A Study of Swedish Mortgage Interest Rates and Swedbank Stock Returns

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Department of Real Estate and Construction Management Thesis no. 198

Real Estate Development and Financial Services Master of Science, 30 credits

Author: Supervisor:

Siyi Yang Stockholm 2012 Han-Suck Song

A Study of Swedish Mortgage Interest Rates

and Swedbank Stock Returns

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Master of Science thesis

Title A Study of Swedish Mortgage Interest Rates

and Swedbank Stock Returns - Time-varying Mortgage Margins and Stock Returns

Author Siyi Yang

Department Real Estate and Construction Management

Master Thesis number 198

Supervisor Han-Suck Song

Keywords Mortgage loan, interest rate, housing market, financial market, bank’s stock return

Abstract

How banks set the mortgage interest rates and the sizes of the mortgage margins they obtain from making mortgage loans always attract attention from households, government authori-ties, politicians and market actors. This thesis studies the relationship between Swedish mort-gage interest rates and mortmort-gage lending institutions’ costs of obtaining funds, and how the gross margins of mortgage interest rates influence the banks stock returns. In general, banks’ mortgage margins are correlated with their funding costs, which are typically reflected in the yields of mortgage bonds (covered bonds), interbank rates (STIBOR) and the repo rate. How-ever the correlations change over time and sometimes the mortgage margins are relatively low and sometimes relatively high. Since mortgage loans play an important role in banks’ lending business, the related interest rate margins should influence banks’ profitability and therefore the performance of their stock. Everything else equal, higher margins should result in higher stock returns.

I have collected and constructed a time-series data set based on Swedbank mortgage rates, Swedbank stock prices, yields on government bonds, yields on mortgage bonds, STIBOR interest rates, and repo rate. Both descriptive analysis and econometric models are applied to analyze the time-varying characteristics of the financial data. The thesis covers unconditional correlation (Pearson correlations), and conditional correlation through applying DCC-GARCH models. Besides, ARCH and DCC-GARCH models are employed to measure the ARCH and GARCH effects of the spread (premium) terms between interest rates.

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Acknowledgement

This thesis has been performed at the master program of Real Estate Development and Finan-cial Services (track: FinanFinan-cial Services) at School of Architecture and the Built Environment, Royal Institute of Technology (KTH).

I would like to thank my supervisor Han-Suck Song for his invaluable suggestion, direction, guidance and patience throughout the entire thesis work.

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1. Introduction

1.1 Background

For most households, home purchases constitute their largest investment, and a majority of the households finance their home purchases by borrowing money from mortgage lending banks. According to a report from the European Central Bank (ECB), mortgages comprise approximately 70% of households’ total debts in the Eurozone (European Central Bank, 2009). In Sweden, which is the country of interest in this thesis, almost two-thirds of the pop-ulation owns a small house or a cooperative apartment (that is, shares in tenant-owner associa-tion), and mortgages comprise about 90% of Swedish household debt (Finansinspektionen, 2012).

Since mid-1990s, Swedish households’ mortgage indebtedness has increased strongly, both in absolute and relative terms. A combination of a favorable macroeconomic environment with falling after-tax real mortgage rates, increasing households’ real disposable income and finan-cial wealth has resulted in a strong increase in real home prices (Sveriges Riksbank, 2011). Besides these macro-economic factors, banks have for many years offered generous lending terms, such as high loan-to-value ratios, and interest only mortgages or mortgages with very low amortization requirements. It is not strange that households’ demand for mortgage loans has increased strongly, and this increase in demand has been matched by a large supply of mortgage loans from the banks. Even if the volume of loans with loan-to-value larger than 85% has decreased since the introduction of the 85% mortgage cap rule in 2010, still many existing mortgages and new mortgages are made with high loan-to-value ratios (Finansinspektionen, 2012). Mortgages also constitute the most important lending activity for the major Swedish banks.

It is obvious that mortgages are important for households’ and banks’ balance sheets (e.g. loan values and home prices) and cash flows (liquidity), as well as profitability. Particularly changes in the level of mortgage interest rates (both nominal and real) affect balance sheets and liquidity. For households with existing mortgages, the impact of changes in mortgage rates on their mortgage spending depends on fixed interest periods and when new mortgage interest rates are determined (for different fixed terms such as 3 months, one year, two years and so on), since interest rates change at random points of times. For households that take out new mortgages for the first time, the level of interest rate for different fixed interest terms will affect their liquidity constraint and how much they want to pay for a new home.

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A combination of high interest rate margins on mortgages and large mortgage lending volume will result in high profitability for the banks. The return on equity – the most important profit-ability measure from a shareholder perspective, is amplified by higher equity multipliers (bank assets divided by bank equity capital). A high return on equity for a bank should, every-thing else equal, be correlated with increases in the stock prices of the bank.

It is in light of this background that I am interested in the relationship between banks’ mort-gage borrowing and lending costs and how they vary over time. Although it is likely that the borrowing and lending rates should tend to move together (at least in a competitive market), the strength of the relationship might vary from one period to another. I am also interested in the (potential) co-movement between interest rate margins and a banks’ stock price.

1.2 Objective and purpose

The main purpose of this paper is to study the strength of correlations between mortgage banks’ costs of obtaining funds and the mortgage interest rates they charge households that borrow money, and how they vary over time. The second purpose is to study the correlations between a bank’s stock returns and interest rate margins.

This paper will mainly focus on one of the major Swedish banks – Swedbank’s mortgage in-terest rates, and the most common costs that Swedish banks pay for obtaining funds, as well as the Swedbank’s stock returns during the same time period.

1.3 Research Problems

To give a more complete and clear picture of this thesis study, the research problems are for-mulated as follows:

1. How do the Swedish banks set their mortgage interest rates according to the funding costs over time? Compare the correlations between mortgage interest rates with different matur-ities and their corresponding funding costs.

2. Are there time-varying volatilities (risk) in the interest rate spread (premium) terms? How does the risk-taking influence the return?

3. How much interest rate margins banks get from their mortgage loans? How do the mar-gins vary over time? And how are the marmar-gins correlated with the bank’s stock return over time?

1.4 Research methods

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this paper computes both unconditional correlations (Pearson correlations) between mortgage interest rates and funding costs, and conditional correlations between mortgage interest rates and funding costs as well as mortgage margins and bank stock returns by estimating DCC-GARCH (Dynamic Conditional Correlations - Generalized Autoregressive Conditional Het-eroscedasticity) models. Since the DCC-GARCH analysis is based on ARCH and GARCH volatility modeling, this paper also includes the volatilities of interest rate spreads.

To cover a longer time period with both upward and downward market tendencies, I examine the data from July 1995 to March 2012. During this time period, the Swedish markets (as well as most other markets) experienced the dot-com boom and the following crash from about 1997 to early 2003, the last global financial crisis.

In order to support the use of DCC-GARCH modeling, I write a shorter literature review on that topic. A literature review on the Swedish mortgage markets is also presented, as it gives an important background to the topic of this thesis.

This is a brief summary of the methods that are applied in this study, more details about them will be included in section 3, section 4 and section 5 respectively.

1.5 Structure

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2. Literature Review

This literature review is divided into two main parts. The first part reviews the relevant litera-ture on Swedish housing and mortgage market and banks’ performance in stock market. The second part reviews the literate on econometric modeling of time-varying volatility and covar-iance (correlation), in which the major econometric tools consist of univariate and multivari-ate GARCH models.

2.1 Review of literature on Swedish mortgage market and banks’ stock returns

Swedish house prices have increased considerably since 1996 with households’ indebtedness also rising substantially (Claussen et al., 2011). Figure 1 shows that real house prices (for one- and two dwelling buildings) have increased by 134 percent since the mid-1990s to the end of 2010. According to Riksbank (2011) (Swedish central bank), the strong boom in house prices can be explained by a favorable macroeconomic environment with falling after-tax real mort-gage rates, and increasing households’ real disposable income and financial wealth. Especial-ly the decline in real mortgage rates seems to be an important factor. A stable low-inflation economy that followed the introduction of the inflation targeting in 1993 by the Riksbank (2% plus/minus 1 %-point) led to both a secular decline in interest rates and lower interest-rate volatility, which contributes to households’ debt affordability and appetite for leverage (IMF, 2011).

Figure 1 The evolution of real house prices in Sweden from 1986 to 2012. Index 1986:1 = 100.

Source: This figure appears in Riksbank (2011, page 69, which in turn refers to Statistics Sweden (SCB) and Riksbank).

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points in the early 1990s which resulted in a sharp asset and real estate price drops and a very serious banking crisis. The sudden and strong increase in real after-tax interest rates that households and corporations faced as a result of new tax law with much lower interest deduc-tions, lower inflation due to the new Riksbank inflation target and severe downturn in the business cycle, at the same time as nominal interest rates were high. After some years of rapid declines in home prices in the early 1990s, the real after-tax rates started to decline and real home prices increased until recent days, as described earlier.

Figure 2 Real after-tax mortgage interest rates (percent) from 1986 to 2012.

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Figure 3 Total households’ debt divided into housing and other personal debt, in percentage of disposable income, from 1980 to 2010.

Source: This figure appears in IMF (2011, page 6, which in turn refers to Statistics Sweden (SCB)).

From mortgage lending banks’ perspective, the increased household borrowing used to fi-nance home purchases, can be expressed as positive mortgage lending growth, increase in loan-to-value ratios (LTV), and an increase in the household lending in relation to total bank lending (Finansinspektionen, 2012) (IMF, 2011). Although there has been a downward trend in the growth rate of mortgage lending since 2007, it has still been positive for many years (see figure 4). Mortgage loan has become a major component of the banks’ loan business, because its collateralized nature apparently decreases the bank credit risk. From 20 years ago, commercial banks began to shift plenty of their assets from commercial loans to mortgage loans (Elyasiani et al., 2010).

Figure 4 Annual percentage rate of mortgage lending growth, from 2007 to 2011.

Source: This figure appears in Finansinspektionen (The Swedish Mortgage market 2012, page 4, which in turn refers to

Statistics Sweden (SCB)).

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ly owned mortgage lending institutions) can be seen in their balance sheets, as mortgages to households constitute a major asset class.

Figure 5 Share of total bank lending in percent, from 1998 to 2010.

Source: This figure appears in IMF (2011, page 6, which in turn refers to Statistics Sweden (SCB)).

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Figure 6 Breakdown of Swedish mortgage institutions' outstanding stock by original fixed interest periods (percent), from 1996 to 2010.

Figure 7 below shows the distribution of new mortgage lending by fixed interest periods. The share of new lending at variable 3-month rates was low from 1996 to 1999, while a majority of households preferred fixed rate periods of between 3 months and 5 years (Lagerwall et al., 2011). Since the second half of 1999, the share of households that took out new mortgage loans with variable 3-month rates was higher than the share of longer fixed rate periods (with man exemption from late 2002 to autumn 2003). Suddenly, the share of new lending at short-term variable rates increased from about 40 percent to 90 percent from the start of 2008 to 2009. This sharp increase coincided with a dramatic fall of nominal 3-month variable mort-gage loan rates (see figure 8 below). It appears that Swedish home prices did not fall during the financial crisis since many households enjoyed both extremely low nominal before-tax and negative after-tax mortgage interest rates.

Figure 7 Breakdown of Swedish mortgage institutions' new lending by original fixed interest periods (percent), from 1996 to 2010.

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The level of the mortgage interest rates that households pay is related to the banks’ costs of obtaining funds; the higher interest rate banks must pay its capital providers, the higher must the interest borrowers pay need to be if banks wants to keep their interest margin constant. The Swedish mortgage lending institutions obtain funds on the Swedish and international cap-ital markets. A large share of the Swedish mortgage lending banks’ financing needs are satis-fied by the issuance of covered mortgage bonds of different maturities such as two and five years. But funding from both short-term deposits from other banks (interbank market) and deposits from household and companies are sources to finance mortgage lending. The interest rate a bank pays when it obtains short-term deposit from other banks is reflected in the Stock-holm Interbank Offered Rate (for instance the important three-month STIBOR). The variable short-term mortgage interest rates should therefore move together with the STIBOR rates. Another important interest rate that to some extent determines banks’ short term funding costs is the Riksbank (Swedish central bank) benchmark interest rate, the repo rate.

Since the difference between the banks’ average mortgage lending and borrowing costs, the interest rate margin, is an important determinant of banks’ profitability and earnings potential, it is of great interest to study how the interest margin has evolved over time. Figure 8 below shows that different interest rates tend to move together over time. Since banks choice and mixture of financing sources change over time, it is difficult to exactly calculate banks’ actual borrowing costs for each time period. However, the stated interest rates should still be able to give a good picture of how funding costs change over time. This reasoning is also applicable for the interest payments banks achieve from their lending.

(a) 3-month mortgage interest rate compared with repo rate and 3-month STIBOR

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(b) 2-year and 5-year mortgage interest rate compared with their corresponding mortgage bond yields

Figure 8 Breakdown of Swedbank mortgage interest rates for different interest rate periods, and repo rate, STIBOR and mortgage bond yields, from 1995 July to 2012 March.

Source: Data have been downloaded from Swedbank and Riksbank web pages.

Interest rate spreads reflect the differences between interest rates or bond yields with various maturities, or the differences between risky bonds’ yields and risk free bond’s yields (Kwark, 2002). It is generally accepted that the interest rate spreads reflect risk premiums and expec-tation of performance of risky loans. Moreover, the fluctuations of interest rate spreads are thought to closely relate to change in default risk throughout the business cycle. The premium is made up of a term premium reflecting the longer maturity of equity in relation to its short-term counterpart, and a risk premium claiming a stochastic payoff based on the other equity within same maturity rank (Abel, 1999). Financial transactions involve not only benefits but also costs (Hoelzl et al., 2010). Mortgage loan is no exception.

Risk taking is thought as one of the most important issues in financial markets, so the risk premium not only shows the benefit bank get from a typical business, but also reflects the risk-taking appetite of banks. Delis and Kouretas claim (2011) a strong negative relationship between low interest rates and banks’ risk taking, in other word, banks will hold more risky assets in the low interest rate environment in the euro area during the period 2001-2008. Moreover, the expansionary monetary policy can improve banks’ risk appetite (Borio & Zhu, 2008). After the financial crisis, more and more researchers, such as Jimenez et al (2008), Loannidou et al (2009), and Brissimis and Delis (2010), devote themselves to discussion of monetary policy to risk taking and get the similar results.

The influence of mortgage interest rate on bank stock return is widely certified (Flannery et al., 1997). He et al. (1996) indicate that all types of mortgage loans, which use property as the collateral, are the explanatory variables of bank stock return. Banker, investors, police makers and academic researchers pay more attention to the impact of interest rates margin on banks’ stock returns, because of the increasing volatility of financial market conditions and lessened profit margins in recent years (Elyasiani & Mansur, 2004). Lolyd and Shick (1977) and

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Chance and Lane (1980) hold the opinion that there is very weak relationship between market interest rate and financial institution’s stock return. However, many research like Lynge and Zumwalt (1980), Flannery and James (1984), and Bae (1990) indicate the negative sensitivity of bank stock returns to interest rates. Akella and Chen (1990) find bank stock returns reflect long-term government bonds yields’ level, but not the short-term counterparts. Moreover, the long-term interest rate and its respective volatility influence more than the short-term one (Mansur & Elyasiani, 1995). Some researchers find the sensitivity of bank stock returns to interest rates varies a lot in different periods (Benink & Wolff, 2000).

Different households choose different borrowing terms, reflected in different fixed credit and interest terms. Since mortgage loan interest payments constitute one of the main factors of periodic household cash outflows, many households pay attention to changes in mortgage interest rates and how the relationship between interest rates for different terms change over time. Since the mortgage rates households that borrow money must pay are related to banks financing costs, it is interesting to study the relationship between banks financing and lending interest rates, and if and how those relationships change over time. Since mortgage loans also constitute a significant part in banks’ lending business, it is also interesting to learn more about the relationship between prices of bank shares and interest rate margins.

2.2 Review of literature on modeling time-varying volatility and correlation

Engle (1982) introduced Autoregressive Conditional Heteroscedasticity (ARCH) process, which permitted the variance to vary over time as a function of lagged error terms, to model the volatility of inflation. As an extension of ARCH model, the Generalized ARCH (GARCH) Model was firstly proposed by Bollerslev (1986). Compared to its original version, GARCH model could capture longer lagged effect by employing fewer parameters. After that, ARCH and GARCH models become to the most common tools applied in the financial time series analysis. Song (1994) employed the ARCH methodology to do the first research in banking area. He regarded ARCH modeling as the appropriate framework for analysis on fi-nance issues. Neuberger (1994) studied the determinants of risk premium by estimating a GARCH model on factor volatilities. And the inspiration for quoting this econometric model to his own research came from Engle et al. (1990b).

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GARCH model. However, there is another equally important model: multivariate GARCH (MGARCH) model. Compared to the univariate one, MGARCH models are flexible to pre-sent the dynamics of both conditional variance and covariance, and their parameters often increase rapidly because of the dimension of the model (Silvennoinen & Teräsvirta, 2008). When considering the relationship between two variables, researchers usually apply the meth-od of calculating correlation coefficients between them. It is widely accepted that correlations between financial variables present completely different performance during good and bad times. Specifically, during “bear market” period correlations increase; however, during “bull market” period correlations move down. Correlation is a widely used method to measure the dependence between market variables (Liow & Lee, 2011). Some investigators explore corre-lations not only between prices but also returns (Engle, 2009). However, correlation might mislead investor to the description of dependence. Because correlation is based on the average deviations from the mean, which does not distinguish between large and small realizations, and make no difference between positive and negative returns as well; moreover, correlation also set preconditions of a linear relationship and a multivariate distribution, which might results in an inevitable significance testing of the risk in the joint extreme event (Poon et al., 2004).

Based on the existing literature, researchers employ both unconditional and conditional corre-lations to measure the correcorre-lations between financial time series. The former one comes from descriptive statistics, and can be achieved through full time period calculation or rolling win-dow method. And the latter one is based on the econometric models, which uses the residuals from estimations on GARCH volatility to estimate the correlation.

Pearson Product Moment Correlation (Pearson's correlation for short) is the most common measurement of unconditional correlation. It is defined as two variables’ covariance divided by the product of their standard deviations. Pearson's correlation reflects the level of linear relationship between pair of variables, and ranges from -1 to +1, which shows the interval of perfect negative and positive linear relationship between two variables (Ahlgren et al., 2003). Compared with unconditional correlations, their conditional counterparts have more complex background. Given two random variables Y and X. Conditional probability distribution of Y is the probability of Y when X is a known value. Conditional variance is the variance under conditional probability distribution, and it plays an important role in ARCH models. In these models, the conditional variances become time varying for the changing information (Bollerslev & Engle, 1993). When the persistence in conditional variances becomes high, the stationarity of series will be influenced.

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3. Description of Data

In this section, I will introduce the data, calculate the risk premiums and term premiums based on the current data and then analyze the descriptive statistics in explicit tables and figures. Besides, I will prepare for the modeling by applying the unit root test to check the stationarity of all the data series.

The data covers financial market interest rates (include repo rate, STIBOR, yields of treasury bill and government/mortgage bonds in this thesis), Swedbank mortgage interest rates, and Swedbank stock returns that transform from the Swedbank stock price index. All the data se-ries are monthly and at the end of month level. In order to simplify the graphics, I drop the “%” from all the data. In other word, all the data in figures and tables are one hundred times as the real one.

The descriptive statistics included data summary, interest rate spreads (both risk premiums and term premiums), which are inputted to the ARGH and GARCH model next section, and exploration on unconditional correlations through different computing methods. And the summary about the data analysis is also contained afterwards.

As a main statistic tool, STATA is always used to manage data, analyze statistics, and plot graphics. In this thesis, all the descriptive statistics and econometric modeling estimations are got from this useful data analysis tool.

3.1 Data collection

3.1.1 Funding costs of mortgage loans

The financial market interest rates come from Riksbank (Swedish central bank) database (Riksbank, 2012). They are used as the funding costs of mortgage loans in this research. In order to make all the data follow the same timer shaft, I use the “Ultimo” calculation method to get the initial time series, which contain Repo rate, 3-month STIBOR, 12-month STIBOR, 3-month treasury bill yield, 2-year Swedish government bond yield, 5-year Swedish govern-ment bond yield, 2-year mortgage bond yield, and 5-year mortgage bond yield. The sample period is from July 1995 to March 2012.

Among these, the repo rates and STIBOR are unique Swedish terms. Repo rate is the interest rate at which banks can deposit or borrow funds from the Riksbank for seven days. Stockholm Interbank Offered Rate (or STIBOR) is the interest rates at which banks borrow unsecured funds from other banks in the Swedish money market (or interbank market). Both repo rate and STIBOR usually play an important role as the funding cost when banks finance their lending.

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year Swedish government bond yields, and 5-year Swedish government bond yields as the match group for mortgage interest rates.

Mortgage bond is a bond based on an array of mortgages on a real estate property such as a house. Generally speaking, bonds that are guaranteed by the pledge of specific assets are called mortgage bonds. Banks, which hold the mortgage loan as their assets, could issue mortgage bond. Mortgage bond yields are the average interest banks have to pay to mortgage bond investors (e.g. insurance companies and fund investors) who lend money to the banks. Some banks might pay higher or lower interest rates when they borrow money, depending on credit risk for instance, but the difference should be small, and the Riksbank data should re-flect the average. Mortgage bond yields are also the major cost for bank financing mortgage lending. After the last financial crisis, Swedish banks fund their mortgage lending primarily from the mortgage bonds.

3.1.2 Swedbank mortgage interest rates

“Swedbank Hypoteks villaräntor” are used as the representative of mortgage interest rates for the research. I select the 3-month Swedbank mortgage interest rates, 2-year Swedbank mort-gage interest rates, and 5-year Swedbank mortmort-gage interest rates into the match group. Ac-cording to the rule of Swedbank presenting the mortgage interest rate, the dates are listed in the line, once changes occur in mortgage interest rates. In other words, before the new record appears in thecolumn, mortgage interest rates keep the same. To get the “end of month” data, I keep the last Swedbank mortgage interest rates every month, as same as the one on the last day of month. In addition, several months data are seem to be absent; I equate the mortgage interest rate with previous month’s one, for the reason of Swedbank only reports new mort-gage rate until they change it (Swedbank, 2012).

Due to the financial crisis, Swedbank did not offer 3-month Mortgage Interest Rates between 2007.09 and 2008.09, so I replaced them by “Swedbank Bolån Direkt 3-month interest rates”, which could be a good substitution for the vacancies.

3.1.3 Swedbank stock returns (based on Swedbank stock prices)

I extract Swedbank stock prices between June 1995 and March 2012 from NASDAQ OMX index (2012). The stock is named as “Swedbank A” in the stock market. Stock prices are daily data; to make all the data at the same line, I use the price for the last day of month to be the monthly “Swedbank stock price”. The Swedbank stock returns are calculated from the follow-ing formulas:

𝑅_!= !!!!!!!_!

! ∗ 100 [1]

Pt means the stock price at the end of month t. The stock prices are transformed into the

arithmetic returns by taking the increase of stock prices from time t-1 to time t, divided by Pt,

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3.2 Descriptive statistics and analysis of data

3.2.1 Data summary

I use the monthly (end of month) data observations of financial market interest rates and Swedbank mortgage interest rates with different maturities. The time span of sample period is 17 years, which contains the dot-com bubble and following crash, and the last global financial crisis.

(a) Repo rate, STIBOR & Swedbank mortgage interest rates

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(c) Mortgage bond yields and Swedbank mortgage interest rates

Figure 9 The evolution of different interest rates, from 1995 July to 2012 March.

Figure 9 shows the evolution of the repo rate, STIBOR, treasury bill yields, government bond yields, mortgage bond yields and Swedbank mortgage interest rates. The different interest rates tended to move strongly together over time, and all interest rates peaked in the beginning of the sample period. They started from the highest point in 1995, gradually decreased in the next 4 years spanning from 1995 through 1999. Then interest rates had a boom at the begin-ning of 21st_{century, and followed by a downward trend between 2002 and 2005. From the}

next year, they began to rise again, and reached the peak in the second half of 2008. Influ-enced by the global financial crisis, the interest rates dropped dramatically. Some short-term lending rates even approached to zero when the repo rate dropped to record-low level in the end of 2009. After that, Riksbank gradually increased the Repo rate, and the price of risk moved in the same way. The new regulations to strengthen financial stability and avoid finan-cial crisis in the future raised the costs for banks, so the mortgage interest rates paid by cus-tomers increased correspondingly. Moreover, the interest rates with shorter due day were more fluctuant, like 3-month Swedbank mortgage interest rate; the long-term rates usually presented a higher return than the shorter ones. As representatives of mortgage interest rates, Swedbank bank mortgage interest rates were obviously higher than their match group like repo rate, STIBOR, treasury bills yield and government bond yields. And mortgage bond yields, which were based on the mortgage loans, had higher rate of return than government bonds; but they also did not exceed mortgage interest rates for the lower risk taking.

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Figure 10 Swedbank stock price index (red line and right axis) and stock returns (blue line and left axis), from 1995 July to 2012 March.

Figure 10 presents the changes in the number of monthly Swedbank stock returns (blue line and left axis) and stock prices in SEK (red line and right axis) over the sample period. Swedbank stock price index began with approximately 60 SEK from mid 1995, and it reached the peak point (above 260 SEK) twice in March 1998 and January 2007 respectively. During the last global financial crisis, the stock price dropped dramatically. After bottomed in the beginning of 2009, it increased again. In this thesis, I use the arithmetic returns as stock re-turns, because the returns computed by other ways, such as log return, show almost the same trend. Due to the transform process, the small lag between stock return and stock price could be found in the figure. Swedbank stock returns mainly fluctuated within the range of 30 and -10 before 21st century, except the extreme negative records in August 1998 and June 1999. There was no obvious reaction on bank’s stock returns during the dot-com bubbles period. The stock returns almost stayed above the level of zero between 2003 and 2006. It experi-enced sharp fluctuations during the global financial crisis. After that, stock returns oscillated back to the normal level again.

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Table 1 Descriptive Statistic of interest rates, stock returns and stock prices, July 1995 - March 2012.

3.2.2 Descriptive statistics of interest rate spreads and economic analysis

The current research covers two kinds of interest rate spreads. One is the term premium, which indicates the differences between the interest rates with the same term but different maturities, such as 5-year Swedbank mortgage interest rates and 3-month Swedbank mortgage interest rates. The other one is risk premium, which presents the differences between the in-terest rates with same maturity but different terms, such as 5-year Swedbank mortgage inter-est rates and 5-year mortgage bonds’ yields.

Term premiums refer to the following items, which are sorted by term categories. Swedbank mortgage interest rate: MR5Y-MR3M, MR5Y-MR2Y, MR2Y-MR3M Mortgage bond: MB5Y-MB2Y

Government bonds: SE5Y-SE2Y, SE5Y-SE3M, SE2Y-SE3M STIBOR: STIBOR12M- STIBOR3M

Risk premiums refer to the following items, which are sorted by maturity categories. 3-month interest rate: MR3M-STIBOR3M, MR3M-SE3M, SE3M-STIBOR3M 2-year interest rate: MR2Y-MB2Y, MR2Y-SE2Y, MB2Y-SE2Y

5-year interest rate: MR5Y-MB5Y, MR5Y-SE5Y, MB5Y-SE5Y

In section 4, all the premiums listed above are inputted to econometric models to test ARCH and GARCH effects of each spread time series.

Figure 11 plots the trends of term premiums. The volatilities of all the series’ value were time varying but not constant. In other word, the spread time series were volatile and fluctuate in an unpredictable manner from period to period. Besides, the big changes in volatilities were always followed by further big changes, and small changes usually came after the former small changes. As a return for financial institutions’ lending activity, the interest rate not only relate to the cost they pay for the funding but also reflect the risk-taking for run a specific loan business. Generally speaking, the long-term loans always have higher interest rates than the short-term loans for the higher risk taking, and their spreads vary over time. This rule also works in bond yields.

Repo STIBOR STIBOR SE SE+GVB SE+GVB MB MB MR MR MR Stock Stock rate 3M 12M 3M 2Y 5Y 2Y 5Y 3M 2Y 5Y Return Price

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(a) Movements over time of term premiums for different pairs of mortgage interest rates

(b) Movements over time of term premiums for different pairs of government bond yields

(c) Movements over time of term premiums for pair of mortgage bond yields and pair of STIBOR Figure 11 The changes of interest rate spreads (term premiums) from 1995 July to 2012 March.

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(a) Movements over time of risk premiums for different pairs of 3-month interest rates (yields)

(b) Movements over time of risk premiums for different pairs of 2-year interest rates (yields)

(c) Movements over time of risk premiums for different pairs of 5-year interest rates (yields) Figure 12 The changes of interest rate spreads (risk premiums) from 1995 July to 2012 March.

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Figure 12 plots the trends of risk premiums. I find the particular volatility clustering effects here: either the low volatility periods or the high volatility periods, they kept for a while. And the volatilities of all spreads changed over time in an arbitrary way. Basically, the changes of risk premiums showed an apparent similarity among them. Some of the risk premiums can be regarded as the margins of mortgage loans with three different maturities. So, this figure also indicates the existence of the time varying effects in interest rate margins, which reflect how the margins banks get from their mortgage loans vary over rime and influence mortgage bor-rowers’ decision in choosing a proper way to finance their house purchase.

And the time varying and clustering effects in the volatility of spread terms will be further supported by estimating ARCH and GARCH models in Section 4.

3.2.3 Descriptive statistics of unconditional correlations and economic analysis

The unconditional correlations, which hold another name as Pearson correlations, are based on the descriptive statistics without estimating models. In this research, I present two kinds of unconditional correlations as the compared group of conditional correlations estimation with DCC-GARCH model in the following chapter.

The most popular statistic formula to measure the constant correlation coefficients is: 𝜌!" = !"#(!,!)

!_!!∙!_!! =

![ !!!! !!!! ]

!!!! [2]

Here, 𝜌!" is the correlation coefficient of the random variables X and Y, 𝜇 is the expected

return, and σ is the standard deviation.

When it comes to the issues of series, the formula [2] could extent to: 𝑟!"= (!!!!)(!!!!) ! !!! (!!!!)! ! _(!!!!)! !!! ! !!! [3]

The first unconditional correlation is the “full time” period correlation, which include the rec-ords for whole sample period from July 1995 to March 2012, and the recrec-ords for three divided periods: July 1995 to December 2000, January 2001 to December 2006, and January 2007 to March 2012. The periods are separated by the global economic events (dot-com boom, and last global financial crisis). It implies unconditional correlation is not unchangeable actually, and they vary a lot in different time periods.

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spectively. The unconditional correlation changed over different time periods, so here is the reason to believe that the constant correlation between two time series is a misunderstanding. A time-varying correlation should be introduced into the study of relationships between pairs of interest rates.

Table 2 Unconditional correlation matrixes of interest rates.

The second unconditional correlation is based on the rolling (moving) windows, which are the typical sample periods used in each time. It is one of the most common ways to get time vary-ing correlations. There are two kinds of windows in the analytical method. One is expandvary-ing windows, and the other is fixed size windows. The previous one means the starting point of window is fixed, and the windows change through the increase of observations, i.e. windows widen gradually. Take following rolling windows I use in research as an example: rolling windows July 1995 - June 1997, rolling windows July 1995 – July 1997, rolling windows July 1995 – August 1997… The latter one is that windows moving on with a fixed window size. For example, the window size is 24 months and step size is one month, then I get rolling win-dow July 1995 – June 1997, rolling winwin-dow August 1995 – July 1997, September 1995 – Au-gust 1997…

Here, researchers extend the basic correlation coefficient to the following equation: 𝜌_!",!" = !"#(!!",!!")

!_!,!"! ∙!_!,!"! [4]

Where 𝜌!",!" is time-varying correlation coefficient at time t with the window size of m

months; 𝑋_!" and 𝑌_!" are the corresponding returns; σX,tm and σY,tm are standard deviations.

In order to simplify data processing, there are five most relevant control pairs kept for each mortgage interest rates. Taking 3-month mortgage interest rate for example, we are interested in its correlations between repo rate, treasury bill yield and STIBOR with the same maturity, and the other two mortgage interest rates respectively. For 2-year and 5-year mortgage inter-est rates, I choose the objects of analysis in the same way: their correlations between repo rate, government bond and mortgage bond yields with the corresponding maturities, as well as the other two mortgage interest rates.

reporate stibor3m stibor12m se3m segvb2y segvb5y mb2y mb5y mr3m mr2y mr5y mr3m 0.9872 0.9867 0.9724 0.9822 0.9283 0.8709 0.9462 0.8862 1

mr2y 0.9520 0.9571 0.9698 0.9634 0.9575 0.9309 0.9803 0.9576 0.9605 1 mr5y 0.8892 0.8808 0.8998 0.8967 0.9286 0.9540 0.9457 0.9859 0.8899 0.9686 1

mr2y 0.9397 0.9648 0.9902 0.9628 0.9925 0.9623 0.9935 0.9556 0.9655 1 mr5y 0.8826 0.8987 0.9304 0.8901 0.9661 0.9899 0.9557 0.9947 0.9086 0.9623 1

mr2y 0.9509 0.9653 0.9658 0.9665 0.9665 0.9673 0.9784 0.9790 0.9538 1 mr5y 0.9044 0.9089 0.9045 0.9121 0.9226 0.9762 0.9348 0.9860 0.9069 0.9803 1

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Figure 13 shows the changes of unconditional correlations between interest rates (yields) by using expanding rolling (moving) windows, and the horizontal axis is the end of each win-dows. All the windows started from July 1995, the first window included 24 months and end-ed in June 1997, and the last window includend-ed 201 months and endend-ed in March 2012. Win-dows have the increment of one month each time.

(a) Unconditional correlations between mortgage interest rates and repo rate

(b)Unconditional correlations between mortgage interest rates and government bond yields

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(c)Unconditional correlations between mortgage interest rates and STIBOR and mortgage bond yields

(d) Unconditional correlations between mortgage interest rates with different maturities

Figure 13 Unconditional correlations between interest rates (yields) by applying expanding rolling (moving) windows. All the windows started from July 1995, the first window included 24 months and ended in June 1997, and the last window included 201 months and ended in March 2012. Windows have the increment of one month each time. The X- axis indicates the windows’ ending time.

From the research method of expanding rolling (moving) windows, I find the unconditional correlations between 3-month mortgage interest rate and repo rate were closed to 1 most of the time. Besides, 3-month mortgage interest rates also showed a high consistency with yields of 3-month treasury bill, which means 3-month mortgage interest rates were influenced by government actions and policies directly and responded with little lags. Compared with 3-month mortgage interest rates, the 2-year mortgage interest rates and 5-year mortgage interest rates presented much lower consistency with repo rate and slightly lower consistency with government bond yields with corresponding maturities; however, they showed very high con-sistency with the returns of their relevant mortgage bond yields even during the period of the last global financial crisis. There was interesting situation that correlation between 3-month mortgage interest rates and 2-year mortgage interest rates moved together with the correlation between 2-year mortgage interest rates and repo rate, and correlation between 3-month

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gage interest rates and 5-year mortgage interest rates followed the same trend with the corre-lation between 5-year mortgage interest rates and repo rate. Depends on the a little bigger effects on the government policy, 2-year mortgage interest rates had higher correlation with 3-month mortgage interest rates than 5-year mortgage interest rates. The correlation between 2-year mortgage interest rates and 5-2-year mortgage interest rates rose gradually after it reached the bottom at June 1998, and dropped again from the financial crisis. Most of unconditional correlations I mentioned presented the downward trend after the crisis, which means the re-search methods or models we used before might become unreliable during the special periods, like last global financial crisis.

Figure 14 reveals the trends of unconditional correlations between interest rates (yields) by applying fixed rolling (moving) windows, and the horizontal axis is also the end of each win-dows. The first window started from July 1995 and ended in June 1997. Then the windows kept the fixed size of 24 months and moved on one month afterwards each time in time axis. Employing the research method of fixed rolling (moving) windows, unconditional correla-tions became more fluctuant, they showed a pronounced trough in 2001, and two troughs after the financial crisis. Expect these distinctions, unconditional correlations I got from fix rolling windows shared the similar general trend with correlations from the expanding rolling win-dows. The 2-year and 5-year mortgage interest rates showed the high correlations with the corresponding mortgage bond yields than the repo rate, especially during the down economy, such as dot-com boom crisis and the last global financial crisis.

(a)Unconditional correlations between mortgage interest rates and repo rate

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(b)Unconditional correlations between mortgage interest rates and government bond yields

(c)Unconditional correlations between mortgage interest rates and STIBOR and mortgage bond yields

(d) Unconditional correlations between mortgage interest rates with different maturities

Figure 14 Unconditional correlations between interest rates (yields) by applying fixed rolling (moving) windows. The first window started from July 1995 and ended in June 1997. Then the windows kept the fixed size of 24 months and moved on one month afterwards each time in time axis. The X- axis indicates the windows’ ending time.

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When using the rolling (moving) window method, it is important to determine an appropriate window size, because the undersize window will lead to a choppy correlation and the oversize window will flatten the result. In addition, there is a distinct drawback of fixed rolling (mov-ing) windows method: when an old observation retreat from the window, a large fluctuation emerges in the correlation, although nothing has happened recently. Thus, it also provides the reason why correlations from fixed window method are wavier.

3.3 Summary

To conclude the descriptive statistics and the analysis, the findings in above section are: Repo rate, STIBOR, treasury bill yields, government bond yields, mortgage bond yields and Swedbank mortgage interest rates tend to move strongly together over time, but the correla-tions between any two of them vary over time, as well as their spread terms. The mortgage loans with shorter maturities are more sensitive to the government actions and policies in fi-nancial area that reflect on the government decided interest rates, such as repo rate, treasury bill yield, and government bond yield; and the interest rates of mortgage loans with longer maturities, like 2-year and 5-year, more correlate with the mortgage bond yields especially during the down economy period. Thus, in order to find out the proper mortgage loans to fi-nance the house purchase, mortgage consumers should pay more attention to the trend of repo rate and related bond yields, as well as the current economic situation.

Because of the high correlations between 3-month mortgage interest rates and 3-month STIBOR, 2-year mortgage interest rates and 2-year mortgage bond yields, and 5-year mort-gage interest rates and 5-year mortmort-gage bond yields throughout the whole research period especially during the financial crisis, 3-month STIBOR, 2-year and 5-year mortgage bond yields are chosen as the funding costs of the mortgage loans with corresponding maturities in the research about how the mortgage interest rate margins affect on the bank’s stock return over time in section 5.

3.4 Preparatory work for model estimation (Unit root test)

Before estimating models upon the data, I apply the Unit root test to check the stationarity of all the series. It is very important to know stationarity of series, because the obvious signifi-cant regression results would be unreliable when the regression is based on nonstationary se-ries. These regressions are called as spurious. More generally, even though the t-statistics is huge, we still cannot reject the null hypotheses, since the significant relationship is false and the results we get are completely meaningless. Actually, there is nothing in common among the series (Hill, Griffiths, & Lim, 2007).

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Table 3 reports the Dickey-Fuller tests results. As can be seen from the table, the time series of 2-year government bond yields, 5-year government bond yields, 2-year mortgage interest rates, 5-year mortgage interest rates show their stationarity at 5% significance level, and other the time series present their stationarity at 1% or even higher significance level. To conclude, all the series are stationary, which means they could be used directly in the model estimation section.

Table 3 Unit root tests results.

*p<.05, **p<.01, ***p<0.001.

Test%Statistic 1%%Critical%Value 5%%Critical%Value 10%%Critical%Value MacKinnon%approximate%p:value%for%Z(t)%

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4. ARCH and GARCH Effects in Spreads

The descriptive statistics of the interest rate spreads and the analysis in last section have pre-sented the initial findings in time varying effects in the volatilities of the premium series. In this section, I will test for the effects in the spreads (premiums) by applying ARCH and GARCH models. And this econometric modeling method could also be used to quantify the increase in return by taking certain amount risk.

The data analysis includes both the econometric results and the discussions from an economic perspective.

4.1 Econometric methodology

To check the ARCH effects of premium series, I regress 𝑒!!on the lagged squared residuals

𝑒_!!!! _{: 𝑒}

!! = 𝛾!+ 𝛾!𝑒!!!! + 𝜈! [5], where 𝜈! is a random term. We have the null hypotheses H0:

𝛾! = 0, which means no ARCH effects; and the alternative hypotheses H1: 𝛾! ≠ 0, which

indicates ARCH effects in the series. T-statistic test of significance is often used to test for the existent of ARCH effects. As an extension of ARCH model, GARCH models explain volatili-ty with similar function of the errors 𝑒!, but include more lags to fit some time series better

(Hill, Griffiths, & Lim, 2007).

Either ARCH effects or GARCH effects present the time-vary volatility of series as well as clustering of changes. More specifically, the value of series varies a lot from period to period in an unpredictable way; and there are periods when high volatilities are followed by further high volatilities and when low volatilities are followed by further low volatilities (Hill, Griffiths, & Lim, 2007).

In order to find out whether ARCH and GARCH effects exist in the spreads series, I estimate ARCH models and three most common GARCH models on all the premium series, and ana-lyze results to give the proper explanation from an economic point of view.

4.1.1 ARCH (1) model

The first model I estimate is ARCH (1) model, which is most basic one in ARCH model esti-mation, and its equations are shown below:

𝑦_!= 𝛽_!+ 𝑒_! ℎ_! = 𝛼_! + 𝛼_!𝑒_!!!! _{, 𝛼}

! > 0, 0 ≤ 𝛼! < 1 [6]

Where 𝑦_! is return, 𝑒_! is error term, ℎ_! is time-varying variance, and 𝑒_!!!! _{is the square of error}

in the previous period. The coefficients 𝛼_! and 𝛼_! should be positive to assure ht above zero,

and 𝛼! should be no more than 1 otherwise variance will keep rising over time and finally

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4.1.2 GARCH (1,1) model

The second model I estimate is GARCH (1,1) model, which derives from ARCH (1) model, but allows having more lags than the primary version. It is an alternative way to catch longer lags with fewer parameters, and is called as Generalized ARCH (Hill, Griffiths, & Lim, 2007). The simplified equations of GARCH (1,1) model are shown below:

𝑦_!= 𝛽_!+ 𝑒_!

ℎ! = 𝛿 + 𝛼!𝑒!!!! + 𝛽!ℎ!!!, 𝛿 > 0, 0 ≦ 𝛼! < 1, 0 ≦ 𝛽! < 1 [7]

Where 𝛿 = 𝛼!− 𝛽!𝛼!. The constant term 𝛿 should be positive, and the coefficients 𝛼! and 𝛽!

should be no less than zero but less than 1. Besides, to ensure the stationarity, we need 𝛼_! + 𝛽_! < 1, otherwise will get a “integrated GARCH”, or IGARCH for short.

In GARCH model, the momentum of volatility change is not only from the lagged square of error 𝑒_!!!! _{, but also via previous variance ℎ}

!!!. Therefore, in some long lags cases, GARCH

show a better performance than ARCH, which means the coefficient in front of ht is

signifi-cant.

4.1.3 GARCH-in-mean model

Considering one of the most common sense of financial economics: the positive relationship exists between risk (here, measured by volatility) and return. While risk increases, the mean return increases, i.e. risky assets’ return should be higher than safe one’s. I estimate the GARCH-in-mean models as the third model on premium series. Its equations are shown be-low:

𝑦! = 𝛽!+ 𝜃ℎ!+ 𝑒!

𝑒_!|𝐼_!!! ∽ 𝑁(0, ℎ_!)

ℎ! = 𝛿 + 𝛼!𝑒!!!! + 𝛽!ℎ!!!, 𝛿 > 0, 0 ≦ 𝛼! < 1, 0 ≦ 𝛽! < 1 [8]

The first one is the mean equation, which presents the effects of volatility on its dependent variable return. The coefficient in front of the conditional variance shows how the return is influenced by risk factor. In order to ensure the positive ht, the constant term 𝛿 should be

above zero. And the coefficients 𝛼! and 𝛽! should be no less than zero but less than 1.

In GARCH-in-mean model, the expected return is no longer a constant value, but it moves together with conditional variance. The usual perspective in financial market is higher risk, higher return. From the opposite point of view, if people want to get the higher return, they should pay the cost that is taking higher risk.

4.1.4 GARCH-in-mean model alternative

The last model I estimate on premium series is based on GARCH-in-mean models but use time-varying standard deviation ℎ! as the substitution for ℎ! in the return equations. The

equations of the last model I employ are shown below: 𝑦_!= 𝛽_!+ 𝜃 ℎ_!+ 𝑒_!

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ℎ_! = 𝛿 + 𝛼_!𝑒_!!!! _{+ 𝛽}

!ℎ!!!, 𝛿 > 0, 0 ≦ 𝛼! < 1, 0 ≦ 𝛽! < 1 [9]

There is an alternative way to write the mean equation, which is also very common to use the standard deviation to present the risk term. The both methods are always used in the financial models. It’s hard to decide which one will be better in a typical model before the t test of sig-nificance. In this alternative GARCH-in-mean model, we have as the same ranges of coeffi-cients as GARCH-in-mean model.

4.2 Econometric results and analysis from an economic perspective

As I mentioned in section 4.1, the t test of significance is used to select the suitable models for the premium series. The critical value of t-statistics at 5% is 1.96. Thus, if absolute values of coefficients’ t-statistics are larger than 1.96, we reject the null hypothesis, and the coefficients are significantly different from zero, i.e. the models are suitable for the time series, and also prove the existence of ARCH or GARCH effects in the time series. Otherwise, we can’t reject the null hypothesis, and the coefficients are not significantly different from zero, i.e. neither ARCH effects nor GARCH effects can be proved. From the financial analysts’ view, volatility is explained as a function of the error terms 𝑒_!, and 𝑒_! are named “news” or “shocks”. There is a positive relationship between shocks and volatility. The econometric models capture the ARCH and GARCH effects or “clustering” effect as large changes in 𝑒_! lead to further large changes through the lagged error term 𝑒_!!! (Hill, Griffiths, & Lim, 2007). In addition, the estimations of GARCH-in-mean models could provide the positive evidence for “high risk, high return received” view, because either volatility or standard deviation is a delegation of risk.

4.2.1 Term premium

Table 4 and Table 5 present model estimations of term premium series, which are the spread between series with same terms but different maturity. Tables include both estimations and their corresponding t-statistics (labeled z-statistic in the Stata results).

1). MR5Y – MR3M

For the spread between 5-year mortgage interest rates and 3-month mortgage interest rates, ARCH (1) model is only effective one. I get the following results:

𝑟_! = 0.803, ℎ_! = 0.067 + 0.907𝑒_!!!!

All the estimated coefficients show the significance in t-statistic test, and satisfy the restricted condition of ARCH (1) model. So ARCH effect exists in this premium series.

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2). MR5Y – MR2Y

Except the GARCH (1,1) model, the other models not only meet the restricted condition of estimations but also show the significance in t test when I estimate the spread between 5-year mortgage interest rates and 2-year mortgage interest rates.

The effective results from ARCH (1) show the ARCH effect on the premium series: 𝑟_! = 0.650, ℎ_! = 0.014 + 0.905𝑒_!!!!

The results from GARCH-in-mean model:

𝑟_! = 0.538 + 0.629ℎ_! ℎ_! = 0.008 + 0.659𝑒_!!!! _{+ 0.279ℎ}

!!!

The estimations not only show the GARCH effect in this premium series, but also indicate that when volatility increase 1 unit, the return term will increase 0.629, which support the common view of financial market: high risk taken, high return received.

The results from GARCH-in-mean alternative:

𝑟_! = 0.524 + 0.363 ℎ_!

ℎ! = 0.010 + 0.689𝑒!!!! + 0.235ℎ!!!

We have when standard deviation increases 1 unit, the return term will increase 0.363. Results also provide support for the mentioned financial market rule.

Table 4 Model estimations of term premium series.

*p<.05, blue marked figure is the insignificant t-value, and red marked figure is the coefficient outside the restricted range. Invalid results is marked with “/”.

ARCH(1,1)

Estimate z1statistic Estimate z1statistic Estimate z1statistic Estimate z1statistic β0 0.803 25.03* 0.650 46.57* 0.332 12.73* 0.611 62.33*

α0 0.067 3.7* 0.014 4.57* 0.045 5.39* 0.007 2.52*

α1 0.907 3.37* 0.905 3.34* 0.815 3.36* 1.153 5.63*

GARCH(1,1)

Estimate z1statistic Estimate z1statistic Estimate z1statistic Estimate z1statistic

β0 0.801 25.97* 0.633 44.69* / / 0.613 62.29*

δ 0.058 2.53* 0.021 4.87* / / 0.006 1.87

α1 0.895 3.35* 1.054 3.52* / / 1.129 5.5*

β1 0.040 0.32 .0.233 .2.11* / / 0.037 0.37

β0 / / 0.538 24.32* / / 0.602 51.76*

θ / / 0.629 2* / / 0.254 1.57

δ / / 0.008 2.84* / / 0.006 2.01*

α1 / / 0.659 2.98* / / 1.096 5.28*

β1 / / 0.279 2.17* / / 0.068 0.68

β0 / / 0.524 15.12* / / 0.586 28.64* θ / / 0.363 2.26* / / 0.163 0.12 δ / / 0.010 3.2* / / 0.006 2.1* α1 / / 0.689 3.1* / / 1.096 5.16* β1 / / 0.235 2.02* / / 0.049 0.54 Term5premium Term5premium Term5premium MB5Y1MB2Y MB5Y1MB2Y MB5Y1MB2Y MB5Y1MB2Y MR2Y1MR3M MR2Y1MR3M MR2Y1MR3M MR2Y1MR3M MR5Y1MR3M MR5Y1MR3M GARCH-in-mean models MR5Y1MR3M MR5Y1MR3M GARCH-in-mean models alternative

MR5Y1MR2Y

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3). MR2Y – MR3M

When estimating models on the spread between 2-year mortgage interest rates and 3-month mortgage interest rates, I only get the valid results from ARCH (1,1) model:

𝑟! = 0.332, ℎ! = 0.045 + 0.815𝑒!!!!

So, ARCH effects are found in this spreads series, but the presence of GARCH effects can’t be confirmed.

4). MB5Y – MB2Y

None of the four models is effective when estimating on the spread between 5-year mortgage bond yields and 2-year mortgage bond yields. So further, both ARCH and GARCH effect are not significant in this premium series. The results from all the models show an oversized coef-ficient in front of 𝑒_!!!! _{. And the coefficients of previous volatility ℎ}

!!! are not significantly

different from zero in GARCH (1,1) and both GARCH-in-mean models. So do the constant term 𝛿 in GARCH (1,1) and coefficients of volatilities in the return equation of both GARCH-in-mean models.

Table 5 Model estimations of term premium series.

*p<.05, blue marked figure is the insignificant t-value, and red marked figure is the coefficient outside the restricted range. Invalid results is marked with “/”.

5). SE5Y – SE2Y

Both GARCH-in-mean models are effective for the term premium series between 5-year gov-ernment bond yields and 2-year govgov-ernment bond yields. We have:

𝑟_! = 0.341 + 0.751ℎ_! ℎ_! = 0.004 + 0.677𝑒_!!!! _{+ 0.313ℎ}

!!! ARCH(1,1)

α0 0.006 1.85 0.038 3.79* 0.033 4.04* 0.015 3.74*

α1 1.146 4.12* 1.017 3.82* 0.901 4.1* 0.727 2.96*

GARCH(1,1)

δ 0.005 1.54 1.040 3.79* 0.041 3.65* 0.016 2.19*

α1 1.117 3.93* 1.040 3.79* 1.011 4.2* 0.729 2.95*

β1 0.032 0.43 -0.038 -0.67 -0.142 -1.59 -0.007 -0.05

θ 0.751 3.22* -0.151 -1.89 -0.137 -0.87 -0.759 -2.74*

δ 0.004 1.98* 0.043 3.11* 0.033 3.03* 0.005 2.09*

α1 0.677 2.63* 1.170 3.66* 0.977 3.91* 0.685 3.02*

β1 0.313 2.25* -0.117 -2.08* -0.045 -0.4 0.284 2.69*

β0 0.283 11.25* 1.435 31.84* 0.705 15.49* 0.029 1.16 θ 0.570 4.43* -0.230 -2.03* -0.141 -0.97 0.750 4.62* δ 0.004 2.49* 0.040 3.18* 0.035 3.15* 0.007 2.83* α1 0.715 2.84* 1.148 3.8* 0.993 4.01* 0.814 3.62* β1 0.269 2.1* -0.090 -1.58 -0.075 -0.74 0.151 1.54 STIBOR12M1:STIBOR3M STIBOR12M1:STIBOR3M STIBOR12M1:STIBOR3M STIBOR12M1:STIBOR3M SE5Y1SE3M SE5Y1SE3M SE5Y1SE3M SE5Y1SE3M SE2Y1SE3M SE2Y1SE3M SE2Y1SE3M SE2Y1SE3M SE5Y1SE2Y SE5Y1SE2Y SE5Y1SE2Y SE5Y1SE2Y Term:premium Term:premium Term:premium Term:premium GARCH-in-mean models

A Study of Swedish Mortgage Interest Rates and Swedbank Stock Returns

A Study of Swedish Mortgage Interest Rates

and Swedbank Stock Returns

Contents

1. Introduction

1.1 Background

1.2 Objective and purpose

1.3 Research Problems

1.4 Research methods

1.5 Structure

2. Literature Review

2.1 Review of literature on Swedish mortgage market and banks’ stock returns

2.2 Review of literature on modeling time-varying volatility and correlation

3. Description of Data

3.1 Data collection

3.2 Descriptive statistics and analysis of data

3.3 Summary

3.4 Preparatory work for model estimation (Unit root test)

4. ARCH and GARCH Effects in Spreads

4.1 Econometric methodology

4.2 Econometric results and analysis from an economic perspective