The relationship between equity prices and credit

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MSC IN ECONOMICS & BUSINESS ADMINISTRATION APPLIED ECONOMICS AND FINANCE

DEPARTMENT OF ECONOMICS

The relationship between equity prices and credit

default swap spreads

An empirical analysis

COPENHAGEN BUSINESS SCHOOL 2009

Handed in: 31. August 2009 Written by:

Ida Buus

Charlotte Renneberg J. Nielsen

Thesis supervisor:

Erik Haller Pedersen The Danish National Bank

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Executive summary

This thesis analyses the relationship between equity prices and credit default spreads (CDS). The CDS is an OTC contract that provides insurance against the risk of default by a particular

company A CDS reflects the credit risk and this credit risk is also present in equity prices as credit risk influence the value of a firm. The relationship between CDS spreads and equity prices is interesting to examine since the nature and direction of this relationship can be used when making economic models, issuing debt and planning arbitrage strategies and the CDS’ played a role in the depth and increase of the crisis that started in 2008. Furthermore due to the young age of the CDS market the available research on the subject is limited and our study will contribute by being the most extensive as far as we know.

We analyse the relationship between equity prices and credit default spreads during the period 2^nd January 2004 to 1^st May 2009 for 265 firms present in S&P 500 in 2002. We examine the daily lead-lag relationship in a vector autoregressive model (VAR) or in the case of co-

integration in a vector error correction model (VECM). Additionally we examine the Spearman Rank correlation, Granger Causality test & Granger-Gonzalo measure.

First, we find that equity prices and CDS spreads are negatively correlated. Second, that equity prices influence CDS spreads and not the other way around. Third, that the relationship is not affected by including exogenous variables in the model. Fourth, that the strength of the relationship increases the higher the credit risk. Fifth, we find that for some sectors the relationship becomes more pronounced the higher the leverage in the sector.

We examine how an increase in credit risk influence the relationship by splitting our data into before and after the beginning of the crisis, in rating, and quartiles. We find that the influence of equity prices on CDS spreads is stronger in the period after the beginning of the crisis than before. This indicates that the relationship between CDS spreads and equity prices is stronger under deteriorating market conditions.

Furthermore we examine how the credit rating of the underlying entity affects the relationship.

We do this by splitting our data in investment grade and high yield. The influence of equity prices on CDS spreads is stronger for the high yield model than the investment grade model.

This indicates that the relationship between CDS spreads and equity prices is stronger the lower the credit rating of the underlying entity.

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At last we examine how the size of the CDS spread effects the relationship. We do this by splitting our data into quartiles. We split the data for index, before and after the beginning of the crisis, high yield, and investment grade. We find that when comparing the quartiles against each otherthe influence of equity prices on CDS spreads is strongest for quartile 4, second strongest for quartile 3, third strongest for quartile 2 and least strongest for quartile 1. Moreover when comparing the quartile models with their respective overall index we find that quartile 3 and 4 are stronger models than the overall model except for the models for high yield and investment grade.

The overall conclusion is that there is a negative relationship between CDS spreads and equity prices and that equity prices lead CDS spreads.

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Acknowledgement

We would like to express our gratitude and give thanks to the people whom help us complete this thesis.

BankInvest for kindly giving us access to Bloomberg and thereby enabling us to get high quality data not otherwise available.

Rasmus Hansen (BankInvest) for continuously inspiration and technical support.

Kirsten Nielsen for editorial support.

Our advisor Erik Haller Pedersen for valuable comments and suggestions.

At last but not least our friends and family for moral support.

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Introduction

Credit risk¹ is a major source of risk for most commercial banks and arises from the possibility that borrowers, bond issuers, and counterparties may default (Hull:2007:255). It appears in almost all financial activities and therefore it is important to measure, price and manage accurately. Credit derivatives can help investors with these issues. Credit derivatives are

financial contracts that transfer the risk between two counterparties without actually transferring the underlying asset.

One kind of credit derivative is credit default swap (CDS). The buyer of a CDS has a credit risk exposure in a firm², typically bonds or loans, and wants to be protected from the risk that the firm e.g. defaults. The seller of a CDS offers to compensate the buyer of a CDS if the firm e.g.

defaults. To receive this protection the buyer of a CDS makes a series of payments to the seller.

In the event of a e.g. default the seller of a CDS has to fulfil his commitment but if a default does not happen the seller of a CDS continue to receive the payments from the buyer of a CDS until the contract expires.

CDS’ were created by JPMorgan Chase in the mid-90’s with the aim to free up capital. At that time JPMorgan Chase had provided a large amount of loans to corporations and foreign governments. By federal law they were required to keep huge amounts of capital in reserve in case any of the loans went bad. They came up with the idea to create the CDS inspired by hedging for fluctuations in interest rates and commodity prices. By using the CDS they could be protected if the loans defaulted and at the same time free up capital. (Phillips:2008:1).

As the market matured and developed in size CDS’ became less a hedging instrument and more a way to speculate for or against the likelihood that particular firms would suffer financial distress or to take advantage of mispricing in the market. The CDS market was largely exempt from regulation by the Securities and Exchange Commission (SEC) and the Commodity Future Trading Commission (CFTC) with the Commodity Futures Modernization Act for 2000, which also provided Enron’s loophole (The Washington Post:2003). As the derivative market exploded in popularity Warren Buffet warned publicly that derivatives were “Financial weapons of mass destructions” (BBC News:2003).

1 Credit risk is defined as risk created by loss associated with the default of the borrower, or the event of credit rating deterioration (Forte:2006:4).

2 For simplicity we will at this point assume that the buyer of a CDS actual has a risk exposure.

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Many agreed with this statement when the credit crisis hit the world economy in mid 2008. The CDS market was accused of causing some of the depth and increased spread of the crisis, and this became obvious when American International Group Inc. (AIG) crashed (Abbott:2009). AIG had sold a lot of CDS contracts and never taken into account that the default intensity increased as it did under the crisis. AIG then became liable to settle a lot of CDS contracts but was not able to fulfil their commitment. They simply gambled that they never had to pay – but when they suddenly had to they went broke (Davidson: 2009). The government later saved AIG by a $180 billion rescue plan. The scenario of AIG was not a unique case.

It was possible for AIG and a lot of other firms to issue CDS contracts for such large amounts for which they did not have the capital in case of a settlement, because the CDS market was not very transparent or regulated (Gillam:2009). CDS are traded over-the-counter (OTC) and there is no central reporting mechanism to determine the price of CDS (Morrissey:2008).

At the time of writing the Obama administration has taken steps to a regulation of the CDS market and proposed a plan to the Congress in August 2009 (Abbott:2009). They proposed that CDS trading should be supervised, new requirements for trade reporting, clearing of standardised contracts and capital backing the trades (Brettell:2009). Combined this should heighten the transparency of the market and limit the counterparty risk. Under the proposal SEC and CFTC should work together to create industry rules (Abbott:2009).

Even though the rules for the regulation of the market are not yet established initiative to clear all standardised contracts has been taken. On 6^th March 2009 Intercontinental Exchange Inc (ICE) established ICE trust, the first clearinghouse for CDS’. It is so far also the only one and has cleared more than $1 trillion in notional volumes in index trades (ICE:2009) and it will expand it operations to also include single name contracts. Moreover JP Morgan Chase, the largest trader of OTC derivatives, has given open access to their CDS pricing system in January 2009 by transferring it to International Swap and Derivatives Association (ISDA) (Pension &

Investment:2009).

All in all a new and more regulated future is set for the CDS market.

1.1 Relation to equity market

CDS spread represent the credit risk in a particular firm and this credit risk is also present in equities. It is expected that when the credit risk of a firm increases the CDS spread will increase – i.e. it becomes more expensive to be protected against the risk of default of the firm as the

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probability of default increases. An increase in credit risk also affects the equity of the firm.

When the credit risk increases the value of the firm is also affected and this will affect the equity price in a negative way. Intuitively there should be a negative relationship between the CDS spread and the equity price of a firm. This means that increased credit risk increases the spread of the CDS and decreases the price of the equity.

The CDS and the equity market differentiate a lot in size, maturity, trade volume and regulation.

Therefore researchers and traders have been interested in analysing how efficient the two markets are when compared and how the interaction is between them. If inefficiencies exist arbitrage between the two markets may be possible.

The CDS market has been a free market without regulations until the crisis, which has made it a very interesting market. A market that has not been regulated in any significant way should self- regulate according to the “invisible hand” theory by Adam Smith. But does this freedom really create an efficient market? Other aspects of the CDS market also have to be considered. The counterparties on the market are only professionals and there are fewer players than on the equity market. Moreover CDS spreads depend on the probability of default of a particular firm and it can be argued that some participants are able to estimate this probability better than others due to more information. For example a bank that works closely with a firm by providing loans, advice etc. is likely to have more information about the real creditworthiness of this firm than other financial institutions that do not have any dealings with this specific firm. Therefore there could be a case of asymmetric information but of course it could also be argued that the two issues are dealt with in two different parts of the bank and that they might not share the same information (Hull:2007:309). These are aspects that increase the probabilities of an inefficient market.

On the other hand, the equity market is probably the most watched market in world. Thousands and thousands of analysts watch its every move. The market reacts fast to new information and sometimes even before the information is public. The major equity markets are very regulated and organised making trading as fast and inexpensive as possible. This may heighten the degree of efficiency but the equity market might also have problems with insider trading – since both instruments depends a lot on firm specific information.

It is interesting to examine the relationship between the CDS spreads and equity prices because of the nature and direction of the relationship and because it is a relation that has not been widely examined. The relationship can be used for example when making economic models, issuing debt and arbitrage strategies. We will cover this in section 12.

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14 1.2 Objectives of the study

The aim of this paper is to examine how equity prices and CDS spreads are related. We find this interesting since both instruments are affected by the current crisis and the relationship between them caught our interest. We expect this relationship to be negative and we expect to find that equity prices influence CDS spreads and not the other way around. Moreover we expect that the degree of influence increases with the size of the spread and in deteriorating market conditions.

The reasons for this will be discussed in section 6 where we will list the hypotheses for our empirical work.

Due to the young age of the CDS market the amount of research available within this area is limited. As far as we know all researchers have found that there exist a negative relationship between the two markets but the strength of the correlation is not unambiguous. The same is valid for the direction of price discovery. Though there is a slight tendency in most research findings that the equity market reacts faster to information and therefore leads the CDS market.

Details of the empirical findings of other researchers will be discussed in section 5.

The limited and ambiguous results of the research give room for further research on the subject.

Our study differentiates from the previously as the time period we examine is longer (5.5 years) and the number of firms (265) we have in our sample is higher. Moreover we cover a time period where the CDS market is more matured than in the previous research and this means that we have been able to get more CDS data than in most of the other research. We have chosen only to consider a selected sample of S&P 500, which is in the US market.

Besides the higher amount of data our time period also include the recent crisis where the CDS played a role. This is a unique opportunity to test how or if the relationship change under more volatile and decreasing conditions. Furthermore we will try to determine how the size of the CDS spread influence the relationship as not previously done. We will also examine if the relationship between CDS spreads and equity prices is influenced by the credit quality and sector of the underlying entity.

We will apply the same techniques as some of the best studies in the field that will be discussed in section 7. Compare to most of the other research papers we will not only consider the Granger Causality test but also analyse the actual estimated models. As far as we know there has not been such an extensive study of this particular subject.

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15 1.3 Problem

The main question this thesis seeks to answer is:

What is the relationship between the CDS spreads and the equity prices?

To answer this we will ask the following sub questions:

- How are CDS spreads and equity prices correlated?

- How do equity prices influence CDS spreads?

- How do CDS spreads influence equity prices?

- To which degree are the results robust?

o To which degree are our results influenced by:

Exogenous variables?

Market conditions?

The rating of the underlying entity?

The size of the CDS spread?

The level of financial leverage in each sector

2 Delimitation

In this thesis we have decided to analyse the relationship between CDS market and equity market for the US market where we have chosen 265 companies from S&P 500. An advantage by

choosing to use only US market data is that we consider only one country. Some studies consider the European market and therefore the analysis will include data from different countries and these might be subject to different laws and regulations, which can make the studies on two different countries less comparable and might loose some explanatory power. It means that country specific issues might affect our results. Moreover the CDS was invented in US and therefore the market in US might be more matured.

When analysing the relationship between CDS spreads and equity prices we decided to look at the “big picture” and not consider specific events such as different initiatives a firm can make, which transfers value between equity holders and creditors. One example could be that a firm announces an unexpected major share buy-back program or increased cash-dividend financed by issuing new debt. This will increase the equity price since the equity holders get cash up front, whereas the credit risk will increase due to higher financial leverage, which increases the CDS spread.

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In the analysis in section 9 we consider the relationship between CDS spreads and equity volatility. It is simply an attempt to further determine the relationship between equity and CDS spreads and not an attempt to simulate the Merton model as we do not include balance sheet data.

Moreover, discussions in this paper are based on the assumption that we are only considering the US market.

3 Structure

The thesis is split in 12 main sections. In section 4 we will describe the theories behind CDS, equity, efficient markets, and the theoretical link between CDS and equity. Section 5 will go through other empirical findings in this area. In section 6,7 and 8 we will describe our hypotheses, the methodology and the data we are using to test them. In section 9 we test our hypotheses and analyse the results. Section 10 will be a discussion of the implication of our results. In section 11 we will give concluding remarks and section 12 is a suggestion for further research.

Figure 0: Structure overview

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4 Theory

4.1 Efficient markets

As described in section 1.1-1.2 we will examine the relationship between equity prices and CDS spreads. We will not only consider if there exists a negative relationship between equity prices and CDS spreads but also if one leads the other in price discovery. In section 1.1 we described characteristics of the two markets and discussed factors that might increase or decrease the level of efficiency. But how is an efficient market determined? We will discuss this in this section.

A market is efficient when the security prices fully reflect all available information. This definition does not take into consideration the costs of trading and acquiring information. It is more realistic to take this into account and therefore the definition is moderated so prices reflect information until the marginal cost of acquiring information and transactions cost no longer exceed the marginal benefit. This means that the investors have incentive to trade the securities until MC = MR. What generally define a market as efficient or inefficient is whether an investor is able to consistently earn abnormal return, e.g. that the investor is able to consistently beat the market and if this is the case the market is inefficient³.

If we find for example that equity prices lead CDS spreads it would mean that an investor would possibly be able to use this information to consistently beat the market when trading CDS’ as he would have knowledge about the future movements of CDS spreads by considering the

movements in equity prices. Public available information is available for both the investors that trade in the CDS market and the investors that trade in the equity market, so if equity prices reacts before CDS spreads it means that the equity market is faster to incorporate new information and thereby must be more efficient.

But this argument is only correct if we do not consider insider trading. If we find that equity prices lead CDS spreads this may be due to a more efficient market but it may also be due to more insider trading in the equity market. If equity prices react to new information before it becomes public and CDS spreads react to new information in the instance it becomes public the CDS market is more efficient than the equity market.

As mentioned we might find in our study that equity prices are leading CDS spreads but due to the aspect of insider trading we cannot say anything about which market is more efficient. To

3 Fama’s (1970) division of efficiency in weak, semi-strong and strong is widely accepted, but since we do not conclude on the level of efficiency in this thesis we will not comment on this further.

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examine which market are efficient event studies is necessary. In event studies it is possible to determine if one of the markets reacts before or after the announcement and compare the reaction time as separately events are examined. This is though beyond the scope of this paper.

This section is meant as a clarification for the reader that a possible lead/lag relationship does not necessarily mean that one market is more efficient than the other. And in this paper we will only consider the influence of one market on the other and not level of efficiency.

4.2 Credit Derivatives

The purpose of this chapter is to give an introduction to the credit derivative market to broaden the understanding of the underlying theories behind a credit default swap.

Credit derivatives are defined as:

“A class of financial instruments, the value of which is derived from an underlying market value driven by the credit risk of private or government entities other than the counterparties to the

credit derivative transaction itself”

(Das:2005:6).

This means that the credit derivative is an instrument to isolate the credit risk from an underlying instrument, called reference entity (Das:2005:29), and transfer the risk between two

counterparties, which a credit derivatives transaction generally consists of. The payoff from the contracts depends on the creditworthiness of one or more firms or countries. This relative new instrument allows firms to trade credit risk much the same way as market risk (Hull:2007:299).

Credit derivatives are Over-The-Counter (OTC) products and this means that they are not traded as equity on official regulated exchanges but the trading is directly between the two

counterparties. It gives the parties the freedom to specify the terms in the contract by negotiation and is therefore less standardized. The trades are usually higher due to the relatively high

transaction cost by negotiation a contract the trades are usually higher. The counterparty risk by OTC trading is also higher than in the exchange-traded market since there are less requirements and standardizing (Hull:2007:28). The ISDA’s documentation and definitions has become the accepted market standard used for both trading and structured transactions (Das:2005:113). But this does not overcome the counterparty risk that OTC trading has. Some products try to

accommodate this by requiring the seller of the protection to make a payment up-front to the protection buyer. These are called funded credit derivatives and include collateralized debt

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obligations, bond obligations, and loans obligations (CDO, CBO, and CLO). Not all credit derivatives are traded as funded and the counterparty risk is still very present when trading credit default swaps (CDS), credit spread options (CSO) etc. Since the credit crisis and the unfunded credit derivatives role in this there is greater outside pressure to regulate the market further.

Therefore more credit derivatives are now being cleared through clearinghouses that act as middlemen in the trade reducing the counterparty risk.

The trading of credit derivatives can be motivated by different reasons and a couple of these are (Goldman Sachs: 2002:slide 1.07):

• To manage credit risk (by using credit derivatives it is easier to transfer credit risk from one party to another.)

• To enable users to diversify credit risk (Exposure to countries, market sectors, and types of financial instruments can selectively be increased or decreased by the involved parties)

• To earn income (Low-cost borrowers with large balance sheets can earn income from parties who want credit exposure without owning assets.)

• To provide access to exposures that would not otherwise be available (e.g. investors can gain access to syndicated loans).

4.3 Credit default swaps

4.3.1 Definition

The most popular credit derivative is the credit default swap (CDS), which is a contract that provides insurance against the risk of default by a particular firm (Hull:2007:299). More precisely a CDS is a bilateral contract between two parties that agree to isolate and transfer the credit risk for a reference entity, usually bond and loans, in case of a pre-defined credit event occurs.

A possible scenario for buying a CDS is that firm A loans 100 millions USD to firm B (reference entity). But firm A knows it is a risky position and they might lose part of or all 100 million USD if the reference entity defaults before the loan is repaid. Firm A is not willing to take this risk so they buy a CDS from firm C. Firm A then becomes the protection buyer and firm C becomes the protection seller.

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Figure 1: CDS transaction

The protection buyer has to pay the periodic payments until the contract expires or the reference entity defaults (see figure 1). In the case of default the protection seller has to pay the protection buyer the sum equal to the face value of the debt owed by the reference entity. This means that the protection buyer obtains the right to sell bonds issued by the reference entity at their face value when a credit event occurs and the protection seller agrees to buy the bonds for their face value when a credit event occurs (Hull:2007:299). The transaction of a CDS results in that the protection buyer has a credit exposure similar to taking a short position while the protection seller has a credit exposure similar to taking a levered long position in the bond (Jersey:2007:3).

So far we have defined a credit event as default of the reference entity. But this was only for simplicity according to the International Swaps and Derivatives Association (ISDA) 1999-2003 terms a credit event includes the following (ISDA:2003):

• Bankruptcy

• Failure to pay

o Borrow money, but not accounts payable o Payment more than $1 million

o After pre-specified grace period

• Obligation default or obligation acceleration

• Repudiation or moratorium

o Mainly applies to sovereigns

• Restructuring

o Reduction or postponement of interest or principal repayments

o Changes in obligation’s seniority causing obligation to become subordinated CDS X-year

contract

Default before year X

Protection buyer pays spread until

default Protection seller

pays face value at default No default in the

period

Protection buyer pays spread

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21 o Deferral or reduction of loan

o Change in currency or composition of material debt obligation

This also illustrates the flexibility of the CDS that the counterparties can agree to terms that are very specific for the individual exposure the protection seller has. However, default are the most popular.

4.3.1.1 Protection buyer – payment of spread

The total amount paid per year to buy protection is known as the CDS spread. Therefore the credit spread is a measure for the compensation the protection seller gets for the risk of default on the underlying security compared to the risk free rate. Calculation of the credit spread is as follows (Das:2005:18):

Credit spread = yield of bond or loan – yield of corresponding risk free security To find the difference between the yield of a risky security and a risk-free security the coupon and maturity of the two securities has to be the same. The spread is paid with a frequency that is decided between the two counterparties and is the cost of protection.

4.3.1.2 Protection seller – payment of face value in case of a credit event

In the case of a credit event the protection seller has to fulfil the CDS contract by paying the protection buyer the default payment, which is equal to the face value of the debt. There are two main types of settlement methods: cash settlement and physical delivery settlement

(Das:2005:86). The physical delivery settlement is the most used settlement method and

“Is structured as the payment of an agreed amount by the seller of protection in exchange for delivery of a defaulted credit asset by the buyer of protection”

(Das:2005:86)

This means that in case of a credit event the protection buyer delivers the bond of the reference entity to the protection seller in exchange for a cash amount of the face value of the debt. This form for settlement assumes that the protection buyer is in possession of the debt of the reference entity.

The other main settlement method is cash settlement, which does not assume the protection buyer to be in possession of the debt of the reference entity. A cash settlement can take form as a post default price, where the payment is based on the price of the reference asset following the

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credit event, or a fixed payment, which is based on a pre-agreed fixed percentage of notional principal (Das:2005:86).

4.3.1.3 Potential speculation

As described in the previous section the cash settlement of a CDS can happen without the protection buyer owning any obligations in the reference entity. So even though CDS contracts can be described as insurance, since it allows debt owners to hedge against credit events – they differ from insurance as there is no requirement to hold the reference entity asset. This lack of requirement means that CDS’ can also be used to speculate on changes in credit spreads or mispricing (Hartmann:2008:4). This means that investors that take long positions in a CDS without having any exposures to the reference entity have a good upside potential for exploiting unjustified spreads between the CDS and the bond market. This also means that investors do not have to worry that much about whether or not the reference entity issues new debt or whether or not the other debt holders are ready to sell their debt or not (Byström: 2004:3).

4.3.2 Valuation of Credit Default Swaps

In order to better understand the relationship between the CDS market and the equity market it is important to know how the CDS is priced and which elements affect the price of the CDS.

The valuation of derivative contracts is the cost of hedging. The pricing relationship between credit derivatives and a cash instrument⁴ is that a risky asset must reflect the return from a risk- free asset plus a risk margin. Risk margin is the compensation the investor is getting for the assumed default risk.

Figure 2: Credit Derivatives - Pricing Relationship

Risk Free

Asset + Risk margin

= Loan or Security

Source: Das (2005:461)

4Cash instruments are financial instruments whose value is determined directly by markets. They can be divided into securities, which are readily transferable, and other cash instruments such as loans and deposits, where both borrower and lender have to agree on a transfer.

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This means that the pricing of a credit default swap should reflect the following factors (Das:2005:489):

• Default probability of the reference entity

• Expected loss given default, which is the recovery rate on the reference entity or the deliverable obligations

• Counterparty risk on the credit default swap

These factors are incorporated into the default probability model, where the CDS is split in two sets of cash flows: A fixed leg and a floating leg. The fixed leg is the spread payments, whereas the floating leg is the contingent cash flow payable by the seller of protection in case of a credit event. The value of the credit default swap is equal to the difference between the present values of the two legs (Troelsen:2008:4).

1 ! "

#

Where:

V_CDS = The value of the credit default swap

DF_t = Discount factor for t₀ to t₁ (the chosen risk-free rate)

SP_n = Marginal survival probability of reference entity from t_n-1 to t_n RR = Recovery rate of the delivered obligation

CDSS = Fee (spread) on credit default swap (bps per annum) AF_t = Accrual factor for t_n-1 to t_n

SP_t = Survival probability of reference entity for t₀ to t₁ 4.3.3 The CDS market in numbers⁵

In this section we give an overview of the development of the CDS market.

5All data in this section is from Bank of International Settlement (BIS) 2009

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The CDS market experienced a steep development as it increased 7 times from 6 trillion USD in 2004 to 42 trillion USD in 2008. In the second half of 2008 the market experienced a contraction and decreased with 27%. When considering the distribution of CDS’ there was a clear

overweight in the first half of 2004 where single-name CDS’ constituted 80% of the total CDS market⁶. Multi-name CDS’ became more widely used and single-name CDS’ part of the total CDS market had decreased to 62% in second half of 2008, which can be seen in figure 3.

Figure 3:Development in single-name and multi-name CDS’

Source: BIS 2009

As our data is on single name CDS we will continue the description of the market using only single name data. From figure 4 it can be seen that almost half of the counterparties in CDS trading is “Other financial institutions” and 1/3 of the counterparties is banks and security firms.

From this it is very clear that all the trading take place between professionals.

6 The other 20% of the market is multi-name CDS which is CDS contracts where the reference entity is more than one name as in portfolios or baskets of default swaps or credit default swap indices (BIS:2006:1)

0 10 20 30 40 50 60 70

Trillions USD

Single-name credit default swaps Multi-name credit default swaps

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Figure 4: CDS single-name 2008-H2 parted on counterparties

Source: BIS 2009

From figure 5 it can be seen that 64% of the single name CDS contracts have a maturity over 1 year to 5 years. This is also consistent with the fact that a 5-year contract is considered the most normal. Contracts with a maturity of 1 year or less is only 7% of the total contracts and this might be due to the fact that there are quite big transaction cost connected to agreeing on a contract. 75% of the contracts are on investment grade (not considering the non-rated).

Figure 5: CDS single-name 2008-H2 parted on maturity

Source: BIS 2009

49%

33%

1%

15%

2%

Other financial institutions

Banks and security firms

Insurance and financial guaranty firms

[ SPVs, SPCs, or SPEs], Hedge funds, Other residual financial customers

7%

64%

29% Maturity of one year or

less

Maturity over 1 year and up to 5 years

Maturity over 5 years

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26 4.4 Equity market

The purpose of this section is to give a short introduction to the equity market in order to be able to better understand elements in the equity price. Equity are traded in a high volume all over the world and in 2008 the total value of share trading in the world was 184,250 trillion USD. The US market constituted 38% of the total share trading and NASDAQ and NYSE are the two largest exchanges in the world. This means that in 2008 the total value of share trading in US was 70,647 trillion USD – which gives a daily turnover of 279 trillion USD (WFE:2008). Even though the numbers are not 100% comparable it is obvious that the equity market is much higher than the CDS market.

Figure 6: Total value of share trading 2008

Source: World Federation of Exchanges 2009

4.4.1 Definition

Equity can be defined as:

“A common stock represent an ownership claim on the earnings and asset of a corporation.

After the holders of debt claims are paid, the management of the firm can either pay out the remaining earnings to stockholders in the form of dividends or reinvest part or all of the

earnings in the business”

(Elton:2007:17)

This means that it is the ownership claims that are being traded on the exchanges. Equity is also characterized by having limited liability. This means that the investor in case of a bankruptcy of the underlying entity is only losing his initial investment and therefore creditors do not have any

62%

2%

15%

21% US

America - without US

Asia - Pacific

Europe - Africa - Middle East

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legal claims on the investor. Moreover an investor gets voting rights by buying a share (Elton:2007:17).

Equity is not only an investment opportunity but is also used for speculation – the price of equity is determined by supply and demand and the volatility of equity is high. Therefore equity is considered as a risky investment. As mentioned before some of the factors affecting the price of equity are the expectations of risk and future return. It is unlikely that all investors have the same expectation but if this would be the case there would not be any trading of equity. The price of equity is the average of all the information and expectations the investors have. Therefore the degree of efficiency in the market is important because it determines how fast information is incorporated into the price of equity.

A lot of time and research have been invested into finding an effective way to determine the future price of equity (Elton:2007:442) and a lot of the trading is driven by the ambition to make above average return. The attempts have ranged from finding a simple rule for selecting equities that will perform above average to hypotheses about broad influences affecting equity prices (Elton:2007:442). If the market is efficient it will not be possible for investors to consistently pick “winners” but the search for an effective method has and still is occupying thousands of people.

In general terms the determinants of a common equity price are a function of firm’s earnings, dividend, risk, cost of money and future growth rate. The problem arises when the factors have to be specified and implemented into a system that uses these concepts to successfully value or select equity (Elton:2007:442).

4.4.2 Valuation models⁷

4.4.2.1 Discounted cash flow model

The discounted cash flow (DCF) model is the model with the most theoretical weight

(Elton:2007:459) and is based on that the value of equity is equal to the present value of the cash flow that the stockholder expects to receive from it⁸ (Elton:2007:443).

PV(equity) = PV(expected future dividends) This can be formalized in the following equation:

7This section is no way exhaustive but just examples of some of the popular valuation models.

8 In academic literature there is a long history of debate about what should be included in cash flow expected from a share. We will here assume as Elton (2007:443) that it is the present value of all future dividends.

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28 _$ %

1 & ' & %₍

1 & '⁽& ) &%_*& _*

1 & '^* %

1 & '& _* 1 & '^*

*

#

Where P₀ is the price today, DIV_t is the dividend received at time t, and P_H is the price at time H.

The DCF model has high popularity in the investment community but only a small fraction of analysts use it. The majority of analysts still value equity by applying some sort of price earnings ratio (P/E) to either present earnings, normalised earnings or forecasted earnings.

(Elton:2007:455)

Another popular form is regression analysis using broad determinants as earnings, growth, risk, time value of money and dividend policy. This approach needs an estimation of the determinants and a weighting of these in the model. (Elton:2007:455)

There is a large range of valuation models and so far none of them have turned out to be superior in the search for above normal performance. The effect of the different models varies also with the efficiency of the market.

4.5 Merton Model

The purpose of this project is to investigate the link between equity price and CDS spreads and so far in our study the link has be augmented for based on previously empirical research but there is also a theoretical background.

A crucial parameter in CDS pricing is the credit risk associated with the underlying entity. This risk is often deducted from the credit rating made by rating agencies. This is quite infrequently revised (and also under some critic) so another opportunity is to deduct the credit risk from the market. Merton (1974) proposed a model that uses equity prices to estimate default probabilities using equity volatilities, equity quotes and balance sheet information. This model made it possible for the credit risk to be estimated on a daily basis, and is crucial for CDS pricing.

The basis of the model is that a firm’s equity is an option on the assets of the firm. For simplicity and to illustrate the model the firm is assumed to have one zero-coupon bond outstanding and the bond matures at T⁹.

We defined the variable in the model as:

V₀: Value of firm’s assets today

9The section that describes and deduct the model is based on Hull (2007:269-272)

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29 V_T: Value of firm’s assets at time T

E₀: Value of firm’s equity today E_T: Value of firm’s equity at time T

D: Amount of debt interest and principal due to be repaid at time T σ_V: Volatility of assets (assumed constant)

σ_E: Instantaneous volatility of equity

Two scenarios are defined as a situation where the firm default and one where there is no default at time T.

Default: If in theory the value of a firm’s assets at time T is smaller than the debt interest and principal due to be repaid at time T (V_T < D) the firm would default and the value of its equity would be zero.

Non-default: If V_T > D the firm should make the debt repayments at time T and the value of equity would be V_T – D (remembering that assets = liabilities + equity), and therefore the firm would not default.

The value of the firm’s equity at time T extracted from the Merton model is:

E_T = max(V_T-D, 0)

This can also be seen as a call option on the value of the assets of the firm with a strike price equal to the repayment required on debt. The Black-Scholes formula for option pricing can then be used to find the value for equity today.

+_$ _$, ^-.,₍ Where

$/ & 0' & 1 ²⁽/ 4 52 1₂√5

And

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₍ 1₂√5

The value of debt today can be defined as the value of the firm’s asset subtracted the value of the firm’s equity (D=V0-E0). The risk neutral probability that the firm will default on debt is N(-d2).

To calculate the probability of default V0 and σ_V need to be calculated because they are not directly observable. But if the firm is publicly traded we can observe E0 (using equity prices).

This means that the Black-Scholes equation provides one condition that must be satisfied by V0

and σ_V and thereafter σ_E can also be estimated.

From a result of stochastic calculus know as Itô’s Lemma the following is found:

1₇+_$ ⁸⁷₈₂1₂_$ or 1₇+_$ ,1₂_$

This provides another equation that must be satisfied by V₀ and σ_V. The equations provide a pair of simultaneous equations that can be solved for V₀ and σ_V.

The most important determinant of CDS spreads is the probability that a credit event involving the underlying references entity occurs. Merton (1974) links this default probability to the equity market valuation and the volatility of equity return. Therefore there is a theoretical background to the hypotheses that there exist an empirical link between the equity market quotes and the CDS spreads.

5 Literature review

In the past decade some empirical work has been done on the relationship between CDS spreads and equity prices. We will go through the empirical work of other researchers who have dealt with basically the same research question, as we will examine.

Financial theories as the Merton model and efficient market theories suggest that the equity market has incorporated the probability of default in the equity price. This is due to the fact that equity holders are more likely to follow the financial conditions/performance of the firm than debt holders, since they are residual owners of the firm.

We have already established that in deteriorating conditions the CDS spread will increase and the equity price decrease. So theoretically there should be a negative relationship between CDS

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spreads and equity prices. As far as we know no other researcher has found a different

relationship when testing this empirically. Bystrøm (2004) investigated the relationship between equity prices and the iTraxx¹⁰ CDS market and found a negative correlation of about 0.5 when using Pearson correlation coefficient and Spearman rank correlation. Furthermore, he confirmed his hypothesis that equity volatility and CDS spreads were positively correlated. Hafer (2008) analysed the correlation between equity quotes and CDS quotes split on sectors over a period of 6 months from March 1 2007 to August 31, 2009 and found a negative correlation of 0.7 using the same techniques as Bystrøm. Lake & Apergis (2009) found that equity across European and US markets were negatively correlated to European CDS spread changes in the period from June 16, 2004 to November 13, 2008 by using error correction (EC) and the multivariable generalized heteroskedasticity in mean (MVGARCH-M) modelling. The same results were found in the Japanese market. Kikuchi (2009) found a negative correlation of 0.95 between the iTraxx Japan and the equity market (TOPIX) using the same technique as Bystrøm. Other Asian studies by Chang, Fung & Zhang (2008) and Ishikawa & Mezrich (2009) also found a very strong negative relationship between CDS spreads and equity prices.

In connection with analysing the relationship between equity prices and CDS spreads a part of the literature is concerned with whether information is embedded at the same time in the CDS market and the equity market. If information is embedded first into one of the markets, there will exist a lead/lag relationship between the two markets. A lead/lag relationship indicates

asymmetric information and can be a sign of inefficiencies between the two markets. A lead/lag relationship between the two markets would not be surprising since they differ in organization, age, number of traders, and liquidity.

When looking at the empirical findings for testing the relationship between the CDS market and the equity market the results are mixed.

Longstaff (2003) was among the first to analyse the lead/lag relationship between equity, bonds, and CDS’ for a sample of 67 single-named CDS firms in the period March 2001 to October 2007 and found no definitive relationship between the three markets.

Lake & Apergis (2009) considered the US and European equity market and found that CDS spreads leaded equity prices in the period 2004 to 2008 by using MVGARCH-M modelling.

Hartmann (2008) used graphical inspections of US and European data for a period of 6 years

10iTraxx is a group of international credit derivative indices that are monitored by the International Index Company (IIC). iTraxx indices cover credit derivative markets in Europe, Asia and Australia

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(2002-2008) and found that CDS spreads leaded equity prices. Furthermore, he found that his results were stronger under deteriorating conditions. Zhang (2005) used cumulated changes in rating-adjusted CDS spreads (CCAS) and cumulative abnormal relative changes of CDS spreads (CARC) on US data in the period 1997-2003 and found that the CDS market leaded the equity market. Chan (2008) analysed the relationship between equity prices and CDS spreads for seven Asian countries in the period 2001-2007 and found by applying VECM, that CDS spreads leaded equity prices in 5 of the 7 markets, and equity prices only leaded in 1 of the 7 markets.

Norden & Weber (2004) analysed individual equity prices, bond spreads, and CDS spreads of 58 international firms in the period 2000-2002 by using a VAR model approach. They found that equity prices leaded CDS spreads in 39 of the 58 firms and that CDS spreads leaded equity prices in 5 of the 58 firms. Forte & Pena (2006) used the VAR model approach to find the relationship between 52 North American and European non-financial firms in the period

September 12, 2001 to June 25, 2003. They found that equity prices leaded CDS spreads in 24 of 65 cases and CDS spreads leaded equity prices in only 5 of the 65 cases. Fung (2008) examined the relationship between the equity prices and the CDS spreads for US data from 2001 to 2007.

They found that the relationship depended on the credit quality of the underlying reference entity. That is, there was mutual feedback of information between equity prices and high yield CDS spreads, whereas equity prices leaded investment grade CDS spreads. They also found that volatility of both high yield and investment grade CDS spreads leaded equity volatility, but also that equity volatility gave some feedback on high yield CDS spreads. Bystrøm (2004) also finds that information flows from the equity market to the CDS market in the period he was examining (2004-2006). Realdon (2007) found that CDS spreads and default intensities seem to be driven by equity prices for five large corporations in the period from January 1, 2003 to June 31, 2006.

As can be seen from the literature review above there is no unambiguous answer to which of the two markets leads the other. The only thing that seems to hold is that there exist a negative relationship between CDS spreads and equity prices. Slightly more studies find though that the equity market leads the CDS market.

6 Hypotheses

In section 4.5 we have established the theory behind CDS spreads and equity prices and the possible relationship indicated by the Merton model and in section 5 covered prior empirical findings. We will use a combination of these two to create our hypotheses. Our hypotheses

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indicate what we expect to find in our analysis. Our methodology section 7 is the link that makes the testing of the hypotheses possible.

H1: The correlation between CDS spreads and equity prices is negative.

Our hypothesis 1 states that the correlation between CDS spreads and equity prices is negative.

According to the Merton theory and the literature reviews we will explain the reasoning behind this. If the value of a firm increases due to for example higher earnings than expected the equity holders will benefit because the equity prices increases. When the value of a firm increases the distance to default also becomes greater. Since the likelihood of default has decreased the cost of debt also decreases. Moreover when the likelihood of default is smaller the price of protection against default also decreases and thereby the spread of the CDS decreases. This inverse relationship is consistent with results of other empirical studies (see Bystrøm (2004), Hafer (2008) and Lake et al. (2009))

We expect to find that the equity prices and CDS spreads are negatively correlated.

H2: Equity prices influence CDS spreads and CDS spreads do not influence equity prices.

Our hypothesis 2 states that equity prices influence CDS spreads and CDS spreads do not influence equity prices and this considers the efficiency of the two markets. In section 4.1 we stated the theory behind efficient markets and it is important because if the two markets are not efficient arbitrage is possible. We will not determine to which degree the two markets are efficient since this usually demand event studies. But instead we will determine if historical equity prices influence current CDS spreads or/and if historical CDS spreads influence current equity prices. This is not the same as determining the degree of efficiency because if we for example find that equity prices leads CDS spreads this may be due to the fact that the equity market is more efficient than the CDS market. However, it may also be due to the fact that there is more insider trading in the equity market and it therefore reacts before the CDS market. This means that the equity market reacts to information before it becomes public while the CDS market reacts to information when it becomes public – and this does not mean that the CDS market is less efficient.

The prior empirical studies (see section 5) did not find consistent results when examining this.

But a slight overweight of the studies found that equity prices influences CDS spreads and not the other way around (Norden & Weber (2004), Forte & Pena (2006), and Fung (2008)). We

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expect this as well also due to the fact that the CDS market is a young market compared to the equity market and the size of the CDS market is approximately 4,000 times smaller than the equity market globally¹¹. Moreover there are thousand and thousand of analysts watching every move of the equity market so it seems logical that it will react before the CDS market. It could though be argued that the CDS market has been unregulated until 2009 and the possibility of insider trading may could be high due to the clientele on the market. But on the other hand there might as well be insider trading on the equity market. All in all we expect to find that historical equity prices influence CDS spreads and not the other way around.

H3: The relationship between CDS spreads and equity prices is still strong when including exogenous variables.

Our hypothesis 3 states that we expect the found relationship between CDS spreads and equity prices still to exist even though we include exogenous variables into our model. This means that the previous found relationship is not simply due to the fact that both CDS spreads and equity prices are influenced by a common 3^rd variable. We will include the same variables as exogenous as Fung (2008).¹²

H4: When the credit risk increases the strength of the relationship between CDS spreads and equity prices increases.

H4.a: The relationship between CDS spreads and equity prices is stronger under deteriorating market conditions.

H4.b: The strength of the relationship between CDS spreads and equity prices becomes more pronounced the lower the credit quality.

H4.c: The strength of the relationship becomes more pronounced the bigger the CDS spreads of the underlying index.

Our hypothesis 4 states that the strength of the relationship between CDS spreads and equity prices increases with an increase in credit risk. The reasoning behind this is that equity bears the ultimate form of credit risk because it represents the most subordinated claim in the capital structure of the firm. Thus equity holders are more likely to monitor the performance of the

11 The data is not directly comparable so the result is not exact.

12 This is not a perfect test and as with every other model there will always be the risk that the found relationship is due to omitted variable problem. We are not able to test the model for all possible exogenous variables.

The relationship between equity prices and credit

MSC IN ECONOMICS & BUSINESS ADMINISTRATION APPLIED ECONOMICS AND FINANCE

DEPARTMENT OF ECONOMICS