi- son and Pennacchi, 1996). The interest rate risk is measured by analyzing the change in the deposit liability7 due to a parallel shift of the market interest rate of 100 basis points (bps).

Jarrow and van Deventer (1998) is another influential paper in the EVM literature. In contrast to Hutchison and Pennacchi (1996), the authors solely focus on the theoretical development of a valuation model for demand deposits and credit card loans under an arbitrage-free setting. Jarrow and van Deventer (1998) shows the deposit rent may be modeled as an exotic interest rate swap when the deposit volume is only dependent on the

6From henceforth, deposits will refer to demand deposits unless stated otherwise. 7The deposit liability is defined as the initial deposit volume less the present value of all future rents. Rent is the net cash flows a bank receives from investing the deposits at a market interest rate less the deposit rate paid to depositors (Hutchison and Pennacchi, 1996; Jarrow and van Deventer, 1998).

8 market interest rate.

Nystrom (2008) extends Jarrow and van Deventer’s (1998) work by developing specific models for the deposit rate and deposit volume respectively. Nystrom (2008) proposed deposit rate model is able to capture how the offered deposit rate is affected by banks favoring customers who deposit large sums. Furthermore, Nystrom’s (2008) proposed deposit volume model is able to capture differences in customer behavior. The completeness of Nystrom’s (2008) suggested models for the deposit rate and the deposit volume makes the models significantly more complex than the ones proposed by Hutchison and Pennacchi (1996), and consequently more difficult to implement in practice.

Hutchison and Pennacchi’s (1996) and Jarrow and van Deventer’s (1998) main contribution is an analytical solution for valuing and measuring interest rate risk in demand deposits. Frauendorfer and Sch¨urle (2003) argue that the analytical solutions are based on simplify- ing and to some extent inadequate assumptions. In contrast to Hutchison and Pennacchi (1996) and Jarrow and van Deventer (1998), O’Brien (2000) develops a numerical model for deposit volume and deposit rate. A prevalent assumption in Hutchison and Pennacchi’s (1996) model is that the deposit rate exhibits a symmetrical behavior in response to changes in the market interest rate. O’Brien (2000) evaluates how Hutchison and Pennacchi’s (1996) assumption affects the interest rate risk estimates by also considering an asymmetric behav- ior of deposit rate changes in the analysis. The asymmetric behavior of the deposit rate is supposed to capture the observed tendency of banks to quickly lower deposit rates during declining market interest rates while being slower with increasing the deposit rates when market interest rates increase (Neumark and Sharpe, 1992; O’Brien, Orphanides and Small, 1994; Rosen, 2007). O’Brien (2000) finds that the estimated interest rate risk is reduced when the deposit rate exhibits a symmetrical behavior. O’Brien’s (2000) findings indicate that the choice of deposit rate model may affect the estimated interest rate risk.

There has not been as much focus in previous literature regarding the impact of macroe- conomic factors on deposit volumes, which may be explained by the fact that their future values are difficult to predict. Jarrow and van Deventer (1998) suggest that unemployment rate and income level may improve the deposit volume modeling. However, no attempt is made to include the variables in their own model. O’Brien (2000) includes household in- come in the model for deposit volume, but simplifies by assuming that it exhibits a constant growth. Carmona (2007) suggests that the unemployment rate may influence the number of individuals in need of short-term funding, as the unemployed may aim to be more cautious with their capital to compensate for their loss of income. This in turn can be related to the volume of demand deposits, as demand deposits are a form of short-term funding.

9 A common characteristic in the aforementioned studies is the focus on U.S. markets. This paper extends this literature by analyzing the applicability of the EVM on a European market. Moreover, macroeconomic factors are mostly excluded in the actual analyses of the previous literature, something this paper addresses.

2.3 Replicating Portfolio Model Framework (RPM)

The aim of the RPM is to mimic the behavior of the demand deposits by constructing a portfolio of market interest rate securities whose returns resemble the deposit rate (Frauen- dorfer and Sch¨urle,2003). RPMs are typically constructed by matching the price and delta8 profile of the demand deposits (Kalkbrener and Willing, 2004) or by solving an optimization problem (Frauendorfer and Sch¨urle, 2003; Maes and Timmermans, 2005).

Maes and Timmermans (2005) construct an RPM using optimization algorithms. The ben- efit of this approach, compared to Kalkbrener and Willing’s (2004), is that no model for the deposit volume is needed. Instead, the optimization problem relies solely on the deposit rates and the market interest rate securities. As RPMs constructed using optimization is not reliant on deposit volume, a disadvantage is that the liquidity risk is not accounted for. Maes and Timmermans (2005) address this by assuming only a part of the deposit volume is invested in the RPM. The authors construct RPMs for the two different optimization cri- teria and evaluate the resulting differences on the corresponding interest rate risk estimates. The two criteria used are maximizing the risk-adjusted margin and minimizing the standard deviation of the margin between the deposit rate and the expected return of the RPM. The authors find the choice of optimization criterion to have little effect on the interest rate risk (Maes and Timmermans, 2005).

Maes and Timmermans (2005) construct their RPMs using historical data and assuming the portfolio weights are constant. Frauendorfer and Sch¨urle(2003) argue the static ap- proach as the one used by Maes and Timmermans (2005) does not adequately account for future changes in the market environment and customer behavior. Frauendorfer and Sch¨urle (2003) address the aforementioned weaknesses by creating a dynamic RPM able to consider future scenarios when determining the portfolio weights. The proposed portfolio is also able to change the portfolio weights in response to changing environments. Frauendorfer and Sch¨urle’s(2003) findings indicate that the dynamic RPM is able to mimic the behavior of the deposit rate better and generate more accurate interest rate risk estimates.

8Delta is a measure of how the price (value) of demand deposits changes with respect to a change in the underlying determinant (in this case deposit rates). For instance, a call option with a delta of 0.5 means that for every 1 SEK the underlying asset increases with the option increase in value with 0.5 SEK.

10 Dewachter (2006) compares the dynamic RPM with the EVM as proposed by Hutchison and Pennacchi (1996) and O’Brien (2000). In contrast to Frauendorfer and Sch¨urle(2003), Dewachter’s (2006) dynamic RPM does not allow the portfolio weights to change in response to changing environment. The author argues the EVM is superior to the RPM as it is not only able to compute the interest rate risk, but also the present value of the deposit liability (Dewachter, 2006). This is supported by Bardenhewer (2007) who finds that the EVM typically provides higher hedging efficiency than the RPM.

This paper contributes to aforementioned literature by extending Dewachter’s (2006) and Bardenhewer’s (2007) analysis of the two different frameworks.

11 3 Theoretical Framework

This section presents the theoretical framework that serves as a basis for this study. First, theoretical concepts for the interest rate modeling are presented. This is followed by a detailed description of the theory behind the EVM and the RPM respectively.

3.1 Market Interest Rate Models

A central aspect of demand deposit modeling, regardless of approach, is the market interest rate as it is assumed to not only be the primary driving factor behind the deposit rates and deposit volumes, but also the return which banks can invest at (Hutchison and Pennacchi, 1996; O’Brien, 2000; Kalkbrener and Willing, 2004). It is consequently essential to properly understand the different market interest rate models that are currently being used. The simulated series of future market interest rates may vary depending on which model is being used, which in turn may affect the estimated interest rate risk.

Models used in the existing literature for simulating stochastic short-term market interest rates typically exhibit mean reversion (Hutchison and Pennacchi, 1996; Jarrow and van Deventer, 1998; O’Brien, 2000; Kalkbrener and Willing, 2004). The mean reversion attribute means the interest rate will tend to move to its average over time. This attribute is crucial to capture since interest rates will most likely not increase or decrease indefinitely as this would greatly affect economic activity. This section aims to provide an overview of the Vasicek model which is used in this paper. The Vasicek model is used since it is prevalent in previous studies on demand deposits (Hutchison and Pennacchi, 1996; O’Brien, 2000), thus the reliability of this study may increase by choosing it. A commonly cited drawback of the Vasicek model is that the interest rates can take negative values (Hull, 2009). A more in-depth argument for this choice of model can be found in section 4.2.

The Vasicek model (Vasicek, 1977) is a so-called one-factor model where the movements in the interest rate are only driven by a single source of market risk. The model was the first of its kind to include mean reversion. The model itself is written as the following stochastic differential equation (Hull, 2009):

drt = a(b − rt)dt + σdWt (3.1)

where Wt is a Wiener process, which together with the standard deviation σ represent the

12 shock factor, i.e. the factor deciding the volatility of the interest rate. The drift term a(b − rt) can be interpreted as the spread between the long term mean level b and the interest rate at time t, multiplied by a, the speed of which the interest rate reverts to the long term mean.

3.2 Economic Value Model Framework (EVM)

In the EVM, the aim is to model future deposit volumes and deposit rates in order to estimate the future “rents” and in extension the value of the deposit liability. The rents are defined as the net cash flows a bank receives from investing the deposits at a short term market interest rate minus the deposit rate paid to depositors:

d Rt = Vt(rt − rt ) (3.2)

d where Rt , Vt , rt and rt is the rent, the deposit volume, the deposit rate, and the market interest rate at time t respectively. It is thus assumed in this study that banks can invest the deposit volume for a return of the short term market interest rate, which is in line with previous research (Hutchison and Pennacchi, 1996; O’Brien, 2000; Dewachter, 2006).

The deposit liability is defined as the current (t = 0) deposit volume (V0) minus the sum of the present value of all the future rents (Rk):

T X L = V0 − ZkRk (3.3) k=1

t Y 1 Z = (3.4) t (1 + 1 r ) k=1 12 k

where L is the deposit liability, T is the time horizon for the simulations, rk is the annualized market interest rate at month k and Zt is the discount factor at time t. The deposit liability is of importance since this is where the interest rate risks are of concern from the banks’ perspective.

13 3.2.1 SARIMAX

The future deposit rates and deposit volumes are modeled with the SARIMAX framework. The SARIMAX model is an extension of the more common Autoregressive model (AR), which is encountered in many of the previous studies (Jarrow and van Deventer, 1998; O’Brien, 2000; Dewachter, 2006). Apart from the AR-components, the SARIMAX model comes with an added seasonal component (S), an integrated part (I), a moving-average part (MA), and exogenous input variables (X). The SARIMAX framework allows for exogenous variables in the modeling of the deposit rate and deposit volume, respectively, which previous studies have indicated might improve the modeling accuracy (see e.g. Jarrow and van Deventer, 1998; Carmona, 2007).

The AR model is a stochastic process in which the output variable, i.e. the future values, are written as a linear combination of lagged values of itself, i.e. its previous values, plus an error term. The benefit of the AR model is that it captures both the deterministic factors and the stochastic residuals (Brockwell and Davis, 2002). The AR model of order p for the time series Yt, where p stands for the number of lags to include, takes the following form:

Φ(B)(Yt − µ) = εt (3.5)

p Φ(B) = 1 − φ1B − ... − φpB (3.6)

where µ is the mean term, εt is white noise, φ1, ..., φp are the parameters of the model, and B is the backshift operator:

i B Yt = Yt−i (3.7)

The AR model can be extended by introducing a Moving-average (MA) polynomial, result- ing in a Autoregressive-Moving-average (ARMA) model. The MA part causes the output variable to also be dependent on previous white noise, i.e. previous random shocks, whereas the AR model is only dependent on the current white noise term. This can be interpreted as a stochastic process where random shocks can have a lasting effect on the output variable over several time periods, e.g. the deposit volume taking several time periods to recover from a bank run. The ARMA model is an extension of Eq. (3.5) and (3.6) and may be

14 written as:

Φ(B)(Yt − µ) = Θ(B)εt (3.8)

q Θ(B) = 1 − θ1B − ... − θqB (3.9)

where the newly introduced θ1, ..., θq are the MA parameters and q is the order of the MA part, i.e. the number of white noise lags.

The series of white noise must be stationary in order for the ARMA model to be of any significance. The definition of stationarity is that the expected value and autocovariance function are independent of the time t (Brockwell and Davis, 2002). If the process turns out to be non-stationary, stationarity can be reached by differencing the process, e.g. modeling the change in interest rate, ∆r, instead of r itself. This differencing step is known as the integrated part (I) of the model. The ARMA model thus becomes the ARIMA model:

Φ(B)(Wt − µ) = Θ(B)εt (3.10)

k Wt = (1 − B) Yt (3.11)

where Wt is the new differenced series of Yt from the ARMA model and k is the number of differences.

When the process shows signs of seasonality, a seasonal component (S) can be included. The SARIMA model is identical to Eq. (3.10) and (3.11) except with a small modification to Eq. (3.11):

k s K Wt = (1 − B) (1 − B ) Yt (3.12)

where Wt is the new differenced series of Yt from the ARIMA model, k is the number of non-seasonal differences, K is the number of seasonal differences, and s is the length of the seasonal cycle. Another option is to directly add the AR and MA terms of the seasonal

15 cycle to Φ(B) and Θ(B) respectively.

Lastly, the X in the SARIMAX model corresponds to the exogenous input variables. Often, the output variable that is modeled will depend not only on its previous values, but also on other exogenous variables. The SARIMAX model is an extension of Eq. (3.12) and can be written as:

X Θ(B) Wt = µ + Ψi(B)Xi,t + εt (3.13) Φ(B) i

r Ψ(B) = ψ0 − ψ1B − ... − ψrB (3.14)

where Xi,t is the i:th exogenous input variable, Ψi is the polynomial backshift operator for the i:th exogenous input variable and r is the number of lags to include for the exogenous input variable.

3.2.2 Box-Jenkins Model Fitting

The parameters of the SARIMAX models is estimated using the Box-Jenkins method, which is the standard methodology when it comes to time series model fitting (Brockwell and Davis, 2002). The first step sets out to identify a suitable model. First, plots of the autocorrelation functions (ACF) of the time series of the dependent variables and exogenous variables are analyzed with regards to stationarity. If the ACF of a particular variable is exponentially decreasing for each lag, stationarity can be concluded. Otherwise, the variable is differenced until stationarity is reached. Once all the variables are stationary, the cross-correlation plots between the exogenous variables and the dependent variables are analyzed. The lag(s) with the highest cross-correlation will be chosen as the exogenous variable(s) to include in the model.

The dependent variables are then regressed on the exogenous variables without the ARMA terms. The resulting ACF and partial autocorrelation function (PACF) plots of the residuals are then analyzed. The PACF plot is analyzed first in order to determine which AR terms to include. AR terms should be included up to the lag where the PACF becomes statistically insignificant. Additionally, sudden spikes in the PACF may indicate seasonality and should thus also be included (e.g. 12 months seasonal data will show a spike in the PACF at lag 12). This process is subsequently repeated for the ACF plot to determine the MA terms.

16 After a model has been selected, the parameters for the ARMA terms and exogenous vari- ables are estimated using the conditional least squares method:

n ∞ X X 2 Minimize (xt − πixt−i) (3.15) t=1 i=1

where xt is the analyzed time series and πi are computed from:

∞ Θ(B) X = 1 − π Bi (3.16) Φ(B) i i=1 where B, Φ and Θ is the backshift operator, AR-parameters and MA-parameters respectively as defined by Eq. (3.7), (3.6) and (3.9) in section 3.2.1.

Finally, the model is validated by testing the residuals of the model. The residuals must be white noise, i.e. independent of each other and have constant mean and variance which are independent of time. The ACF and PACF plots of the final residuals are analyzed for this purpose. Furthermore, a chi-square test with the null-hypothesis that the residuals are white noise is computed using the Ljung-Box formula:

m X r2 χ2 = n(n + 2) k (3.17) m n − k k=1 where m is the lag and:

n−k P atat+k t=1 rk = n (3.18) P 2 at t=1

where at is the residual series of length n.

The constructed models are evaluated based on their standard error and Akaike Information Criterion (AIC) score. The AIC score is a commonly used measure for model selection and is a measure of how well the estimated model represent the “true” model (Brockwell and Davis, 2002). The lower the AIC score, the closer the estimated model represents the “true

17 model” (Brockwell and Davis, 2002). The formula for AIC is as follows:

n P 2 at ! AIC = ln t=1 + 2p n (3.19) n where p is the number of parameters in the model, including the white noise term.

3.2.3 Interest Rate Risk

Interest rate risk is defined as the risk that an investment’s value will change as a result of changes in the interest rates (SFSA, 2014). Typically, this is reflected in the fact that the interest rates used to calculate an investment’s present value changes, thus affecting the present value. With demand deposits, interest rate risk is also manifested in that changes in market interest rate may affect depositors’ behavior. For example, increasing market interest rates might lead to customers withdrawing money and seeking more profitable alternatives elsewhere. This results in changes in the deposit volume, and thus also the rents and the deposit liability. In short, the present value of the deposit liability is affected by interest rate risk not only in terms of discount factors, but also in terms of the deposit volume.

Traditional interest risk measures typically only consider the first source of risk (Hutchison and Pennacchi, 1996) and are thus not directly applicable for demand deposits. Instead, the interest rate risk in the EVM is in this study estimated by calculating the interest rate elasticity. This choice of measure is in line with the interest rate risk measure used by O’Brien (2000) and Dewachter (2006). Elasticity is a measure of how sensitive an asset is to its underlying variable (Bodie, Kane and Marcus, 2014). The aim is to measure how the value of the deposit liability changes subject to parallel shifts in the market interest rate yield curve. From Eq. (3.3) it can be seen that the deposit liability is a function of the deposit rate, the deposit volume, and the market interest rate. Additionally, the deposit rate and volume are both dependent on the market interest rate as well. The interest rate elasticity will therefore be able to capture all of the aspects of which shifts in the market interest rate affect the deposit liability.

After applying the parallel shifts to the future market interest rate yield curve, a new deposit liability Lnew is calculated. The interest rate elasticity (IRE) is then calculated as:

18 L IRE = new − 1 (3.20) L

with L and Lnew computed in accordance to Eq. (3.3). Because the IRE can take positive and negative values, the interest rate risk will be assessed from the absolute value of the IRE. For example, a larger absolute value in the IRE means that the interest rate risk is higher.

3.3 Replicating Portfolio Model Framework (RPM)

An alternative approach for modeling the dynamics and estimating the interest rate risk in demand deposits is the RPM. In the RPM, the dynamics of a bank’s deposits are estimated by transforming it into a portfolio of market interest rate securities with known maturities. The idea is to mimic the dynamics of the deposit volume with a portfolio of market interest rate securities (Frauendorfer and Sch¨urle,2003).

Optimization criteria commonly used in the RPM are maximizing the risk-adjusted margin or minimizing the variance between the portfolio return and deposit rate over time (Maes and Timmermans, 2005). The idea behind the former criterion is to maximize the profit banks receive from investing the deposit volume in a portfolio of market interest rate securities. The latter criterion is typically used to mimic the behavior of the demand deposits (Frauendorfer and Sch¨urle, 2003). This paper focuses on the latter criterion as the primary aim is to replicate the deposits dynamics. The optimization problem may be formulated as:

Minimize Variance of (rp − R) n X subject to wi = 1, (3.21) i=1

wi ≥ 0.

n P where R is the deposit rate and the portfolio return rp = wiri, i.e. equal to the sum of i=1 the returns of each individual asset multiplied with the allocated weight invested in asset i (wi). The first constraint states that the portfolio weights shall add up to one, i.e. it ensures that no money is unused. Finally, the second constraint prohibits the undertaking of any short positions. This constraint is included to improve comparability with previous studies (Maes and Timmermans, 2005; Frauendorfer and Sch¨urle,2003).

19 3.3.1 Interest Rate Risk

A benefit of the RPM is that the interest rate risk may be estimated with traditional measures such as duration. This is feasible since the replicating portfolio and not the actual deposits is used for estimating the interest rate risk. Duration measures the approximate change in value due to a parallel shift of the market interest rate yield curve (BCBS, 2004). A duration measure typically associated with RPM is the Macaulay duration (Maes and Timmermans, 2005; Dewachter, 2006), which is defined as:

n X D = wimi (3.22) i=1

where wi is the portfolio weight invested in security i and mi is its maturity. Macaulay duration (D) is expressed in the weighted average time to repayment. The main advantage of the Macaulay duration is that it estimates the average time the deposited capital is expected to remain at the bank. However, it is not an explicit measure of how the deposit value changes due to changes in the market interest rate. Instead, the following formula may be used:

∆P = −D∆y (3.23) P where P and ∆P is the portfolio value and change in portfolio value respectively and D is Macaulay duration as specified in Eq. (3.22). This formula estimates the change in portfolio value due to small changes (parallel shifts) in the portfolio yield ∆y (Hull, 2009). This measure allows for a direct comparison of the interest rate risk estimate of the RPM with the corresponding estimate from the EVM since unit of measure is changed. Similar to the EVM, the interest rate risk in the RPM will be viewed from an absolute value perspective as well. This means that a larger absolute value in the change of portfolio value indicates a higher interest rate risk.

20 4 Methodology

This section introduces the methods used to answer the research questions of the study. The four key issues of this study are the choice of model for the market interest rate, the deposit rate and the deposit volume and how to measure the interest rate risk. The remainder of this section describes the selected models in this study. First, the market interest rate model used in both frameworks is presented. Next with regards to RQ1, the models for the EVM are elaborated upon, followed by a detailed explanation of the models for the RPM. To an- swer RQ2, the demand deposits are grouped into SA and TA, as well as private accounts and corporate accounts. Lastly, the limitations, validity and reliability of the study are discussed. An overview of the overall workflow for the EVM and RPM is presented below in Figure 4.1.

Vasicek model

EVM RPM

Market Interest Rate Market Interest Rates

Deposit Rates Portfolio Optimization

Deposit Volumes Interest Rate Risk

Deposit Rents

Deposit Liability

Interest Rate Risk

Figure 4.1: Illustration of the workflow for the EVM and the RPM approaches applied in this study.

21 4.1 General Method

The general method of this study is based on stochastic simulation, where the interest rate risk is analyzed based on future forecasted scenarios. Stochastic simulation is together with backtesting two of the most common techniques in analyzing non-maturing liabilities (see e.g. Hutchison and Pennacchi, 1996; O’Brien, 2000; Kalkbrener and Willing, 2004). The main difference between the two methods is that stochastic simulation considers future scenarios in the analysis whereas backtesting only utilizes historical data. Each method is associated with different advantages and disadvantages.

The main advantage of backtesting is the use of real world data to evaluate the developed models. This enables one to determine how well the model would have been in the past (Hagin and Kahn, 1990). Still, a disadvantage of backtesting is that the obtained result may be sensitive to the selected time period of study (Hagin and Kahn, 1990). Selecting a too long time period may lead to the inclusion of old data with little relevance to the current deposit dynamics. Analogously, a too short time period may lead to an exclusion of significant events which may have had an impact on the current deposit dynamics. Moreover, backtesting implicitly assumes future dynamics will resemble the current ones, which is not always the case (Frauendorfer and Sch¨urle,2003).

The cited drawbacks of backtesting are addressed in stochastic simulation. The main benefit of stochastic simulation is that multiple future scenarios are used in the analysis. This alleviates the need for assumptions regarding the future development of deposit dynamics (Frauendorfer and Sch¨urle,2003). Still, the added benefit of stochastic simulation comes with increased complexity as all included factors in the analysis must be simulated. This may be cumbersome, especially in the case of demand deposits which require models for the market interest rate, deposit rate, deposit volume and other exogenous variables such as macroeconomic indicators. Further, caution should be taken as the difficulty to implement the model increases as the number of variables in the model increases. For these cited reasons, it is important to construct as simple models as possible without sacrificing the predictive ability when using stochastic simulation techniques.

By using stochastic simulation, this study is able to consider different scenarios of future developments of the deposit market in the analysis. This study runs Monte Carlo simulations to obtain 1000 different scenarios for 20 years into the future, starting in January 2015. These simulated scenarios serve as basis for the analysis of the EVM and the RPM. The 20-year time horizon is selected since the 20-year interest rate swap is the security with the highest maturity available for the construction of the replicating portfolios. This time horizon is lower than the time horizon used by O’Brien (2000) and Dewachter (2006), whose

22 time horizons are 30 years and 40 years respectively. A longer time horizon results in higher deposit rents, lower deposit liabilities and an increased uncertainty in the forecasts. The results produced from this study should therefore be seen as a more conservative estimate of the deposit liability and the interest rate risk.

4.1.1 Demand Deposit Categorization

The demand deposit accounts are defined in this study as deposit accounts without re- strictions on the number of withdrawals/deposits that the account holder can make. This definition is in line with previous studies (see e.g. Jarrow and van Deventer, 1998). The two main types of demand deposits are savings accounts (henceforth SA) and transaction accounts (henceforth TA). SA are typically used for saving money, while TA are for everyday banking needs such as shopping transactions. As a result, the volumes of TA will usually have more frequent fluctuations than the volumes of SA, while also paying lower deposit rates than SA (Hutchison and Pennacchi, 1996; O’Brien, 2000). Because of these differences, this study separates demand deposits into SA and TA, which is in line with Hutchison and Pennacchi (1996) and O’Brien (2000). To extend on the previous literature, this study further investigates private (personal) accounts and corporate accounts separately, as cor- porations often have the possibility to negotiate higher deposit rates because of their higher capital base.

4.2 Market Interest Rate Model

As explained in section 3.1, the market interest rate is a central aspect in both frameworks since it typically seems to not only be the primary driving factor behind the deposit rates and deposit volumes, but also the return which banks may invest at. This study utilizes the one-factor Vasicek model to simulate the market interest rate for a couple of reasons. First, as the Vasicek model is commonly used in previous studies on demand deposits (Hutchison and Pennacchi, 1996; O’Brien, 2000), reliability and comparability can be increased by using the model. Furthermore, the Vasicek model allows for negative interest rates, something frequently cited as a disadvantage, whereas modified versions of the Vasicek model, such as the Cox-Ingersoll-Ross model9, removes this possibility (Hull, 2009). With the current negative interest rate environment on the Swedish market in consideration, the possibility for negative interest rates in the Vasicek model may be a desirable attribute. Although the negative interest rate environment may merely be a temporary occurrence, it can be argued as to why it is significant and should be considered: First, the current interest

9A more detailed description of the model can be found in Cox, Ingersoll and Ross (1985).

23 rate environment provides evidence that negative interest rates are not as implausible as previously believed. Furthermore, Zeytun and Gupta (2007) find the difference in interest rate estimates of the Cox-Ingersoll-Ross model and the Vasicek model to be minimal. With these cited reasons in mind the Vasicek model is chosen in this paper under the belief that the current negative interest rates are significant enough to warrant their inclusion in this study’s probability space of possible events.

The following is the discrete time Vasicek model used in this study:

√ rt = rt−1 + a(b − rt−1)∆t + σ ∆tzt (4.1)

where rt is the short term market interest rate at time t, zt is a random variable with standard normal distribution N(0,1), and σ is the volatility of the interest rate. The drift term a(b − rt−1) can be interpreted as the spread between the long term mean level b and the interest rate at time t − 1, multiplied by a, the speed of which the interest rate reverts to the long term mean. The model is mean reverting and stationary for all a > 0, which are desirable traits when modeling interest rates as mentioned in the literature review.

The parameters a, b and σ are estimated by the maximum likelihood method using historical monthly interest rate data. As all the other data used in this study are also on a monthly basis, the time steps will be monthly increments, resulting in ∆t being equal to 1. Breusch- Pagan test is used to ensure the residuals of the model are normally distributed with a constant variance. Breusch-Pagan is a test for heteroskedasticity in the estimated model, i.e. whether the variance of the residuals is dependent on the values of the explanatory variables (Woodridge, 2013).

4.3 Economic Value Model Framework (EVM)

As described in section 3.2, the main aspect of the EVM is to estimate future rents in order to calculate the deposit liability. As the rents are dependent on the future deposit rates and deposit volumes, it is necessary to derive predictive models for these. The models are constructed using the Box-Jenkins method as described in section 3.2.2. The market interest rate used for the EVM approach is the 1-month STIBOR.10 This choice is based upon previous research using market interest rates of a similar maturity (Hutchison and Pennacchi, 1996; O’Brien, 2000; Dewachter, 2006).

10Stockholm Interbank Offered Rate

24 4.3.1 Deposit Rate Model

In accordance with Hutchison and Pennacchi (1996), O’Brien (2000) and Dewachter (2006), the deposit rate model used in this study is a function of the short term market interest rate and lagged values of the deposit rate itself. Furthermore, as the market concentration has been proven to be correlated with the deposit rates (Hannan and Prager, 2006; Rosen, 2007), such a variable is also included in the analysis. Drawing from the SARIMAX framework from section 3.2.1, the following model is used:

Θ(B) (1 − B)k(1 − Bs)K rd = Ψ (B)r + Ψ (B)x + cI + ε (4.2) t 1 t 2 t [rt−rt−1>0] Φ(B) t

d where rt is the deposit rate at time t, rt is the market interest rate, xt is the market concentration variable, and c is a constant. I is the indicator function which takes the value 1 if the market interest rate have increased over the last month and otherwise is 0. This intends to capture the asymmetric behavior of deposit rates as banks tend to quickly lower deposit rates during declining market interest rates while being slower with increasing the deposit rates when market interest rates increase (Neumark and Sharpe, 1992; O’Brien, Orphanides and Small, 1994; Rosen, 2007). The unknown parameters and the resulting model are estimated and presented in section 6.2.1.

Market concentration is measured by the Herfindahl-Hirschman Index (HHI). It is one of the most widely used measure of market concentration and widely used in previous studies

(Neumark and Sharpe, 1992; Hannan and Prager; 2006; Rosen, 2007). HHI (xt) is defined as (Rosen, 2007):

n X 2 xt = γi (4.3) i=1

where γi is the market share of bank i. The index returns a value between 0 and 1 where the former indicate a perfectly competitive market and the latter a monopoly market.

4.3.2 Deposit Volume Model

The deposit volume model is a function of lagged values of itself, the spread between the market interest rate and the deposit rate, and several macroeconomic variables. The spread, which is also included by O’Brien (2000), is a way to incorporate the opportunity costs

25 depositors face, as only including the deposit rate may be misleading. By including them separately, multicollinearity might be an issue since the deposit rate is a function of the market interest rate. Building upon the suggestions of Jarrow and van Deventer (1998), O’Brien (2000), and Carmona (2007), the macroeconomic variables included in this paper are the gross domestic product, unemployment rate, and the monetary aggregate. Once again using the SARIMAX framework from section 3.2.1, the following model is suggested:

k s K d Θ(B) (1 − B) (1 − B ) Vt = µ + Ψ1(B)(rt − rt ) + Ψ2(B)Gt + Ψ3(B)Ut + Ψ4(B)Mt + Φ(B) εt (4.4)

where Vt, rt, Gt, Ut, Mt, is the deposit volume, the market interest rate, the gross domestic product, the unemployment rate and the monetary aggregate at time t respectively. Finally, d rt is the deposit rate at time t as determined by Eq. (4.2). The unknown parameters and the resulting model are estimated and presented in section 6.2.2.

4.3.3 Interest Rate Risk

The interest rate risk in the EVM is estimated numerically with the interest rate elasticity (IRE) presented in Eq. (3.20). In order to calculate the change in the deposit liability due to parallel shifts in the market interest rates yield curve, 1000 future 20-year paths of market interest rates are simulated. The average path is then used to discount the future rents, as well as to simulate the future 20-year deposit rates and deposit volumes. The deposit volume used to calculate the rents are the lower limit of the 95% confidence interval of the simulated volume. This is to take a more conservative approach by not overestimating the future growth rate, as the case bank in this study has sustained a relatively high growth rate in the last decade. The market interest yield curve is constructed by compounding the simulated market interest rates. The interest rate elasticity is then calculated for parallel shifts of 100 and 200 bps in the simulated market interest rate yield curve, which is in accordance with BCBS (2004) recommendations.

This particular method for constructing the yield curve and estimating the interest rate risk is used to increase comparability with previous studies using a similar approach (Hutchison and Pennacchi, 1996; O’Brien, 2000). By measuring the elasticity subject to parallel shifts in the market interest rate yield curve, Eq. (3.20) is equivalent to the interest rate risk formula used in the RPM (Eq. (3.23)). This allows for a comparison with the results obtained from the RPM approach. While there are other analytical approaches to measuring interest

26 rate risk such as the Modified duration11, they are not fit for this study since a numerical approach is applied here (Monte Carlo simulations), hence the numerical IRE method being more suited. To further increase comparability with the RPM approach, the interest rate risk will be calculated for the 10- and 15-year time horizons as well12 (see section 4.4).

4.4 Replicating Portfolio Model Framework (RPM)

The following section provides a detailed description regarding the construction of the repli- cating portfolio. The purpose of constructing an RPM is to compare its interest risk es- timates with corresponding estimates for the EVM as stated in the second research ques- tion.

This study develops a dynamic RPM since previous studies find it to be superior to static RPMs (see e.g. Dewachter, 2006). The main benefit of the dynamic RPM is that the optimal portfolio is constructed based on both historical and future deposits dynamics. This is typically illustrated in two ways (Frauendorfer and Sch¨urle, 2003):

♦ Multiple future scenarios are simulated and used in constructing the optimal portfolio.

♦ The portfolio weights are allowed to change dynamically to better replicate the future deposit dynamics.

In this study, the constructed RPM only incorporates the first cited benefit. To let the portfolio weights remain constant, this study assumes the portfolio is reinvested every month with the same weights. While banks in practice typically are more active in reallocating their replicating portfolios to match the in- and outflow of demand deposits, the reason why the portfolio weights are not allowed to change dynamically is due to the added complexity it requires. Though it may improve the obtained findings, the increased complexity is very difficult to implement due to its computational demands (Bardenhewer, 2007).

The portfolio is constructed by minimizing the variation between the portfolio return and the deposit rate as formulated by Eq. (3.21). As discussed in section 3.3, this criterion is com- monly used when the primary aim is to mimic the behavior of the demand deposits.

The optimal portfolio weights are determined by simulating 1000 different scenarios for 20 years into the future of each asset (i.e. the market interest rate securities) and deposit rate. For each scenario, the optimal portfolio weights with regards to the problem formulation

11Modified duration is defined as the percentage derivative of price with respect to yield. 12This is done by only using the first 10 and 15 years of the simulated 20-year paths.

27 in Eq. (3.21) are determined. The final portfolio weight wi for asset i is computed as the average weight allocated to asset i of every scenario:

1000 P wi k (4.5) w = k=1 i 1000

k where wi is the optimal weight of asset i in the final portfolio, and wi is the allocated weight to asset i in scenario k. To simulate future scenarios, models for the deposit rates and the market interest rate securities need to be developed. The deposit rate model is developed as described in section 4.3.1 and the market interest rate securities are modeled with the one-factor Vasicek model as described in section 4.2.

Analogously to previous studies (see e.g. Kalkbrener and Willing, 2004; Maes and Tim- mermans, 2005), the replicating portfolio in this study consists of liquid short-term and long-term maturity securities. The short-term market interest rate securities are the 1-day, 1-week, 1-month, 3-month and 6-month STIBOR. The long-term market interest rate secu- rities are 1-year, 2-year, 3-year, 5-year, 7-year, 10-year, 15-year and 20-year swap rates.13 A cited drawback of the RPM is that the obtained findings are typically sensitive to the choice of longest maturity security included in the portfolio (Kalkbrener and Willing, 2004). This paper addresses this issue by constructing three different RPMs for three different choices of the longest maturity security. The three portfolio constructions are: the 20-year portfolio which contains all securities, the 15-year portfolio which exclude the 20-year swap, and the 10-year portfolio which contain securities with a maturity of 10 years and below.

4.4.1 Interest Rate Risk

After constructing the replicating portfolio, the next step is to compute the interest rate risk. To allow for a direct comparison with the corresponding estimates of the EVM and subsequently answer the second research question, this paper use the interest rate risk measure defined by Eq. (3.22-3.23). This choice of measure is in line with Dewachter (2006) and Maes and Timmermans (2005) except for the unit of measure, as the mentioned studies uses Macaulay duration as defined in Eq. (3.22). Because the Macaulay duration report the interest rate risk in a different unit of measure than the interest rate elasticity used in the EVM, a direct comparison between the two frameworks is unattainable. This issue is solved by Eq. (3.22). To allow for a direct comparison and thus answering the second

13The dataset is described in detail in section 5.4.

28 research question, the interest rate risk is estimated for parallel shifts of 100 bps and 200 bps in the market interest rate yield curve. The yield curve will be constructed with the market interest rate securities mentioned in the previous section.

4.5 Limitations

Regarding the methodology, two limitations of this study should be kept in mind. The first concerns the time series modeling used in the construction of the deposit rate and deposit volume. Time series modeling involves to a large extent trial and error in determining the number of lags the included variables should have. This trial and error procedure is carried out manually which means it is not feasible to evaluate all possible model combinations in the analysis.14 Though this might result in an arbitrary model construction, this is to a large extent mitigated by the use of Box-Jenkins framework. As discussed in section 3.2.2, the Box-Jenkins framework provide a systematic way to identify suitable model combinations which reduces the number of model combinations to evaluate.

As accounted for section 4.4, an assumption is made regarding the construction of the replicating portfolio. Typically, dynamic RPM also allows the portfolio weights to change continuously to better reflect the market conditions (Frauendorfer and Sch¨urle,2003). This study assumes the portfolio weights to be constant for simplifying reasons. As mentioned in section 4.4, allowing the portfolio weights to change continuously is difficult to implement due to the required computational power (Bardenhewer, 2007).

4.6 Reliability and Validity

Reliability refers to the absence of differences in results if the research were repeated and is typically important in quantitative research. A high level of reliability implies one would obtain the same result if the study is repeated (Collis and Hussey, 2014). Since this study is of quantitative nature, the reliability is inherently good. Stochastic simulation methods as this study relies upon are typically based on a random shock term for generating future scenarios. Per definition it is impossible to replicate something which is random. In attempt to mitigate this and further improve the reliability and replicability, 1000 different scenarios are simulated in the analysis. This is expected to improve the accuracy of the study as the interest rate risk is estimated based on the average scenario, which reduces the possibility of

14To illustrate the cumbersome work testing all possible model combinations may involve, assume an AR(1) process should be fitted to a time series with 130 observations. Just for this simple case there exists 129 different AR(1) model combinations that could be tried.

29 an extreme scenario distorting the findings. Moreover, as the random shock term is assumed to follow a gaussian distribution, the average scenario is always expected to converge to the “true” average scenario as the number of generated scenarios increase.

Validity concerns how well the obtained findings measure the examined phenomena (Collis and Hussey, 2014). In this study, a number of selections from both a data collection and methodological perspective is made to improve the validity. Regarding the data collection15, this study utilizes a unique dataset provided by one of Sweden’s four largest retail banks. The dataset contains information of the deposited capital and offered deposit rate for all demand deposit accounts provided by the bank between 2004 to 2015. The rest of the data is of secondary nature gathered from reliable and established sources, which minimizes the possibility of measuring errors. From a methodological standpoint, the selected models are chosen with regards to previous research to ensure they are capable of accurately capture the deposit dynamics and avoiding interpretation errors. Still, no model, regardless of how well it may perceive to be, can predict the exact future as it is based on certain assumptions which means the validity of any model could always be disputable.

15The dataset is described in section 5.

30 5 Data

This section introduces the dataset used in this study. The data regarding the historical deposit volumes and deposit rates is a unique dataset provided by one of Sweden’s four biggest retail banks. The data for the macroeconomic variables and the market interest rate securities are of a secondary nature. All of the data are given in nominal values, i.e. the inflation is not adjusted for. The reason why the data is not adjusted for inflation is that deposits are regarded as a part of banks’ liabilities. Thus, adjusting for inflation leads to an underestimation of banks deposit liabilities which is not sensible from a risk management perspective. The remainder of this section discusses each data type and the required data treatment more in detail.

5.1 Deposit Volumes16

The data for the deposit volumes consists of 132 monthly observations between January 2004 and December 2014. The dataset is provided by a major Swedish retail bank and contains information from all their demand deposit accounts on the Swedish market. Only deposit accounts with the base currency SEK is included in this study to avoid issues regarding currency risks. Since the bank, which is not disclosed for business reasons, offers several different demand deposit accounts that share many similarities, the data is grouped into SA and TA. A more detailed disposition of the demand deposit accounts cannot be disclosed for business reasons. Moreover, the data is analyzed on an aggregate level as well as on a customer level. On a customer level, the analysis focuses on private individual accounts and corporate accounts separately. The historical deposit volumes on an aggregate and customer level are displayed in Figure 5.1. More detailed illustrations of respective category is provided by Figures A.1-A.4 in Appendix A. Worth noting is that the case bank in this study has a much larger volume for private accounts than for corporate accounts. The divide between SA and TA is more evenly distributed in terms of volume. It can be seen that the TA volumes fluctuate significantly more than the SA. The growth rates are quite similar for all categories except the corporate SA, whose volume development saw two large growth spurts between 2007-2009 and 2011-2013. This is more clearly visible in Figure A.2.

16The deposit volume data presented in this study is scaled for business reasons.

31 ·105 4 SA Private SA Corporate TA Private 3.5 TA Corporate

3

2.5

2 MSEK 1.5

1

0.5

0 2006 2008 2010 2012 2014 Year

Figure 5.1: The deposit volume (in MSEK) from 2004 to 2014. From top to bottom: the red area represents TA Corporate, yellow area rep- resent TA Private, light blue area represents SA Corporate and the blue area represents SA Private.

5.2 Deposit Rates

The deposit rates for the different account types have been computed implicitly. This is done since some depositors receive a higher deposit rate as they deposit more capital. Analogously to the data of the deposit volume, the deposit rate data is provided by the case bank. The data contains the total amount every customer receives each month for depositing their capital at the case bank. The deposit rate is computed on a monthly basis by:

Amount paid to depositors month i Deposit rate at month i = (5.1) Deposit volume month i

The deposit rate data consists of 132 monthly observations from January 2004 to December 2014. The deposit rates for the different account types are illustrated in Figure 5.2. For reference the STIBOR 1-Month is also provided. It is clear that the deposit rates for SA are

32 almost always higher than for TA, while corporate deposit rates are generally higher than private ones. The market interest rate is always higher than the deposit rates, as should be expected. The differences become smaller as the general level of interest rates decreases. The plot also suggests that the SA follow the fluctuations of the market interest rate more closely than the TA.

6 SA Private SA Corporate TA Private 5 TA Corporate STIBOR1M 4

% 3

2

1

0 2006 2008 2010 2012 2014 Year

Figure 5.2: The deposit rates for SA and TA on a private and corporate level, from 2004 to 2014. For reference the STIBOR 1-Month is also provided.

5.3 Macroeconomic Variables

The macroeconomic variables included in this study are the unemployment rate, gross do- mestic product, monetary aggregate and market concentration as measured by HHI. The latter is used in the model construction for the deposit rate while all the others are used in the modeling of the deposit volume. A detailed presentation of each variable is provided below.

5.3.1 Unemployment Rate

The unemployment rate is included in the deposit volume analysis as Carmona (2007) sug- gests it reflects the number of individuals that are in need of short term funding. If this relation is existent, the deposit volume is expected to decline as unemployment rate rise, i.e. the deposit volume is inversely correlated with the unemployment rate. Unemployment is defined as people between 15 and 74 years of age that have searched for an employment

33 but not worked for the past four weeks (Statistics Sweden, 2014). Unemployment rate is the proportion of unemployed to the entire workforce. The data of the unemployment rate in Sweden is collected from Statistics Sweden (2014) and consists of 132 monthly observa- tions between January 2004 and December 2014. The historical unemployment rates are illustrated by Figure A.5 in Appendix A.

5.3.2 Gross Domestic Product

Previous studies (Jarrow and van Deventer, 1998; O’Brien, 2000) have suggested that in- cluding people’s income level may improve the deposit volume modeling as people typically deposit capital to save for future consumption. Therefore, income level should be positively correlated with deposit volume. This study uses nominal values of gross domestic product (GDP) as a proxy for a population’s income level. It is not adjusted for inflation in order to achieve congruence with the deposit volume and the deposit rate data. GDP is a measure of the economic growth in a country. The GDP measure used in this study is defined as the sum of the final uses of all goods and services. It is measured using the production approach, which measures the value added by producers (Statistics Sweden, 2010). This measure is used as a proxy for income level as it is argued that the more value added by the producers, the more is distributed to the employees in terms of increased salaries. The Swedish GDP data is collected from Statistics Sweden (2015) and consists of 44 observations spanning from Q1 2004 to Q4 2014 on a quarterly basis. Since the GDP data consists of cumulative GDP over entire quarters, the GDP in this study is broken down into monthly data points in congruence with the data for deposit rates and volumes. This is done by linear interpolation and assuming that a quarter’s GDP is distributed uniformly over the three corresponding months. Linear interpolation is a simple method which fill in the missing data points by taking the arithmetic average of the two adjacent data points (Eriksson, 2008). The final time series is displayed by Figure A.6 in Appendix A.

5.3.3 Monetary Aggregate

Monetary Aggregate is examined as a possible explanatory variable of the deposit volume. The definition of monetary aggregate used is the so-called M0, which is defined as the total amount of physical cash and coins in Sweden (Statistics Sweden, 2014). The data is collected from Statistics Sweden (2015) and consists of 132 monthly observations between January 2004 and December 2014. The time series is illustrated by Figure A.7 in Appendix A.

34 5.3.4 Market Concentration

Previous research (see e.g. Neumark and Sharpe, 1992; Rosen, 2007) is in unison that market concentration affects the offered deposit rate. Because of this, market concentration, as measured by HHI, is included in the analysis of the deposit rate. In this study, market share is defined in terms of bank i’s total deposits in relation to the total deposits in the Swedish bank market. This definition is in line with Hannan and Prager (2006) and Rosen (2007), thus it is expected to improve the reliability of this study. The data contains market shares of every bank operating in Sweden and is collected from Swedish Bankers’ Association. The data consists of 11 observations spanning from January 2004 to January 2014 on a yearly basis. The data has been interpolated to a monthly basis with linear interpolation. Since the data for the market concentration only spans to January 2014, linear extrapolation is applied to extract monthly values of HHI between January 2014 and December 2014. Linear extrapolation is a method where a tangent line is constructed based on the arithmetic mean of the two adjacent points, which is then used to make short-term predictions of the data (Harder, 2005). The final dataset consists of monthly observations between 1st January 2004 and 1st January 2015 and is displayed by Figure A.8 in Appendix A.

5.4 Market Interest Rate Securities

The market interest rate securities used in the EVM and the RPM are:

♦ 1-day, 1-week, 1-month, 3-month and 6-month STIBOR.

♦ 1-year, 2-year, 3-year, 5-year, 7-year 10-year, 15-year and 20-year swap rates for SEK interest rate swaps.

The data is collected from Bloomberg and consists of 132 monthly observations per security between January 2000 and December 2014. The historical time series for the market interest rate securities are displayed in Figure 5.3.

35 7 1d STIBOR 7d STIBOR 1m STIBOR 3m STIBOR 6 6m STIBOR 1y Swap 2y Swap 5 3y Swap 5y Swap 7y Swap 10y Swap 4 15y Swap 20y Swap % 3

2

1

0 2002 2004 2006 2008 2010 2012 2014 Year

Figure 5.3: STIBOR and Swap rates between 2000 and 2014. Note that the longer the maturity the security has, the less it fluctuates over time. Data Source: Bloomberg.

36 6 Results and Analysis

In this section, the empirical results are presented and analyzed with regards to the research questions of this study. First, the parameters and simulated values of the market interest rate model are presented. This is followed by the results from the EVM, which include the final models for the deposit rates and the deposit volumes as well as the interest rate risk estimates. Finally, the section is concluded by the results from the RPM, where the different optimal portfolios are presented together with their corresponding interest rate risks.

6.1 Market Interest Rate Model

The first step in both EVM and RPM is to estimate the interest rate model which is used to forecast future developments of the market interest rates. Recall that the discrete Vasicek model as described by Eq. (4.1) is used to simulate the market interest rates. The obtained parameters for the STIBOR 1-Month are presented in Table 6.1.

Table 6.1: The statistics of the estimated market interest rate model. */**/*** denotes significance at the 10%, 5%, and 1% levels respectively. Recall from√ Eq. (4.1) that the fitted Vasicek model is formulated as: rt = rt−1 + a(b − rt−1)∆t + σ ∆tzt

Parameter Estimate Std Error t-statistic p-value a 0.01645*** 0.0054 3.06 0.0024 b 0.01238 0.0143 0.87 0.3869 σ 0.00209 Adjusted R2 0.9922 Breusch-Pagan p-value 0.0706

As seen in Table 6.1, the speed of reversion variable a is statistically significant at the 1% level, while the long term mean b is not statistically significant at the 10% level. This is due to the historical market interest rates used in calibration of the model, which include large fluctuations during the period of which the data was available. It is thus difficult to fit a long term mean with high statistical significance. Despite that, the adjusted R2 is 0.9922, indicating the model is suitable as it is able to explain 99.22% of the variations of the dependent variable rt. This value may seem remarkably high, but this suggests that the market interest rate is heavily dependent on its own most recent value. This most likely helps explain why the majority of the well-known market interest rate models include the rt−1 variable (see e.g. Vasicek, 1977; Cox, Ingersoll, and Ross, 1985). Furthermore, the

37 Breusch-Pagan test for heteroscedasticity suggests that heteroscedasticity can be rejected at the 5% level, meaning that the error terms are uncorrelated and normally distributed with constant variance, which is in line with the assumptions made beforehand.

The long term mean of 1.238% is low considering that the inflation target is set at 2% (Swedish National Bank, 2014). This is merely a result of the historical evolution of the STIBOR 1-Month, which has a declining trend for the last couple of decades. Furthermore, the relatively high p-value of 38.69% leads to more uncertainty in the forecast, which suggest that the long term mean may not be perfect. This seemingly low forecasted market interest rate results in a more conservative estimate of the future deposit rents and liabilities, which is sensible from a risk management perspective. It is difficult to put the results from the fitted market interest rate model in relation to the previous demand deposit research (e.g. Hutchison and Pennacchi, 1996; O’Brien, 2000), since the statistics and diagnostics are never reported. The fitted model together with the 20-year forecast and the historical market interest rates are shown in Figure 6.1.

6 STIBOR 1m Modeled STIBOR 1m

5

4

% 3

2

1

0 2008 2012 2016 2020 2024 2028 2032 Year

Figure 6.1: The historical and modeled values of STIBOR 1-Month from 2004 to 2034. The simulated values from 2015 to 2034 are the average of 1000 simulated paths from the Monte Carlo simulation.

6.2 Economic Value Model Framework (EVM)

The results from the EVM are presented in this section. First, the parameters and diagnos- tics of the final deposit rate models are presented, which is then followed by the presentation of the deposit volume models. Finally, the interest rate risk is presented and analyzed. All

38 of the results are separated into SA and TA on an aggregate level and then further divided into private and corporate accounts. The key findings of the EVM are as follows:

♦ The deposit rate models are all similar across the account types: the included terms are the lag 1 AR term and the lag 0 spread variable. Neither market competition nor the asymmetry term are found to improve the models.

♦ The deposit volume models vary more between account types: all of the models include the lag 12 AR term, suggesting that a 1-year seasonality exists. Models for TA also include a lag 1 AR term. TA and corporate accounts are more responsive to changes in the spread variable compared to SA and private accounts respectively. None of the macroeconomic variables (GDP, Unemployment, and Monetary aggregate) improve the models significantly.

♦ The interest rate risk is lower for SA compared to TA, and lower for corporate accounts compared to private accounts. The interest rate risk also decreases as the simulated time horizon decreases.

Since the plots used in the Box-Jenkins model fitting steps consist of over 300 individual graphs, they will not be attached to this paper, but are instead available upon request.

6.2.1 Deposit Rate Model

The Box-Jenkins method for model fitting described in section 3.2.2 are applied in order to fit SARIMAX models for the deposit rates. Results from this process show that the best suited models for the deposit rates include only the lag 1 AR component and the lag 0 component of the market interest rate. Both the dependent variable (deposit rate) and the exogenous variable (market rate) are differenced once for the sake of stationarity. The models take the following form:

d 1 (1 − B)rt = ψ1,0(1 − B)rt + εt (6.1) 1 − φ1B

The estimated parameters and test statistics are presented in Table 6.2. For the plots of ACFs, PACFs and cross-correlations used in the Box-Jenkins model fitting steps, see Appendix C.

39 Table 6.2: The statistics of the estimated deposit rate models. */**/*** denotes significance at the 10%, 5%, and 1% levels respec- tively. The final fitted model is of the following form: d 1 (1 − B)r = ψ1,0(1 − B)rt + εt t 1−φ1B

Parameter Estimate Std Error t-statistic p-value SA Aggregate

φ1 -0.43307*** 0.08042 -5.39 <0.0001

ψ1,0 0.67577*** 0.02547 26.53 <0.0001 TA Aggregate

φ1 -0.32057*** 0.0858 -3.74 0.0003

ψ1,0 0.29647*** 0.015 19.77 <0.0001 SA Private

φ1 -0.42365*** 0.08086 -5.24 <0.0001

ψ1,0 0.66834*** 0.0258 25.91 <0.0001 SA Corporate

φ1 -0.35479*** 0.08368 -4.24 <0.0001

ψ1,0 0.74432*** 0.03111 23.93 <0.0001 TA Private

φ1 -0.26878*** 0.08791 -3.06 0.0027

ψ1,0 0.20665*** 0.01498 13.79 <0.0001 TA Corporate

φ1 -0.34622*** 0.08358 -4.14 <0.0001

ψ1,0 0.49602*** 0.02395 20.71 <0.0001

The parameters of the deposit rate models are significant at the 1% level across the board. This indicates that the market interest rate and the lag 1 AR component is sufficient in explaining the deposit rates when using the SARIMAX framework. The market interest rate parameter ψ1,0 takes larger values for SA compared to TA, and also for corporate accounts compared to private accounts. This indicates that SA and corporate accounts follow the market interest rate more closely than their counterparts. Moreover, the small standard errors of the parameters, especially for the market interest rate, suggest that they are sufficient in predicting the deposit rates. The fitted models and the simulated deposit rates together with the historical deposit rates are shown in Figure 6.2 and Figure 6.3.

40 6 Modeled STIBOR 1m SA Aggregate TA Aggregate 5 Modeled SA Aggregate Modeled TA Aggregate 4

% 3

2

1

0 2008 2012 2016 2020 2024 2028 2032 Year

Figure 6.2: The historical and modeled values of deposit rates for the aggre- gate SA and the aggregate TA from 2004 to 2034. The simulated deposit rates from 2015 to 2034 are averages based on the 1000 simulated market interest rates (STIBOR 1-Month). The modeled STIBOR 1-Month is also shown for reference.

6 Modeled STIBOR 1m SA Private SA Corporate 5 TA Private TA Corporate Modeled SA Private 4 Modeled SA Corporate Modeled TA Private Modeled TA Corporate

% 3

2

1

0 2008 2012 2016 2020 2024 2028 2032 Year

Figure 6.3: The historical and modeled values of deposit rates separated into private and corporate along with SA and TA from 2004 to 2034. The simulated deposit rates from 2015 to 2034 are averages based on the 1000 simulated mar- ket interest rates (STIBOR 1-Month). The modeled STIBOR 1-Month is also shown for reference.

41 As can be seen from Figure 6.2 and Figure 6.3, the deposit rates for TA are generally lower than for SA, which helps explain why they are less affected by changes in the market interest rate. It is also evident that corporate accounts receive a higher deposit rate than private accounts.

Both the market concentration variable and the asymmetry term are found to be statistically insignificant at the 10% level for all models, whilst also not improving the AIC score of the models upon inclusion, thus being excluded from the final model. See Table 6.3 for the AIC scores and standard errors of the models which are used to compare the models with each other. Appendix B lists the detailed statistics for the market concentration variable and the asymmetry term.

Table 6.3: The AIC and standard error (Std Error) of the tested de- posit rate models. r, x, and I indicate that the model includes the market interest rate, the market competition variable (HHI), and the asymmetry term respectively. The lags of the included market inter- est rate (0 lag) and market competition (0 lag) variables are chosen according to the Box-Jenkins model fitting method and are shown in Appendix B. Lower AIC and Std Error indicate a better model.

r r, x r, I r, x, I SA Aggregate AIC -1483.29 -1481.85 -1482.02 -1480.56 Std Error 0.000835 0.000837 0.000836 0.000838 TA Aggregate AIC -1643.54 -1641.73 -1641.8 -1639.99 Std Error 0.000453 0.000454 0.000454 0.000456 SA Private AIC -1481.59 -1480.13 -1480.14 -1478.66 Std Error 0.000841 0.000842 0.000842 0.000844 SA Corporate AIC -1443.91 -1442.77 -1443.29 -1442.12 Std Error 0.000971 0.000971 0.000969 0.00097 TA Private AIC -1653.82 -1651.85 -1652.16 -1650.19 Std Error 0.000436 0.000437 0.000437 0.000438 TA Corporate AIC -1512.55 -1511.68 -1510.55 -1509.68 Std Error 0.000747 0.000747 0.00075 0.000749

42 6.2.2 Deposit Volume Model

Again, the Box-Jenkins model fitting method is used to fit SARIMAX models to the deposit volumes. The best suited models for the deposit volumes include a mix of AR and MA components, with the spread between the market interest rate and the deposit rate as the only exogenous variable. Both the dependent variable (deposit volume) and the exogenous variable (spread) are differenced once for the sake of stationarity. The models take the following form:

θ(B) (1 − B)V = µ + ψ (B)(r − rd) + ε (6.2) t 1 t t φ(B) t

The models differ from each other in the different account and client categories with regards to the lags of the ARMA and spread terms. The final models together with the estimated parameters and test statistics for the deposit volumes are presented in Table 6.4. For the plots of ACFs, PACFs and cross-correlations used in the Box-Jenkins model fitting steps, see Appendix C.

43 Table 6.4: The parameter estimates and statistics of the estimated deposit volume models for all accounts and clients categories. */**/*** denotes significance at the 10%, 5%, and 1% levels respectively.

Equation Parameter Estimate Std Error t-statistic p-value SA Aggregate µ 589.34*** 205.4 2.87 0.0048

3 d 1−θ1B φ12 0.64228*** 0.07652 8.39 <0.0001 (1 − B)Vt = µ + ψ1,3B (1 − B)(rt − rt ) + 1−φ B εt 12 θ1 -0.27109*** 0.08854 -3.06 0.0027 ψ1,3 130070*** 43390 3 0.0033 TA Aggregate µ 558.99*** 158.4 3.53 0.0006 φ1 -0.45754*** 0.07061 -6.48 <0.0001 2 d 1−θ2B (1 − B)Vt = µ + ψ1,2B (1 − B)(rt − r ) + 12 εt φ 0.42645*** 0.07118 5.99 <0.0001 t 1−φ1B−φ12B 12 θ2 0.29746*** 0.09211 3.23 0.0016 ψ1,2 -203950** 92770 -2.2 0.0298 SA Private µ 531.21*** 188.8 2.81 0.0057 φ 0.65625*** 0.07511 8.74 <0.0001

44 3 d 1−θ1B 12 (1 − B)Vt = µ + ψ1,3B (1 − B)(rt − rt ) + 1−φ B εt 12 θ1 -0.24634*** 0.08913 -2.76 0.0066 ψ1,3 94619** 39980 2.37 0.0195 SA Corporate µ 24.991 62.34 0.4 0.6892

2 d 1−θ1B φ1 0.78160*** 0.07011 11.15 <0.0001 (1 − B)Vt = µ + ψ1,2B (1 − B)(rt − rt ) + 1−φ B εt 12 θ1 -0.34818*** 0.08644 -4.03 <0.0001 ψ1,2 -21423** 8971 -2.39 0.0184 TA Private µ 310.99*** 88.74 3.5 0.0006 φ1 -0.48590*** 0.06952 -6.99 <0.0001 2 d 1−θ2B (1 − B)Vt = µ + ψ1,2B (1 − B)(rt − r ) + 12 εt φ 0.42611*** 0.06948 6.13 <0.0001 t 1−φ1B−φ12B 12 θ2 0.46738*** 0.08835 5.29 <0.0001 ψ1,2 -115420** 54720 -2.11 0.0369 TA Corporate µ 258.47* 146.2 1.77 0.0796 1 d 1 φ1 -0.22034*** 0.07181 -3.07 0.0026 (1 − B)Vt = µ + ψ1,1B (1 − B)(rt − rt ) + 1−φ B−φ B12 εt 1 12 φ12 0.60911*** 0.07538 8.08 <0.0001 ψ1,1 -98862 60600 -1.63 0.1053 From Table 6.4 it is clear that the SARIMAX framework with the spread variable as an exogenous input variable is sufficient in modeling the deposit volumes. The spread variable and the mix of AR and MA components are mostly statistically significant at the 1% level. The mean constants (µ) are positive also statistically significant at the 1% level for the majority of the models, suggesting a continued growth in future deposit volumes. In general, the volumes for SA are found to have a more delayed reaction to the changes in spread (i.e. higher lag on the spread variable) compared to TA. The same discrepancy exists for corporate accounts and private accounts, with the latter showing a more delayed reaction. While all 12 models incorporate a 12 month seasonal component (φ12B ), the TA also include an AR1 term, i.e. the 1-month lag (φ1B), which has a negative coefficient. Since the dependent variable (the deposit volume) is differenced once, the negative AR1 term means that the new change in volume will be negatively correlated to the most recent change in volume. This is evident in Figure A.1-A.4 in Appendix A, where the volumes for TA fluctuate much more than for SA.

Table 6.4 also shows that the parameter for the spread variable takes negative values for all models except the private SA (and as result also the aggregated SA since the private portion is substantially larger than the corporate). This means that the volume for private SA is positively correlated to changes in the spread (note that the spread is also differenced once), while the other accounts are negatively correlated. As seen in Figure 5.2 and Eq. (6.1), the nominal value of the spread increases as market interest rates increase. The negative spread coefficient in the volume models can thus be interpreted as private clients being more inclined to deposit money into their SA during increasing market interest rates, while choosing to keep their money in TA during decreasing market interest rates. Since salary is normally automatically transferred to TA, the aforementioned phenomenon could be explained by private clients not bothering to transfer the new influx of capital to their SA during decreasing market interest rates, and vice versa for increasing market interest rates. For corporate accounts, this discrepancy between SA and TA does not exist. Corporate clients are more inclined to withdraw capital from both SA and TA during rising interest rate environments and deposit capital during declining interest rate environment.

The fitted models and the simulated deposit volumes together with the historical deposit volumes are presented in Figure 6.4-6.9.

45 ·105 4.5 SA Aggregate Modeled SA Aggregate 4 Upper 95% Lower 95% 3.5

3

MSEK 2.5

2

1.5

1 2008 2012 2016 2020 2024 2028 2032 Year

Figure 6.4: The historical and modeled values of the deposit volume for the aggregate SA from 2004 to 2034. Included are the lower and upper limits of the 95% confidence interval for the simulated values from 2015 to 2034.

·105 4 TA Aggregate Modeled TA Aggregate Upper 95% 3.5 Lower 95%

3

2.5 MSEK 2

1.5

1 2008 2012 2016 2020 2024 2028 2032 Year

Figure 6.5: The historical and modeled values of the deposit volume for the aggregate TA from 2004 to 2034. Included are the lower and upper limits of the 95% confidence interval for the simulated values from 2015 to 2034.

46 ·105 4 SA Private Modeled SA Private Upper 95% 3.5 Lower 95%

3

2.5 MSEK 2

1.5

1 2008 2012 2016 2020 2024 2028 2032 Year

Figure 6.6: The historical and modeled values of the deposit volume for private SA from 2004 to 2034. Included are the lower and upper limits of the 95% confidence interval for the simulated values from 2015 to 2034.

·104 SA Corporate 6 Modeled SA Corporate Upper 95% Lower 95%

4

2 MSEK

0

−2

2008 2012 2016 2020 2024 2028 2032 Year

Figure 6.7: The historical and modeled values of the deposit volume for corporate SA from 2004 to 2034. Included are the lower and upper limits of the 95% confidence interval for the simulated values from 2015 to 2034.

47 ·105 2.6 TA Private Modeled TA Private 2.4 Upper 95% Lower 95% 2.2 2 1.8 1.6 MSEK 1.4 1.2 1 0.8 2008 2012 2016 2020 2024 2028 2032 Year

Figure 6.8: The historical and modeled values of the deposit volume for private TA from 2004 to 2034. Included are the lower and upper limits of the 95% confidence interval for the simulated values from 2015 to 2034.

·105 2 TA Corporate Modeled TA Corporate 1.8 Upper 95% Lower 95% 1.6 1.4 1.2 1 MSEK 0.8 0.6 0.4 0.2 2008 2012 2016 2020 2024 2028 2032 Year

Figure 6.9: The historical and modeled values of the deposit volume for corporate TA from 2004 to 2034. Included are the lower and upper limits of the 95% confidence interval for the simulated values from 2015 to 2034.

48 Figure 6.7 show that the lower limit of the 95% confidence interval for the simulated corpo- rate SA volume becomes negative after year 2020. This is a result of the estimated µ having low statistical significance along with a high standard error (see Table 6.4). The reason µ was difficult to fit relative to the models for the other types of accounts is because the his- torical corporate SA volume has a significantly different profile, characterized by two growth spurts in-between otherwise flat growths, which could not be explained by the exogenous variables included in this study either. Possible explanations may be acquisitions/losses of major corporate clients, but without the necessary data, these are mere speculations.

The exogenous macroeconomic variables are found to be either statistically insignificant or not leading to a significant improvement enough to warrant the added complexity when included. Table 6.5 presents the AIC scores and standard errors of the models which are used to compare the models with each other. It is clear that the AIC scores and standard errors are more or less the same for the different combinations of macroeconomic variables. The largest improvement can be seen in the deposit volume model for corporate TA, where including all three macroeconomic variables improves the AIC score and the standard error by 4.2% each. This is a relatively small improvement considering the addition of three extra variables that has to be modeled on their own as well. This in turn would increase the uncertainty in the forecast even more. Appendix B lists the detailed statistics for the macroeconomic variables.

49 Table 6.5: The AIC and standard error (Std Error) of the tested deposit volume models. S, G, d U, and M indicate that the model includes the spread variable (rt − rt ), the GDP variable, the unemployment variable, and the monetary aggregate variable respectively. The lags of the included variables are chosen according to the Box-Jenkins model fitting method and are shown in Appendix B. Lower AIC and Std Error indicate a better model.

S S, G S, U S,M S, G, U S, G, M S, U, M S, G, U, M SA Aggregate AIC 2091.8 2090.2 2093.1 2093.5 2090.2 2091.3 2094.6 2090.6 Std Error 842.9 834.6 843.8 845.3 831.3 834.9 845.8 829.5 TA Aggregate AIC 2411.2 2406.7 2413.2 2409.9 2408.4 2402.6 2411.8 2404.6 Std Error 2718.6 2661.6 2729.6 2695.0 2669.1 2609.5 2704.5 2620.3 SA Private AIC 2069.4 2068.6 2070.8 2071.4 2069.0 2070.5 2072.6 2070.6 Std Error 772.4 766.8 773.4 775.4 765.4 769.7 776.2 767.3 SA Corporate AIC 1730.2 1731.7 1694.9 1732.2 1696.4 1733.6 1696.8 1754.7 Std Error 194.8 195.2 197.8 195.6 198.3 196.0 198.6 250.8 TA Private AIC 2338.0 2339.3 2339.8 2337.6 2341.1 2339.5 2339.6 2341.5 Std Error 2047.3 2049.6 2053.6 2036.0 2056.3 2043.7 2044.3 2052.0 TA Corporate AIC 2203.7 2189.2 2124.4 2202.2 2109.2 2191 2123.4 2111.2 Std Error 1143.2 1077.4 1163.4 1132.4 1090.7 1080.7 1154.3 1095.3

6.2.3 Interest Rate Risk

The liabilities and interest rate elasticities estimated from the simulated 10-, 15- and 20-year horizons, respectively, are shown in Table 6.6. The interest rate elasticities are estimated from a +100 and +200 bps parallel shift in the simulated market interest rate yield curve. Since the asymmetry term is not included in the deposit rate models, the interest rate elasticities are symmetric, i.e. the interest rate elasticity subject to a -100 bps shift is equal to that of a +100 bps shift but with opposite signs.

50 Table 6.6: The estimated interest rate elasticity for the three different time horizons T (10, 15 and 20 years) subject to parallel shifts of the simulated market interest rate yield curve. The deposit liabilities (L) are the pre-shifted values, shown as percentages of the deposit volumes at t=0 (January 2015). ∆L indicates the percentage change in deposit liability as a result of a +100 (+200) bps parallel shift in the simulated market interest rate yield curve. Higher absolute value indicate higher interest rate risk. Since the asymmetry term is not included in the deposit rate models, the interest rate elasticities are symmetric, i.e. the interest rate elasticity subject to a -100 bps shift is equal to that of a +100 bps shift but with opposite signs.

Change in deposit liability value due to a 100 bps (200 bps) increase in market interest rates ∆L (T=20 years) ∆L (T=15 years) ∆L (T=10 years) SA Aggregate -5.99% (-10.83%) -4.57% (-8.49%) -3.10% (-5.92%) TA Aggregate -14.46% (-25.79%) -10.53% (-19.30%) -6.85% (-12.88%) SA Private -6.25% (-11.30%) -4.76% (-8.85%) -3.23% (-6.16%) SA Corporate17 -4.83% (-7.87%) -3.60% (-6.15%) -2.38% (-4.28%) TA Private -16.38% (-29.23%) -11.94% (-21.88%) -7.77% (-14.62%) TA Corporate -7.77% (-13.89%) -5.94% (-10.90%) -4.09% (-7.70%)

The first thing from Table 6.6 to note is that all of the deposit liabilities for the different categories decrease in value when the market interest rates are shifted upwards. This is because the spread between the deposit rates and the market interest rate increases with increasing market interest rates. An increased spread results in higher deposit rents and thus a bigger decrease in deposit liability. This is slightly counteracted by the changes in deposit volumes which generally decrease with increasing market interest rates (recall the negative spread coefficient from Table 6.4). Declining volumes result in lower rents, but the effect on the deposit liability from the decline in volume is only marginal compared to the impact from the increased spreads, which is why the interest rate elasticities still remain negative. Furthermore, it is clear that the interest rate risk becomes smaller as the simulated time horizon shortens. This is simply explained by the fact that the amount of rents are increased as the time horizon increases.

It is also evident that TA are more exposed to changes in the market interest rates (i.e. higher interest rate risk) compared to SA. This is in line with this study’s previous findings that the deposit rates of SA follow the market interest rate more closely than those of TA. Since the rents (and thus liabilities) are functions of the spread between the deposit rates and the market interest rate, the rents will not be significantly altered during a parallel shift in the market interest rate if the deposit rate follows suit, as the spread will stay roughly

17The deposit volume used to estimate the interest rate elasticity for corporate SA is the actual forecasted volume, as opposed to the lower limit of the 95% confidence interval used for the other volumes. This is due to unexplainable behavior in the historical volumes for corporate SA, resulting in a model with higher uncertainty which produces a lower 95% limit that takes negative values. The implications of this choice will be further discussed in section 7.1.

51 the same. Because the spread increases more for TA after an upward shift in the market interest rate than for SA, the rents of TA will see a bigger increase. This results in a bigger decrease in liability value which in turn results in TA having a higher interest rate elasticity compared to SA. The same line of reasoning can be applied to the differences in interest rate elasticity between corporate accounts and private accounts: the higher deposit rates for corporate accounts follow the market interest rates more closely, thus resulting in a lower interest rate elasticity than for private accounts. Furthermore, recall that the private SA is the only category where the volume is positively correlated to the spread. This means that the volume (and thus rents) of private SA increases when the market interest rates are shifted upwards, while the other account types experience a decrease in volume. Still, the larger increase of spreads on the TA categories have a bigger impact on the deposit liabilities, as both the TA categories have higher elasticities than private SA despite its increase in volume.

Finally, the interest rate elasticities from the 20-year horizon are similar to the results of O’Brien (2000), who obtained results of -12% and -15% for a +100 bps parallel shift for SA and TA respectively. On the other hand, Hutchison and Pennacchi (1996) obtained interest rate elasticities of -0.4% and -6.7% for a +100 bps parallel shift for SA and TA respectively. This is more comparable to the results from the 10-year horizon in this study. These similarities indicate that the results obtained in this study are reasonable.

6.3 Replicating Portfolio Model Framework

This section presents the results from the RPM. First, the results from the portfolio con- structions are presented. Analogous to the analysis of the EVM model, the analysis of SA and TA is first done on an aggregate level and then on a customer level for private and corporate clients respectively. This is followed by an analysis of the estimated interest rate risks of the optimal portfolios. The key findings of the RPM are as follows:

♦ The first part of the analysis concerns the construction of the optimal portfolios for TA and SA on an aggregate level and a customer level. Three different portfolios are constructed: the 10-year, the 15-year and the 20-year portfolio. The results indicate that the portfolio allocations for the TA and SA differ slightly. Typically, the portfolios for the TA allocates a larger weight to the security with the longest maturity. Similar trends is observable between private accounts and corporate accounts with the former typically allocating more weight to the security with the longest maturity.

♦ In general, the portfolio allocations are sensitive to the portfolio maturity. All the

52 portfolios except the 10-year portfolios allocate most weight to the security with the longest maturity. In contrast, the 10-year portfolios allocate most weight to the 1-week STIBOR.

♦ The previous point is reflected in the interest rate risk estimates as the 10-year port- folios generate significantly lower estimates than the 20-year and 15-year portfolios. Still, the interest rate risk is higher for all TA compared to SA, and for private accounts compared to corporate accounts.

6.3.1 Portfolio Construction

The optimal portfolios are constructed by solving the optimization problem described by Eq. (3.21) for 1000 different future scenarios obtained from the Monte Carlo simulations. Replicating portfolios for three different maturities are constructed: 10 years, 15 years and 20 years. The optimal portfolios for the aggregate level of TA and SA are presented in Table 6.7. The optimal 20-year and 15-year portfolios for both account types allocate the largest weight to the security with the longest maturity in the portfolio. The optimal 20-year and 15- year portfolios for TA (SA) allocate 95% (68%) and 91% (63%) to the security with longest maturity respectively. This result may be interpreted as the capital deposited in demand deposit accounts remains at the bank for a prolonged period. Moreover, the results indicate that money deposited in TA remains at the bank for a longer period than money deposited in SA. In general, the findings seem to confirm the popular view among practitioners that deposited capital remains at the bank for a long time. Still, the large allocations to the security with maximum maturity indicate that the optimal 20-year and 15-year portfolios are very risky and not suitable for hedging purposes. Furthermore, the results for the 10- year portfolio for both the TA and SA strongly indicate that the optimal portfolios are sensitive to the choice of maximum maturity security included in the portfolio. In contrast to the 20-year and the 15-year portfolios, the 10-year portfolios allocate the largest weight to the 1-week STIBOR. Consequently, this result contradicts the findings of the 20-year and 15-year portfolio which indicated that the deposited capital in TA and SA remains at the bank a long time. Note that the optimal portfolio allocations based on the problem formulation in Eq. (3.21) are determined based on the covariance between the securities and the deposit rate. Thus, the difference in results between the 10-year portfolios and the 20-year and 15-year portfolios are likely due to the 10-year swap rate having a lower correlation with the deposit rate than the other securities. In total, the findings provide support to Kalkbrener and Willing’s (2004) conclusion of the RPM being sensitive to the choice of securities used in constructing the portfolio.

53 Table 6.7: The optimal 20-year, 15-year, and 10-year portfolios to the optimization problem described by Eq. (3.21). The portfolios are modeled for the aggregate SA and the aggregate TA. The portfolio allocations are given in percent. Minimum variance specifies how well the portfolio replicate the behavior of the deposit rate, with the lower value the better.

SA Aggregate TA Aggregate 20-year Portfolio 15-year Portfolio 10-year Portfolio 20-year Portfolio 15-year Portfolio 10-year Portfolio Minimum Variance 0.0081% 0.0093% 0.00117% 0.0089% 0.0110% 0.0153% Market Interest Rate Security STIBOR 1 Day 0.32% 1.20% 6.49% 0.50% 1.23% 5.79% STIBOR 1 Week 10.76% 17.09% 55.80% 1.67% 5.46% 54.65% STIBOR 1 Month 0.00% 0.00% 0.04% 0.28% 0.61% 1.09% STIBOR 3 Month 16.77% 14.71% 15.91% 2.53% 1.45% 1.69% STIBOR 6 Month 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% Swap 1-year 2.61% 2.23% 1.81% 0.08% 0.00% 0.00% Swap 2-year 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% Swap 3-year 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% Swap 5-year 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% Swap 7-year 0.93% 0.67% 0.58% 0.00% 0.00% 0.00% Swap 10-year 0.51% 0.82% 19.38% 0.06% 0.04% 36.79% Swap 15-year 0.05% 63.27% Omitted 0.00% 91.20% Omitted Swap 20-year 68.06% Omitted Omitted 94.88% Omitted Omitted

To examine if the variability of the optimal portfolio weights is present on a more granular level, further analysis is made on a customer level. Both SA and TA are further segmented into private and corporate accounts, where the former refers to accounts owned by private individuals and the latter corporations. The results for the SA and TA are displayed in Table 6.8 and 6.9 respectively. The observed patterns in the portfolio allocations for the respective portfolios at the aggregate level are also observed at the customer level. Analogous to the aggregate level, the optimal 20-year and 15-year portfolios at the customer level allocates most weight to the security with the longest maturity. This is observed both when TA and SA are segmented on a private and corporate client level. Moreover, the results presented in Table 6.8 and 6.9 support the observed pattern at the aggregate level, showing that the capital deposited in TA remains at the bank longer than the capital in SA. The results also indicate that the capital deposited in SA and TA by private clients remains at the bank longer than the capital deposited by corporate clients. This may be interpreted as corporate clients being more active in their capital management than private clients, and this behavior is more pronounced for SA. Analogous to the findings on the aggregate level, the results on a customer level is also sensitive to the choice of portfolio maturity. As before, most weight are allocated to the 1-week STIBOR when the longest maturity of the securities included in the portfolio is 10 years. Subsequently, this implies that the majority of capital in SA and TA only remain at the bank for a short time period, contradicting the results of the 20-year and 15-year portfolios. Similar to the aggregate level, the difference in results between the 10-year portfolios and the other portfolios are likely due to the 10-year

54 swap rate having a lower correlation with the deposit rate than the other securities. This only further highlights the RPM’s sensitivity to the choice of included securities, providing further support to Kalkbrener and Willing’s (2004) results.

A natural extension of the RPM is to use the constructed portfolios to hedge the interest rate risk in demand deposits. Overall, the low variance between all constructed portfolios and the deposit rates suggests that the portfolios mimic the deposit rates closely. This implies that the portfolios may be interesting for hedging purposes. Yet, as previously mentioned, the large allocation to the security with the longest maturity in the 20-year and 15-year portfolios for both the SA and TA makes them risky to use for hedging. In contrast, the 10- year portfolio seems more sensible to use for hedging from a risk management perspective since it allocates most capital to the 1-week STIBOR rather than tying up the capital for several years. Still, it is not able to track the deposit rates as closely as the 20-year and 15-year portfolios. It is also interesting to note that hedging private and corporate accounts separately does not result in a significant improvement from hedging accounts on an aggregate level. In conclusion, a bank interested in using a replicating portfolio for hedging purposes face a trade-off between capital commitment and hedging efficiency.

Table 6.8: The optimal 20-year, 15-year and 10-year portfolio to the optimization problem described by Eq. (3.21). The portfolios are modeled for SA and separated into private and corporate accounts. The portfolio allocations are given in percent. Minimum variance specifies how well the portfolio replicate the behavior of the deposit rate, with the lower value the better.

SA: Private Corporate 20-year Portfolio 15-year Portfolio 10-year Portfolio 20-year Portfolio 15-year Portfolio 10-year Portfolio Minimum Variance 0.0084% 0.0099% 0.0126% 0.0081% 0.0092% 0.0114% Market Interest Rate Security STIBOR 1 Day 1.01% 1.90% 7.03% 0.75% 2.07% 8.12% STIBOR 1 Week 9.86% 16.61% 60.15% 12.72% 18.86% 54.48% STIBOR 1 Month 0.00% 0.00% 0.60% 0.00% 0.03% 0.55% STIBOR 3 Month 11.78% 10.22% 10.98% 18.73% 16.49% 17.09% STIBOR 6 Month 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% Swap 1-year 1.51% 1.21% 0.90% 2.66% 2.30% 1.88% Swap 2-year 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% Swap 3-year 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% Swap 5-year 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% Swap 7-year 0.30% 0.22% 0.23% 1.08% 0.92% 0.83% Swap 10-year 0.44% 0.53% 20.10% 0.84% 1.10% 17.05% Swap 15-year 0.00% 69.31% Omitted 0.11% 58.22% Omitted Swap 20-year 75.10% Omitted Omitted 63.12% Omitted Omitted

55 Table 6.9: The optimal 20-year 15-year, and 10-year portfolios to the optimization problem described by Eq. (3.21). The portfolios are modeled for TA and separated into private and corporate accounts. The portfolio allocations are given in percent. Minimum variance specifies how well the portfolio replicate the behavior of the deposit rate, with the lower value the better.

TA: Private Corporate 20-year Portfolio 15-year Portfolio 10-year Portfolio 20-year Portfolio 15-year Portfolio 10-year Portfolio Minimum Variance 0.0094% 0.0116% 0.0163% 0.0080% 0.0098% 0.0134% Market Interest Rate Security STIBOR 1 Day 0.35% 1.07% 5.31% 1.02% 1.80% 6.90% STIBOR 1 Week 0.92% 4.01% 53.38% 4.16% 9.01% 56.00% STIBOR 1 Month 0.21% 0.32% 0.88% 0.72% 1.41% 2.08% STIBOR 3 Month 1.47% 0.80% 1.09% 5.27% 3.36% 3.21% STIBOR 6 Month 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% Swap 1-year 0.00% 0.00% 0.00% 0.60% 0.33% 0.10% Swap 2-year 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% Swap 3-year 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% Swap 5-year 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% Swap 7-year 0.00% 0.00% 0.00% 0.05% 0.01% 0.01% Swap 10-year 0.02% 0.00% 39.34% 0.39% 0.34% 31.71% Swap 15-year 0.00% 93.79% Omitted 0.00% 83.73% Omitted Swap 20-year 97.03% Omitted Omitted 87.79% Omitted Omitted

6.3.2 Interest Rate Risk

One of the goals of this study is to evaluate how the interest rate risk estimates differ for the respective frameworks. This interest rate risk for the RPM is estimated by Eq. (3.23) and defined as the percentage change in portfolio value due to a parallel shift in the portfolio yield (i.e. the market interest rate securities). The results are presented in Table 6.10. Note that the interest rate risk is symmetric, i.e. the change in portfolio value subject to a -100 bps shift is equal to that of a +100 bps shift but with the opposite sign.

56 Table 6.10: The interest rate risk for the optimal 20-year, 15-year, and 10-year portfolios to the optimization problem described by Eq. (3.21) for every account category. The interest rate risk is estimated as the change in portfolio value subject to a +100 (+200) bps parallel shift in the market interest rate yield using Eq. (3.23). Higher absolute value indicate higher interest rate risk. The interest rate risk is symmetric, i.e. the change in portfolio value subject to a -100 bps shift is equal to that of a +100 bps shift but with the opposite sign.

Change in portfolio value due to a 100 bps (200 bps) increase in market interest rates 20-year Portfolio 15-year Portfolio 10-year Portfolio SA Aggregate -13.8051% (-27.6101%) -9.6813% (-19.3625%) -2.0466% (-4.0932%) TA Aggregate -18.9903% (-37.9806%) -13.6896% (-27.3792%) -3.6947% (-7.3894%) SA Private -15.1317% (-30.2633%) -10.5056% (-21.0111%) -2.0748% (-4.1496%) SA Corporate -12.8737% (-25.7474%) -8.9752% (-17.9504%) -1.8348% (-3.6697%) TA Private -19.4123% (-38.8246%) -14.0723% (-28.1447%) -3.9479% (-7.8958%) TA Corporate -17.6203% (-35.2407%) -12.6088% (-25.2176%) -3.1928% (-6.3857%)

The interest rate risk estimates displayed in Table 6.10 indicate that the interest rate risk varies depending on the portfolio maturity. This is expected as the optimal portfolios for the different maturities either allocate most weight to the security with the longest maturity or have a different composition to the others (10-year portfolio). The interest rate risk to a 100 bps change for the 20-year (15-year) portfolio varies between 12.9% (10.0%) and 19.4% (14.1%) depending on the account classification. The interest rate risks for the 10- year portfolios are significantly lower than for the other portfolios, which are caused by the optimal 10-year portfolios allocating a large weight to the 1-week STIBOR. A more interesting insight is the observed trend in the interest rate risk estimates for the different portfolios. Analogous to the interest rate risk estimates of the EVM, the interest rate risk for the RPM is higher for TA and private clients than for SA and corporate clients respectively. Overall, the different interest rate risk estimates for the different portfolios, account, and client types are expected given the varying portfolio allocations presented in Table 6.7-6.9. This observed variability in the interest rate risk estimates highlights a disadvantage of the RPM, i.e. its sensitivity to the choice of securities included in the portfolio. Consequently, this implies that a bank using the RPM to assess the interest rate risk in demand deposits should be cautious when interpreting the obtained estimates.

57 7 Discussion

The purpose of this section is to put the results and analysis from section 6 into the con- text of this study’s research questions. The first sub-section answers to the first research question:

♦ RQ1: How does the modeling of demand deposit rates and volumes differ between account and client categories?

This is followed by the sub-section dedicated to the second research question:

♦ RQ2: How do the interest rate risk estimations from the EVM compare to those of the RPM?

Finally, a discussion regarding the sustainability aspect of this study is held.

7.1 Model differences: Account and Client Categories

With regards to RQ1, the results from this study show that there are indeed a few differences between the account and client categories when it comes to modeling of the deposit rate and volume. The deposit rate models are quite similar across the categories, where the included components in the models are identical: the lag 1 AR component and the lag 0 market interest rate. This essentially means that the deposit rate can be sufficiently explained by the current market interest rate and the deposit rate of last month. The only differences between categories are the coefficients of the components, mainly for the market interest rate, which suggest that deposit rates of SA follow the market interest rate closer than those of TA. This is in line with the results of Hutchison and Pennacchi (1996) and O’Brien (2000). Moreover, the same dynamics can be seen on a client level, where deposit rates for corporate accounts follow the market interest rate closer than private accounts. This could be due to corporate clients having dedicated finance divisions continously monitoring the interest rates, prompting banks to pay deposit rates that are more in line with the market interest rate in order to retain the clients. Private clients may lack the knowledge or resources to closely monitor their finances, thus allowing banks to eke out larger spreads.

The model differences between account and client categories are more prominent in the deposit volume models. The volumes of TA react faster to changes in the spread between the market interest rate and the deposit rate compared to the volumes of SA. The nature and purpose of the two account types could be a possible explanation to this discrepancy

58 in reaction time. SA are intended for saving purposes and their volumes have historically been more stable than TA. It can thus be interpreted that SA require spread changes over a longer period of time before they start to have an effect on the volumes. Furthermore, the volumes of corporate accounts are also quicker to react to the interest rate spread than private accounts. This can be explained by the same line of reasoning as with the deposit rates, where corporations are more likely to continuously monitor their finances.

The distinctions between the SA and TA are more pronounced for private clients than for corporate. The volumes of corporate accounts are negatively correlated to changes in the spread regardless of being SA or TA. This suggests that corporate clients will withdraw money during increasing market interest rates and deposit money during declining market interest rates. This is reasonable since financing via debt typically gets more expensive in environments with high market interest rates, thus prompting corporations to use their cash reserves rather than taking expensive loans. On the other hand, the results indicate that private clients deposit money (which may originate partly from their TA) in their SA during increasing market interest rates. This contrast to corporate clients could be due to private clients’ lack of better alternatives or lack of knowledge/time to pursue said alternatives.

Another interesting point is that all categories show strong signs of seasonality in the deposit volumes. The periodicity of the seasonality is 1 year which is seen in the lag 12 AR com- ponent in every volume model. This is something that no previous research have accounted for, but makes sense since specific events that could affect demand deposits volumes occur every year, such as tax refunds, holiday season shopping and summer vacation.

The distinctive volume of corporate SA is important to discuss. As explained in section 6.2.2, the peculiar development of the historical corporate SA volume results in an increased uncertainty in the forecasted volume. This is visible in Figure 6.7, where the forecasted future volumes have a much wider spread between the upper and lower 95% confidence intervals. Because the lower 95% forecast scenario seem highly unlikely when compared to the other account and client categories, the actual forecasted volume is used in the interest rate risk calculations in the EVM (recall that RPM does not take volumes into consideration). This could lead to the interest rate risk for corporate SA being relatively high in comparison to the other categories. Still, the growth of the actual forecasted volume for corporate SA is still very modest in relation to even the lower 95% volumes of the other categories. If anything, this suggests that the interest rate risk for corporate SA is estimated rather conservatively.

Finally, none of the macroeconomic variables (GDP, Unemployment, and Monetary aggre-

59 gate) are found to significantly improve the deposit volume models, whilst neither market competition nor the asymmetry variable improve the deposit rate models. The largest im- provement can be seen in the deposit volume model for corporate TA, where including all three macroeconomic variables improves the AIC score and the standard error by 4.2% each. This is a relatively small improvement considering the addition of three extra variables that has to be modeled on their own as well, which in turn increases the uncertainty of the forecasts.

One likely explanation to why the exogenous variables do not improve the models is that some of the variables are linearly interpolated to monthly data. Since the model fitting method is based on the cross-correlations between the dependent variable and the input variables, the interpolated data could give misleading signals. The asymmetry variable, which intends to capture banks’ alleged asymmetric behavior when setting deposit rates, may be more significant if daily market interest rate/deposit rate data is used instead. The difference in the time it takes for banks to raise/lower deposit rates in response to increasing/declining market interest rates could possibly be a matter of days as opposed to months. Furthermore, most of the aforementioned variables included in this study are based on results or suggestions from previous studies (see e.g. market concentration from Hannan and Prager, 2006). The vast majority of these previous studies are done in the U.S. market, whose banking sector may differ from the Swedish market. The banking sector in Sweden is dominated by four major banks, whilst having a relatively lack of smaller boutique firms (Swedish Bankers’ Association, 2015). This difference in market compositions is a possible explanation to why the variables did not prove to be as significant as in the previous studies.

7.2 Interest Rate Risk Comparison of EVM and RPM

In view of RQ2, the impact on the interest rate risk estimates based on the choice of modeling framework is investigated. As displayed in Table 6.6 and Table 6.10, the magnitude of the interest rate risk varies depending on the selected framework and time horizon. The interest rate risks from the RPM vary to a greater extent between time horizons compared to those from the EVM. In line with the findings of Kalkbrener and Willing (2004), the obtained results shows that the interest rate risks from the RPM vary significantly depending on the securities included in the portfolios.

For the 20- and 15-year horizons, the RPM consistently yields higher interest rate risk estimates than the EVM regardless of the account and client categories. The discrepancy in the interest rate risk estimates between the EVM and the RPM are more pronounced

60 for SA than TA. This pattern is the most distinct for corporate SA in the 20-year horizon where the RPM estimates the interest rate risk, to a 100 bps market interest rate change, to be almost 166% larger than the EVM. The observed discrepancy is slightly reduced for the 15-year horizon. In contrast, the interest rate risk estimates for the 10-year horizon differ from the aforementioned pattern. In this case, the EVM yields higher interest rate risk estimates than the RPM with the discrepancy now being more distinct for TA than SA.

Despite the differences in magnitude of the obtained interest rate risk estimates from the EVM and the RPM, the observed pattern in terms of which account and client category are consistent in both frameworks. Regardless of the choice of framework, TA are found to be riskier than SA. These results are in line with the findings of Hutchison and Pennacchi (1996) and O’Brien (2000). Analogously, private accounts are found to be more exposed to interest rate risk than corporate accounts. The aforementioned results are to be expected since the deposit rates of SA and corporate accounts follow the market rate closer than their counterparts (recall the more detailed analysis in section 6.2.3).

The variability in the interest rate risk estimates between the EVM and RPM are likely due to the choice of interest rate risk measure in respective framework. In the EVM, the interest rate risk is derived from the deposit liability which is a bank’s net liability after the rents are deducted from the deposit volume. This is a direct method of estimating the interest rate risk since the actual deposited capital is used to determine how the deposit liability changes with respect to changes in the market interest rate. In contrast, the RPM estimates the interest rate risk based on the duration of a portfolio, consisting of market interest rate securities, that replicates the demand deposit behavior as closely as possible. This may be seen as an indirect method since the replicating portfolio and not the deposit volume is used to assess the interest rate risk. The reason as to why the RPM generates higher interest rate risk estimates for the 15- and 20-year horizons is due to the large portfolio weight allocated in the security with the longest maturity in the replicating portfolio (Table 6.7-6.9). Analogously, the reason why the RPM yields lower interest rate risk estimates for the 10-year horizon than the EVM is due to the large portfolio allocation in short term securities (see Table 6.7-6.9).

Since the RPM estimates the interest rate risk based on a replicating portfolio, the inter- est rate risk is sensitive to the choice of market interest rate securities used and how the portfolio is constructed. This may explain the obtained differences in the interest rate risk estimates between the EVM and RPM. Since the RPM aims to mimic the deposit behavior, the maturity and the portfolio weight of each security indicate the time the deposited capital is expected to remain at the bank. To clarify the chain of thought, recall that the optimal

61 portfolio for TA on an aggregate level allocates 94.88% to the security with the 20-year maturity (Table 6.7). Consequently, this means the RPM predicts that 94.88% of the de- posited capital is expected to remain at the bank for 20 years. However, the expected time the demand deposits are projected to stay at the bank is dependent on the selected market interest rate securities. For instance, for the 20-year portfolio in this study, the three securi- ties with the longest maturities are the 10-year, 15-year and 20-year swap rates. Therefore, this implies that the RPM predicts the deposited capital is withdrawn every 5 years, i.e. after 10, 15 and 20 years respectively. This simplifying assumption is a shortcoming with the RPM as demand deposits are in practice typically withdrawn more continuously than the RPM implies. While this may be mitigated by including more market interest rate se- curities with different maturities, this solution is also associated with additional complexity. In contrast, the EVM is able to compute the in- and outflow of the deposit volumes on a monthly basis, which should improve the interest risk estimates.

Another limitation of the RPM that is important to mention is the duration based measure used for assessing the interest rate risk. Despite it being a commonly used measure, it is only an approximate measure of the interest rate risk for small changes in the market interest rate. This may explain why the discrepancy in the interest rate risk estimates from the EVM and the RPM is amplified for larger shifts in the market interest rate.

Still, the EVM in this particular study faces a similar problem as the RPM, namely that the interest rate risk varies for the different choices of time horizons, albeit not as much as for the RPM. For the EVM, it is theoretically possible to find a time horizon large enough where the cumulative present value of future deposit rents converges to a fix value, as long as the rents’ growth rate is less than the market interest rate. But because of the nature of the data used in this study, it is difficult to arrive at this convergence. First of all, the downward trend in the historical 1-month STIBOR leads to a relatively low long term mean in the forecasted market interest rates. Meanwhile, the case bank enjoyed strong growth in deposit volume during the last decade. As a result, the forecasted deposit rents show continued growth as they are a function of the deposit volume, even when the deposit volume used to calculate rents are chosen as the lower 95% confidence interval limit. With higher market interest rates and slower deposit volume growth, convergence may well be reached, thus making the EVM approach more favorable as the number of assumptions can be further reduced.

62 7.3 Sustainability

In light of the 2008 financial crisis, regulatory authorities have implemented several measures to assert the sustainability of financial markets. One of the most prominent actions is the enactment of stricter capital requirements to account for the unexpected risks banks may face. Despite the employment of stricter regulations, no explicit guidelines regarding the interest rate risk management of demand deposits have been implemented. From a sustainability perspective, the absence of explicit guidelines is worrying since one of banks’ primary functions is to facilitate saving and lending in the society (Swedish National Bank, 2014). Banks commonly perform this function by transforming demand deposits from parties with abundant capital to credits for parties in need of capital. The lack of guidelines for managing the interest rate risk in demand deposits is one of the reasons that motivated this study. The findings of this study may contribute to the sustainable development of financial industries in two ways: first, it highlights the magnitude of the inherent interest rate risk in demand deposit and the importance to account for it. Second, this study provides two modeling frameworks which allow banks to measure the interest rate risk of demand deposits. By adequately capturing the risks in demand deposits, banks may in extension perform their societal role as financial intermediaries more efficiently and solidify themselves in times of economic recessions.

63 8 Conclusion

Since the future volumes and deposit rates of demand deposits are unknown, correctly in- corporating demand deposits into capital and funding planning poses a significant challenge as it requires a clear understanding of the underlying risks. As a result, the purpose of this study is to empirically evaluate the modeling of the valuation and interest rate risk in demand deposits, with the main goal of this study being the following:

♦ How can demand deposit rates, volumes, and interest rate risk be modeled?

This study is hereby concluded by putting the two research questions in relation to this goal. The demand deposits are first separated into different categories: savings accounts (SA), transaction accounts (TA), private accounts, and corporate accounts. The two most prominent frameworks for modeling demand deposits in existing literature are then exam- ined. These frameworks are the Economic Value Model (EVM) and the Replicating Portfolio Model (RPM).

The main findings of this study show that the deposit rates and volumes can be sufficiently modeled with the widely-used time series framework SARIMAX. The deposit rates can be explained by their own lagged values and the market interest rate, while market concen- tration and asymmetric deposit rate policy are not explanatory. The deposit volumes can be explained by the spread between the market interest rate and the deposit rate, together with lagged values of itself and moving-average terms. The macroeconomic variables GDP, Unemployment, and Monetary aggregate are not explanatory for the deposit volumes.

The results show that there are differences within the different types of demand deposits when it comes to the modeling of deposit rates and volumes. The deposit rates of SA and corporate accounts follow the market interest rate closer than their counterparts, while taking higher values as well. Furthermore, the deposit volumes of TA and corporate accounts are found to be more reactive to changes in the interest rate spread than their counterparts. As a result, the interest rate risks, which are dependent on the deposit rates and volumes, are also different between categories. In both the EVM and RPM, SA and corporate accounts are observed to have a lower exposure to interest rate risk than their counterparts. These differences suggest that it may be wise to separate demand deposits into various categories when modeling their dynamics.

The comparison between the EVM and the RPM shows that the RPM arrives at higher interest rate risks for the 15- and 20-year horizons, and vice versa for the 10-year horizon. The differences in the interest rate risks produced by the two frameworks are reduced for

64 smaller changes in the market interest rate. Both frameworks yield interest rate risks that are dependent on assumptions regarding the time horizon, although it can theoretically be made independent in the case of EVM which is an advantage of the EVM.

There a few delimitations and limitations of the study which affects the generalizability of the findings. The first delimitation is the sole focus on the Swedish demand deposit market. Consequently, the findings are subject to Swedish regulations which may differs from other jurisdictions. Therefore, it is left to future research to evaluate the generalizability of the constructed models in other demand deposits markets. Another delimitation of this study is the focus on the interest rate risk in demand deposits. Since demand deposits are also exposed to liquidity risk, future research could seek to develop a more comprehensive modeling framework by extending the models of this study to also capture the liquidity risk in demand deposits.

A limitation of the results is the difficulty to model future market interest rate. While this study implemented the commonly used Vasicek model (see e.g. Hutchison and Pennacchi, 1996), the presence of a negative trend in historical Swedish market rates resulted in a rela- tively low long-term interest rate. With this in mind, an interesting area for future research would be to extend this study by considering alternative interest rate modeling frameworks such as the Heath-Jarrow-Morton framework. Nevertheless, the findings of this study pro- vide banks valuable tools for implementing a prudent interest rate risk management.

65 References

Bank of Japan (2014). Survey on Core Deposit Modeling in Japan: Toward Enhancing Asset and Liability Management, Bank of Japan Report and Research Paper.

Bardehewer, M. (2007). Modeling Non-maturity products. In: Matz, L. and Neu, P. eds. Liquidity Risk Measurement and Management. Wiley, pp. 220-256.

Basel Committee on Banking Supervision (2004). Principles for the Management and Su- pervision of Interest Rate Risk.

Bodie, Z., Kane, A. and Marcus, A.J. (2014). Investments. Tenth Edition. McGraw-Hill Education, New York, USA.

Brockwell, P.J. and Davis, R.A. (2002). Introduction to Time Series and Forecasting. Sec- ond Edition. Springer-Verlag, New York, USA.

Carmona, G. (2007). Bank Failures Caused by Large Withdrawals: An Explanation Based Purely on Liquidity. Journal of Mathematical Economics, vol. 43.

Collis, J. and Hussey, R. (2014). Business Research: A practical guide for undergraduate and postgraduate students. Fourth Edition. Palgrave Macmillan, London, England.

Cox, J.C., Ingersoll J.E. and Ross S.A. (1985). A Theory of the Term Structure of Interest Rates, Econometrica, vol. 53.

Dermine, J. (2015). Basel III leverage ratio requirements and the probability of bank runs, Journal of Banking and Finance, vol. 53.

Dewachter, H., Lyrio. M. and Maes, K. (2006). A Multi-Factor Model for the Valuation and Risk Management of Demand Deposits, working paper, National Bank of Belgium.

Eriksson, G. (2008). Numeriska Algoritmer med MATLAB. Royal Institute of Technology Data Science department, Stockholm, Sweden.

Finansinspektionen (2014). FI:s metoder f¨orbed¨omningav enskilda risktyper inom pelare 2.

Fraundorfer, K. and Sch¨urle,M. (2003). Management of non-maturing deposits by multi- stage stochastic programming, European Journal of Operational Research, vol. 151.

66 Goldstein, I. and Pauzner, A. (2005). Demand Deposit Contracts and the Probability of Bank Runs, Journal of Finance, vol. 60.

Hagin, R.L. and Khan, R.N (1990). What Practitioners Need to Know about Backtesting, Financial Analyst Journal, vol. 46.

Hannan, T. H. and Prager, R. A. (2006). Multimarket bank pricing: An empirical investi- gation of deposit interest rates. Journal of Economics and Business, vol. 58.

Harder, D.W. (2005). Topic 6.4: Extrapolation. https://ece.uwaterloo.ca/ dwharder/NumericalAnalysis/06LeastSquares/extrapolation/complete.html Accessed: 2015-05-04.

Hull, J.C. (2009). Options, Futures and Other Derivatives. Seventh Edition. Pearson Education, New Jersey, USA.

Hutchison, D. and Pennacchi, G.G. (1996). Measuring Rents and Interest Rate Risk in Imperfect Financial Markets: The Case of Retail Bank Deposits. The Journal of Financial and Quantitative Analysis, vol. 31.

Jarrow, R. A. and van Deventer, D. R. (1998). The arbitrage-free valuation and hedging of demand deposits and credit card loans. Journal of Banking & Finance, vol. 22.

Kalkbrener, M. and Willing, J. (2004). Risk management of non-maturing liabilities. Jour- nal of Banking & Finance, vol. 28.

Maes, K. and Timmermans, T. (2005). Measuring the interest rate risk of Belgian regulated saving deposits, National Bank of Belgium, Financial Stability Review.

Neumark, D. and Sharpe, S. A. (1992). Market Structure and the Nature of Price Rigidity: Evidence from the Market for Consumer Deposits. The Quarterly Journal of Economics, vol. 107.

Nystr¨om,K. (2008). On deposit volumes and the valuation of non-maturing liabilities. Journal of Economic Dynamics and Control, vol. 32.

O’Brien, J. M. (2000). Estimating the Value and Interest Rate Risk of Interest-Bearing Transaction Deposits. Division of Research and Statistics, Board of Governors, Federal Reserve System.

67 O’Brien, J. M., Orphanides, A. and Small, D. (1994). Estimating the Interest Rate Sen- sitivity of Liquid Retail Deposits. Proceedings of a Conference on Bank Structure and Competition, Chicago Federal Reserve Bank.

Rosen, R. J. (2007). Banking market conditions and deposit interest rates. Journal of Banking & Finance, vol. 31.

Statistics Sweden (2010). Quaterly National Accounts Inventory: Sources and methods for Swedish National Accounts.

Statistics Sweden (2014). Begrepp och Definitioner AKU.

Statistics Sweden (2014). Finansmarknadsstatistik december 2014.

Swedish National Bank (2014). Den svenska finansmarknaden.

Vasicek, O. (1977). An Equilibrium Characterization of the Term Structure. Journal of Financial Economics, vol. 5.

Wooldridge, J.M. (2013). Introductory to Econometrics: A modern approach. Fifth Edition. South-Western, Ohio, USA.

Zeytun, S. and Gupta, A. (2007). A Comparative Study of the Vasicek and the CIR model of the Short Rate. Published reports, Fraunhofer Institut Techno- und Wirtschaftsmathe- matik.

68 Appendix

Appendix A - Complementing Data

·105 1.8

1.6

1.4

1.2

1

MSEK 0.8

0.6

0.4

0.2

0 2006 2008 2010 2012 2014 Year

Figure A.1: The deposit volume (in MSEK) placed in pri- vate SA from 2004 to 2014.

·104

2.4 2.2 2 1.8 1.6 1.4 1.2 MSEK 1 0.8 0.6 0.4 0.2 0 2006 2008 2010 2012 2014 Year

Figure A.2: The deposit volume (in MSEK) placed in cor- porate SA from 2004 to 2014.

69 ·105 1.6

1.4

1.2

1

0.8 MSEK 0.6

0.4

0.2

0 2006 2008 2010 2012 2014 Year

Figure A.3: The deposit volume (in MSEK) placed in pri- vate TA from 2004 to 2014.

·104 8

7

6

5

4 MSEK 3

2

1

0 2006 2008 2010 2012 2014 Year

Figure A.4: The deposit volume (in MSEK) placed in cor- porate TA from 2004 to 2014.

70 10

9

8 % 7

6

5 2006 2008 2010 2012 2014 Year

Figure A.5: The unemployment rate in Sweden between 2004 and 2014. Data source: Statistics Sweden (2015).

·106 1.05

1

0.95

0.9

0.85 MSEK 0.8

0.75

0.7

0.65 2006 2008 2010 2012 2014 Year

Figure A.6: The nominal gross domestic product (GDP) in MSEK between 2004 and 2014. Data source: Statistics Sweden (2015).

71 ·105 1.05

1

0.95

0.9 MSEK 0.85

0.8

0.75 2006 2008 2010 2012 2014 Year

Figure A.7: The monetary aggregate supply (M0) in Sweden between 2004 and 2014. Data source: Statistics Sweden (2015).

0.18

0.18

0.18

0.17

0.17

0.16 2006 2008 2010 2012 2014 Year

Figure A.8: Market concentration (HHI) between 2004 and 2014. The HHI takes values between 0 and 1, where 0 indicate a perfectly competitive market and 1 a monopoly. Data source: Swedish Bankers’ Association (2015).

72 Appendix B - Model Parameter Diagnostics

Table B.1: Displays the p-values of HHI and assymetry term for different deposit rate model combinations for all account and client categories. The variables are defined as: x = HHI and I = As- symetry term. The leftmost column displays the variables included in the model. The lag of the variable is stated in the parenthesis. For instance, the first model combination under SA Aggregate which only says x(o) means that this deposit rate model only include the macroeconomic variable HHI and it has lag 0. Analogously x(2) and I(0)means the model include the HHI with lag 0 and the assymetry term with lag 0. Note that the higher the p-value the less significant is the variable.

x I SA Aggregate x (0) 0.4613 I (0) 0.3994 x (0), I (0) 0.4702 0.4070 TA Aggregate x (0) 0.6673 I (0) 0.6150 x (0), I (0) 0.6628 0.6117 SA Private x (0) 0.4689 I (0) 0.4639 x (0), I (0) 0.4770 0.4720 SA Corporate x (0) 0.3603 I (0) 0.2466 x (0), I (0) 0.3702 0.2533 TA Private x (0) 0.8588 I (0) 0.5662 x (0), I (0) 0.8673 0.5698 TA Corporate x (0) 0.2940 I (0) 0.9535 x (0), I (0) 0.2955 0.9431

73 Table B.2: Displays the p-values of the macroeconomic variables for different deposit volume model combinations for all account and client categories. The variables are defined as: G = GDP, U = Unemployment Rate and M = Monetary Aggregate. The leftmost column displays the macroeco- nomic variables included in the model. The lag of the variable is stated in the parenthesis. For instance, the first model combination under SA Aggregate which only says G(2) means that this deposit volume model only include the macroeconomic variable GDP and it has lag 2. Analogously G(2), U(0) and M(1) means the model include the GDP with lag 2, the unemployment rate with lag 0 and monetary aggregate with lag 1. Note that the higher the p-value the less significant is the variable.

GUM GUM SA Aggregate TA Aggregate G (2) 0.0441 G (0) 0.0118 U (0) 0.3258 U (0) 0.9381 M (1) 0.5659 M (2) 0.0685 G (2), U (0) 0.0158 0.0951 G (0), U (0) 0.0097 0.5749 G (2), M (1) 0.0268 0.3190 G (0), M (2) 0.0026 0.0120 U (0), M (1) 0.2887 0.4986 U (0), M (2) 0.7041 0.0609 G (2), U (0), M (1) 0.0061 0.0532 0.1941 G (0), U (0), M (2) 0.0029 0.9888 0.0146 SA Private TA Private G (2) 0.0807 G (2) 0.3960 U (0) 0.3576 U (0) 0.6327 M (0) 0.8909 M (2) 0.1161 G (2) , U (0) 0.0420 0.1528 G (2), U (0) 0.4109 0.6621 G (2), M (0) 0.0794 0.7987 G (2), M (2) 0.7820 0.1798 U (0), M (0) 0.3049 0.7043 U (0), M (2) 0.9283 0.1351 G (2), U (0), M (0) 0.0341 0.0944 0.4770 G (2), U (0), M (2) 0.7773 0.9142 0.2050 SA Corporate TA Corporate G (1) 0.4670 G (0) <0.0001 U (5) 0.9142 U (6) 0.5111 M (1) 0.8364 M (0) 0.0564 G (1), U (5) 0.4912 0.9384 G (0), U (6) <0.0001 0.3499 G (1), M (1) 0.4495 0.7347 G (0), M (0) <0.0001 0.6314 U (5), M (1) 0.8563 0.7975 U (6), M (0) 0.9210 0.0890 G (1), U (5), M (1) 0.4712 0.8461 0.7037 G (0), U (6), M (0) <0.0001 0.4333 0.9739

74 Appendix C - Model Residual Correlation Plots

1 1

0.5 0.5

0 0 Correlation Correlation

−0.5 −0.5

−1 −1 2 4 6 8 10 12 14 16 18 20 22 24 2 4 6 8 10 12 14 16 18 20 22 24 Lag Lag (a) The ACF plot. (b) The PACF plot.

Figure C.9: The ACF plot (left) and PACF plot (right) for the Deposit Volume model for SA Aggregate. The blue dashed lines indicate the boundaries of the 95% confidence interval.

1 1

0.5 0.5

0 0 Correlation Correlation

−0.5 −0.5

−1 −1 2 4 6 8 10 12 14 16 18 20 22 24 2 4 6 8 10 12 14 16 18 20 22 24 Lag Lag (a) The ACF plot. (b) The PACF plot.

Figure C.10: The ACF plot (left) and PACF plot (right) for the Deposit Volume model for TA Aggregate. The blue dashed lines indicate the boundaries of the 95% confidence interval.

75 1 1

0.5 0.5

0 0 Correlation Correlation

−0.5 −0.5

−1 −1 2 4 6 8 10 12 14 16 18 20 22 24 2 4 6 8 10 12 14 16 18 20 22 24 Lag Lag (a) The ACF plot. (b) The PACF plot.

Figure C.11: The ACF plot (left) and PACF plot (right) for the Deposit Volume model for SA Private. The blue dashed lines indicate the boundaries of the 95% confidence interval.

1 1

0.5 0.5

0 0 Correlation Correlation

−0.5 −0.5

−1 −1 2 4 6 8 10 12 14 16 18 20 22 24 2 4 6 8 10 12 14 16 18 20 22 24 Lag Lag (a) The ACF plot. (b) The PACF plot.

Figure C.12: The ACF plot (left) and PACF plot (right) for the Deposit Volume model for SA Corporate. The blue dashed lines indicate the boundaries of the 95% confidence interval.

76 1 1

0.5 0.5

0 0 Correlation Correlation

−0.5 −0.5

−1 −1 2 4 6 8 10 12 14 16 18 20 22 24 2 4 6 8 10 12 14 16 18 20 22 24 Lag Lag (a) The ACF plot. (b) The PACF plot.

Figure C.13: The ACF plot (left) and PACF plot (right) for the Deposit Volume model for TA Private. The blue dashed lines indicate the boundaries of the 95% confidence interval.

1 1

0.5 0.5

0 0 Correlation Correlation

−0.5 −0.5

−1 −1 2 4 6 8 10 12 14 16 18 20 22 24 2 4 6 8 10 12 14 16 18 20 22 24 Lag Lag (a) The ACF plot. (b) The PACF plot.

Figure C.14: The ACF plot (left) and PACF plot (right) for the Deposit Volume model for TA Corporate. The blue dashed lines indicate the boundaries of the 95% confidence interval.

77 1 1

0.5 0.5

0 0 Correlation Correlation

−0.5 −0.5

−1 −1 2 4 6 8 10 12 14 16 18 20 22 24 2 4 6 8 10 12 14 16 18 20 22 24 Lag Lag (a) The ACF plot. (b) The PACF plot.

Figure C.15: The ACF plot (left) and PACF plot (right) for the Deposit Rate model for SA Aggre- gate. The blue dashed lines indicate the boundaries of the 95% confidence interval.

1 1

0.5 0.5

0 0 Correlation Correlation

−0.5 −0.5

−1 −1 2 4 6 8 10 12 14 16 18 20 22 24 2 4 6 8 10 12 14 16 18 20 22 24 Lag Lag (a) The ACF plot. (b) The PACF plot.

Figure C.16: The ACF plot (left) and PACF plot (right) for the Deposit Rate model for TA Aggre- gate. The blue dashed lines indicate the boundaries of the 95% confidence interval.

78 1 1

0.5 0.5

0 0 Correlation Correlation

−0.5 −0.5

−1 −1 2 4 6 8 10 12 14 16 18 20 22 24 2 4 6 8 10 12 14 16 18 20 22 24 Lag Lag (a) The ACF plot. (b) The PACF plot.

Figure C.17: The ACF plot (left) and PACF plot (right) for the Deposit Rate model for SA Private. The blue dashed lines indicate the boundaries of the 95% confidence interval.

1 1

0.5 0.5

0 0 Correlation Correlation

−0.5 −0.5

−1 −1 2 4 6 8 10 12 14 16 18 20 22 24 2 4 6 8 10 12 14 16 18 20 22 24 Lag Lag (a) The ACF plot. (b) The PACF plot.

Figure C.18: The ACF plot (left) and PACF plot (right) for the Deposit Rate model for SA Corpo- rate. The blue dashed lines indicate the boundaries of the 95% confidence interval.

79 1 1

0.5 0.5

0 0 Correlation Correlation

−0.5 −0.5

−1 −1 2 4 6 8 10 12 14 16 18 20 22 24 2 4 6 8 10 12 14 16 18 20 22 24 Lag Lag (a) The ACF plot. (b) The PACF plot.

Figure C.19: The ACF plot (left) and PACF plot (right) for the Deposit Rate model for TA Private. The blue dashed lines indicate the boundaries of the 95% confidence interval.

1 1

0.5 0.5

0 0 Correlation Correlation

−0.5 −0.5

−1 −1 2 4 6 8 10 12 14 16 18 20 22 24 2 4 6 8 10 12 14 16 18 20 22 24 Lag Lag (a) The ACF plot. (b) The PACF plot.

Figure C.20: The ACF plot (left) and PACF plot (right) for the Deposit Rate model for TA Corpo- rate. The blue dashed lines indicate the boundaries of the 95% confidence interval. The PACF plot suggests that there is a significant correlation at lag 3. By adding the AR term with lag 3 to the model, the model scores an AIC of -1524.10 and Std Err of 0.000712. This is a negligible change from the final model which has an AIC of -1512.55 and Std Err of 0.000747. This is the reason why the lag 3 AR term is excluded from the final model, even though the ACF and PACF plots suggest the opposite.

80