Quantifying the illiquidity spread : an estimation and comparison of illiquidity measurements.

(1)

Quantifying the illiquidity spread:

an estimation and comparison of

illiquidity measurements

Maarten Ruissaard

Master’s Thesis to obtain the degree in Financial Econometrics

University of Amsterdam

Faculty of Economics and Business Amsterdam School of Economics

Author: Maarten Ruissaard

Student nr: 10664009

Date: September 17, 2014

Universitiy supervisor: prof. dr. H.P. Boswijk

Second reader: dr. S.A. Broda

(2)

Abstract

This study aims to provide an analysis on measuring the illiquidity spread on corporate bonds and covered bonds. In particular we focus on practical illiquidity measurements for insurance companies presented by Hibbert et al. (2009) and make a connection between what is written within the Solvency II framework. We find that the illiquidity measurements presented in the literature are not of practical use for insurance companies because they are perceived as too theoretic to be used in practice. We use daily data on corporate bonds and covered bonds and employ a vector error correction model to investigate Granger Causality tests and impulse response functions. We present evidence that the illiquidity level in the corporate bond market follows the illiquidity level of the covered bond market method. Furthermore, we describe the decomposition of the total spread risk Solvency II Capital Requirement (SCR) and use a vector error correction model to estimate the illiquidity spread risk SCR. We find that the illiquidity spread risk SCR is significantly present in the total spread risk SCR which stresses the importance of including an illiquidity premium in the Solvency II framework. Based on our research on the total spread risk SCR we conclude that in the absence of model uncertainty the credit spread risk SCR for corporate bonds and covered bonds that mature within one-to-three years are similar and therefore we could question the perception of covered bonds being less risky than corporate bonds.

(3)

Preface

First of all I would like to thank my academic supervisor prof. dr. Peter Boswijk for sharing his critical views and support. Also I would like to thank Tijn Schulting MSc for his practical input on this topic during my internship at EY. The actuary department of EY (formerly known as Ernst & Young) consists of multiple service lines aimed at supporting insurance companies, pension funds, banks, asset managers and individuals. This thesis was written as a result of clients needing to comply with the upcoming Solvency II regulations. The quantification of illiquidity spreads on their investments is a topic currently widely discussed by insurance companies because of the long-term nature of their liabilities.

(5)

1 Introduction

Recent financial crises have made policy makers, investors and researchers aware of the effects that illiquidity can have on the stability in financial markets. The turmoil in the markets in 2008 has sparked new questions regarding the perception of liquidity risk. The illiquidity risk premium is an additional return on financial assets that are not actively traded. Amihud & Mendelson (1986) define the notion of illiquidity as ”the discount that a seller concedes or the premium that a buyer pays when executing a market order”. Ambrose & Park (2012) re-fer to illiquidity as the result of a wedge between fundamental asset value and the market price. Insurance companies have long-term and highly predictable liabilities. For example, an-nuity portfolios consist of stable cash flows that continue for a long period. Due to their long-term nature, the portfolios are resistent to illiquidity shocks. To replicate the liabilities, insurance companies can thus hold illiquid assets to obtain an illiquidity markup on the total spread instead of holding only liquid assets. The main goal of this thesis is to estimate the illiquidity premium using different illiquidity measurement techniques and investigate possi-ble relations between the illiquidity levels of different markets.

Illiquidity cannot be directly measured (Amihud (2002)) and is therefore a very elusive concept. In the literature there is no clear consensus on how illiquidity should be measured. For each market, different ways of calculating the illiquidity premium are described. Authors that are concerned with this topic have mainly focused on illiquidity estimation methods re-garding the ”more liquid” assets.

As of 2016 the Solvency II regulations state that an additional term to the risk-free rate should be added to value insurance liabilities in a market consistent way. Since 2009 the European Insurance and Occupational Pensions Authority (EIOPA) has proposed several techniques to cope with the illiquidity of liabilities. But there is not a clear consensus on how illiquidity should be estimated. In this study we give an overview of what is written about the inclusion of an illiquidty premium within Solvency II.

Next to the techniques that are presented in the Solvency II regulations to measure illiq-uidity, Hibbert et al. (2009) propose several practical methods of estimating the illiquidity premium of financial assets. This paper explores these multiple measures of illiquidity and assesses the relation between illiquidity levels across different assets. Using econometric tech-niques we measure the illiquidity dynamics between both calculation methods for corporate bonds and covered bonds. Since these financial instruments comprise a large part of the in-vestment portfolio of insurance companies, it is of interest to investigate the short-term and long-term dynamics between the illiquidity measurements.

Within the literature and Solvency II different names for the illiquidity premium have been defined. For sake of clarity, in this paper the term ”illiquidity premium” is used for all calculation methods that are used to deal with the illiquidity in assets. In addition, a distinc-tion is made between the nodistinc-tions of funding liquidity and market liquidity. Funding liquidity refers to degree in which a company is capable of attracting funding. For example, a bank is vulnerable to bank-runs which cause the bank to have reduced funding liquidity. Market liquidity is considered as the relative capability of finding a counter party that takes on the

(6)

other side of the trade (Brunnermeier & Pedersen (2009)). Due to the long-term nature of their assets and liabilities, insurance companies do not have to cope with funding liquidity as much as banks do. In this paper we refer to market liquidity when liquidity related topics are discussed.

This paper makes several contributions to the literature. Through the analysis on the per-formance of the different illiquidity estimation methods, we found numerous relations between the illiquidity levels across the corporate bond and covered bond market. The first contribu-tion is that where illiquidity measurements are often measured independent of other financial assets, our analysis focuses on the impact of an illiquidity shock to an asset and its resulting impact on the level of illiquidity of another financial asset. If a relation exists this can have significant consequences on the investment portfolio of an insurance company. Secondly, our econometric approach focuses on the existence of potential cointegrating relationships across different markets. Whereas many papers have the availability over weekly or monthly data, our analysis is conducted using daily data which allows us to analyze the short-term dynamic interactions between markets. We also conduct analysis on the long-term memory of the vector error correction (VECM) model by imposing a heterogeneous auto regressive (HAR) model that is capable of measuring weekly and monthly effects of illiquidity estimations on the present level of illiquidity. This paper ends with an analysis on the derivation of the spread risk Solvency II Capital Requirements (SCR) for a corporate bond and covered bond portfolio of a large Dutch insurance company. Assuming that the total spread risk SCR consists of a credit spread risk SCR and an illiquidity spread risk SCR, we use the VECM representation to simulate a one-year ahead forecast to obtain the illiquidity spread risk SCR.

To sum up, we are interested in providing answers to the following research questions: • What is included in the literature on risk management and measurement of an illiquidity

premium on financial instruments? Is there evidence of illiquidity spill-over effects

between the corresponding markets?

• What regulations does Solvency II currently impose on measuring illiquidity?

• Is there a relation between the illiquidity levels measured in the corporate bond market and the covered bond market?

• What proportion of the spread risk SCR can be attributed to illiquidity?

This paper starts with an overview of the different illiquidity measurements presented in the literature. In particular studies that have conducted econometric analysis on this topic are presented. Secondly, section 3 describes what is written on the estimation and inclusion of an illiquidity premium within Solvency II. Third, the calculation of the illiquidity measurements as described by Hibbert et al. (2009) are explained in section 4 followed by an analysis of the descriptive statistics. Section 5 presents an analysis on the short-term dynamic interactions between the illiquidity measurements using a VECM model. The analysis is continued by a study on the long-term memory of the VECM model using a HAR model. Finally, we present the derivation of the Solvency II Capital Requirements regarding the total spread risk of the corporate bond and covered bond portfolios of a large Dutch insurance company.

(7)

2 Literature review

2.1 Characteristics of illiquidity

The relationship between illiquidity and asset pricing has been studied extensively. Several studies, e.g., Amihud & Mendelson (1986), Amihud (2002) and Bao et al. (2011) have em-pirically shown that illiquidity has an increasing effect on the expected returns of corporate bonds. Amihud & Mendelson (1986) and Amihud & Mendelson (2006) modeled the effects of the bid-ask spread on expected returns and found a positive relationship between the illiq-uidity measurement and expected returns. Bekeat et al. (2007) find evidence that market illiquidity is an important driver of expected returns in emerging markets. In their research Longstaff et al. (2005) show that a significant amount of the non-default component is related to illiquidity. Bao et al. (2011) prove that illiquidity accounts for a substantial part of the size and the cross-sectional variation of the yield spread.

Kyle (1985) contributes to the literature by making a distinction between three types of market liquidity. ”Tightness”, which is described as the cost of turning around a position over a short period of time. ”Depth”, the size of an order that is able to affect the price level. The third type referred to as ”resiliency” is defined as the speed at which prices recover from a random, uninformative shock. A market is called liquid if it has a high level of tightness, is deep and has a level of resiliency such that prices are at their underlying value.

From what follows from the study by Amihud (2002) his analysis on measuring illiquidity showed that illiquidity is not easily observable and cannot be captured in one single measure. Therefore proxies are used to estimate illiquidity. Illiquidity is affected by transaction costs, search costs and price impacts. These different aspects suggest that there is no single measure that captures liquidity for all assets.

2.2 Illiquidity measurements

The bid-ask spread is a widely used measurement for measuring illiquidity in corporate bonds. Amihud & Mendelson (1986) state that the ask price consists of a premium that is the result of an immediate purchase. The bid price consists of a concession enforced by the immediate sale of an asset. Therefore, they consider the difference between the bid and ask price as a measure of illiquidity. The illiquidity measure is calculated as the average of the monthly quoted spread and can be formalized as follows:

ILLIQCOR_iy = 1

Diy Diy

X

d=1

[P_i,dAsk− P_i,dBid], (1)

where P_i,dAsk and P_i,dBid denote the daily ask and bid price respectively for corporate bond i in

year y. Diy is the total number of days of data available.

Although widely used, the degree of liquidity in corporate bonds that is explained by the bid-ask spread does not capture all aspects of liquidity. Bao et al. (2011) argue that the types of market liquidity regarding market depth and resiliency are not captured with the bid-ask spread. They found some salient properties of illiquidity in corporate bonds. In particular, they argue that age and maturity have an increasing effect on illiquidity while the issuance

(8)

size of corporate bonds has a decreasing effect. Bao et al. (2011) constructed a more direct measure of illiquidity in which the lack of liquidity in a corporate bond gives rise to transitory effects on the price of the asset. It is argued that these transitory price movements result in a negative autocovariance in relative price changes. This measure captures substantially more illiquidity than the ordinary bid-ask measurement is capable of and results in the following formula:

ILLIQCOV_t = −Cov(∆pt, ∆pt+1), (2)

where pt is the price of the corporate bond at time t and ∆pt = pt− pt−1. Other than its

transitory nature, no further dynamics concerning illiquidity are assumed known. For exam-ple, Bao et al. (2011) state that when the illiquidity process follows an AR(1) process the

measure of illiquidity becomes: (1 − ρ)σ2_{/(1 + ρ). Here σ denotes the instantaneous volatility}

and ρ is the persistence coefficient.

Amihud (2002)’s illiquidity measurement for stocks, ILLIQV OL

iy , is based on the daily

price response associated with one dollar of trading volume. He performs a cross-sectional study based on the following formula:

ILLIQV OL_iy = 1 Diy Diy X t=1 |R_iyd| V OLDiyd . (3)

Riydis the return on stock i on day d of year y. V OLDiyddenotes the daily volume in dollars.

The model introduced by Fama & French (1993) is a three-factor asset pricing model which in comparison to the ordinary capital asset pricing model contains two more factors, namely, the excess returns of small market capitalization over large market capitalization and of value stocks over growth stocks. Chan & Faff (2005) use the pricing model to show that companies with higher book-to-market and smaller size ’appear’ to earn large risk-adjusted returns. In their research they generated a mimicking portfolio for illiquidity by extending the procedure of Fama & French (1993). The mimicking portfolio is based on the share turnover ratio. This ratio divides the volume of shares traded per month by the quantity of shares on issue for that month. This procedure is repeated for each month. For each calendar year the average turnover ratio is calculated and ranked in categories: liquid, moderately liquid and illiquid. They include an illiquidity factor in the Fama and French three-factor asset pricing model and test the restrictions of this model using the generalized method of moments approach. Their findings suggest that there is strong evidence of model improvement when including the share turnover factor in the model.

Except for corporate bonds, the literature written on illiquidity of financial assets does not agree to which proportion illiquidity is priced in assets. In a large study on corporate bond illiquidity Chen et al. (2007) study the level of illiquidity of more than 4000 corporate bonds using several measures. They find an illiquidity spread of 8-25 basis points (bps) for AAA-rated bonds and 59-459 bps for B-rated bonds. The study demonstrates the implica-tions of a decrease in credit rating on the level of the illiquidity spread.

(9)

2.3 Econometric analysis

With the available tools for measuring illiquidity across different markets, it is possible to an-alyze how liquidity shocks spread through markets within the financial sector. There is little literature about liquidity dynamics across markets, but the few studies give an impression of the spill-over effects of illiquidity across multiple markets.

Zhu (2006) presented empirical findings confirming that corporate bond spreads move to-gether with credit default swap spreads in the long run. In the paper Zhu (2006) extended existing studies by exploring potential short run dynamics using econometric methods and used a data set consisting of daily credit default swaps and corporate bond data. He proved the existence of cointegrating relationships between the credit spreads of both assets and specified a vector error correction model to examine the relative importance of the two mar-kets. The author showed that bonds spreads do not necessarily move together with the credit default swap spreads in the short run.

Buckles (2008) developed a liquidity index for the private real estate market and calibrated the joint behavior of price and liquidity using a vector auto regressive (VAR) model. The liquidity index is derived from the Transactions-Based Price Index and Transactions-Based Supply Index. Using cointegration analysis the paper showed that a linear combination of both indices can be interpreted as a measure of private market liquidity. The sample consists of monthly data. The author found a significant coefficient of 3.7 basis points between the 12-month lagged liquidity index and the price index. Contrastingly, a one point increase in the liquidity index 18 months ago has a negative effect of 5.4 basis points on the price index today. From the interpretation of the coefficients of the liquidity index equation Buckles (2008) found that a one point increase in the price index resulted in a 2.17 point increase in the liquidity index. Impulse response functions revealed that the price adjustment process is more chaotic than the liquidity adjustment process.

An extensive analysis of the spill-over effect of liquidity shocks across four markets, namely the stock market, the credit default swap market, the corporate bond market and the private real estate market is given by Ambrose & Park (2012). Their research provides evidence suggesting that liquidity spill-over effects spread quickly across these financial markets. Their illiquidity measures are based on existing methods of Amihud (2002), Bao et al. (2011), which are presented in section 2.2, and two self developed measurements for estimating private asset market illiquidity. By including private market illiquidity they directly tested the liquidity-shock spill-over effects across private and public markets. Results from their VAR model indicate that bond market liquidity Granger Causes CDS market liquidity with a 2-month lag. The results also suggest that a positive bond market liquidity shock has a negative effect on CDS market liquidity with a two-month lag and thus the illiquidity level in the CDS mar-ket reduces. Granger Causality tests show that stock marmar-ket liquidity Granger Causes bond market liquidity with a two-month lag and a bi-directional Granger Causality relation exists between private market liquidity and bond market liquidity.

Results from the VAR regression show that the coefficient for the bond illiquidity estimate on the CDS illiquidity level is significant for the 2-month lag, indicating that a positive shock that lowers the liquidity in the bond market has a positive effect on the liquidity of the CDS market. This result suggests a flight-to-liquidity effect since the demand of CDSs increase

(10)

as a result of a decrease in the liquidity in the corporate bond market. In addition, Am-brose & Park (2012) find a flight-to-liquidity effect between the private and public real estate market. The presence of the liquidity spill-over effect is confirmed by the impulse response functions which show a change in the liquidity levels of the markets after a standard deviation shock is applied to a particular market. The impulse response functions show that the shocks only have a temporary effect of 2 months before the illiquidity level returns to its original level. In this section we have given an overview of different illiquidity measurements and re-lations between the illiquidity levels across different markets. The different illiquidity esti-mation methods described in the literature review are in practice regarded as too theoretic. More interesting are the illiquidity premium calculation methods presented in the Solvency II framework as these methods serve with the sole purpose of estimating illiquidity for insurance companies. Solvency II presents a regulative environment which insurers will have to com-ply with in 2016. The next section gives an overview of the illiquidity premium estimation methods that have been presented over the last few years under Solvency II.

3 Solvency II

During the financial crisis credit institutions holding complex financial instruments ran into liquidity problems and questions were posed regarding the robustness of the risk system of financial institutions like insurance companies. The turmoil in the financial sector increased the awareness of risks that insurance companies are exposed to and highlighted the impor-tance of proper risk management and measurement. These circumsimpor-tances led to a new regime in which the supervision and regulation of insurance companies were pooled in one directive, the Solvency II Directive. The guidelines and regulations will hold as of 2016.

Solvency II will introduce a new harmonized regulatory regime for European insurance companies. Its objectives are a greater protection for policyholders and a deeper integration in the European insurance market. The regime has a three-pillar structure, each governing a different aspect of the Solvency II requirements. The first pillar consists of the quantitative requirements including the calculation of technical provisions and the solvency capital re-quirements. The second pillar deals with the qualitative aspects such as the risk management process. The third pillar contains the improvement of the disclosure requirements to enhance market transparency. Firms are obliged to disclose certain information publicly, which will bring in market discipline and help to ensure the stability of insurers.

The Solvency II Directive that has been adopted by the Council of the European Union and the European Parliament in November 2009 states that the reserves for the liabilities have to be equal to a best estimate and a risk margin. The best estimate is a probability-weighted average of the firm’s cash flows, discounted at the risk-free rate. The risk margin should be kept at a certain threshold to ensure that the value of the technical provisions is equivalent to the amount insurance undertakings would require in order to meet its obligations.

Under Solvency II firms are also allowed to value their liabilities using a replicating port-folio approach. If future cash flows of insurance liabilities can be replicated using financial instruments for which a consistent market valuation is available then the value of the technical

(11)

provisions can be set equal to the value of the replicating portfolio. This replaces the need to calculate the best estimate and a risk margin. Then, the replicating illiquid assets contain discount rates that include an illiquidity premium. This method implies that the illiquidity premium can be deduced from illiquid but default-free financial instruments that replicate the liabilities. The market-consistent valuation introduced by the Solvency II directive has consequences for insurers. Their liabilities are discounted at the risk-free rate, which implies that given the low level of interest rates, the value of the liabilities will significantly increase. The insurance industry argues that the market-consistent valuation should not be applied to them as their liabilities consist mostly of long-term highly predictable cash flows.

The European Insurance and Occupational Pensions Authority (EIOPA) works alongside the national supervisory authorities to protect the financial soundness of insurers and occupa-tional pension providers in order to protect consumers. As of 2009, CEIOPS, the predecessor of EIOPA opened the discussion whether an illiquidity premium should be included in the spread of illiquid investments. Although the group was aware of the importance of the in-clusion of an illiquidity premium, no clear guidelines were set on how the premium should be calculated. The Solvency II Directive therefore did not pose any restrictions on the esti-mation of the illiquidity premium. As of 2013 EIOPA provided a quantitative measurement in reaction to the request of the European Commission reported in the Quantitative Impact Study 5. In this report several approaches to cope with illiquidity were introduced:

• The Matching Adjustment allows insurers to add an illiquidity premium to the discount rate. The Matching Adjustment may only be applied to portfolios under certain condi-tions. The qualifying long-term assets and liabilities should have fixed cash flows and the credit quality should be on investment grade level. The level of the premium is not set by EIOPA and therefore does not depend on a transparent formula.

• The Counter Cyclical Premium allows the European Insurance Supervision to set higher discount rates during times of crisis to cope with the extra need to raise capital. In such way the premium deals with the reduction of pro-cyclicality and temporary financial distress that firms can run into in times of crisis. The premium can only be applied after EIOPA has granted permission.

• The Volatility Balancer is a permanent markup on the risk-free rate and can include a top-up in case in exceptional market circumstances. Where the spread of a reference investment portfolio exceeds twice a particular company investment portfolio, the spread would be adjusted for that market. The discount rate is increased by 20% of the excess spread between a country-specific investment portfolio and a currency (for example euro-dominated) reference investment portfolio.

The Counter-Cyclical premium received a lot of criticism due to its complexity to implement and time-intensive nature as EIOPA has to decide whether the premium is applicable to an investment portfolio. EIOPA therefore recommends that the Counter-Cyclical Premium be replaced by the Volatility Balancer, which would operate automatically meaning that EIOPA does not need to activate it or otherwise take a decision.

Under Solvency II different approaches to include a markup for illiquidity were presented. This section showed that there is no clear consensus yet on how insurance companies should

(12)

deal with illiquidity and in particular on how to estimate illiquidity. Hibbert et al. (2009) propose several practical methods for calculating an illiquidity premium. We will make a comparison and explore the presence of a relation between the illiquidity measurements. Next section describes these illiquidity measurements based on corporate bond and covered bond data and discusses their corresponding descriptive statistics.

4 Estimating illiquidity

4.1 Practical illiquidity measures

The measurability of illiquidity in financial assets is a topic that is high on the agenda of accountants and actuaries. Illiquidity premia calculation methods have been studied in both a theoretical as well as a practical setting. In this section we measure illiquidity using two widely used illiquidity estimation methods and explore the relation between these measure-ments. In the rest of the paper we will use the esimated illiquidity series for the specification of a model and the estimation of the illiquidity spread risk SCR.

Hibbert et al. (2009) describe two methods to estimate the illiquidity premium. The Neg-ative Basis CDS Method is based on the relation between corporate bonds and uses data from the CDS market to estimate the credit spread on corporate bonds. A CDS provides insurance to a protection buyer in case the entity defaults. The CDS spread therefore describes the credit risk of the firm and can intuitively be viewed as the market price for credit risk. A second method described by Hibbert et al. (2009) makes use of the data from the covered bond market. The covered bond market is known for its low level of credit risk and the spread over the risk-free rate is therefore viewed as a markup for illiquidity.

First, the Negative CDS Basis method and the Covered Bond method introduced by Hibbert et al. (2009) are described. Second, a comparison is made between their respective descriptive statistics.

4.2 Negative CDS Basis Method

This section describes an arbitrage-free derivation of the spread of a CDS, that is used in the derivation of the illiquidity levels estimated by the Negative CDS Basis Method. This method compares the spread on a corporate bond with the spread of a CDS with the same maturity and currency. A credit default swap is a contract in which one party buys protection by hedging the risk that a bond of a given issuer will default. The protection buyer pays a premium to the protection seller in return. It is important to make a clear distinction between the CDS spread and the CDS premium since these definitions are often perceived incorrectly as equivalents. The CDS premium is the fee that is paid on a regular basis for the protection offered and is set such that the value of the contract is zero at time of issuing. When the contract is settled the price of the CDS fluctuates as a result of market movements. The value of the contract becomes different from zero. The CDS spread is the premium in basis points that makes the value of the contract zero again. The spread can be derived implicitly from the (historic) market values of the CDS contract. We are interested in the CDS spread because the derivation of the illiquidity spread requires the prices of the CDSs that make the

(13)

value of the contract zero.

Following Duffie (1999) it can be shown by using the no-arbitrage principle that the spread of a corporate floating rate bond over a default free bond is equal to the CDS premium. Empirical results from Hull et al. (2004) prove that the relationship between the CDS premium and the bond spread is negative. The presence of this relationship implies the existence of other components priced in the spread of corporate bonds. One aspect of the residual part of the spread can be attributed to illiquidity risk. Longstaff et al. (2005) make the assumption that corporate bond yield spreads are calculated as the yield on a corporate bond minus the yield on a risk-less bond. They also argue that the non-default component of the spread is strongly related to illiquidity and that the CDS premium is a direct measure of the default component. Given these assumptions the illiquidity premium is formulated as follows:

Corporate bond spread = Corporate bond yield − risk-less bond yield

IlliquidityP remium = −CDS basis = Corporate bond spread − CDS spread (4)

Hull & White (2000) describe that the price of a CDS is determined by the probability of default, the recovery rate and the maturity of the CDS. The probability of default is de-termined by the financial rating of the corresponding bond. Rating agencies like Moody’s, Standard and Poor’s and Fitch provide ratings of corporate bonds underlying the correspond-ing credit default swap. The recovery rate reflects the total amount of firm value that can be retrieved given that the firm defaults. As the term of a CDS contract increases, the probabil-ity that a firm defaults increases. A higher markup is required by the protection seller which results in a higher CDS spread.

To derive the CDS spread several assumptions are made. The moment of default can happen at any moment in the life of a corporate bond. n denotes the term of a CDS in years. The CDS premium is paid annually. In case of a default at time t the premium is paid until time t. Interest is compounded continuously.

Suppose we are given the following:

• ptis the risk-neutral conditional default probability of a default in period [t − 1, t] given

that no default has occurred in period [0, t − 1];

• qt is the probability of no default over period [0, t];

• R denotes the recovery rate which is assumed constant over time;

• vt is defined as the present value of 1$ at time t;

• c is the market value of the CDS premium denoted in basis points of the total amount of protection (N ) that is bought by the protection buyer.

Given the definition of the conditional default probability pt, the survival probability can be

formalized by: qt=Qn_t=1(1 − pt).

The expected value of the CDS premium is the discounted value of the CDS premia until default occurs and can be formalized by:

N · c

n

X

t=1

(14)

The expected value of the losses given default occurs is denoted as: N · (1 − R) n X t=1 e−rtptqt−1. (6)

For the no-arbitrage principle to hold the expected value of the CDS premia should be equal to the expected value of the losses in case of a default.

As described by Hull & White (2000) the probability of default can be estimated by:

pt= 1 − e−λt, (7)

with λ denoting the average default intensity between time 0 and time t. Hull & White (2000)

argue that the average default intensity over a life of a bond is approximately: λ = spread_1−R .

Setting the present value of the CDS premia equal to the expected losses and substituting (7) for pt yields: N · c n X t=1 e−rtqt−1= N · (1 − R) n X t=1 e−rtptqt−1 c n X t=1 e−rt t−1 Y i=1 (1 − pi) = (1 − R) n X t=1 e−rtpt t−1 Y i=1 (1 − pi) c n X t=1 e−rt t−1 Y i=1 e−spreadi1−R i = (1 − R) n X t=1 e−rt(1 − e−spreadt1−R t) t−1 Y i=1 e−spreadi1−R i

The recursive formula consists of variables which are known except for spread at time t and can therefore be solved. The spread series obtained from the formula are used to derive the illiquidity spread using the Negative CDS Basis approach.

4.2.1 Data

The CDS market values are provided by the Thomas Reuters database. In order to make sure the CDS market values consists solely of a credit risk component, data is used from financial firms that are listed in the iTraxx index. This index consists of a family of credit default swap products covering Europe, Australia and Japan. Its constituents are 125 investment grade companies issuing CDSs with a maturity from 1 to 20 years. In this study only financial entities constituted in Europe were selected as our study is focused on measuring illiquidity in Euro dominated markets. The time series consists of daily data and is denominated in basis points. The selected firms are either banks or insurers and have a sample period as of December 2007 until January 2014 and comprise around 180.000 observations. An overview of the selected financial entities can be found in the appendix (Table 8).

Corresponding to the CDSs of the particular financial entities, we retrieve the yields for all bonds issued during the sample period. For each date and maturity the corresponding CDS spread is obtained using linear interpolation. The selection of corporate bonds was subject to the following conditions:

(15)

• bonds may not be structured or subordinated;

• only bonds which have a fixed coupon rate are included;

• bonds have to be denominated in the same currency as the corresponding CDS are. After the filtering process based on the conditions above a total of 47 corporate bonds have been selected with contracts ending between 2014 and 2022. Daily data is available for all bonds, but the sample size differs substantially between bonds. Out of 47 bonds 20 have data available since 2007. To cope with the missing data the corporate bonds have been classified into buckets. The buckets consist of corporate bonds with similar maturities and credit rating. An illiquidity index of these buckets is created by taking equal averages between the series. The corporate bonds with maturities ranging between 2014 and 2016, 2017 and 2019, 2020 and 2022 are grouped together. As the maturity date of each corporate bond is different, we assume to set each maturity date on the 30th of June for each year. The filtered data resulted in the 2020-2022 bucket to have a diminished sample size that only starts in 2011. Therefore we continued our analysis with the 2014-2016 and 2017-2019 bucket.

For the analysis it is crucial to make a distinction between the credit rating of each financial institution. Through Bloomberg the credit ratings of the banks and insurance companies were obtained from Standard & Poor’s, Moody’s and Fitch. Since the rating agencies can differ in their assigned ratings we assumed the following selection criteria for the determination of the credit rating:

• If all three rating agencies assign a different rating the middle rating is chosen;

• If two rating agencies assign the same rating and the third differs from these, then the rating that is assigned by the majority is chosen.

The sample consists of investment grade bonds with a credit rating ranging between AA and BBB. In the appendix (Table 8) a list is shown of the ratings assigned to the firms. As a risk-free rate the ECB AAA curve is used. This curve consists of interest rates of AAA countries within the Euro zone. Daily quotes are available for a maturity of 1 to 20 years. For each date and maturity the corresponding interest rate is found using linear interpolation.

4.2.2 Descriptive statistics

Figure 2 gives an overview of the illiquidity levels for each credit rating for the two liquidity buckets. The illiquidity premium for the constituents of the curve which credit rating reduces from A to BBB in Figure 2 (a) shows clear spikes in 2008 and 2011. The significant increases in illiquidity premium in 2009 can be attributed to the credit crisis that started in the United States. The clear spike in 2011 occurs at the same time when the (still ongoing) Euro crisis was at its peak. The Euro crisis is characterized by a large increase in interest rates as a result of severe economic downturns in Greece, Portugal and Spain. The lower credit rating has a negative impact on the liquidity of corporate firms reflecting a higher illiquidity premium. Table 1 shows the descriptive statistics of the two liquidity buckets denominated in percent-ages. For different credit ratings and their transitions, the statistics show the impact of the credit rating on the illiquidity premium. To avoid possible time effects all credit rating downgrades have occurred in 2012. The descriptive statistics therefore allow us to make a comparison between curves in which a credit rating transition has occurred. The average

(16)

illiquidity premium increases for the 2014-2016 bucket when the credit rating decreases. We observe that the average illiquidity spread for the 2017-2019 bucket is higher when compared to the 2014-2016 bucket. For example, the illiquidity premium for the companies which credit rating were downgraded from A to BBB lies 69 bps higher for the 2017-2019 year curve in comparison to the 2014-2016 year curve. The average illiquidity premium for the curve that transitions from a credit rating of A to BBB is 239 bps while the AA curve that transitions to an A credit rating has an average illiquidity premium of 129 bps. In the transition of credit rating we observe that a decrease in credit rating has an increasing effect on the standard deviation. A result that was expected, as it is normally assumed that a decrease in credit rating results in a more volatile illiquidity premium.

The analysis performed by Hibbert et al. (2009) is done on a sample period different from the sample period studied in this paper. Their sample consists of investment grade corporate bonds that mature in three to five years and the iTraxx CDS index. The year 2008 is contained in both studies and we observe comparing graphs that the illiquidity premium estimated by Hibbert et al. (2009) is close to the calculated premia of the 2017-2019 bucket. The estimated illiquidity premium for the AA curve of the 2014-2016 liquidity bucket is also in line with the findings by Chen et al. (2007).

0.0% 1.0% 2.0% 3.0% 4.0% 5.0% 2008 2009 2010 2011 2012 2013 AA AA->BBB A->BBB

(a) Illiquidity spreads of 2014-2016 year buckets

0.0% 1.0% 2.0% 3.0% 4.0% 5.0% 6.0% 7.0% 2008 2009 2010 2011 2012 2013 A AA->A A->BBB

(b) Illiquidity spreads of 2017-2019 year buckets Figure 2: Illiquidity spreads

(17)

Descriptive statistics 2014 - 2016 2017 - 2019 Credit rating AA AA → BBB A → BBB A AA → A A → BBB Mean 0.75 0.98 1.70 1.01 1.29 2.39 Median 0.68 0.91 1.44 1.02 1.11 2.21 Maximum 2.17 2.40 4.60 2.20 3.40 6.01 Minimum 0.19 0.10 0.88 0.28 0.57 0.61 Standard deviation 0.34 0.51 0.74 0.40 0.56 1.20 Skewness 1.27 0.36 1.35 0.17 1.35 0.91 Kurtosis 4.68 2.22 4.14 2.49 4.47 3.29 Observations 1579 1579 1579 1579 1579 1579

Table 1: Descriptive statistics of illiquidity premia calculated using the Negative CDS Basis method

4.3 Covered Bond Method

The Covered Bond method is a more direct measure of illiquidity as described by Hibbert et al. (2009) since it involves choosing a pair of financial instruments which are assumed to offer equivalent cash flows for a portfolio. Compared to an ordinary bond, the holder of a covered bond has a priority claim on a managed pool of high-grade assets. Aside from the fact that the issuer of a covered bond is required to pay back the bond in event of default, the bonds are backed by assets such as public sector loans and pooled mortgages. Therefore the investor has a dual appeal on the issuer. Given the high credibility of these instruments minimal default risk is expected. In the absence of default risk of both instruments the illiquidity premium is calculated as:

IlliquidityP remium = Covered bond index yield − risk-f ree rate (8)

4.3.1 Data

To ensure the credit risk in covered bonds is reduced to a minimum, we conducted analysis on covered bonds that have an AAA or AA credit rating. Pfandbriefe are one of the oldest issued covered bonds and originated in Germany. Due to the dual nature of protection cov-ered bonds have not experienced a default since 1900. Packer et al. (2007) have shown that covered bond prices have been robust to idiosyncratic shocks to both issuer creditworthiness and the value of the covered pools. At their peak in 2003 over 1100 billion of issued Pfand-briefe were outstanding. Therefore we chose to use the PfandPfand-briefe yields as the covered bond index yield. We retrieve the data from the Reuters database. The sample consists of yields with a sample period from 2002 to 2014. Terms ranging from one to fifteen years have been collected yielding over 40.000 observations.

As a risk-free rate three different curves have been evaluated. Hibbert et al. (2009)

considered using the ECB AAA rate. Since the Pfandbriefe are originated in Germany and the German government bond yields have the AAA status, another option would be to use the German ”Bund” yields. Under Solvency II a swap rate is used when determining the risk-free rate. The fixed nature and minor default of these rates prove to be more reliable than the

(18)

ordinary variable deposit rates. In Figure 3 an overview of the risk-free rates is given. The figure shows that the spread between the ECB AAA rate and the German government bond yields is very small. The swap curve follows a similar pattern as the other two curves but lies consistently higher. A plausible explanation for this is that the swap spread at any maturity reflects the credit risk associated with banks that provide swaps compared to government issued bonds. The German government bond is considered as the most trustworthy amongst all European countries and the bond yield curve is also comprised in the ECB AAA curve. Besides its creditworthiness, the bund yields data contains more observations than the ECB AAA bond yields. The stable nature of the German government bond and the larger sample size give us reason to continue with the German government bond yields as a proxy for the risk-free rate. -1% 0% 1% 2% 3% 4% 5% 6% 2007 2008 2009 2010 2011 2012 2013 ECB AAA 1YR SPOT RATE

SWAP CURVE 1YR

GERMAN GOVERMENT BOND YIELD 1YR

Figure 3: Risk-free rates

4.3.2 Descriptive statistics

Figure 4 shows the difference between the Pfandbriefe yields and the ECB AAA rate for different terms. Figure 4 (a) shows the whole sample and the sample used in Figure 4 (b)

corresponds to the sample of the Negative CDS Basis method. The one year illiquidity

spread shows a clear spike in comparison to the other curves. The distinctive peak for the one-year curve in 2008 does not return in the results presented by Hibbert et al. (2009). A possible explanation for this is that in their research Hibbert et al. (2009) use different covered bonds since our sample consists solely of German covered bonds. From Figure 4 (a) it can be seen that a negative illiquidity premium was estimated in 2004 and 2005 for the one year illiquidity premium. Although this result is not intuitive, a plausible explanation for this result are the extremely low bond spreads and a different quotation basis used for the instruments. Comparing the graphs between both studies we find that the illiquidity premia estimated in our study are comparable to the results found by the authors during the sample period 2005-2008.

(19)

-0.5% 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014-2016 2017-2019 2020-2022 2023+

(a) Whole sample

0.0% 0.4% 0.8% 1.2% 1.6% 2.0% 2.4% 2008 2009 2010 2011 2012 2013 2014-2016 2017-2019 2020-2022 2023+ (b) Reduced sample Figure 4: Illiquidity premium using Covered Bond method

Table 2 gives an overview of the descriptive statistics of the illiquidity premium in per-centage points calculated using the Covered Bond method based on the German Pfandbriefe and the German covered bond yields. The sample period is adjusted to the sample from the Negative CDS Basis method to make a comparison between the two methods possible. The average illiquidity premium is 75bps, 103 bps, 87 bps and 72 bps for the 2014-2016, 2017-2019, 2020-2022, 2023+ maturities, respectively. One surprising aspect of the results is that the average illiquidity premium does not increase as the term increases. For example, the average 2023+ year spread is found to be on a lower level than the average 2020-2022 year spread. This result was not expected as an increasing term normally has a negative effect on the liquidity of the firm. In addition, when we observe the standard deviation we see that the standard deviation for short term liquidity premium is higher in comparison to the medium to long-term liquidity premium.

Descriptive statistics name 2014 - 2016 2017 - 2019 2020 - 2022 2023+ Mean 0.75 1.03 0.87 0.72 Median 0.70 1.00 0.81 0.69 Maximum 2.24 1.63 1.50 1.55 Minumum 0.12 0.31 0.35 0.08 Standard deviation 0.44 0.27 0.25 0.35 Skewness 0.96 -0.04 0.50 0.39 Kurtosis 3.63 2.46 2.41 2.16 Observations 1579 1579 1579 1579

Table 2: Descriptive statistics of illiquidity premia using the Covered Bond method

4.4 Comparison

Before a comparison is made between the two methods described in the previous section, the following things should be kept in mind: both methods are proxies for calculating an

(20)

illiq-uidity premium. The unobservable nature of the true illiqilliq-uidity premium makes us cautious when interpreting our findings. The analysis is conducted during one of the most turbulent financial times in history with multiple crises occurring during this period. The disruption in the markets possibly has had a biased effect on the illiquidity premia.

From Figure 2 (a) and 4 (b), we observe that all curves follow similar patterns. with the curve that decreases from an A credit rating to a BBB rating being the biggest outlier. A plausible conjecture for the fact that this curve is higher than the rest, is the large shift in credit rating that occurred for the underlying constituents.

Comparing the descriptive statistics of the AA curves for both illiquidity measurements in Table 1 and 2 we observe that the average illiquidity premium for both buckets is exactly equal. The average illiquidity premia for the corporate bonds in the 2014-2016 bucket that have been downgraded are estimated higher than its covered bond counterpart. A plausible conjecture for this result is that the decrease in credit rating did not occur for the covered bonds in the sample. Covered bonds ordinarily do not suffer from credit rating downgrades and contain little credit risk. A noteworthy result is that the standard deviations of both methods do not consistently increase when the maturity increases. From Table 1 it is clear that the illiquidity premium becomes more volatile as the maturity and credit rating decrease. The illiquidity series that followed from the Negative CDS Basis method and Covered Bond method proved to be close to each other. Based on the graphs and the descriptive statistics we conclude that the illiquidity levels captured by both methods are equaly able in estimating illiquidity. Using the estimated illiquidity spreads we are able to investigate the presence of a relation between the illiquidity measurements. The following section describes different econometric models and tests to find possible spill-over effects between the illiquidity levels of the corporate bond and covered bond market.

5 Dynamic interaction between illiquidity measurements

This section provides results on the relation dynamics between the illiquidity levels estimated by the Negative CDS Basis method and the Covered Bond method. By specifying a VAR model we calibrate the behavior of the levels of illiquidity between markets. In addition, we specify a VECM model after we check for cointegration between the illiquidity measurements. We investigate the linear dependencies between the 2014-2016 year illiquidity curves estimated by both methods. Using the VECM representation we conduct a Granger Causality test and investigate the impulse response functions to evaluate the impact of the relationship between the illiquidity measurements. Finally, we perform a model misspecification test by investigating the long-term memory of the VECM model with the use of a HAR model. Given the previous research done on the illiquidity estimates we expect a relationship to some degree between the illiquidity estimates.

5.1 Vector auto regressive model

The illiquidity series estimated from the Negative CDS Basis method and Covered Bond method displayed in Figure 5 show that both series are non-stationary. We performed a unit root test on both series to confirm our hypothesis of the non-stationarity. For both series

(21)

0.0% 0.4% 0.8% 1.2% 1.6% 2.0% 2.4% 2008 2009 2010 2011 2012 2013 NEGATIVE CDS LIQUIDITY INDEX

COVERED BOND LIQUIDITY INDEX

Figure 5: Time series 1-3 year illiquidity estimates

the test failed to reject the null hypothesis, implying that we can not reject the hypothesis that both series are integrated of order 1. If a linear combination appears stationary then a cointegrating relationship exists.

The endogenous relationship between the two series can be analyzed by answering the fol-lowing questions: how does illiquidity in the bond market influence illiquidity in the covered bond market and vice versa? A VAR model is useful to explore the relationship between the two markets and is specified as follows:

LIQBON Dt LIQCOVt =a b + Pp

i=1α1,iLIQBON Dt−i

Pp

i=1α2,iLIQBON Dt−i

+ Pp j=1β1,jLIQCOVt−j Pp j=1β2,jLIQCOVt−j +1,t 2,t , where:

• a and b are constants; • p = the number of lags; • t = the time index;

• LIQBON D = The liquidity index estimated using the Negative CDS Basis approach;

• LIQCOV = The liquidity index estimated using the Covered Bond approach;

• is a vector corresponding to the error term;

• αi, and βi are coefficients for lag i.

For the decision process of selecting the optimal lag-length we performed a lag-length test

on the series LIQBON D and LIQCOV. The Likelihood ratio statistic, Final prediction error

and Akaike criterion indicate an optimal lag-length of eight. Contrastingly, the Hannan-Quin and Schwarz criterion indicate a lag order of 2. We are interested in the impact of variables that are lagged for a week. This argument together with the fact that the majority of the tests indicate a lag order of eight, made us chose a VAR model that includes eight lags. After

conducting analysis on the level of serial correlation in the variables LIQBON D and LIQCOV

(22)

The VAR estimation results are displayed in Table 9 in the appendix. Overall, only a small amount of the variables is significant. The impact of the significant variables on the dependent variables is very small and conclusions from these relations can not be deduced since the presence of a possible cointegrating relation will most likely have an effect on the estimation results.

More interesting are the results from a Granger Causality test to check whether the past values of one variable contain information that help predict another variable. It allows us to test the existence of a relation between the liquidity levels of different markets. ”X is said to Granger-cause Y” if Y can be better predicted using the histories of both X and Y than using the histories of Y alone. Here the null hypothesis is formalized as ”X does not Granger-cause Y”. In Table 3 the results of the Granger Causality test are presented. The test uses chi-square statistics and probabilities to measure causality between the variables.

From the table we deduce that the null hypothesis that LIQBON D does not Granger Cause

LIQCOV and vice versa is rejected at the 5% significance level. We hence find evidence that

both series are useful in forecasting each other.

Furthermore, we analyzed the impulse response functions to track the responses of a systems variable to a brief shock. Figure 6 gives an overview of the impulse response functions. We find that a shock to the illiquidity level has a constant impact on the illiquidity level and

does not die out as time passes. The point estimates of LIQCOVton LIQBON Dt in Figure 6 (b)

show that there is a relation between the illiquidity levels as calculated by the Negative CDS

Basis method and Covered Bond method. A shock to LIQBON Dt has an impact on LIQCOV t

of around 2 basis points. Contrastingly, this impact is not present the other way around

(Figure 6 (c)). Finally, similar results following from a shock on LIQBON Dt to LIQBON Dt

are applicable to the effects on LIQCOVt after a shock on LIQCOVt.

LIQBON D does not Granger Cause LIQCOV Chi-square Degrees of Freedom Prob

55.799 8 0.000

number of observations: 1570

LIQCOV does not Granger Cause LIQBON D Chi-square Degrees of Freedom Prob

18.606 8 0.017

(23)

.00 .01 .02 .03 .04 .05 1 2 3 4 5 6 7 8 9 10 Point estimate – 2 S.E.

Response of LIQ_BOND to one shock in LIQ_BOND

(a) LIQBON Dt on LIQCDSt

.00 .01 .02 .03 .04 .05 1 2 3 4 5 6 7 8 9 10 Point estimate – 2 S.E.

Response of LIQ_BOND to one shock in LIQ_COV

(b) LIQBON Dt on LIQCOVt

-.01 .00 .01 .02 .03 .04 .05 1 2 3 4 5 6 7 8 9 10 Point estimate – 2 S.E.

Response of LIQ_COV to one shock in LIQ_BOND

(c) LIQCOVt on LIQBON Dt

-.01 .00 .01 .02 .03 .04 .05 1 2 3 4 5 6 7 8 9 10

Response of LIQ_COV to one shock in LIQ_COV

(d) LIQCOVt on LIQBON Dt

(24)

5.2 Vector error correction model

Since the Dicky-Fuller test on both series demonstrated the presence of a unit root, we evaluate the Johansen test (Johansen (1992)) to evaluate the presence of cointegrating rela-tionships between the series. The trace test (Table 10) indicates one cointegrating equation at the 5% level. Since cointegration has been detected between the series we know that there exists a long-term equilibrium relationship. We therefore apply a VECM model in order to evaluate the short-run properties of the cointegrated series. A VECM model considers the first-differenced versions of the series and imposes cointegrating relationships. It poses restrictions on the coefficients of the VAR model such that the errors of the regression are stationary series. The illiquidity premium series in Figure 5 show that no clear linear trend is present. The levels of the series indicate a non-zero mean such that the inclusion of a constant is justified. Using the representation of a VAR model we rewrite it as follows to obtain a VECM model.

Xt=

p

X

i=1

γiXt−i+ t

∆Xt= c + (γ1− I)Xt−1+ (γ2− I)Xt−2+ · · · + (γp− I)Xt−p+ t

= c + " _p X i=1 γi− I # − p X i=2 γi∆Xt−1− · · · − p X i=p γi∆Xt−p+1+ t = c + ΠXt−1− p−1 X i=1 Ψi∆Xt−i+ t, where Π =Pp−1

j=1+1γj and Ψ =Pp−1i=1αi− I. Π can be decomposed in a part that reflects

the speed of convergence to equilibrium denoted by α, and a vector β that contains the

cointegrating relationships, such that Π = αβ0. Rewriting the VAR model for LIQBON Dt

and LIQCOVt in VECM form results in the following equations:

∆LIQBON Dt = c1+ α1β 0   LIQBON Dt−1 LIQCOVt−1 c  + p X i=0

Φ∆LIQBON Dt−i+

p

X

i=0

Ψ∆LIQCOVt−i+ 1t

∆LIQCOVt = c2+ α2β 0   LIQBON Dt−1 LIQCOVt−1 c  + p X i=0

Φ∆LIQBON Dt−i+

p

X

i=0

Ψ∆LIQCOVt−i+ 2t.

The estimation results of the VECM model for the illiquidity estimates can be found in

Table 4. The cointegrating vector is significant and β specifies the relation between LIQBON Dt

and LIQCOVt as:

β   LIQBON Dt−1 LIQCOVt−1 c 

= LIQBON Dt−1− 0.639LIQCOVt−1− 0.272

From the significant variables displayed in Table 4 some interesting results can be derived. First of all, the speed-of-conversion vector α is only significant for the dependent variable ∆LIQBON Dt. The relation shows that the lagged levels of ∆LIQBON Dt have an impact on the

(25)

levels of ∆LIQCOVt. Secondly, the first-differenced one-day lagged corporate bond variable

is significant for both ∆LIQBON Dt and ∆LIQCOVt but is small in impact. ∆LIQBON Dt−1

reflects that a one percentage point increase of the illiquidity measured one day ago has a decreasing effect on the illiquidity level in the corporate bond market and an increasing effect on the covered bond market illiquidity level. Furthermore we see that the five-day lagged corporate bond market illiquidity measure has an impact of 0.05 percentage points on the current level of illiquidity. We also find a significant relation between dependent variable

∆LIQCOVt and ∆LIQBON Dt−7. In contrast with the regression results of the VAR model in

Table 9 this relationship is now positive.

A first impression of the second column of Table 4 is that we see more significant lagged

variables of ∆LIQCOVt in comparison to the lagged variables of ∆LIQBON Dt. The two-day

to seven-day lagged variables of ∆LIQCOVt are all significant. The impact of all variables

is similar as the coefficients show that a one percentage point increase in the level of illiq-uidity in the covered bond market results in an increase of around 0.07 percentage points

in ∆LIQBON Dt. These results show that there is a very clear link between the estimated

illiquidity in the covered bond market and the illiquidity in the corporate bond market. The relation shows that illiquidity measured in the corporate bond market follows from the illiq-uidity level in the covered bond market with a weekly delay. As illiqilliq-uidity in the covered bond market has a delayed effect on the illiquidity in the corporate bond market, this could imply that there is a ”portfolio rebalancing” effect as proposed by Kodres & Pritsker (2002). This effect arises when investors adjust their portfolios as a result of an idiosyncratic shock to the liquidity level of a market. The adjustment process has an effect on other assets within the portfolio resulting in changes in the illiquidity level of these assets. In addition we find a

significant relation between ∆LIQCOVt−1 and ∆LIQBON Dt of -0.12 percentage points, which

shows that the illiquidity measured by the Covered Bond approach decreases after the illiq-uidity increased one day ago, ceterus paribus.

Summing up, these findings suggest there is one relation found between the lagged

vari-ables of ∆LIQBON Dt and ∆LIQCOVt and that is for ∆LIQBON Dt−1 variable. With an impact

of 0.08 percentage points the influence is very small. The regression of the lagged variables of

∆LIQCOVt on ∆LIQBON Dt gives strong evidence that the illiquidity level of the corporate

(26)

Table 4: VECM estimates

Error correction: ∆LIQBON Dt ∆LIQCOVt

α -0.021429 0.007062 (0.00526) (0.00583) [-4.07631]* [1.21033] ∆LIQBON Dt−1 -0.092991 0.088527 (0.02559) (0.02841) [-3.63344]* [3.11659]* ∆LIQBON Dt−2 -0.028101 0.021185 (0.02569) (0.02852) [-1.09364] [0.74287] ∆LIQBON Dt−3 0.030892 0.051766 (0.02565) (0.02847) [1.20434] [1.81835] ∆LIQBON Dt−4 0.007879 0.036298 (0.02557) (0.02838) [0.30807] [1.27880] ∆LIQBON Dt−5 0.052321 0.016997 (0.02550) (0.02830) [2.05214]* [0.60067] ∆LIQBON Dt−6 0.039491 -0.008061 (0.02546) (0.02826) [1.55098] [-0.28525] ∆LIQBON Dt−7 0.056528 0.019184 (0.02540) (0.02819) [2.22582]* [0.68061]

Error correction: ∆LIQBON Dt ∆LIQCOVt

∆LIQCOVt−1 0.042859 -0.128158 (0.02323) (0.02578) [1.84494] [-4.97061]* ∆LIQCOVt−2 0.062794 -0.046073 (0.02341) (0.02598) [2.68226]* [-1.77320] ∆LIQCOVt−3 0.070374 -0.049333 (0.02348) (0.02607) [2.99656]* [-1.89266] ∆LIQCOVt−4 0.072249 -0.026855 (0.02355) (0.02614) [3.06758]* [-1.02734] ∆LIQCOVt−5 0.070966 0.018990 (0.02359) (0.02618) [3.00826]* [0.72528] ∆LIQCOVt−6 0.052322 -0.002430 (0.02358) (0.02617) [2.21881]* [-0.09285] ∆LIQCOVt−7 0.055968 -0.007597 (0.02357) (0.02616) [2.37458]* [-0.29043] Constant -0.000120 -0.000306 (0.00103) (0.00114) [-0.11680] [-0.26748] Cointegrating vector

Variable: LIQBON Dt−1 LIQCOVt−1 Constant

Estimate: 1.000000 -0.639499* -0.271792

Standard errors in ( ) and t-statistics in [ ] * Statistically significant at the 5% level

Using the VECM representation we tested for Granger Causality and checked the impulse response functions. In Table 5 the results from the Granger Causality test are displayed. The chi-square statistics and probability values under the null-hypothesis show that there is a

(27)

causal relationship between ∆LIQBON Dt and ∆LIQCOVt since the null hypothesis is rejected.

It implies that ∆LIQCOVt follows ∆LIQBON Dt in the short-run. This result confirms the

finding of the significant variable α1 which suggested there is a relation between the lagged

variables of ∆LIQBON Dt on ∆LIQCOVt. The null hypothesis for the test that ∆LIQCOVt

does not Granger cause ∆LIQBON Dt is not rejected. This finding contrasts with the Granger

Causality test using the VAR specification which rejected the null hypothesis. The fact that

α2 is not significant supports the rejection failure. Taken together, these results suggest that

a shock to the illiquidity level of the corporate bond market Granger Causes the covered bond market illiquidity, but not vice versa.

Granger Causality Tests

∆LIQBON D does not Granger Cause ∆LIQCOV

Chi-square Degrees of Freedom Prob

33.915 8 0.000

∆LIQCOV does not Granger Cause ∆LIQBON D

Chi-square Degrees of Freedom Prob

14.897 8 0.061

Table 5: Granger Causality Tests

To confirm the findings of the cointegration test we evaluate the impulse response functions

of ∆LIQBON D and ∆LIQCOV. We notice that the responses are very similar to the effects

seen in Figure 6 when the VAR specification was used. This shows that the fit of the VECM model does not differ from the VAR model since similar patterns are visible. The graphs give a clear picture of the general trend in the course of the shock during a period. The similar graphs indicate that the shocks applied are not model specific.

(28)

.00 .01 .02 .03 .04 .05 1 2 3 4 5 6 7 8 9 10 Point estimate

Response of LIQ_BOND to one shock in LIQ_BOND

(a) LIQBON Dt on LIQBON Dt

.00 .01 .02 .03 .04 .05 1 2 3 4 5 6 7 8 9 10 Point estimate

Response of LIQ_BOND to one shock in LIQ_COV

(b) LIQBON Dt on LIQCOVt

-.01 .00 .01 .02 .03 .04 .05 1 2 3 4 5 6 7 8 9 10 Point estimate

Response of LIQ_COV to one shock in LIQ_BOND

(c) LIQCOVt on LIQBON Dt

-.01 .00 .01 .02 .03 .04 .05 1 2 3 4 5 6 7 8 9 10 Point estimate

Response of LIQ_COV to one shock in LIQ_COV

(d) LIQCOVt on LIQCOVt

Figure 7: Impulse response functions

5.3 Long-term memory

Since the VECM model is only capable of exploring the dynamic relationships between the illiquidity estimates for a short-term, it is interesting to investigate the long-term memory of the VECM model. To model this we implement a model that is based on the Heterogenous Autoregressive model, also known as HAR model introduced by Corsi (2009). This model is based on the idea that market agents influence the level of volatility on a different frequency. Therefore the model copes with this by implementing the volatility independently, but jointly in a regression. This offers the opportunity to model weekly and monthly influences of the illiquidity level on the present level through a simple regression. The HAR model therefore serves as a misspecification test to check whether the model captures long-term memory. Implementing the HAR model brings us to the following model:

LIQBON Dt = c + LIQBON Dt−1+ LIQCOVt−1+ LIQBON DW EEKt−1

(29)

LIQCOVt = c + LIQBON Dt−1+ LIQCOVt−1 + LIQBON DW EEKt−1

+ LIQCOV W EEKt−1 + LIQBON DM ON T Ht−1 + LIQCOV M ON T Ht−1,

where LIQBON Dt−1 is the previous day illiquidity level, LIQBON DW EEKt−1 the previous week

average daily illiquidity level and LIQBON DM ON T Ht−1 is the previous month average daily

illiquidity level. The same definitions hold for the illiquidity variables from the Covered Bond method.

From the plotted series in Figure 5 it can be observed that the error terms are most likely not homoskedastic. To test this we perform the White heteroskedasticity test to determine if the errors have the same scatter through the series. The test for homoskedasticity is re-jected at the 5% significance level. In our ordinary least-squares regression we therefore allow for heteroskedastik-consistent standard errors. To draw more accurate inferences from the parameters we constructed the model using a heteroskedastic and autocorrelation consistent (HAC) covariance matrix.

Table 6 and 7 display the regression results using the HAR model for dependent variables LIQBON Dt and LIQCOVt respectively. From Table 6 it can be seen that the impact of the

significant variables on LIQBON Dt is small. The only variables that are significant are the

present covered bond illiquidity variable and the one-day lagged variables for both measures. For example, a percentage point increase of the illiquidity level from the covered bond market has a negtive impact of 0.18 percentage points on the level of liquidity in the corporate bond market. Based on these statistics we did not find any proof of long-term memory present in the VECM model. We can therefore say that the model is well specified.

In Table 7 the results from the HAR regression for dependent variable LIQCOVt are

dis-played. The results are similar to the results with respect to the regression on LIQBON Dt.

A one percent point liquidity increase in the one-day lagged LIQBON Dt variable results in

an increase of 0.19 percentage points of LIQCOVt. We see that the effects of an increase of

the one-day lagged LIQCOVt variable has an impact of 0.95 percentage points on the present

illiquidity level.

The results show that we cannot conclude that there is a proven long-term memory in the VECM model. Unlike papers from Buckles (2008) and Ambrose & Park (2012) the long-term memory between markets was not found using the HAR model. A possible explanation for this is the fact that in our sample two severe liquidity crises occurred, resulting in very high levels of illiquidity.

(30)

Regression output using HAR model

Variable Coefficient Std.Error t-Statistic Prob.

LIQBON Dt−1* 0.961826 0.019164 50.19035 0.0000

LIQCOVt−1* 0.086058 0.021796 3.948287 0.0001

LIQBON DW EEKt−1 0.017907 0.024536 0.729840 0.4656

LIQCOV W EEKt−1 -0.037058 0.029200 -1.269088 0.2046

LIQBON DM ON T Ht−1 0.001454 0.020205 0.071984 0.9426

LIQCOV M ON T Ht−1 -0.038296 0.020622 -1.857067 0.0635

Constant* 0.006008 0.002611 2.300556 0.0215

Observations 1561

Table 6: Regression output using the HAR model with dependent variable LIQBON Dt

Regression output using HAR model

Variable Coefficient Std.Error t-Statistic Prob.

LIQBON Dt−1* 0.060430 0.018505 3.265608 0.0011

LIQCOVt−1* 0.932890 0.021136 44.13783 0.0000

LIQBON DW EEKt−1 -0.030090 0.025332 -1.187805 0.2351

LIQCOV W EEKt−1 0.051878 0.029549 1.755677 0.0793

LIQBON DM ON T Ht−1 -0.025801 0.020097 -1.283843 0.1994

LIQCOV M ON T Ht−1 0.007986 0.020077 0.397746 0.6909

Constant 0.001761 0.002820 0.624391 0.5325

R-squared 0.989482

Observations 1561

Table 7: Regression output using the HAR model with dependent variable LIQCOVt

Using the VECM representation we find numerous relations between the illiquidity level of the corporate bond market and covered bond market. Although relations are present, the impact on the illiquidity levels followed from a shock is small. In addition we did not find prove of long-term memory captured in the VECM model. The VECM model representation can be used to forecast illiquidity levels. Under Solvency II, insurers will have to determine the total spread risk Solvency II Capital Requirements. Our study has presented evidence of the presence of illiquidity in the total spread. The following section describes the decomposition of the total spread risk SCR and uses the VECM model to estimate the illiquidity spread risk SCR.

6 Decomposing the spread risk SCR

Insurers are allowed to follow either the standard Solvency II capital requirements formula or create their own internal models. In this section we focus on the calculation of the spread capital requirements as is aligned by the standard Solvency II Capital Requirements (SCR) model. The total SCR consists of six individual risk components:

(31)

• market risk;

• life underwriting risk; • counter party default risk; • health underwriting risk; • operational risk;

• non-life risk.

The total SCR formula is defined as: SCRtotal=

s X

i,j

ρi,j× SCRi× SCRj,

where SCRidenotes the Solvency II capital requirement for the corresponding risk component

i and ρi,j is the correlation factor between two risk components. For this study we elaborate

further on the market risk component. According to EIOPA market risk arises from the level or volatility of market prices of financial instruments. The market risk module is divided in six sub-risk modules:

• interest rate risk; • spread risk; • property risk; • equity risk; • currency risk; • concentration risk.

We study the spread risk component as liquidity risk is considered to be attributed to spread risk. According to SCR 5.79 (EIOPA (2014)) spread risk results from: ”the sensitivity of the value of assets, liabilities and financial instruments to changes in the level or in the volatility of credit spreads over the risk-free rate”. The spread risk module applies to corporate bonds, credit derivatives and covered bonds which are evaluated in this paper. To assess the impact of a widening of the spreads on the value of the bonds, the market value of the bonds are multiplied by a factor that is calibrated to deliver a shock consistent with the 99.5% Value-at-Risk (VaR). The shock factors are multiplied by the modified duration of the corresponding bond. The modified duration is a measure of price sensitivity and is defined as the percentage change in price for a unit change in yield. In Table 11 the spread risk factors as imposed by EIOPA (2014) are displayed. For each credit rating a change in the level of the credit quality has an impact on the value of the bonds.

From a large insurer we obtained an investment portfolio consisting of 60 corporate bonds and covered bonds. The bonds all have an AA rating. We use the constituents of the iBoxx Covered Bond index to construct a covered bond portfolio. The iBoxx Covered Bond index is a

Quantifying the illiquidity spread : an estimation and comparison of illiquidity measurements.