Application of a liquidity premium proxy in the market-consistent valuation of liabilities

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proxy in the market-consistent

valuation of liabilities

Reinder J. van Velze

Master’s Thesis to obtain the degree in Actuarial Science and Mathematical Finance University of Amsterdam

Faculty of Economics and Business Amsterdam School of Economics

Author: Reinder J. van Velze Student nr: 5948894

Email: reinderj@me.com Date: August 28, 2015

Supervisor: dhr. prof. dr. R.J.A. (Roger) Laeven Second reader: dhr. dr. T.J. (Tim) Boonen

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Abstract

Given the ongoing discussion regarding a liquidity premium and the importance in the valuation of liabilities, this thesis answers the fol-lowing research question: ’What is the impact of a liquidity premium proxy on the market-consistent valuation of liabilities?’ To find out, we first start with a scientific overview of liquidity regarding assets and liabilities. By explaining the risk liquidity imposes for an investor, we introduce the liquidity premium. This thesis shows that there is no scientific literature that explains or explores the estimation of a liq-uidity premium for liabilities. Therefore, we introduce three ‘general’ estimation methods that quantify a ‘benchmark’ liquidity premium for assets and qualify as a proxy for liabilities. The most practical estima-tion method is conducted and the resulting liquidity premium proxy is reviewed. The estimated liquidity premium proxy turns out to be of a significant size and has a relatively large standard deviation. This raises the question whether the application of a liquidity premium in the market-consistent valuation of liabilities is justifiable. Besides the quantification of a proxy, the current state of affairs regarding the inclusion of a liquidity premium within Solvency II is clarified. And last but not least, the steps taken to apply a liquidity premium in the market-consistent valuation of liabilities are explained.

Keywords Liquidity premium, liquidity premium proxy, illiquidity premium, liquidity, Match-ing Adjustment, Solvency II, insurance, liabilities, CDS basis method, Structural model method, Covered Bond Spreads method, Direct approach, Structural approach, market-consistent valu-ation, hold-to-maturity view

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Preface

Thank you!

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Introduction

When the first draft of the Solvency II framework was introduced in 2009 a liquid-ity premium was not taken into account (CEIOPS, 2009a, p. 10). This started a firm discussion whether or not a liquidity premium should be included in the Solvency II framework. Note that this discussion concerns the application of a liquidity premium in the valuation of liabilities, not regarding assets. For assets, the application of a liquidity premium is widely accepted.

For assets, a liquidity premium is a compensation that makes an investor indifferent between a liquid asset and an identical but less liquid asset. Thus, illiquidity imposes a risk that the investor wants to be compensated for. Estimating such a compensation is a complex procedure, since liquidity is not directly observable. All assets, except for cash, are subject to different levels of liquidity and a liquidity premium is time dependent (Amihud et al., 2006, p. 270).

For liabilities, this is different. Liabilities are not actively traded on a market unlike assets, so why should illiquid liabilities be discounted with a liquidity premium?

First, it is possible to quantify liquidity for liabilities. Pritchard and Turnbull (2009), describe a stochastic process that captures the predictability of the liability cash flows. If we would apply their method to, for example, a plain vanilla annuity that has no lapse option, then it would say that this liability has highly predictable cash flows. Meaning that the plain vanilla annuity is illiquid.

From an insurer his point of view, implementing a liquidity premium would affect the value of technical provisions; the larger the liquidity premium, the lower the valuation of technical provisions. However, empirical studies show that a very uncommon scenario exists which has a negative liquidity premium. For an insurer, a lower value of technical provisions means holding on to a lower reserve (Hibbert et al., 2009b, p. 11).

From a policyholder his point of view, a lower value of technical provisions means that an insurer has a larger likelihood that he can not foresee in his future obligations. On the other hand, applying a liquidity premium would mean that liabilities can be backed up with illiquid assets, which are less expensive than equivalent liquid assets.

There is also the regulatory point of view. If an insurer holds predictable liabilities, then from a hold-to-maturity perspective he can back up the liabilities by investing in illiquid assets. All though, this conflicts with the market-consistent view of Solvency II. Market-consistent valuation requires that liabilities are priced by assets with reliable prices, however illiquid assets do not have reliable prices (Perotti et al., 2011).

If parties would agree on the application of a liquidity premium and found a way to implement this within the insurance regulations, then there are also practical issues that need to be considered. For example, how to quantify the liquidity premium for liabilities?

Given the ongoing discussion regarding a liquidity premium and the importance in the valuation of liabilities, this thesis answers the following research question: ‘What is the impact of a liquidity premium proxy on the market-consistent valuation of

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2 Reinder J. van Velze — A liquidity premium for liabilities

ties?’ To find out, we first start with a scientific overview of liquidity regarding assets and liabilities. By explaining the risk liquidity imposes for an investor, we introduce the liquidity premium. This thesis shows that there is no scientific literature that explains or explores the estimation of a liquidity premium for liabilities. Therefore, we introduce three ‘general’ estimation methods that quantify a ‘benchmark’ liquidity premium for assets and qualify as a proxy for liabilities. The most practical estimation method is con-ducted and the resulting liquidity premium proxy is reviewed. The estimated liquidity premium proxy turns out to be of a significant size and has a relatively large standard deviation. This raises the question whether the application of a liquidity premium in the market-consistent valuation of liabilities is justifiable. Besides the quantification of a proxy, the current state of affairs regarding the inclusion of a liquidity premium within Solvency II is clarified. And last but not least, the steps taken to apply a liquidity premium in the market-consistent valuation of liabilities are explained.

The structure of this thesis is as follows. The second chapter explains liquidity for both assets and liabilities and introduces a liquidity premium. The third chapter is a time-line that summarizes the major developments in the realization of a liquidity pre-mium within the European-wide risk-based supervisory framework Solvency II. Chapter four explains the steps taken to apply a liquidity premium in the market-consistent val-uation of liabilities. Chapter five conducts one of the benchmark methods and estimates a liquidity premium proxy for liabilities.

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Liquidity and a liquidity premium

This chapter explains the concept of liquidity for both assets and liabilities and intro-duces the liquidity premium, a compensation for the risk that an investor bears due to illiquidity.

2.1 Liquidity, assets and liabilities

Liquidity can be interpreted in different ways. For assets, liquidity is defined as the ease the assets can be traded, but for a trader, liquidity is defined as the ease he can fulfill his cash-flow commitments. These two types of liquidity are known as ‘market liquidity’ and ‘funding liquidity’ respectively (Brunnermeier and Pedersen, 2008, p. 1). In this thesis, the definition market liquidity is meant when referred to liquidity.

Assets

Where liquidity stands for the ease of trading an asset, illiquidity means that an asset is very difficult or impossible to trade. Literature shows that liquidity (or illiquidity) has a significant effect on asset pricing. Amihud et al. (2006, pp. 270, 271) acknowledge this effect and reviewed and discussed this literature. In their paper, they discuss four sources of illiquidity that might affect asset pricing. These illiquidity sources are:

• Transaction costs: asset trading results in transaction costs such as administration costs or brokerage fees.

• Private information: not every player has access to the same resources of informa-tion; the buying/selling party never knows if the counter-party makes his decisions based on private information. The informed party will benefit at the expense of the uniformed party.

• Demand pressure and inventory risk: if an investor his need to sell an asset is high, he is dependent on the demand side. This might result in a situation that the investor has to settle for less. In the case that there is no natural buyer, a potential buyer might be interested in the asset to resell it on a later time if he gets compensated for the risk of price changes while he holds on to the asset.

• Search friction: it can be difficult and costly to locate a buyer/seller for a given asset. The search might result in financing costs and the delay might lead to opportunity costs.

So, by definition a liquid asset is easily sold for its market price and above-mentioned illiquidity sources affect the liquidity, resulting in extra costs for the seller. This is in accordance with the work of Amihud and Mendelson (1986, pp. 223-224). By investigat-ing the effect of the bid-ask spread (which they used as a proxy for liquidity) on asset

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pricing, they found out that an increasing bid-ask spread positively affects the asset price. This means that the more liquid the asset, the higher its price.

So, theory and empirical evidence suggest that a buyer is compensated in the form of a discount for buying an illiquid asset. Take for example two assets with identical cash-flows which differ only in liquidity. As they are offered for the same price, the buyer is more interested in the more liquid asset, there it is easier for the buyer to trade again. So, from the buyer his point of view is the less liquid asset the less attractive one, there it comes with (more) liquidity risk. If we want the buyer to be indifferent between the two assets then the buyer should be compensated for the liquidity risk. This compensation is known as a liquidity premium (Amihud et al., 2006, p. 292).

Amihud and Mendelson (1986) measured liquidity on the basis of the bid-ask spread. This suggests that liquidity is not a constant factor, but differs over time. Amihud et al. (2006, p. 324) explain that in times of crisis illiquid assets are less attractive. The fall of the European real estate prices during the financial crisis of 2007-2008 is a clear example (MSCI, 2015).

Liabilities

If we extend the definition of a liquid asset to a liquid liability, it means the ease with which a liability can be traded. This sounds logical, but practically there is a problem; there is no market to sell and buy liabilities. Therefore, this definition is not applicable for liabilities. How should one capture a liability its liquidity then? Well, due to the lack of research and literature, there is no universally accepted method to capture liquidity of liabilities (IAA, 2009, p. 55).

Pritchard and Turnbull (2009) explain a possible approach to capture the liquidity of liabilities and so do CFO Forum et al. (2010). Noted that both methods are non-academic, they both capture liquidity by estimating the predictability of the liability cash flows. CRO Forum (2009, p. 23): “A liability is liquid if the liability cash flows are not reasonably predictable.” So, the predictability of future cash flows represents the liquidity of the liabilities. The predictability on its turn depends on the characteristics of the liability, a plain vanilla annuity for example can be called illiquid.

CRO Forum (2011, p. 3) states that predictability of liabilities should be measured on portfolio level. The policy characteristics influence the predictability of the cash flows, so lead penalties for early withdraws overall to a smaller surrender rate, but demographic effects, as mortality rates, also influence the predictability. Where the policy characteristics and demographic effects are unreliable for a single person, for a whole portfolio they can be representative. For these and other reasons the CRO Forum believes that the predictability should be measured on portfolio level rather than policy level.

2.2 A liquidity premium for assets

The previous paragraph introduced the liquidity premium and stated that literature is well known with this phenomenon for assets. This paragraph explains what a liquidity premium is and discusses the theoretical and empirical existence of a liquidity premium for assets.

2.2.1 What is a liquidity premium?

A liquidity premium was first mentioned by Constantinides (1986, p. 1) who investigated the effect of transaction costs on asset prices. During his investigation he found a second-order effect of transaction costs on the liquidity premium. He defined the liquidity premium as the compensation in expected return for a less liquid (risky) asset with

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trading costs that makes a buyer indifferent from a liquid (not risky) asset with no trading costs. Where Constantinides defined the liquidity premium as a compensation in expected return, Vayanos (2004, p. 1) defined the liquidity premium as the price difference between two very similar assets which differ in liquidity.

Constantinides and Vayanos their definitions are not contradictory, but complement each other. Amihud and Mendelson (1986) described that liquidity affects the price of assets and expected returns and Acharya and Pederson (2005) showed that the higher the liquidity of an asset the higher the price or the lower the expected return.

Liquidity affects asset pricing, but what affects a liquidity premium? According to Constantinides (1986), Acharya and Pedersen (2005) and Amihud et al. (2006) are transaction costs the main illiquidity source affecting the size of a liquidity premium. The literature showed that higher transaction costs leads to lower sizes of the liquidity premium.

Vayanos (2004, pp. 1-2) showed that a liquidity premium is positively correlated with volatility. This has to do with the financial term ‘a flight to liquidity’, meaning that investors seek to sell their more illiquid (risky) assets to buy liquid (less risky) assets. Thus, times of high volatility are known for a large liquidity premium.

Furthermore, Amihud et al. (2006, pp. 281-282) showed that clientele effects are time varying and also play a role in the estimation of a liquidity premium. The likelihood of the need to sell affects the size of a liquidity premium; a high likelihood results in a large liquidity premium.

Above mentioned literature compared two identical assets that differ in liquidity, we name the liquidity premiums that results from their estimations a ‘relative liquidity pre-mium’. Conversely, there is an absolute liquidity premium. Auckenthalera et al. (2015) used a hypothetical, perfectly liquid bond to estimate an absolute liquidity premium. This thesis holds on to the relative liquidity premium, because liquidity is already a complex subject and the implementation of hypothetical bonds would make the process even more complex (Amihud, 2006, p. 270).

So, from the point of view of an investor a liquidity premium represents a compen-sation for bearing liquidity risk. If the investor has a hold-to-maturity strategy, a liq-uidity premium represent the annual expected compensation. A liqliq-uidity premium is time-dependent and influenced by the need for liquidity of the investor. In times of high market stress and when the investor has a large likelihood of needing to sell, he can expect a large liquidity premium.

2.2.2 Theoretical and empirical evidence of a liquidity premium in assets

A liquidity premium compensates for the risk of liquidity that an investor bears, but is this risk actually reflected in the market price of the asset? This paragraph provides a brief summary of the theoretical and empirical evidence for the existence of a liquidity premium in assets.

Theoretical evidence

In their paper ‘Liquidity and Asset Prices’ Amihud et al. (2005, p. 273) discuss the effect liquidity has on asset pricing. Asset pricing theory signifies that two assets with exactly the same cash flows should have exactly the same price, otherwise one can obtain arbitrage opportunities. However, literature provides examples of no arbitrage when comparing differently priced assets with exactly the same cash flows. Following Amihud et al. (2005, p. 272), this is explained by the different levels of liquidity of the assets.

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This is agreed on by other researchers. Duffie (1999) showed that there is a difference between the selected bond spread and the CDS premium, while theoretically this should be equal. This difference is called the negative basis and Longstaff et al. (2005, p. 2243) showed that this difference is due to liquidity and can be used to estimate a liquidity premium, as the following equation shows:

Liquidity premium = −negative basis = corporate bond spread − CDS premium By regressing the non-default component of the bond spread on liquidity proxies, Longstaff et al. (2005, p. 2242) showed that the coefficient of the average bid-ask spread of the corporate bonds is significant and positive. This means that when the bond becomes more illiquid, the non-default component becomes larger. The CDS premium lacks this non-default component that depends on the level of liquidity, so by subtracting the bond spread from the CDS premium a liquidity premium is estimated.

Empirical evidence

Amihud et al. (2005, p. 273) not only discussed the theoretical loopholes regarding a liquidity premium for assets, they also reviewed and assembled various empirical stud-ies. Their work was continued by Hibbert (2009) who assembled the significant research of the last twenty years and published an overview of the various studies, see figure2.1. After summarizing the research, both Amihud et al. and Hibbert came to the same con-clusion; a liquidity premium is no myth, it exists. Below are three empirical examples that support their conclusion.

Boudoukh and Whitelaw (1991) explained the price differences of (almost) identical government bonds with their model by taking liquidity into account. By using a direct approach (see section 4.1for more information about the direct approach) they found out that highly liquid Japanese benchmark bonds have a significant lower yield than similar government bonds. The liquidity premium ranged between 30bps and 100bps in the time-period they studied (Boudoukh and Whitelaw, 1991 & Amihud et al., 2005, p. 336).

Longstaff (2004) compared the yields of a zero coupon U.S. Treasury bond with identical bonds issued by the U.S. government agency Refcorp. Both bonds have the same credit rating, but treasury bonds are more liquid. For the period studied, the results show a significant difference between both yields. Longstaff finds an average liquidity premium between 10bps and 16bps.

Dimson and Hanke (2002) used a regression analyses to estimate a liquidity premium that applies as a discount factor. By comparing a portfolio of equity index-linked bonds with an equity index with identical cash-flows, they showed that the difference in price was explained by the factor liquidity. For the period studied, the weighted average of the liquidity premium is 2.71%.

2.2.3 Liquidity premium estimation methods for assets

Based on the work of Amihud et al. (2005), Hibbert et al. (2009a, p. 17) grouped the existing literature concerning the quantification of a liquidity premium in four dif-ferent approaches; the Microstructure, Direct, Structural model and Regression-based approach. Below, each approach is explained briefly and linked to relevant literature. This subsection sticks to an overview of the possible approaches, Chapter4will explain and review three actual estimation methods.

• Microstructure approach: the models developed are mainly intended to explain the effect of liquidity on asset pricing, in particular the effect of clientele effects and

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Figure 2.1: an overview of various liquidity premium studies, assembled by Hibbert et al. (2009a, p. 16).

transaction costs. The compensation that makes an investor indifferent between a liquid asset and an equivalent, liquid asset represents the liquidity premium. Examples: Constantinides (1986) and Acharya and Pedersen (2005).

• Direct approach: the price or yield of an asset or portfolio is compared to an equivalent, but less liquid, pair of assets or asset portfolios. The difference in price represents a liquidity premium for the less liquid asset or portfolio. Because the direct approach estimates a liquidity premium directly from two assets, it is some-times referred to as a model-free approach. Examples: Boudoukh and Whitelaw (1991) and Longstaff et al. (2005).

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used to estimate a fair spread for an illiquid bond. The fair spread withholds expected losses based on the default probability and a credit risk premium. Sub-tracting the fair spread from a market spread results in a residual spread, which is interpreted as a liquidity premium. Example: Webber and Churm (2007).

• Regression-based approach: besides that this approach can be used to explain the differences in liquidity, it is used to estimate a liquidity premium. Based on different liquidity proxies the size of a liquidity premium is estimated. Examples: Dimson and Hanke (2002) and Longstaff (2004).

2.3 A liquidity premium for liabilities

As mentioned in section2.1, there is a lack of scientific literature concerning a liquidity premium for liabilities. The available papers that discuss this subject are mainly writ-ten by consultancies as Barrie & Hibbert, actuarial associations as the International Actuarial Association (IAA) and insurance regulators as the European Insurance and Occupational Pensions Authority (EIOPA). Though, these papers explain the valuation of liabilities when a liquidity premium is included, but do not explain how the liquidity premium is actually estimated.

What liquidity premium or in what form a liquidity premium can be used in the valuation of liabilities is not known for sure until Solvency II is officially in force. At this moment, it seems that a liquidity premium in the form of a Matching Adjustment will be included in Solvency II (see Chapter3for the major developments and current status of a liquidity premium in Solvency II). Though, so far there is no scientific literature that explains the estimation of a Matching Adjustment. To get an idea about the magnitude of the impact a liquidity premium has on the liabilities valuation, we will estimate a proxy and discuss the potential impact. Chapter 4 will introduce and discuss three possible estimations methods that will qualify as a proxy and Chapter 5 will conduct the most practical estimation method and discuss the estimated proxy.

Taking the empirical estimations of a liquidity premium for assets into account (section 2.2.2), implementing a liquidity premium could significantly affect the value of the technical provision. The larger the liquidity premium, the lower the technical provisions. However, there is the scenario of a negative liquidity premium, as empirical studies show this is possible, but not very common (Hibbert et al., 2009b, p. 11).

The incorporation of a liquidity premium in the price of illiquid assets does not automatically mean that a liquidity premium should be reflected in the price of liabil-ities. This would only be possible in the extreme case wherein liability cash flows are perfectly replicated by hypothetical assets. In this extreme case, the liquidity premium incorporated in the asset price is then reflected in the price of the liability (Pritchard and Turnbull, 2009, p. 5).

So, it could be argued that the application of a liquidity premium in the valuation of predictable liabilities is justifiable. In the remainder of this thesis, the term ‘liquidity premium’ refers to the liquidity premium in the valuation of liabilities, unless stated otherwise.

2.4 Liquidity Premium Vs. Illiquidity Premium

Where the European Commission (EC) uses the term ‘illiquidity premium’ in their official documentation concerning Solvency II, the term Liquidity premium is used in the gross of the research papers and articles. In their paper, Barry & Hibbert explain that both terms are used for the same purpose; a liquidity premium is expressed as the difference in price between a liquid and less liquid equivalent asset and a illiquidity pre-mium is expressed as the difference in interest rate. Figure2.2visualizes this example

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-‘LP’ stands for liquidity premium and ‘ILP’ for illiquidity premium. The graph clearly shows that the liquidity premium is used as a premium in price and that the illiquidity premium is an adjustment to the yield.

Figure 2.2: price versus interest rate for assets. LP = liquidity premium, ILP = illiq-uidity premium.

In Solvency II the liquidity premium is conducted as an increase of the risk-free term structure, but the term ‘liquidity premium’ is more widely used. Therefore, this thesis will continue with the term liquidity premium (Solvency II Wire, 2011a).

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Chapter 3

Timeline: a liquidity premium

within Solvency II

This chapter describes the major developments in the realization of a liquidity premium within the European-wide risk-based supervisory framework Solvency II.

Note: Within this thesis the term liquidity premium is used. This can cause some con-fusion there the term ‘illiquidity premium’ is used within the Solvency II frame-work. Both terms are used for the same purpose, but ‘Liquidity premium’ is the more conventional term (Hibbert, 2009, p. 1). Chapter 2.4 provides a clear and comprehensive explanation.

3.1 Intro

In the end of 2009, the European Commission (EC) released the Solvency II Directive (2009/138/EC). This was the first draft of the European-wide risk-based supervisory framework Solvency II. Its purpose is to replace the nine existing European supervision guidelines of the insurance market (DNB, 2014). This replacement will have a large impact on the daily business of the European insurance market. For example, the in-surance framework of the United Kingdom (UK) allows insurers to include a liquidity premium when discounting liabilities (CEIOPS, 2009b, p. 117). Though, the first draft of Solvency II did not allow for the application of a liquidity premium in the valuation of liabilities. Figure 3.1is an overview of all the major developments discussed in this chapter.

3.2 Solvency II Directive

The Solvency II Directive released by the EC was the first draft of Solvency II and did not contain any indication of a liquidity premium. The discussion that preceded this decision is listed below.

In Juli 2009, the Committee of European Insurance and Occupational Pensions Super-visors (CEIOPS, a European Union financial regulatory institution that was replaced in January 2011 by EIOPA) (2009a) published Consultation Paper No. 40 (CP 40). This paper consults on the matter concerning the relevant risk-free interest rate term structure used for the assessment of the technical provisions under Solvency II. In their paper, CEIOPS presents their opinions whether the discount rate should include a liq-uidity premium (2009a, pp. 10, 36). This is brief and concise expressed. It states that the great majority of the CEIOPS members are against this inclusion and that some CEIOPS members recommend to further investigate the issue. CEIOPS stated that part of the industry finds it plausible to use a liquidity premium for predictable liabilities,

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Figure 3.1: timeline of the major developments in the realization of a liquidity premium under Solvency II. On the left side the release dates of the documents and on the right side the form of a liquidity premium at that point in time.

but counters that there is no generally acknowledged method to derive a reliable liquid-ity premium. This seems to be their foremost argument.

The absence of a liquidity premium concerned some of the key players within the insur-ance market, as they do not agree with the outcomes of CP 40 regarding the liquidity premium. In the paper Summary of comments on CEIOPS-CP-40/09, (2009b) CEIOPS summarized the arguments and concerns of several parties regarding this issue. In this paper a substantial number of stakeholders highly recommends to further investigate the liquidity premium before taking any drastic decisions. For example:

• Association of British Insurers: they note that a liquidity premium should be further investigated in order to find an appropriate approach. A working group consisting of CEIOPS members, the industry and experts would be suited for this task (P.2).

• Barrie & Hibbert: in their paper, Barrie & Hibbert (2009) dicuss the CP 40 draft. They note for example that there exist several methods to compute an estimation of a liquidity premium and that these each of these methods offers valuable infor-mation. They state that the technical challenges in the estimation of the liquidity

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premium should not play a role in the rejection of a liquidity premium. They conclude that the current proposal by CEIOPS should be reviewed.

• Comit Europen des Assurances (CEA, now: Insurance Europe): in their comments, the CEA agrees with the minority of the CEIOPS members to further investigate the issue (pp. 9, 10).

After taking the comments on their draft of CP 40 into account, CEIOPS (2009c) returned in October 2009 with the updated version of CP 40, which they refer to as ‘former CP 40’. This paper was presented as the final advice of CEIOPS. Even though, this update contained a larger section for a liquidity premium, their former opinion did not change (pp. 10, 11). All though, they added that a liquidity premium may be allowed for as a transitional measure if a liquidity premium is already used in the current line of business (p. 17).

Annex B of the paper summarizes and discusses the issues concerning their disap-proval. One of the arguments to support their cause is that a liquidity premium leads to a significant decrease of technical provisions, which means that the level of protection of policyholders will be limited (p. 11). Nevertheless the overall aversion for a liquidity premium, CEIOPS stated that it is prepared to start a more in depth investigation provided that this investigation follows within the scope of Solvency II.

3.3 Liquidity Premium Task Force

CEIOPS arguments in former CP 40 to disapprove for the application of a liquidity premium did not satisfy the wishes of a large part of the insurance market. So, quickly after the release of former CP 40 a CEIOPS meeting was set up to discuss the possibilities of an in depth investigation of a liquidity premium. This led - as was asked for by stakeholders in the insurance market and now approved for by CEIOPS - to a working group called ‘Task Force’ which was assigned with the task to foresee (from a technical point of view) in a guide concerning the inclusion of a liquidity premium in the risk-free rate for discounting technical provisions.

In March 2010 the Task Force completed their report. Where a large part of the insurance market was hoping for approval, the report did not include a final recommen-dation whether or not to apply a liquidity premium.

After the Task Force report, the opinions of the CEIOPS members whether to in-clude a liquidity premium were still widespread. Though, the rapport did state that the research and the assumptions could be a good starting point if the EC decides to take a liquidity premium into account (Bernardino, 2010, p.3). Also, the task force preferred a permanent solution above a transitional one, as was suggested in Former CP 40 (CEIOPS, 2010a, p. 24). An important statement within the paper is that a representative of the EC agreed that the inclusion of a liquidity premium fits within the scope of the Directive (CEIOPS, 2010a, p. 9).

3.4 QIS5

The Task Force report was positive, but whether to include a liquidity premium or not is up to the EC.

On July 5, 2010, the EC presented the final version of the Quantitative Impact Study ‘QIS5 Technical Specifications’ (QIS5). This impact study was meant to test the practicability of the Solvency II modules in practice to get an idea about the financial impact for insurers. In April, three months before releasing the final QIS5, the EC already announced that they incorporated the conclusions of the Task Force in QIS5 (Bernardino, 2010, p. 3).

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As announced, the final QIS5 paper included the liquidity premium as a discount rate in the valuation of the liabilities (CEIOPS, 2010b, p.50). Paragraph TP.3.1., under section V.2.3., states that an insurer qualifies for a liquidity premium bucket of 0%, 50%, 75% or 100%. Which liquidity bucket applies depends on the conditions that are described in this section. For example, to qualify for a liquidity premium of 100% an insurer has to meet the following three conditions (TP.3.5.):

• the policies are only exposed to longevity risk and expense risk;

• the insurer is exempt from any risk subject to any form of surrender;

• there are no future cash-flows planned in the technical provisions of the policies and all premiums are already paid.

So, after a lot of research, performed by both the regulators and industry, a liquidity premium was included in the Solvency II Framework. This decision was wished for by a large part of the industry, but still not widely supported.

After the QIS5 release a discussion rose regarding artificial volatility affecting prod-ucts with long-term guarantees under Solvency II and the liquidity premium not being adequate to permanently resolve this issue (CEA, 2011, p. 1, 5).

3.5 Counter-Cyclical Premium and Matching Adjustment

In the draft for the Omnibus II Directive, released in October 2011, the Counter Cycli-cal Premium (CCP) was introduced as a substitute for the liquidity premium. Under market consistent valuation, a factor as liquidity can cause short-term volatility by un-der or over pricing the assets (SolvencyIIwire.com, 2011b). The CCP minimizes this short-term volatility, like the liquidity premium. But, unlike the liquidity premium, it also deals with exposure to sovereign debt. Also, where the liquidity premium within QIS5 was meant to apply permanent, the CCP is introduced as a so called crisis mea-sure. Insurers may only apply the CCP when markets are in times of high market stress (Solvency II wire, 2011b).

After its introduction, the CCP was criticized by experts and stakeholders. For ex-ample, a panel of experts stated in an article on voxeu.org that the suggested CCP is not even counter-cyclical. They stated that in times of high market stress, the CCP does what is expected, it reduces short-term volatility, but when the market performs extraordinarily well, the CCP does not build a buffer to compensate for a period of high market stress (Daniels et al., 2012).

Besides the CCP, the EC introduced the Matching Adjustment (MA); a method meant to eliminate artificial volatility on the balance sheet of insurers that hold products with long-term guarantees. As Insurance Europe (2013, p.6) explains, artificial volatility oc-curs when insurers are wrongful exposed to losses on forced sales of assets. An insurer holding products with long-term guarantees is less exposed to movements in the bid-ask spread of assets, but market-consistent valuation takes these movements into account, which can lead to wrongful exposure to losses on forced sales.

3.6 LTGA

In June 2013, EIOPA presented their new and last impact study ‘Long-Term Guarantee Assessment’ (LTGA). The study outlines the practicability of the Solvency II modules to get an idea about the financial impact on insurers with long-term liabilities and discusses the CCP and the MA.

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Regarding the CCP, EIOPA recommends to replace this premium with the Volatility Balancer (VB); a simpler, more transparent method. Some keys points of the VB:

• where the CCP was determined by CEIOPS, the VB is a more predictable and comparable measure (p. 154);

• the VB is a permanent solution, so not only applied in times of high market stress (p. 18);

• insurers are not allowed to apply the VB with unit-linked products and when the MA is already included (p. 18);

• the VB does not affect the SCR (p. 148).

Besides the VB, the Classical Matching Adjustment (besides the Classical Matching Adjustment, there is the Extended Matching Adjustment. The Classical Matching Ad-justment enhances the definition that we stated before in this chapter. CEIOPS advises within the LTGA to exclude the Extended Matching Adjustment (LTGA, p. 17). In this thesis, the Classical Matching Adjustment is meant with Matching Adjustment (MA).) is supported by the impact study. EIOPA tested different premiums to minimize short-term volatility on the balance sheet and they concluded that the MA performed best (EIOPA, 2013, p. 90). The Actuarial Association of Europe (AAE) (2013, p. 22) sum-marized some key differences between the QIS5 liquidity premium and the LTGA MA. The differences are presented in table3.1.

According to DNB (2013), which was actively involved in the realization of the LTGA, the insurance market broadly supports the LTGA and its recommendations.

3.7 Omnibus II Directive

The Omnibus II Directive (Omnibus) complements the Solvency II Directive and con-tains the LTGA recommendations; it included the MA and Volatility Adjustment (VA). The EC states that artificial volatility on the balance sheet should be minimized (Eu-ropean Commission, 2014, p. 5). Insurers holding products with long-term guarantees are allowed, if the conditions under article 77b of the Omnibus are met, to include the MA to the relevant risk-free interest rate term structure for discounting technical pro-visions. Article 77b.3 of the Omnibus states that the MA should not be applied when the Volatility Adjustment (VA) is already in use. Where the LTGA speaks of ‘Volatility Balancer’ the Omnibus uses the term ‘Volatility Adjustment’, though both papers use the different terms for the same meaning (Conn & Sharp, 2014, p. 2). The next section describes the MA and the VA.

In November 2014 CEIOPS published a consultation paper regarding the risk free in-terest rate. This paper provided an update regarding the latest standings of the MA and the VA at that moment, in short:

• where, under QIS5, the CCP was applicable in times of high market stress, the MA and the VA are both permanent measures;

• the VA is an adjustment that applies to the liquid part of the liabilities in order to deal with the unintended short-term volatility on the balance sheet. The MA on the other hand is meant to deal with the artificial volatility affecting the balance sheet regarding products with long-term guarantees, the illiquid part of the balance sheet (p. 6);

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Table 3.1: the QIS5 liquidity premium versus the LTGA Matching Adjustment.

QIS5 LP MA

Reference Portfolio

An official European insti-tution should supervise and calculate the liquidity pre-mium; this should be in-line with the updates regarding the basic risk-free interest rate (CEIOPS, 2010a, p. 11).

The MA depends on the as-set portfolio of an insurer, it therefore is specific for an in-surer. (EIOPA, 2013, p. 75) - EIOPA provides the Fun-damental Spreads to calculate the MA (EIOPA, 2013, p. 45). Formula QIS5 does not provide a

defi-nite formula. The Task Force report presents some options to determine a liquidity pre-mium (CEIOPS, 2010a, p. 6)

The MA differs per asset type: Current spread -MAX(default risk, x% his-toric spread) (AAE, 2013, p. 22).

Application Permanent, applied as liquid-ity buckets: 0% - 50% - 75% - 100%. Which bucket ap-plies depends on the con-ditions described in section V.2.3. (CEIOPS, 2010b, p. 50).

Permanent measure that dif-fers per asset type.

Asset re-strictions

N/A An insurer must show that he can meet several conditions regarding the ALM, before applying the MA (CEIOPS, 2013, p. 75).

Ring-fencing

N/A It protects assets that back up the predictable portfolio of li-abilities from the risk of forced sales (CEIOPS, 2013, p.76). Cash-flow

matching

N/A Cash-flow matching is the ba-sis of the MA (CEIOPS, 2013, p.76).

SCR treat-ment

It is only meant for the risk of a decrease of the liq-uidity premium, which leads to an increase of the value of the technical provisions (CEIOPS, 2010b, p. 132).

Yes, it has impact on the SCR, but in a positive way. The MA reduces the SCR spread (LTGA, p. 75).

• to maintain and pursue transparency in the European market, EIOPA manages the VA and MA (p. 10). EIOPA publishes the VA and an estimate of the fundamental spread - the spread that is accountable for the unintended risk for products with long-term guarantees - which is used for the calculation of the MA (p. 6);

• the VA is based on 65% of the currency spread (underlying a reference portfolio of yield curves and indices on yields) minus the risk correction and the currency spread (p.41). Calculating the VA results in a constant that is expressed in basis points. Applying the VA leads to a parallel shift of the risk-free interest rate term structure. The shift applies till the last liquid point (p. 44);

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• where the VA is set by EIOPA, insurers calculate the MA individually. Though, EIOPA has an important stake in the MA; they provide the Fundamental Spreads to calculate the MA (p. 45). Calculation of the adjustment results in a single number and is insurer specific; it depends on the composition of the eligible assets. Like the VA, the MA is expressed in basis points and applied as a parallel shift of the risk-free interest rate term structure (p. 45).

3.8 Conceptual framework of the MA and the VA

On February 28, 2015, EIOPA (2015) released their latest technical document regarding the risk-free interest rate term structure. The document presents the values of the VA and provides the fundamental spread for insurers to calculate the MA. EIOPA released the document such that insurers can prepare and get a feeling for what is expected when Solvency II is set in place on the 1st of January 2016. EIOPA will update the fundamental spread and the VA at least every quarter (p. 39).

3.8.1 Conceptual framework of the VA

EIOPA summarizes the VA as follows: “For each relevant currency, a volatility adjust-ment is an adjustadjust-ment to the relevant risk-free interest rate term structure based on 65% of the risk-corrected currency spread between the interest rate that could be earned from bonds, loans and securitisations included in a reference portfolio for that currency and the rates of the relevant basic risk-free interest rate term structure.” - (p. 40, section 143)

So the VA is based on the risk-corrected currency spread and is currency dependent. To determine the VA per country, EIOPA takes the following steps.

Step 1: the risk-corrected currency spread

EIOPA first calculates the risk-corrected currency spread which follows from the cur-rency spread (S) and the risk correction (RC). EIOPA uses a curcur-rency representative portfolio of assets and a currency reference portfolio of yield market in-dices to deter-mine respectively the S and RC (p. 40, section 144 and 145). Then the risk-corrected currency spread is calculated as follows:

SRCcrncy = RC − S.

Step 2: the currency VA

For each currency there is the currency VA (p. 42, secion 150):

V Acrncy = 0.65 ∗ SRCcrncy

Step 3: country specific increase

Each country under the Solvency II Framework has their own country specific VA. This is determined by including a country specific value to the currency VA. This country specific value is calculated by the corrected country spread minus twice the risk-corrected currency spread, the resulting value has to be positive and the risk-risk-corrected country spread should be at least 100 basis points, otherwise the value is set to zero (p. 42, section 152):

max(SRCcountry− 2 ∗ SRCcrncy, 0), if SRCcountry > 100.

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Finally, Step 3 leads to the total VA:

V Atotal = 0.65 ∗ (SRCcrncy+ max(SRCcountry− 2 ∗ SRCcrncy, 0)),

with the restriction (p. 43, section 156):

SRCcountry> 100, otherwise: V Atotal = V Acrncy.

So, the VA is a single value that is the same for all insurers in a specific country (p. 43, section 158).

3.8.2 Conceptual framework of the MA

EIOPA summarizes the MA as follows: “The matching adjustment is an adjustment to the basic risk-free interest rate, based on the spread on an undertakings own assigned portfolio of matching assets, less a Fundamental Spread that allows for default and down-grade risk.” - (p. 45, section 165)

So, the MA is based upon an insurer his own asset portfolio and a Fundamental Spread (FS). The insurer therefor calculates the MA itself. To maintain uniformity, EIOPA publishes the Fundamental Spreads for each asset class, duration and credit quality step (p. 45, section 166 + 167).

The calculation of the MA was already defined in the Omnibus II Directive (p.23, article 77c):

M A = A − B − C, (3.1)

with:

• A = “the annual effective rate, calculated as the single discount rate that, where applied to the cash flows of the portfolio of insurance or reinsurance obligations, results in a value that is equal to the value in accordance with Article 75 (Omnibus II Directive) of the portfolio of assigned assets;” - (European Commission, 2014, p. 23, article 77c(1)(a)(i));

• B = “the annual effective rate, calculated as the single discount rate that, where applied to the cash flows of the portfolio of insurance or reinsurance obligations, results in a value that is equal to the value of the best estimate of the portfolio of insurance or reinsurance obligations where the time value of money is taken into account using the basic risk-free interest rate term structure;” - (European Commission, 2014, p. 23, article 77c(1)(a)(ii));

• C = Fundamental Spread.

The FS depends on the type of asset. There is a distinction made between ‘central government and central bank bonds’ and ‘assets other than central government and central bank bonds’. In the case that the credit spreads are unreliable there is a back up for the FS that depends on the long-term average of the spread (p. 56, 59).

3.9 Conclusion

From no liquidity premium under the Solvency II Directive to the MA and the VA under the Omnibus II Directive. According to the latest updates released by EIOPA and the European Commission, insurers may apply a liquidity premium in the form of the MA and the VA within the Solvency II Framework. Both measures are widely supported by the insurance industry. With the conceptual frameworks defined in the Technical Document of February 2015, the insurance market is ready to implement both adjustments.

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Chapter 4

The valuation of predictable

liabilities

Both CRO Forum (2011) and Pritchard and Turnbull (2009) developed a market-consistent valuation methodology for illiquid (predictable) liabilities. Their method-ologies follow the same steps, but underlying estimation methods differ. Briefly, these steps come down to:

Step 1: estimate a liquidity premium proxy;

Step 2: replicate the fixed liability cash flows by a portfolio of liquid assets;

Step 3: estimate the proportion of the liquidity premium that applies;

Step 4: discount the replicated portfolio by the risk-free curve that includes the applicable liquidity premium.

In other words, the predictable liabilities are valued by a replicating portfolio of liquid assets (Step 2). These ‘expensive’ liquid assets are discounted by an adjusted risk-free curve (Step 4) to estimate the market-consistent value of the predictable liabilities. This adjust risk-free curve withholds the applicable liquidity premium proxy (Step 3 and Step 1). These steps are all explained in their own section.

4.1 Step 1: estimate a liquidity premium proxy

This section introduces three estimation methods that qualify for the estimation of a liquidity premium proxy. We estimate a proxy based on assets, because their is no lit-erature that explains how the liquidity premium is estimated for liabilities.

Below are the three methods explained, according to Hibbert et al. (2009b, p.2) this are three ‘general’ estimation methods that estimate a, as they call it, ‘benchmark’ liquidity premium for assets. They are named ‘Benchmark’, because the liquidity premiums are primarily indicative.

• CDS basis method: by a credit default swap (CDS) a third party assures to refund the default value of a bond that is borrowed by a company, which in return pays the CDS premium. This CDS premium is then compared to the spread of a default corporate bond and a non-default risk-free bond. The difference between the premium and spread is the negative basis, which can be interpreted as the yield difference between a less liquid and liquid bond, also known as a liquidity premium (Longstaff et al., 2005, pp. 4, 5 & Hibbert et al., 2009b, p. 9).

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• Structural model method: the yield of a corporate bond portfolio (the market spread) is compared to the fair spread calculated by the Merton model. The fair spread is the cost/yield of a risk-free bond that is equivalent to a corporate bond (credit risk premium) and an option on the firms assets (default probability). The difference between the market spread and fair spread is a residual spread, which is interpreted as a liquidity premium (Webber and Churm, 2007, p. 534 & Hibbert et al., 2009b, p. 7).

• Covered Bond Spreads method: this Direct approach compares covered bonds with swaps, the difference in yield represents a liquidity premium (Hibbert et al., 2009b, p. 9).

4.1.1 CDS basis

As explained in the previous paragraph, the CDS basis method is a Direct approach that estimates a liquidity premium by determining the negative basis, as is shown by equation 4.1(Longstaff et al., 2005).

Liquidity premium = −negative basis = corporate bond spread − CDS premium. (4.1) Longstaff et al. (2005) also present an alternative explanation, as they state that a liquidity premium can be seen as the residual spread in the following equation:

Synthetic def ault bond = A + B + C, (4.2)

with:

• A = non-default bond;

• B = CDS protection seller position;

• C = residual spread.

Following Longstaff et al. (2005) their approach requires an adequate sample of corporate bonds, a data set of CDS premiums for equivalent maturities and a data set of risk-free bond indices. The actual calculation can be done in two different ways. Hibbert et al. (2009b, p. 6) introduce two easy-to-compute methods, both depending on a CDS index: • Method 1: choose a portfolio of bonds that matches the maturity and constituents of the CDS index, for example an iTraxx index. The liquidity premium then follows from subtracting a Swap spread and an iTraxx CDS index from a synthetic bond index;

• Method 2: choose a CDS index and a separate bond index with similar maturi-ties, but keep in mind that the underlying constituents may not be aligned. The liquidity premium is estimated by subtracting a Swap spread and an iTraxx CDS index from an iBoxx bond index.

In Method 1 are the bonds better matched with the constituents of the CDS index then in Method 2, this can lead to biased results for Method 2. Conversely, matching the CDS index requires a sufficient sample of bond data.

The CDS basis method is simple and relatively easy to perform, but is dependent on the data availability. The reliability of the estimated liquidity premium can be questioned there the method is sensitive to the sample choice and to mismatches concerning the data. Where theoretically the CDS spread measures the pure credit risk, practically the CDS may include the counter-party risk (Hibbert et al., 2009b, p. 6). So, the reliability of the results can be questioned but this is compensated by the method its simple and clear approach.

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4.1.2 Structural model

The Structural model is based on the Merton model that is used to estimate a fair spread for an illiquid bond. The fair spread is the cost/yield of a synthetic combination of a risk-free bond, equivalent to the corporate bond, and an option on the firms assets. In other words the fair spread withholds the credit risk premium and the expected losses based on the default probability. Because the option on the firms assets can be explained as a call option on a firms total assets, with the face value of debt as the strike the fair spread, the fair spread is free of liquidity risk. Subtracting the fair spread from a market spread results in a residual spread, which is interpreted as a liquidity premium (Webber and Churm, 2007, pp. 534-535). Figure4.1 visualises the decomposition of the market spread.

In practice, the options of the firm that are to be valued do not trade and are therefore difficult to value, the Merton model tackles this problem. The model assumes that the firms assets follow the geometric Brownian motion (this is the non-negative variation of the Brownian motion ). The Merton model is based on the following input:

• a risk-free interest rate;

• the firm its initial value of the total assets;

• the volatility of the firms assets;

• assumptions for the firm its maturity of debt and its face value.

Figure 4.1: the market spread, fair spread and residual spread according to the structural model. Note that this figure is not in proportion.

Hibbert et al. (2009b, p. 8) summarized the steps followed by the Merton model. In step 4 they differ from the Merton model by adding a ‘short binary option on bankruptcy cost’. They they believe that legal implications significantly affect the valuation of debt. The bankruptcy costs are captured by the value of a put option that pays a fixed amount if the assets are below the threshold at bond maturity. Hibbert et al. (2009b, p. 8) their summarized steps:

1. Set the implied level of debt at bond maturity to be consistent with historic cumu-lative default rates assuming firm assets exhibit volatility in line with de-leveraged firm-specific equity volatility.

2. Set option volatility based on observed market option costs and de-leverage as-sumption.

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4. Price the synthetic corporate bond using the Merton model as a risk free bond plus a short put option plus a short binary option on bankruptcy cost.

5. Liquidity premium = market spread Fair spread (yield on corporate bond)

The Structural model requires input that is difficult to require, for example the de-fault probability of the balance sheet. Therefore, Hibbert et al. (2009b, p. 8) made the following assumptions to simplify the process:

• simplified default probability of the balance sheet: the default of the balance sheet is in-line with historic long-term default frequencies;

• assuming that the firms assets follow the geometric Brownian motion: the asset volatility and interest rate are constant and non-stochastic;

• debt is taken into account as a single zero-coupon bond;

• default is ignored until maturity.

Besides the simplified assumptions the following data and parameters are required:

• Data: interest rates, market spreads and the firms asset volatility.

• Parameters: dividend yield expectations, expected default rates, estimate for the average cost of bankruptcy and for average firm leverage.

The Structural model is the most complex method of the three; it requires complex estimations and expert judgement. On the other hand, the model has a theoretical foundation and the input data is ‘relative’ easy to obtain, as it is fore-handed in most major economies. The reliability of the results can be questioned; the residual spread is sensitive to the estimations of the parameters, to the choice of input data and to the assumptions made.

4.1.3 Covered Bond Spreads

The Covered Bond Spreads method is also a Direct approach; it compares covered bond yields with swap yields (Hibbert et al., 2009b).

Hibbert et al. (2009b, p. 9) note that covered bonds are assumed to be ‘practically’ risk-free. A covered bond is known for its extra security; the issuer has a priority claim on one or more third parties to pay the holder in case of default. But, is this extra secu-rity a solid argument for defining covered bonds as risk-free? Packer et al. (2007, p. 47) think so: “covered bonds offer an alternative to develop country government securities for bond investors interested in only the most highly rated securities.” In their research, Packer et al. tested the robustness of the covered bonds regarding credit risk and its underlying securities. They concluded that the covered bonds are robust in these cases; this suggests that differences in yields between covered bonds and swaps are due to liquidity risk.

By assuming that covered bonds are practically risk-free, a liquidity premium is es-timated by subtracting the swap yield from a covered bond index yield for every time step of the selected period. The following equation illustrates this:

LPt= Covered Bond Index Y ieldt− Swap Y ieldt. (4.3)

In their research paper, Hibbert et al. (2009b, p. 9) state that the market data is not sufficient to extract a pure covered bond yield curve. Therefore, they propose a proxy: a

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mix of European AAA-rated covered bonds with the restriction that the proxy matches the duration of the swaps.

The Covered Bond Spreads method is simple and relatively easy to perform. Besides that the availability of data is is a large restriction for this method, it can be questioned whether there are other risks than liquidity affecting the spread, credit risk for example.

4.1.4 Conclusion

All three methods have in common that they are relatively simple and intuitive. The structural model is the most complicated of the three and requires expert judgement for its model calibration. Opposed to this is the availability of data, which is available for most major economies and the theoretical foundation of the model. The CDS basis and covered bond spreads methods are known for their simplicity, but requiring data can be a challenge or even impossible. All three models are sensitive to their input data and parameters. The reliability of the methods depends on the data availability and model assumptions.

4.2 Step 2: replicate the fixed liability cash flows by a

portfolio of liquid assets

Both Pritchard and Turnbull (2009, pp. 6-7) and CRO Forum (2011) use a replicating portfolio to value the liabilities in their approach. CFO Forum also describes a Monte-Carlo simulation model, but this model will not be explained in this thesis.

A replicating model is used to replicate the fixed liability cash flows by a portfolio of liquid assets. This way the fixed liabilities are valued by a replicating portfolio of liquid assets.

The advantage of a replicating portfolio is that it provides an objective and quanti-tative estimation of fixed liabilities. The disadvantage is that a replicated portfolio, even a perfectly replicated one, represents market risks, but does not capture demographic risks or policyholder risks (Pritchard & Turnbull, 2009, pp. 5, 6).

4.3 Step 3: estimate the proportion of the liquidity

pre-mium that applies

The proportion of the liquidity premium that applies stands for the ratio of illiquidity of the liabilities. Where Pritchard and Turnbull (2009) follow a stochastic model to estimate this ratio, CFO Forum (2011) follows the technical specifications of QIS5.

QIS5 simplified the process by introducing a so-called ‘bucket approach’; a liquidity premium accounts for 0%, 50%, 75% or 100%, depending on the liability characteristics (CEIOPS, 2010b, p. 50). A more ‘sophisticated’ approach, as Turnbull (2009, p. 2) de-scribes it, would be by determining the predictability of the liability cash flows with a stochastic model.

The approach followed by Pritchard and Turnbull (2009, p. 6) defines the liabilities liquidity risk as the portion of forced sales that is the result of misestimating the liquidity cash flows. Liquidity is in their opinion the function of the likelihood of forced liquida-tions and the cost of such forced liquidaliquida-tions. They made the simplifying assumption that any interaction between these two parameters can be ignored. The approach:

1. First make a stochastic projection of the replicated portfolio (that follows from Step 2) and the liabilities for the duration of the latter. Then subtract the pro-jected replicated portfolio cash flows from the propro-jected liability cash flows, this

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results in the net cash flow for each time step of the projection. The net cash flow is the part that needs to be invested (if positive) or funded (if negative) at each time step. If the net cash flow needs to be funded, than this can lead to disinvestments from the replicated portfolio.

2. The previous step leads to a ‘not disinvested’ ratio per time step for each trial of the stochastic process. This ratio is called the ‘Predictability Ratio (PR)’. A PR of 1 stands for highly predictable cash flows (illiquid) and a PR of 0 stands for unpredictable cash flows (liquid). This step can be simplified by taking the PR as the average of the array of PRs per time step.

3. When the PR is determined, a stochastic process is used to determine its proba-bility distribution.

The resulting distribution represents the predictability of the liabilities and by choosing a significance level the predictability of the liabilities are expressed in a single value. For example, when a significance level of 0.005% is chosen, this means that when in 995 of the 1000 runs a maximum of 10% of the cash flows is disinvested then the portion of the liquidity premium applicable is 90%.

4.4 Step 4: discount the replicated portfolio

If Steps 1 till 3 are successfully resolved, then we have an applicable liquidity premium proxy for liabilities. The applicable proxy is used to estimate the market-consistent value of the predictable liabilities. First add the applicable proxy to the risk-free curve and then discount the replicated portfolio of liquid assets (Pritchard & Turnbull, 2009).

Turnbull (2009) states that above-mentioned approach works for simple liabilities, but needs careful consideration when applied to complex liabilities. As an example, he explains that a lump sum option attached to a deferred annuity contract counters the effect when discounted with the adjusted risk-free curve. There is no further literature that explains how complex liabilities should be discounted.

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Chapter 5

A liquidity premium proxy

This chapter estimates a liquidity premium proxy following the CDS benchmark method discussed in Chapter4.

5.1 CDS basis method

The CDS basis method describes two possible approaches to estimate a liquidity pre-mium: Method 1 and Method 2 (the methods differ in the composition of the CDS yield, see section 4.1.1). Method 2 is chosen over Method 1 there the data is more easy to obtain and more easy to perform.

The data used to estimate the liquidity premium proxy by Method 2 is extracted from the financial database Datastream, accessed from the account of the University of Amsterdam (UvA). The data extracted from Datastream are the following variables:

• IBOXX EURO CORP. 3-5Y AAA - RED. YIELD (corporate bond yield to re-demption);

• DS ITRAXX EUROPE 5Y (EOD)CONT SERIES - CDS PREM. MID (CDS premium in bps);

• ICAP EURO VS LIBOR IR SWAP 5Y - MIDDLE RATE (swap interest rate);

• GOVT. AAA-RATED - SPOT RATE,5 YR. - RED. YIELD (government bond yield to redemption).

For the iBoxx, iTraxx and Swap spread, European daily data is used from the sample period 01-01-2007 till 01-31-2014 (the iBoxx data is not available from 01-31-2014 till 11-28-2014). In their research Hibbert et al. (2009b) used data with a maturity of 5 years, so for the data within this thesis a maturity of 5 years is also used.

The liquidity premium is estimated by subtracting a Swap spread and an iTraxx CDS index from an iBoxx bond index, as is shown by the following equation:

LP = iBoxx − iT raxx − Swap spread. (5.1)

The Swap spread in equation 5.1follows from the difference between a Swap yield and a government bond yield.

Figure 5.1 provides an overview of the yields of the iBoxx, iTraxx and Swap spread used for equation (5.1). At the start of the sample, 2007-2008, the spread between the iBoxx and iTraxx is very large (300-400 bps), this becomes smaller and smaller towards the end of the sample period and by the end of 2014, the spread even becomes negative. At the end of 2008 one can observe a large spike for the iBoxx yield, this is explained by the fall of Lehman Brothers in September 2008.

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Figure 5.1: an overview of the iBoxx and iTraxx yields and the Swap spread for the sample period. With the yield in hundreds of bps on the y-axis and the date on the x-axis.

Figure5.2shows the estimated liquidity premium. As was expected by interpreting the yields in Figure 5.1, the liquidity premium starts rather large (it fluctuates between 300 and 400 bps) and becomes negative at the end of the sample period. After Lehman Brothers collapsed, September 2008, the liquidity premium hits its top: 525.75 bps.

A negative liquidity premium is not intuitive, but not impossible as it means that illiquid liabilities are preferred above their liquid equivalents. This seems to be the case when observing the extremely low bond prices in Figure 5.1; for a period in 2013 the iBoxx graph dives even below the iTraxx graph. On the other hand there are some uncertainties concerning the data that need to be taken into account. Besides that the iBoxx and the iTraxx are not well matched, there is the uncertainty surrounding the CDS spread. Where theoretically the CDS spread measures the pure credit risk, practically the CDS may include the counter-party risk (Longstaf et al., 2005, p. 5). These issues might affect the estimated liquidity premium, though are not further researched.

The set of liquidity premiums for the sample period 01-01-2007 till 01-31-2014 is summarized in Table 5.1. The average liquidity premium is estimated on 176.77 bps and has a standard deviation of 145.14 bps. The estimated mean seems plausible when compared to the summary of empirical evidence by Hibbert et al. (2009a, p. 14), though the relatively large standard deviation is reason for concern. This indicates that the sample mean does not represent the sample period well. Figure5.2 underpins this con-clusion; the liquidity premium decreases from almost 400bps to almost -40bps. Splitting the sample period might provide more realistic estimations.

The global financial crisis, known as the credit crisis, started during the summer of 2007 and continued under the name ‘Eurocrisis’ at the end of 2009. The sample period will be divided on the hand of these two events, taking the start and end dates of both events not to accurate. The first period, Period 1, runs from 01-01-2007 till 12-31-2009 and the second period, Period 2, runs from 01-01-2010 till 01-31-2014.

Table 5.2 shows the estimated liquidity premiums for both periods. The sample mean for period 1 and Period 2 are 320.76 and 70.87 bps respectively and the standard deviations decreased to 79.24 and 73.94 bps respectively. Dividing the sample period in two periods improves the quality of the results, as both means give a better indication of the period they represent. Though, the standard deviation of Period 2 (73.94 bps) is large when compared to the sample mean (70.05 bps).

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Figure 5.2: the liquidity premium estimated by equation (5.1). With the yield in hundreds of bps on the y-axis and the date on the x-axis.

Table 5.1: the summary statistics for the liquidity premium over the sample period 01-01-2007 till 01-31-2014. Summary statistics Mean (bps) 176.77 Median (bps) 167.45 Max (bps) 525.75 Min (bps) -40.28 St. Dev. (bps) 145.14 Skewness 0.25 Kurtosis -1.21 Observations 1850

Table 5.2: the summary statistics of the estimated liquidity premiums for Period 1 (01-01-2007 till 12-31-2009) and Period 2 (01-01-2010 till 01-31-2014).

Summary statistics - P1 Summary statistics - P2

Mean (bps) 320.76 Mean (bps) 70.87 Median (bps) 349.38 Median (bps) 70.05 Max (bps) 525.75 Max (bps) 248.28 Min (bps) 167.37 Min (bps) -40.28 St. Dev. (bps) 79.24 St. Dev. (bps) 73.94 Skewness -0.26 Skewness 0.41 Kurtosis -0.98 Kurtosis -1.01 Observations 784 Observations 1066

Application of a liquidity premium proxy in the market-consistent valuation of liabilities

proxy in the market-consistent

valuation of liabilities

Reinder J. van Velze

Contents

Preface

Introduction

Liquidity and a liquidity premium

2.1

Liquidity, assets and liabilities

2.2

A liquidity premium for assets

2.3

A liquidity premium for liabilities

2.4

Liquidity Premium Vs. Illiquidity Premium

Chapter 3

Timeline: a liquidity premium

within Solvency II

3.1

Intro

3.2

Solvency II Directive

3.3

Liquidity Premium Task Force

3.4

QIS5

3.5

Counter-Cyclical Premium and Matching Adjustment

3.6

LTGA

3.7

Omnibus II Directive

3.8

Conceptual framework of the MA and the VA

3.9

Conclusion

Chapter 4

The valuation of predictable

liabilities

4.1

Step 1: estimate a liquidity premium proxy

4.2

Step 2: replicate the fixed liability cash flows by a

portfolio of liquid assets

4.3

Step 3: estimate the proportion of the liquidity

pre-mium that applies

4.4

Step 4: discount the replicated portfolio

Chapter 5

A liquidity premium proxy

5.1

CDS basis method