An Empirical Analysis of the CDS-Bond Basis in Sovereign Debt Markets

Scott Smith

April, 2006

Introduction

A credit default swap (CDS) is an over-the-counter financial instrument that permits the transfer of credit risk between parties. In a credit default swap, a protection seller agrees to compensate a protection buyer in the event that a particular entity (the reference entity), such as a corporation or sovereign country, experiences a credit event. In return, the protection buyer pays the seller a periodic fee. Thus, CDS contracts are basically a form of insurance.

CDS contracts are linked to cash bond markets by arbitrage relationships much like equity and bond futures are linked to their respective cash markets. However, unlike many derivative markets, the arbitrage is less apparent. CDS contracts are not written on individual securities; instead, they are written on an issuer. Any bond or loan associated with the reference entity can be delivered in the event of default, creating a natural cheapest-to-deliver option for protection buyers that are not present in the cash market. Further, CDS generally are written for a tenor of five years, meaning that it is difficult or impossible to create a maturity-matched hedge for a given instrument. Finally, since default is an ill-defined concept, there may be disagreement as to whether a credit event has actually occurred. As a result of these and other factors, spreads in the two markets often diverge even though they represent similar underlying credit risks. The dynamics of this difference between CDS and cash bond spreads, or basis, is thus a natural target for relative value traders.

In this paper, we will begin with an overview of CDS contracts. We will explain the most common uses and derive a valuation model. We will then present a method for comparing spreads in the two markets using risk-neutral default intensities. Using this technique, we will calculate the CDS-bond basis for a number of sovereign issuers. We will analyze the statistical behavior of the basis, determine whether a non-zero basis persists, and look for causal relationships between spreads in the two markets.

Overview of Credit Default Swaps

A CDS contract is an unfunded instrument that transfers credit risk from a protection buyer to a protection seller in exchange for a period fee. This fee is set such that the present value of the fee payments equals the expected present value of the potential obligations of the protection seller in the event of a default event. Thus, a CDS contract has zero value at initiation.

If the reference entity does not experience any credit events, then the protection buyer simply continues paying the protection seller a fee until the contract expires (usually after five years). In the event that a credit event does occur, then the buyer can deliver any obligation of the reference entity to the seller at par (although cash, rather than physical, settlement is becoming more common). Thus, a CDS contract behaves much like a put option on the firm’s debt for the protection buyer.

Often, parties will want to terminate a contract before it matures. This can be achieved in a number of ways. A party (xxx)

Since the term “credit event” can be defined in many different ways, market participants have agreed on a set of definitions laid out by the International Securities Dealers Association (ISDA) in 2003. ISDA’s 2003 definitions include several types of credit events[1]:

1. Failure to pay: if an entity fails to make scheduled payment of coupon or principal

2. Bankruptcy: if an entity files for bankruptcy

3. Obligation default or acceleration: if any of the entity’s obligations have become payable prior to maturity (generally excluded in corporate contracts but still used in some emerging market contracts)

4. Repudiation or moratorium: if a government or other authority enacts laws that make it impossible for an entity to repay its debt

5. Restructuring: if the principal or interest due on an obligation is decreased or the maturity date extended; could also be triggered by changing the priority of obligations or the currency in which they will be paid

As an example of the ambiguity inherent in the term “credit event”, one could look to the case of Xerox in the summer of 2002[2]. Xerox’s creditworthiness had been steadily declining before this time. Shortly before a substantial bank revolver came due, Xerox negotiated an extension of the repayment date. The extension was agreed to by both parties, but according to the terms of many CDS contracts, it could have been defined a credit event. As a result of this case, ISDA updated its definitions to include the word “mandatory” in the restructuring clause to prevent bilateral agreements from triggering a credit event.

The restructuring clause has been by far the most contentious aspect of CDS contracts. ISDA now has four different versions of the restructuring clause. This means that contracts on the same reference entity may have different terms and trade at different spreads. In an attempt to standardize the market (to improve transparency and liquidity), many market participants are advocating dropping this clause completely.

Uses of Credit Derivatives

The primary participants in the CDS market are banks, insurance companies, corporations, and asset managers. Banks and corporations are net buyers of protection, while insurance companies are net sellers[3]. Among asset managers, some players sell protection in order to enhance returns, while others (such as convertible bond arbitrageurs) use them to hedge credit risk in their strategies.

Hedging credit risk

Many market participants who buy protection are looking to hedge exposure to an entity. For instance, banks often extend loans to corporations. Rather than securitizing these loans (which may damage the bank’s relationship with its customer), the bank can simply buy protection in the CDS market and nullify its credit exposure. Similarly, firms such as pension funds, and insurance companies often use CDS contracts to limit exposure to bonds that are experiencing credit erosion. Instead of selling the bonds and incurring a mark-to-market loss, the firms continue to hold the bonds and simply buy protection via CDS contracts.

Regulatory capital relief

Banks are a major player in the CDS market. According to the terms of the Basel Accord, banks need to hold capital in relation to their loan exposure. However, since the rules favor OECD banks and sovereigns (exposure to an A-rated OECD bank requires less capital than exposure to an AAA-rated corporation)[4]. As a result, banks often use credit derivatives to transfer exposure from corporations to OECD banks. They will buy protection from an OECD bank on their corporate portfolios in order to minimize the amount of capital they need to hold.

Yield enhancement

When yields are low, entities such as investment banks and hedge funds often sell protection in the CDS market. Such a strategy is similar to the strategy of writing deep out-of-the-money puts on a firm in an attempt to enhance yields.

Arbitrage

Many hedge funds use CDS contracts as a part of their trading strategies. For instance, firms who engage in convertible bond arbitrage generally purchase convertible bonds and buy protection. This leaves them with an option on common equity that is stripped of credit risk[5]. Thus, much like interest-rate derivatives can be used to hedge curve risk in trading strategies, CDS can be used to hedge credit risk.

Arbitrage Principles

The cash bond and CDS markets are linked by arbitrage principles like all cash-derivative markets. In order to determine the nature of this relationship, one needs to find a portfolio of tradable instruments that replicates the cash flows of the CDS contract. Disregarding counterparty risk, the following trades would replicate the cash flows of a CDS contract:

· Buy a bond corresponding to the reference entity in the cash market

· Finance the bond by selling it in the repo market

· Sell an interest rate swap to hedge the interest rate risk inherent in the cash bond

Combining these trades with protection from a CDS contract yields a trade with no cash flows at either initiation or at termination. In the event of no default, the loan is repaid with the principal payments from the bond. In the event of default, the CDS will be triggered, thus providing the difference between the bond’s par value and its recovery rate. In either case, the net principal payments for the trade will be zero.

By no-arbitrage principles, since there is no initial outlay, the value of the cash flows from the trade should be zero. We have just demonstrated that the combination of the cash bond and protection offsets the loan payment. All that is left are the intervening payments: the coupons from the bond, flows from the swap, loan payments, and protection payments. Thus, the net value of these payments must also be zero[6].

Rearranging the payments, we find the following:

Thus, the CDS spread should equal the spread to swaps of a cash bond less the repo spread (or the “specialness” of the repo). If , then it would be profitable to buy the cash bond and buy protection. Since highly rated firms can buy cash bonds and fund close to LIBOR, they will exploit this situation and drive the spreads together ( is essentially zero in this case since the firm is funding on their balance sheet at or near LIBOR). Thus, these situations are exceedingly rare. In contrast, if , then it would be profitable to short the cash bond and sell protection. However, in many cases, is negative (it is difficult to short bonds). Therefore, it is possible for CDs spreads to exceed cash spreads for extended periods of time (the spread will be bounded by ).

Valuation

The valuation of a credit default swap requires a number of inputs including default rates, recovery rates, and interest rates. Most valuation models fall into two categories: structural and reduced form. Structural models are generally based on Merton’s option pricing model. They attempt to model the path of an entity’s assets and liabilities. Using these predictions, a probability of default (when assets fall below liabilities) can be determined.

Reduced form models attempt to derive default probabilities from cash bond prices. There are two degrees of freedom associated with reduced-form models: the probability of default and the recovery rate. Since prices can only eliminate one degree of freedom, the other must be determined exogenously. Generally, recovery rates are estimated based on historical default data. In the corporate market, recovery rates are generally a function of sector and somewhere in the neighborhood of 40%. Sovereign recovery rates are often lower since there is no legal structure to enforce asset distribution (for instance, a sovereign could simply refuse to pay its debt, whereas a corporation would be forced to liquidate and distribute its assets to bondholders). Cash bond prices are then used to calculate the probability of default.

One of the most common reduced form models was proposed by Hull and White[7]. It assumes that default rates, recovery rates, and interest rates are independent and that there is no counterparty risk (although the latter constraint was lifted in a subsequent paper).

To derive their model we must first define the following:

: risk-neutral default intensity density at time t (conditional)

: survival probability at time t

: risk-neutral default probability density at time t (unconditional)

: discount factor at time t

: accrued interest at time T

: risk-neutral recovery rate

Using this model, the first step in pricing a plain vanilla CDS involves finding the risk-neutral default probability density function .

We start with the survival probability. The unconditional probability of default is simply

The conditional probability of default is

Rearranging yields

Integrating leads to

This is the survival probability as a function of the hazard rate. The risk-neutral probability density is then simply the product of the hazard rate and the survival probability:

The probability that a credit event will occur by time T can be defined as

Likewise, the probability that no credit event will occur is

In the event that a default does occur, the protection buyer will receive a payment equal to

Integrating this over the default density function and discounting to the present yields

This is the value of the contingent leg of the swap.

To value the fixed leg, one must discount the conditional fixed payments back to the present. Thus, the value of the fixed leg is simply

The spread that equates the value of these two legs is thus the “price” of the contract:

Comparing CDS Spreads to Bond Spreads

In order to compare CDS spreads to spreads in the cash market, a par-implied spread should be calculated for a bond[8]. Often, spreads in the bond market are quoted as Z-spreads, or the amount by which the curve would need to shift in parallel for the discounted value of a riskless bond with the same cash flows to be equal to the observed market price of the bond. This technique suffers from a major drawback, however: CDS contracts are struck at par whereas bonds can trade at any value. In the no default case, this is not significant, but in the event of default, it is.

Let us assume that investor A were to buy a bond at $80 and investor B were to sell protection in the CDS market. If the bond were to default with a recovery value of $40, investor A would realize a loss of $40. However, investor B would be delivered a bond worth $40 and be obligated to exchange it for $100 (par), resulting in a loss of $60. Thus, a protection seller is exposed to more risk than a bond holder when bonds are trading below par. This means that comparable CDS spreads should be wider than predicted by bond Z-spreads. Similarly, comparable CDS spreads should be lower than bond Z-spreads when bonds are trading at a premium.