Demand Deposits: Valuation and Interest Rate Risk Management821427/FULLTEXT01.pdf · Demand Deposits: Valuation and Interest Rate Risk Management YANG LU KEVIN VISVANATHAR Master

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:Vardering och Ranteriskhantering

Yang LuKevin Visvanathar

Examensarbete INDEK 2015:29KTH Industrial Engineering and Management

Industrial ManagementSE-100 44 STOCKHOLM

Demand Deposits:Valuation and Interest Rate Risk Management

Yang LuKevin Visvanathar

Master of Science Thesis INDEK 2015:29KTH Industrial Engineering and Management

Industrial ManagementSE-100 44 STOCKHOLM

Sammanfattning

Till foljd av finanskrisen 2008 har regulatoriska myndigheter infort mer strikta regelverk foratt framja en sund finansiell riskhantering hos banker. Trots avistakontons okade betydelsefor banker har inga regulatoriska riktlinjer introducerats for hur den associerade ranteriskenska hanteras ur ett riskperspektiv. Avistakonton ar forknippade med tva faktorer somforsvarar utvarderingen av dess ranterisk med traditionella ranteriskmetoder: de saknaren forutbestamd loptid och avistarantan kan andras nar sa banken onskar. Med hansyntill detta gap fokuserar denna studie pa att empiriskt analysera tva modelleringsramverkfor att vardera och mata ranterisken hos avistakonton: Economic Value Model Framework(EVM) and Replicating Portfolio Model Framework (RPM). Analysen genomfors genom attinitialt ta fram modeller for hur avistarantan och volymen pa avistakonton utvecklas over tidmed hjalp av ett modernt och unikt dataset fran en av Sveriges storsta kommersiella banker.Studiens resultat indikerar att modellerna for avistarantan och avistavolymen inte forbattrasnar makroekonomiska variabler ar inkluderade. Detta ar i kontrast till vad tidigare studierhar foreslagit. Vidare visar studiens resultat att det modellerna skiljer sig nar avistakontonaar segmenterade pa en mer granular niva. Slutligen pavisar resultatet att EVM producerarranteriskestimat som ar mindre kansliga for antanganden an RPM.

Nyckelord: avistakonton, ranterisk, marknadsranta, stokastisk simulering, nuvarde, rep-likerande portfolj, sparkonto, transaktionskonto

i

Abstract

In the aftermath of the financial crisis of 2008, regulatory authorities have implementedstricter policies to ensure more prudent risk management practices among banks. Despitethe growing importance of demand deposits for banks, no policies for how to adequatelyaccount 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 usingstandardized models: they lack a predetermined maturity and the deposit rate may bechanged 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 twodifferent frameworks: the Economic Value Model Framework (EVM) and the ReplicatingPortfolio Model Framework (RPM). To analyze the two frameworks, models for the demanddeposit rate and demand deposit volume are developed using a comprehensive and noveldataset provided by one the biggest commercial banks in Sweden. The findings indicate thatincluding macroeconomic variables in the modeling of the deposit rate and deposit volumedo not improve the modeling accuracy. This is in contrast to what has been suggested byprevious studies. The findings also indicate that there are modeling differences betweendemand deposit categories. Finally, the EVM is found to produce interest rate risks withless 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 Lonnbark for the introduction of this topic andtheir continuous support throughout this process. Furthermore, we would also like to thankour supervisor Gustav Martinsson at the Royal Institute of Technology for his invaulableadvice and support. Finally, we would like to express our gratiude to our families and friendsfor their constant support.

Stockholm, May 2015Yang 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


3.2.1 SARIMAX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.2.2 Box-Jenkins Model Fitting . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2.3 Interest Rate Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18



4 Methodology 21

4.1 General Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.1.1 Demand Deposit Categorization . . . . . . . . . . . . . . . . . . . . . 23

4.2 Market Interest Rate Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23


4.3.1 Deposit Rate Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.3.2 Deposit Volume Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 25



iv


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


6.2.1 Deposit Rate Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

6.2.2 Deposit Volume Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 43


6.3 Replicating Portfolio Model Framework . . . . . . . . . . . . . . . . . . . . . 52

6.3.1 Portfolio Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . 53


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 Figures4.1 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 Tables6.1 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 theoffered deposit rate may be changed at the bank’s discretion.

Deposit Liability - The net deposit liability banks’ owe customers. Defined as the currentdeposited 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 measuringthe interest rate risk in demand deposits.

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

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

M0 - A measure of the monetary aggregate in an economy. Defined as the total amount ofphysical 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 shortterm 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 periodto high interest rate.

STIBOR - Stockholm Interbank Offered Rate, which is the average rate banks at theSwedish 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 2014for 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 areprovided 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 expectedto 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; Nystrom,

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 ofzero 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 Schurle, 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; Nystrom, 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 depositrate 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 Schurle (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 Schurle, 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 Schurle, 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 Schurle (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 Schurle

(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

Schurle’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 theunderlying determinant (in this case deposit rates). For instance, a call option with a delta of 0.5 meansthat 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 Schurle (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.


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:

Rt = Vt(rt − rdt ) (3.2)

where Rt , Vt , rdt 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):

L = V0 −T∑k=1

ZkRk (3.3)

Zt =

t∏k=1

1

(1 + 112rk)

(3.4)

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)

Φ(B) = 1− φ1B − ...− φpBp (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:

BiYt = 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)

Θ(B) = 1− θ1B − ...− θqBq (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)

Wt = (1−B)kYt (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):

Wt = (1−B)k(1−Bs)KYt (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:

Wt = µ+∑i

Ψi(B)Xi,t +Θ(B)

Φ(B)εt (3.13)

Ψ(B) = ψ0 − ψ1B − ...− ψrBr (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:

Minimize

n∑t=1

(xt −∞∑i=1

πixt−i)2 (3.15)

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

Θ(B)

Φ(B)= 1−

∞∑i=1

πiBi (3.16)

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:

χ2m = n(n+ 2)

m∑k=1

r2kn− k (3.17)

where m is the lag and:

rk =

n−k∑t=1

atat+k

n∑t=1

a2t

(3.18)

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:

AIC = ln

( n∑t=1

a2t

n+ 2p

)n (3.19)

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

IRE =LnewL− 1 (3.20)

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.


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 Schurle, 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 Schurle, 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)

subject to

n∑i=1

wi = 1,

wi ≥ 0.

(3.21)

where R is the deposit rate and the portfolio return rp =n∑i=1

wiri, i.e. equal to the sum of

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 Schurle, 2003).

19


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:

D =

n∑i=1

wimi (3.22)

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

P= −D∆y (3.23)

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

Market Interest Rate

Deposit Rates

Deposit Volumes

Deposit Rents

Deposit Liability

Interest Rate Risk

Market Interest Rates

Portfolio Optimization

Interest Rate Risk

EVM RPM

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 Schurle, 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 Schurle, 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).


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:

(1−B)k(1−Bs)Krdt = Ψ1(B)rt + Ψ2(B)xt + cI[rt−rt−1>0] +Θ(B)

Φ(B)εt (4.2)

where rdt 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):

xt =

n∑i=1

γ2i (4.3)

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:

(1−B)k(1−Bs)KVt = µ+ Ψ1(B)(rt − rdt ) + Ψ2(B)Gt + Ψ3(B)Ut + Ψ4(B)Mt + Θ(B)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,

rdt 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.


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).


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 Schurle, 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:

wi =

1000∑k=1

wik

1000

(4.5)

where wi is the optimal weight of asset i in the final portfolio, and wki 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.


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 Schurle, 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 129different 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

2006 2008 2010 2012 20140

0.5

1

1.5

2

2.5

3

3.5

4·105

Year

MSEK

SA PrivateSA CorporateTA PrivateTA Corporate

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

Deposit rate at month i =Amount paid to depositors month i

Deposit volume month i(5.1)

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.

2006 2008 2010 2012 20140

1

2

3

4

5

6

Year

%

SA PrivateSA CorporateTA PrivateTA CorporateSTIBOR1M

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

2002 2004 2006 2008 2010 2012 20140

1

2

3

4

5

6

7

Year

%1d STIBOR

7d STIBOR

1m STIBOR

3m STIBOR

6m STIBOR

1y Swap

2y Swap

3y Swap

5y Swap

7y Swap

10y Swap

15y Swap

20y Swap

Figure 5.3: STIBOR and Swap rates between 2000 and 2014. Note that thelonger the maturity the security has, the less it fluctuates over time. DataSource: 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. */**/*** denotessignificance at the 10%, 5%, and 1% levels respectively. Recall from Eq. (4.1) that thefitted 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.

2008 2012 2016 2020 2024 2028 20320

1

2

3

4

5

6

Year

%

STIBOR 1m

Modeled STIBOR 1m

Figure 6.1: The historical and modeled values of STIBOR 1-Month from 2004 to2034. The simulated values from 2015 to 2034 are the average of 1000 simulatedpaths from the Monte Carlo simulation.


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:

(1−B)rdt = ψ1,0(1−B)rt +1

1− φ1Bεt (6.1)

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:(1−B)rdt = ψ1,0(1−B)rt + 1

1−φ1Bεt

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

2008 2012 2016 2020 2024 2028 20320

1

2

3

4

5

6

Year

%Modeled STIBOR 1mSA AggregateTA AggregateModeled SA AggregateModeled TA Aggregate

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 ratesfrom 2015 to 2034 are averages based on the 1000 simulated market interestrates (STIBOR 1-Month). The modeled STIBOR 1-Month is also shown forreference.

2008 2012 2016 2020 2024 2028 20320

1

2

3

4

5

6

Year

%

Modeled STIBOR 1mSA PrivateSA CorporateTA PrivateTA CorporateModeled SA PrivateModeled SA CorporateModeled TA PrivateModeled TA Corporate

Figure 6.3: The historical and modeled values of deposit rates separated intoprivate and corporate along with SA and TA from 2004 to 2034. The simulateddeposit 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 alsoshown 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 themarket interest rate, the market competition variable (HHI), and theasymmetry term respectively. The lags of the included market inter-est rate (0 lag) and market competition (0 lag) variables are chosenaccording to the Box-Jenkins model fitting method and are shown inAppendix 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:

(1−B)Vt = µ+ ψ1(B)(rt − rdt ) +θ(B)

φ(B)εt (6.2)

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-valueSA Aggregate

(1−B)Vt = µ+ ψ1,3B3(1−B)(rt − rdt ) + 1−θ1B

1−φ12Bεt

µ 589.34*** 205.4 2.87 0.0048φ12 0.64228*** 0.07652 8.39 <0.0001θ1 -0.27109*** 0.08854 -3.06 0.0027ψ1,3 130070*** 43390 3 0.0033

TA Aggregate

(1−B)Vt = µ+ ψ1,2B2(1−B)(rt − rdt ) + 1−θ2B

1−φ1B−φ12B12 εt

µ 558.99*** 158.4 3.53 0.0006φ1 -0.45754*** 0.07061 -6.48 <0.0001φ12 0.42645*** 0.07118 5.99 <0.0001θ2 0.29746*** 0.09211 3.23 0.0016ψ1,2 -203950** 92770 -2.2 0.0298

SA Private

(1−B)Vt = µ+ ψ1,3B3(1−B)(rt − rdt ) + 1−θ1B

1−φ12Bεt

µ 531.21*** 188.8 2.81 0.0057φ12 0.65625*** 0.07511 8.74 <0.0001θ1 -0.24634*** 0.08913 -2.76 0.0066ψ1,3 94619** 39980 2.37 0.0195

SA Corporate

(1−B)Vt = µ+ ψ1,2B2(1−B)(rt − rdt ) + 1−θ1B

1−φ12Bεt

µ 24.991 62.34 0.4 0.6892φ1 0.78160*** 0.07011 11.15 <0.0001θ1 -0.34818*** 0.08644 -4.03 <0.0001ψ1,2 -21423** 8971 -2.39 0.0184

TA Private

(1−B)Vt = µ+ ψ1,2B2(1−B)(rt − rdt ) + 1−θ2B


µ 310.99*** 88.74 3.5 0.0006φ1 -0.48590*** 0.06952 -6.99 <0.0001φ12 0.42611*** 0.06948 6.13 <0.0001θ2 0.46738*** 0.08835 5.29 <0.0001ψ1,2 -115420** 54720 -2.11 0.0369

TA Corporate

(1−B)Vt = µ+ ψ1,1B1(1−B)(rt − rdt ) + 1


µ 258.47* 146.2 1.77 0.0796φ1 -0.22034*** 0.07181 -3.07 0.0026φ12 0.60911*** 0.07538 8.08 <0.0001ψ1,1 -98862 60600 -1.63 0.1053

44

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

models incorporate a 12 month seasonal component (φ12B12), 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

2008 2012 2016 2020 2024 2028 20321

1.5

2

2.5

3

3.5

4

4.5·105

Year

MSEK

SA AggregateModeled SA Aggregate

Upper 95%

Lower 95%

Figure 6.4: The historical and modeled values of the deposit volume for theaggregate SA from 2004 to 2034. Included are the lower and upper limits of the95% confidence interval for the simulated values from 2015 to 2034.

2008 2012 2016 2020 2024 2028 20321

1.5

2

2.5

3

3.5

4·105

Year

MSEK

TA AggregateModeled TA Aggregate

Upper 95%

Lower 95%

Figure 6.5: The historical and modeled values of the deposit volume for theaggregate TA from 2004 to 2034. Included are the lower and upper limits of the95% confidence interval for the simulated values from 2015 to 2034.

46

2008 2012 2016 2020 2024 2028 20321

1.5

2

2.5

3

3.5

4·105

Year

MSEK

SA PrivateModeled SA Private

Upper 95%

Lower 95%

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

2008 2012 2016 2020 2024 2028 2032

−2

0

2

4

6

·104

Year

MSEK

SA CorporateModeled SA Corporate

Upper 95%

Lower 95%

Figure 6.7: The historical and modeled values of the deposit volume for corporateSA 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

2008 2012 2016 2020 2024 2028 20320.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6·105

Year

MSEK

TA PrivateModeled TA Private

Upper 95%

Lower 95%

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

2008 2012 2016 2020 2024 2028 20320.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2·105

Year

MSEK

TA CorporateModeled TA Corporate

Upper 95%

Lower 95%

Figure 6.9: The historical and modeled values of the deposit volume for corporateTA 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,U , and M indicate that the model includes the spread variable (rt − rdt ), the GDP variable, theunemployment variable, and the monetary aggregate variable respectively. The lags of the includedvariables are chosen according to the Box-Jenkins model fitting method and are shown in AppendixB. 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


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 thepre-shifted values, shown as percentages of the deposit volumes at t=0 (January 2015). ∆L indicates thepercentage change in deposit liability as a result of a +100 (+200) bps parallel shift in the simulated marketinterest rate yield curve. Higher absolute value indicate higher interest rate risk. Since the asymmetry termis not included in the deposit rate models, the interest rate elasticities are symmetric, i.e. the interest rateelasticity 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 forecastedvolume, as opposed to the lower limit of the 95% confidence interval used for the other volumes. This isdue to unexplainable behavior in the historical volumes for corporate SA, resulting in a model with higheruncertainty which produces a lower 95% limit that takes negative values. The implications of this choicewill 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 thebetter.

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). Theportfolios are modeled for SA and separated into private and corporate accounts. The portfolio allocations are givenin percent. Minimum variance specifies how well the portfolio replicate the behavior of the deposit rate, with the lowervalue the better.

SA: Private Corporate




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%



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 givenin percent. Minimum variance specifies how well the portfolio replicate the behavior of the deposit rate, with the lowervalue the better.

TA: Private Corporate




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%




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 theoptimization problem described by Eq. (3.21) for every account category. The interest rate risk isestimated as the change in portfolio value subject to a +100 (+200) bps parallel shift in the marketinterest rate yield using Eq. (3.23). Higher absolute value indicate higher interest rate risk. Theinterest rate risk is symmetric, i.e. the change in portfolio value subject to a -100 bps shift is equalto 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

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Statistics Sweden (2014). Finansmarknadsstatistik december 2014.

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Vasicek, O. (1977). An Equilibrium Characterization of the Term Structure. Journal of

Financial Economics, vol. 5.

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Zeytun, S. and Gupta, A. (2007). A Comparative Study of the Vasicek and the CIR model

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matik.

68

Appendix

Appendix A - Complementing Data

2006 2008 2010 2012 20140

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8·105

Year

MSEK

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

2006 2008 2010 2012 20140

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

·104

Year

MSEK

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

69

2006 2008 2010 2012 20140

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6·105

Year

MSEK

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

2006 2008 2010 2012 20140

1

2

3

4

5

6

7

8·104

Year

MSEK

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

70

2006 2008 2010 2012 20145

6

7

8

9

10

Year

%

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

2006 2008 2010 2012 20140.65

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05·106

Year

MSEK

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

71

2006 2008 2010 2012 20140.75

0.8

0.85

0.9

0.95

1

1.05·105

Year

MSEK

Figure A.7: The monetary aggregate supply (M0) in Sweden between 2004 and2014. Data source: Statistics Sweden (2015).

2006 2008 2010 2012 20140.16

0.17

0.17

0.18

0.18

0.18

Year

Figure A.8: Market concentration (HHI) between 2004 and 2014. The HHItakes values between 0 and 1, where 0 indicate a perfectly competitive marketand 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 fordifferent deposit rate model combinations for all account and clientcategories. The variables are defined as: x = HHI and I = As-symetry term. The leftmost column displays the variables includedin the model. The lag of the variable is stated in the parenthesis.For instance, the first model combination under SA Aggregate whichonly says x(o) means that this deposit rate model only include themacroeconomic variable HHI and it has lag 0. Analogously x(2) andI(0)means the model include the HHI with lag 0 and the assymetryterm with lag 0. Note that the higher the p-value the less significantis 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 modelcombinations 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. Forinstance, the first model combination under SA Aggregate which only says G(2) means that thisdeposit volume model only include the macroeconomic variable GDP and it has lag 2. AnalogouslyG(2), U(0) and M(1) means the model include the GDP with lag 2, the unemployment rate withlag 0 and monetary aggregate with lag 1. Note that the higher the p-value the less significant is thevariable.

G U M

SA Aggregate

G (2) 0.0441

U (0) 0.3258

M (1) 0.5659

G (2), U (0) 0.0158 0.0951

G (2), M (1) 0.0268 0.3190

U (0), M (1) 0.2887 0.4986

G (2), U (0), M (1) 0.0061 0.0532 0.1941

SA Private

G (2) 0.0807

U (0) 0.3576

M (0) 0.8909

G (2) , U (0) 0.0420 0.1528

G (2), M (0) 0.0794 0.7987

U (0), M (0) 0.3049 0.7043

G (2), U (0), M (0) 0.0341 0.0944 0.4770

SA Corporate

G (1) 0.4670

U (5) 0.9142

M (1) 0.8364

G (1), U (5) 0.4912 0.9384

G (1), M (1) 0.4495 0.7347

U (5), M (1) 0.8563 0.7975

G (1), U (5), M (1) 0.4712 0.8461 0.7037

G U M

TA Aggregate

G (0) 0.0118

U (0) 0.9381

M (2) 0.0685

G (0), U (0) 0.0097 0.5749

G (0), M (2) 0.0026 0.0120

U (0), M (2) 0.7041 0.0609

G (0), U (0), M (2) 0.0029 0.9888 0.0146

TA Private

G (2) 0.3960

U (0) 0.6327

M (2) 0.1161

G (2), U (0) 0.4109 0.6621

G (2), M (2) 0.7820 0.1798

U (0), M (2) 0.9283 0.1351

G (2), U (0), M (2) 0.7773 0.9142 0.2050

TA Corporate

G (0) <0.0001

U (6) 0.5111

M (0) 0.0564

G (0), U (6) <0.0001 0.3499

G (0), M (0) <0.0001 0.6314

U (6), M (0) 0.9210 0.0890

G (0), U (6), M (0) <0.0001 0.4333 0.9739

74

Appendix C - Model Residual Correlation Plots

2 4 6 8 10 12 14 16 18 20 22 24−1

−0.5

0

0.5

1

Lag

Correlation

(a) The ACF plot.

2 4 6 8 10 12 14 16 18 20 22 24−1

−0.5

0

0.5

1

Lag

Correlation

(b) The PACF plot.

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

2 4 6 8 10 12 14 16 18 20 22 24−1

−0.5

0

0.5

1

Lag

Correlation

(a) The ACF plot.

2 4 6 8 10 12 14 16 18 20 22 24−1

−0.5

0

0.5

1

Lag

Correlation

(b) The PACF plot.

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

75

2 4 6 8 10 12 14 16 18 20 22 24−1

−0.5

0

0.5

1

Lag

Correlation

(a) The ACF plot.

2 4 6 8 10 12 14 16 18 20 22 24−1

−0.5

0

0.5

1

Lag

Correlation

(b) The PACF plot.

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

2 4 6 8 10 12 14 16 18 20 22 24−1

−0.5

0

0.5

1

Lag

Correlation

(a) The ACF plot.

2 4 6 8 10 12 14 16 18 20 22 24−1

−0.5

0

0.5

1

Lag

Correlation

(b) The PACF plot.

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

76

2 4 6 8 10 12 14 16 18 20 22 24−1

−0.5

0

0.5

1

Lag

Correlation

(a) The ACF plot.

2 4 6 8 10 12 14 16 18 20 22 24−1

−0.5

0

0.5

1

Lag

Correlation

(b) The PACF plot.

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

2 4 6 8 10 12 14 16 18 20 22 24−1

−0.5

0

0.5

1

Lag

Correlation

(a) The ACF plot.

2 4 6 8 10 12 14 16 18 20 22 24−1

−0.5

0

0.5

1

Lag

Correlation

(b) The PACF plot.

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

77

2 4 6 8 10 12 14 16 18 20 22 24−1

−0.5

0

0.5

1

Lag

Correlation

(a) The ACF plot.

2 4 6 8 10 12 14 16 18 20 22 24−1

−0.5

0

0.5

1

Lag

Correlation

(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.

2 4 6 8 10 12 14 16 18 20 22 24−1

−0.5

0

0.5

1

Lag

Correlation

(a) The ACF plot.

2 4 6 8 10 12 14 16 18 20 22 24−1

−0.5

0

0.5

1

Lag

Correlation

(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

2 4 6 8 10 12 14 16 18 20 22 24−1

−0.5

0

0.5

1

Lag

Correlation

(a) The ACF plot.

2 4 6 8 10 12 14 16 18 20 22 24−1

−0.5

0

0.5

1

Lag

Correlation

(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.

2 4 6 8 10 12 14 16 18 20 22 24−1

−0.5

0

0.5

1

Lag

Correlation

(a) The ACF plot.

2 4 6 8 10 12 14 16 18 20 22 24−1

−0.5

0

0.5

1

Lag

Correlation

(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

2 4 6 8 10 12 14 16 18 20 22 24−1

−0.5

0

0.5

1

Lag

Correlation

(a) The ACF plot.

2 4 6 8 10 12 14 16 18 20 22 24−1

−0.5

0

0.5

1

Lag

Correlation

(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.

2 4 6 8 10 12 14 16 18 20 22 24−1

−0.5

0

0.5

1

Lag

Correlation

(a) The ACF plot.

2 4 6 8 10 12 14 16 18 20 22 24−1

−0.5

0

0.5

1

Lag

Correlation

(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 plotsuggests that there is a significant correlation at lag 3. By adding the AR term with lag 3 to themodel, the model scores an AIC of -1524.10 and Std Err of 0.000712. This is a negligible changefrom the final model which has an AIC of -1512.55 and Std Err of 0.000747. This is the reason whythe lag 3 AR term is excluded from the final model, even though the ACF and PACF plots suggestthe opposite.

80

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