Limited Arbitrage Analysis of CDS-Basis Trading

Qi SHANG∗ q.shang@lse.ac.uk

First version: Dec 2009 This version: Nov 2011

Abstract

This paper proposes a continuous-time limited arbitrage model in which time-varying fund-ing costs and demand pressure on two markets with identical assets jointly results in the twomarkets offering different expected excess returns. I apply the model to illustrate the riskyarbitrage nature of CDS basis trading in closed-form and derives a number of predictionsthat have favorable empirical evidence. The CDS basis became very negative during the2007/08 financial crisis and was slow to converge to zero, which seems to violate text-bookno arbitrage conditions. However, poor funding liquidity and market liquidity during thisperiod implies high funding costs and demand pressure. According to the model, the twoassets therefore earn different risk premia and CDS basis trading, which takes opposite po-sitions on the two markets, becomes a risky arbitrage that earns non-zero expected returnin excess of the funding costs. High level of market frictions can also destruct predictabilityof credit spread term structure slope on future credit spread changes and distort prices tothe extent that providing liquidity is not rewarded with positive expected excess return. Onthe empirical side, I find evidence that basis trading is exposed to systematic risk factorsand factors in the form of TED spread or Federal Fund Rate sqaured times corporate bondmarket trading volume has some short-term predictive power on abnormal basis tradingprofit. I also find consistent evidence suggesting that the size and volatility of realizedbasis trading return is increasing in the severity of the two main market frictions and basistrading profit is increasing in the underlying’s time-to-maturity.

∗I owe special thanks to Dimitri Vayanos and Kathy Yuan for their many comments and suggestions.Also, I am very grateful to Mikhail Chernov, Amil Dasgupta, Daniel Ferreira, Stephane Guibaud, ShiyangHuang, Dong Lou, Philippe Mueller, Christopher Polk, Zhigang Qiu, Michela Verardo, Jean-Pierre Zigrandand seminar participants at the LSE/FMG PhD Seminar for many helpful suggestions. All remaining errorsare my own.

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1 Introduction

As summarized in Gromb and Vayanos (2010), costs and demand shocks faced by arbi-trageurs can prevent them from eliminating mis-pricings on the markets and therefore gen-erate market anomalies. I propose a model that illustrate how the interaction of exogenoustime-varying funding cost and exogenous demand pressure faced by arbitrageurs results intwo assets with identical payoffs having different expected excess return. This result implytaking opposite positions on these two assets is a risky arbitrage that is expected to earnprofit in excess of funding costs. I then use CDS basis trading as an example to showimplications of the model.

Tuckman and Vila (1990) showed that exogenous price discrepancies between two assetswith identical cash-flows do not necessarily create arbitrage opportunities if there’s shorting-selling cost. As show in Gromb and Vayanos (2010), without other frictions, the discrep-ancies between the expected returns of the two assets should compensate exactly for thefunding costs so that an arbitrageur is still expected to earn zero excess return. In contrary,my model suggests arbitrageur can earn a risky profit even after adjusting for the fundingcosts if the funding costs are time-varying and arbitrageur faces demand pressure.

The demand pressure faced by the arbitrageurs is another important source of market fric-tion that contributes to the rise of market anomalies. Investors other than arbitrageurs canhave endogenous demand shocks that arise via different channels,1 but a number of papershave focused on the pricing implications given exogenous demand shocks. These theoreticaldemand-based papers include Garleanu, et.al.(2009), Naranjo (2009) and Vayanos and Villa(2009). By assuming exogenous underlying asset prices, Garleanu, et.al.(2009) and Naranjo(2009) solved derivative prices endogenously to show that exogenous demand shocks andfrictions in arbitrageurs’ trading can drive derivative prices away from conventional pricesimplied by the no-arbitrage conditions. Naranjo (2009) considered extra funding cost facedby arbitrageurs as the friction limiting her ability to eliminate price discrepancies on thefutures and underlying markets. However, he assumed the underlying asset’s price as ex-ogenously given, so the market frictions only have impact on the futures price but not onthe underlying market, which is unrealistic as derivative markets’ trading do have impacton underlying price.

My paper is the closest to Vayanos and Vila (2009) in that prices on all markets are en-dogenized so frictions on one market affect all markets. Vayanos and Villa (2009) studiedarbitrage across different Treasury bonds maturities, i.e. assets with different cash-flows,and there’s no other frictions than the demand shocks from other preferred habitat in-vestors. However, my paper introduces an additional friction, which is the time-varyingfunding costs, to show that two assets with identical cash-flows can earn different expectedexcess return, which implies profitability yet risk for a cross-market arbitrage trade. The

1See Gromb and Vayanos (2010) for details.

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two assets with identical cash-flows are two defaultable bonds, one represents corporatebond, while the other represents a synthetic corporate bond position created by writinga CDS protection and default-free lending.2 Trading corporate bonds through repo andreverse-repo generates additional funding costs that are sensitive to default intensity of thebonds. Therefore I model the funding costs as functions of default intensity. Although theassumption on funding costs are not fully endogenized, a clear motivation in the Appendixalong with empirical findings by Gorton and Metrick (2010) justify this assumption, whichis further supported by a recent paper by Mitchell and Pulvino (2011), which illustrates theconsequence of funding liquidity failure on arbitrage activities from practitioners’ perspec-tives.

I apply the model’s implications on CDS basis trading, which turned out to be a riskyarbitrage activity in the 2007/08 crisis. Credit default swap (CDS) is an OTC contract inwhich one party pays the other party a periodical fee (the CDS premium) for the protectionagainst credit events of an underlying bond, in which case the protection seller pays theprotection buyer for the loss from the underlying bond. The CDS market offers hedgers andspeculators to trade credit risks in a relatively easy way. It is a fast growing market withvast market volume. The exact way to trade CDS has experienced some significant changesin the recent years following hot debates over the role it plays in the 2007/08 financial crisis.In the past, the two parties of a CDS trade agree on the CDS premium that makes theCDS contract having zero value at origination. Then as conditions change in the life of thiscontract, it has a marked-to-market value that is not zero. Following the implementationof the so-called CDS Big-Bang regulations on the North American markets in April 2009,the CDS premia are fixed at either 100bps or 500bps, and the two parties exchange anamount of cash at origination to reflect the true value of the contract. For instance, if thereasonable CDS premium should be 200bps, then the protection buyer pays the protectionwriter a certain amount of money at the beginning, and then pays CDS premium at 100bpseach period. This is certainly a change in order to make the market more standardized andmore liquid, however, the CDS market is still very opaque and illiquid.

Theoretical papers such as Duffie (1999) and Hull and White (2000) showed a parity be-tween CDS price and credit spread under the no-arbitrage condition, i.e. investors who holda defaultable bond and short a CDS (buy protection) on this bond is effectively holding adefault-free bond and thus should earn the risk free return. In other words, the CDS basis,which is CDS premium minus the credit spread, should be zero if basis trading earns onlyrisk free return. This zero basis hypothesis is supported by some empirical works includingHull, et. al.(2004), Blanco, et. al.(2005) and Zhu (2006) using relatively early data. How-ever, practitioners observe positive or negative basis at times and many investors engage inbasis trading. Buying a bond and CDS protection is known as negative basis trading, whileshorting a bond and writing CDS protection is called positive basis trading. Meanwhile,

2The equivalence of synthetic corporate bond and writing CDS plus lending will be illustrated in the nextsection.

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recent work by Garleanu and Pedersen (2009) and Fontana (2010) showed large negativebasis persisted since the summer of 2007. As shown in Figure 1, during the 2007/08 crisis,the CDS basis become very negative for a long period, which contradicts text-book arbi-trage argument, yet negative basis trading still lost money even at quite negative CDS basislevel. In this paper, I reveal the risky arbitrage nature of CDS basis trading in closed-formand find empirical evidence that supports the model.

To justify the deviation from the law of one price on the CDS and corporate bond markets,Garleanu and Pedersen (2009) attributes two otherwise identical assets’ different exposuresto risk factors to the different level of exogenous margin requirement on the two markets.Alternatively, I model the riskiness of CDS basis trading as the result of the interactionof funding illiquidity and market illiquidity. Under a demand-based framework in whicharbitrageurs trade to meet demand pressure posed by local investors, the risk-aversion ofarbitrageurs and the presence of demand pressure results in arbitrageurs requiring risk pre-mium for the positions they take. They also face time-varying funding costs on the twomarkets, which results in the two assets may have different risk exposures and thus carrydifferent level of risk premia. The co-existence of time-varying funding cost and demandpressure makes CDS basis trading a risky arbitrage. As shown in the model, without any oneof these two sources of friction, CDS basis trading doesn’t generate expected excess profit.In a special case, even if the arbitrageurs take the exact opposite positions on the CDS mar-ket and corporate bond market so that they are completely protected from defaults, theystill have non-zero exposures to other risk factors. Therefore, CDS basis trading is in factrisky arbitrage and it is reasonable for the CDS basis to deviate from zero under severe mar-ket frictions, when the above mentioned market illiquidity assumptions are likely to be met.The model also generates results that highlight the arbitrageurs’ inability to correct pricedistortion under market frictions and offers a number of results on term structure properties.

The model predictions are supported by empirical data. Using Markit CDX and iBoxxIndices data and corporate bond data from TRACE, I find the size and volatility of realizedbasis trading excess return is increasing in the degree of market frictions. The model’spredictions that basis trading profit is increasing in underlying maturity and the size ofCDS basis is increasing in corporate bond market trading volume are also supported bythe data. I perform a number of regression tests to show that basis trading is exposed tosystematic risk factors and some interaction terms of funding cost and market liquidity havepredictive power on abnormal basis trading profits. As predicted by the model, I also showthat the predictability of credit spread term structure slope on future credit spread changecan disappear when market frictions are high.

Empirical work by Fontana (2010) found that funding costs variables are important in ex-plaining CDS basis changes, while Bai and Collin-Dufresne (2010) explained cross-sectionalvariations in CDS basis with funding liquidity risk, counterparty risk and collateral quality.However, their results concerned only on the changes in CDS basis, which according to my

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model doesn’t determine the profitability of basis trading in the presence of funding costs.My paper is also related to a number of empirical works in explaining credit spread andCDS price movements such as: Collin-Dufresne, et. al.(2001), Elton, et. al.(2001), Huangand Huang (2003), Blanco, et. al.(2005), Tang and Yan (2007), and Ellul, et. al.(2009)among others. A recent work of Giglio (2011) proposed a novel way of inferring impliedjoint distribution of financial institution’s default risk from the CDS basis, which shows therole of counterparty risk in widening CDS basis.

The next section introduces model set-up while Section 3 solves the model under two casesand provides a number of results on the expected excess return of basis trading and the termstructure properties of credit spread and basis trading profits. I then carry out empiricalstudy in Section 4 to verify theoretical results. Finally, Section 5 concludes the paper.

2 The Model

2.1 The Markets

In a continuous time economy with a horizon from zero to infinity, there are two defaultablebond markets C and D, each with a continuum of zero-coupon defaultable bonds with facevalue of one and time to maturity τ , τ ∈ (0, T ]. Denote the time t prices of these bonds byP ct (τ) and P

dt (τ) respectively. The coupon rate is assumed to be zero so as to derive closed

form solutions. Assume all bonds on the two markets are issued by the same entity, so thata bond on market C has identical cash-flow as the bond with the same time to maturity onmarket D. Therefore, the model is in line with other limited-arbitrage models in derivingprice discrepancies between assets with identical cash-flows under market frictions. Whenapplying equilibrium results to explain real world phenomenon, I refer to bond market Cas the cash market, which corresponds to the corporate bond market, and bond market Das the derivative market, which corresponds to the CDS market plus default-free lending.The linkage between synthetic defaultable bond position and CDS plus default-free lendingis given at the end of this subsection.

Upon the exogenous default of the underlying entity, the bond holder loses L fractionof the bond’s market value. To keep the model tractable, I assume L is constant. Nowsuppose Nt is the counting process for the underlying bond’s default time T ′, which is adoubly-stochastic stopping time3. Nt = 0 if no default happens before time t and Nt = 1if default happens before time t. Here, I model Nt as a counting process with a intensityλ̃+ λt. In general:

Nt =∫ t0

(λ̃+ λs)ds+Mt (1)

3refer to Duffie (2004) for full explanation

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where Mt is a jump martingale that jumps to one at the time of default. The stochastic λtfollows the Ornstein-Uhlenbeck process:

dλt = κλ(λ̄− λt)dt+ σλdBλ,t (2)

I also assume that the money invested into money market account generates instantaneousreturn at an exogenous short rate rt, which also follows an Ornstein-Uhlenbeck process:

drt = κr(r̄ − rt)dt+ σrdBr,t (3)

In early literature such as Duffie (1999), the equivalence of defaultable bond and CDS plusdefault-free lending is best illustrated in the case of floating rate notes (FRN), i.e. thecash flow of a defaultable FRN is the same as the cash flow from writing CDS protectionplus the cash flow of a default-free FRN. Without using FRNs, the equivalence can beseen in the following way: Assume the zero-coupon defaultable bond holder gets the facevalue 1 dollar at maturity in the absence of default, but gets the default-free present valueof this 1 dollar and loses L fraction of the bond’s pre-default market value in the case ofdefault. As for the CDS, assume the CDS premium is paid up-front so that unless there’sa default, there’s no cash-flow between the two parties except at the origination of the con-tract. Then assume the CDS protection writer also invests in the money market accountan amount with future value of 1 dollar. Therefore, if there’s no default, the CDS writer’stotal payoff at maturity is the 1 dollar from the money market account. If there’s default,the CDS writer pays fraction L of the defaultable bond’s market value before default, andwithdraws from the money market account to get the present value of the 1 dollar. So theCDS writer’s total payoff is also default-free present value of 1 dollar minus L fraction of thebond’s market value before default. Therefore, the cash-flow from CDS writing and default-free lending replicates that of a defaultable bond. Hence I refer one of the two defaultablebond markets in the model as the derivative market, which corresponds to the CDS market.

When applying model’s predictions to real world phenomenon, I define negative basis trad-ing as buying cash bond C and selling derivative bond D, which corresponds to buyingcorporate bond through borrowing and buying CDS protection. In the contrary, positivebasis trading is defined as buying derivative bond D and selling cash bond C, which corre-sponds to shorting corporate bond and writing CDS protection.

2.2 The Agents and Demand Pressure

There are two type of agents, arbitrageurs and local investors. The continuum of risk-averse arbitraguers can trade any amount on the two bond markets, and therefore rendersthe prices arbitrage free. At any time t, the continuum of arbitrageurs are born in time tand die in t + dt, so arbitrageur’s utility is to trade off instantaneous mean and variance.The arbitrageurs have zero wealth when they’re born, so an arbitrageur’s time t wealthWt = 0. Denote the arbitrageur’s amount invested on the cash market for maturity τ byxct(τ) and the amount invested on the derivative market for maturity τ by x

dt (τ).

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Local investors are segmented into the two markets. Denote the cash market investors’amount invested by zct (τ), and the derivative market investors’ amount invested by z

dt (τ).

Assume both markets have zero supply. At equilibrium, the arbitrageurs and local in-vestors clear both markets, i.e. xct(τ) + z

ct (τ) = 0 and x

dt (τ) + z

dt (τ) = 0, which implies

xct(τ) = −zct (τ) and xdt (τ) = −zdt (τ).

A positive zit, i = c, d corresponds to local investors’ excess demand while a negative zit

corresponds to local investors’ excess supply. A negative zit means the arbitrageurs have apressure to buy and a positive zit means they have a pressure to short. In general, assumethe local investors’ demand are:

zit(τ) = θ̄i(τ) + θi(τ)zt (4)

dzt = κz((̄z)− zt)dt+ σzdBz,t (5)

where i = c, d. θ̄i(τ) and θi(τ) are functions of τ . Assume the three Brownian Motions Br,t,Bλ,t and Bz,t are independent.

In reality, large excess demand/supply from local investors exist on both the CDS mar-ket and the corporate bond market. The excess supply of bond can be the result fromregulation restricted fire-sale of bonds by insurance companies or simply a flight to qualityduring crisis while the excess demand of bond can come from large inflows into bond marketfunds. On the other hand, excess demand or supply on the CDS markets can come from thehedging demand from banks who hold bonds/loans or those who gain exposure to defaultrisk from other credit derivative market positions. Sometimes the local investors’ demandon the two markets can be exactly the opposite. As documented by Mitchell and Pulvino(2011) and also in other practitioners’ articles, some banks that hold corporate bonds andCDS protection on these underlying bonds unwound their positions after the Lehman Col-lapse in order to get more cash. Their trades introduce negative zct and positive z

dt with the

same absolute value. In this scenario, the arbitrageurs face exactly the opposite demandpressures from the two markets. A special case of my model investigates this scenario indetail in the following sections.

The presence of demand pressure has implications on asset pricing because the arbitra-guers, who provide liquidity by clearing the markets , need to be compensated for the riskexposure they get by doing so. As summarized by Gromb and Vayanos (2010), severalkinds of demand pressure effects on treasury bonds, futures and options markets have beenstudied.4 Without other frictions, demand pressure alone doesn’t generate pricing discrep-ancies between assets with identical cash-flows. My model of defaultable bonds differ fromthese models in the introduction of the time-varying funding costs, which work togetherwith demand pressure in causing pricing discrepancies.

4By Vayanos and Villa (2009), Naranjo (2008), and Garleanu, et.al. (2009) respectively

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2.3 Funding costs

In the real world, buying bonds through borrowing (repo) and short-selling through reverse-repo incurs funding costs in excess of the short rate. I assume that the exogenous fundingcosts are linear functions of λt:

hit(τ) = αi(τ)λt + δi(τ) i = c, d 0 < αi < L (6)

In the Appendix A I provide motivations for this assumption by solving for the optimal hair-cuts applied in repo and reverse-repo. Given exogenous interest rates, the cost of borrowingusing the defaultable bond as collateral is shown to be increasing in the default intensityrisk λt. This is because the amount that can be borrowed using the bond as collateral isdecreasing in λt. Therefore, when λt is higher, the borrower has to borrow more at theun-collateralized rate, and therefore incur more borrowing costs. The short-selling cost isalso shown to be increasing in λt. The short-seller will be asked to put more cash collat-eral to borrow the bond for sale when λt is higher because the bond is more risky whichmakes the short-seller more likely to default on the obligation to return the bond. As aresult, the short-seller lends more at collateralized rate, less at uncollateralized rate, there-fore earns less (incurs more short-selling costs). The above rationale is supported by theempirical evidence found by Gorton and Metrick (2010) that the repo hair-cut is increasingin the riskiness of collaterals. Mitchell and Pulvino (2011) also justify the above assumptionfrom a practitioner’s perspective. This funding cost models both the borrowing cost andshort-selling cost, so it reduces arbitrageur’s wealth regardless of the direction of her trades.

If trading on the CDS market is frictionless, then αd(τ) and δd(τ) can be set as zeros.However, although the CDS market used to have extremely low funding costs due to itslow margin requirement, it is not frictionless. During the 2007/08 crisis, counterparty riskin CDS contract led to the raise in margin requirement on the CDS market. Counterpartyrisk refers to the possibility that protection writers may default on their obligation to paythe buyers upon the default of the underlying, or the possibility that protection buyersdefault on their obligation to pay the CDS premium. CDS protection writers were asked toput more collaterals than before, while protection buyers were asked to pay CDS premiumup-front. These changes made CDS having comparable funding costs as trading corporatebonds. An alternative way for CDS protection writers to provide collateral that was widelyused in practice is for them to buy a CDS on their own names for the protection buyer froma third party. In this way, if the CDS writer defaults, the buyer can still get paid by the thirdparty. Therefore, the CDS protection writer incurs additional periodical cost that equalsto the CDS premium on themselves. If the CDS writer’s default can only be triggered bythe underlying’s default, then this additional cost should be increasing in the underlying’sdefault intensity. So it’s also reasonable to assume funding costs as an increasing functionof λt even when making the analogy between derivative market D and the CDS market.

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2.4 The Arbitrageurs’ Optimization Problem

The representative arbitrageur’s problem is:

maxxct ,x

dt

[Et(dWt)−γ

2V art(dWt)] (7)

dWt = [Wt −∫ T0xct(τ)dτ −

∫ T0xdt (τ)dτ ]rtdt

+∫ T0xct(τ)[

dP ct (τ)P ct (τ)

− LdNt]dτ +∫ T0xdt (τ)[

dP dt (τ)P dt (τ)

− LdNt]dτ

−∫ T0|xct(τ)|hct(τ)dτdt−

∫ T0|xdt (τ)|hdt (τ)dτdt (8)

In the above dynamic budget constraint, Wt is the representative arbitrageur’s wealth attime t and is assumed to be zero. γ is her risk aversion coefficient. Ignoring τ , xct is theamount of her cash bond trade and xdt is the amount of her derivative bond trade. So thefirst term on the right hand side of the dynamic budget constraint gives the amount earnedby her money market account. The arbitrageur’s wealth is also affected by changes in thecash and derivative bond prices, as well as jumps upon default. Additionally, trading onthe cash and derivative markets incurs funding cost at the rate of hct(τ) and h

dt (τ). These

costs reduce arbitrageur’s wealth regardless of the direction of her trades, so the costs aremultiplied by the absolute value of arbitrageur’s trade.

3 Main Theoretical Results

3.1 Understanding the First Order Conditions

I first derive the arbitrageur’s F.O.C.s and provide intuition and definition that facilitatediscussions in later subsections. Ignoring τ where it doesn’t cause confusion, the F.O.C.sare derived as follows.

Lemma 1. The Arbitrageur’s F.O.C.s are:

µct − rt − hct∂|xct |∂xct

− L(λ̃+ λt) = LΦJ,t + Σσj(∂P ct∂j

/P ct )Φj,t (9)

µdt − rt − hdt∂|xdt |∂xdt

− L(λ̃+ λt) = LΦJ,t + Σσj(∂P dt∂j

/P dt )Φj,t (10)

where µct and µdt are the expected returns of bond C and D, conditional on no default, and

ΦJ,t = γL∫ T0

[xct(τ) + xdt (τ)]dτ(λ̃+ λt) (11)

Φj,t = γσj∫ T0

[xct(τ)(∂P ct∂j

/P ct ) + xdt (τ)(

∂P dt∂j

/P dt )]dτ (12)

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j = λ, r, z are the market prices of risks.

Proof. see Appendix.

The left hand side of the F.O.C.s is the instantaneous expected excess return, hereafterEER, and the right hand side is the risk premium. The EER is the expected return of anasset in excess of the short rate and the funding cost. The EER equals the risk premiumwhich equals exposure to risk times the market price of risk. By construction, bond C andbond D have the same exposure to the jump risk of default, which carries market price ofrisk ΦJ,t. Their exposures to other market prices of risks Φj,t, j = λ, r, z depend on equilib-

rium terms ∂Pit

∂j /Pit , i = c, d. In later subsections, I solve for these exposures explicitly to

show that in the presence of time-varying funding costs, the two bonds can have differentexposure to the same factor, which leads them to have different total risk premium andhence different expected excess returns.

Subtracting the first F.O.C. from the second one gives the total expected excess returnof the so-called negative basis trade. In contrary, subtracting the second F.O.C. from thefirst one gives the expected excess return of positive basis trade. Formally, I make thefollowing definition.

Definition 1: Negative basis trading (nbt) is defined as buying bond C and selling bond Dfor the same time-to-maturity (which corresponds to buying corporate bond through borrow-ing and buying CDS protection); Positive basis trading (pbt) is defined as selling bond Cand buying bond D for the same time-to-maturity (which corresponds to shorting corporatebond and writing CDS protection plus lending).

EERnbt = Σσj(∂P ct∂j

/P ct −∂P dt∂j

/P dt )Φj,t (13)

EERpbt = Σσj(∂P dt∂j

/P dt −∂P ct∂j

/P ct )Φj,t (14)

The difference in the instantaneous expected returns of the two assets equals funding costdifference plus the expected excess return of basis trading. For instance,

µct − µdt = (hct − hdt ) + EERnbt (15)

Based on the F.O.C.s, equilibrium results are solved using the market clearing conditionthat on each market, the optimally derived quantities of the arbitrageurs plus those from thelocal investors equals zero. To solve the model in closed-form, I make further assumptionson the local investors demand and derive equilibrium results in the following two cases.

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3.2 Equilibrium under Constant Demand Pressure

3.2.1 Solutions

In this subsection, I assume that the local investors’ demand on the two markets are con-stants, i.e. θi(τ) = 0 and zit(τ) = θ̄

i(τ) = zi(τ), i = c, d. This assumption removes thedemand shock factor zt from the model, I therefore conjecture that the bond prices to takethe following form:

P ct (τ) = e−[Acλ(τ)λt+A

cr(τ)rt+C

c(τ)] (16)

P dt (τ) = e−[Adλ(τ)λt+A

dr(τ)rt+C

d(τ)] (17)

where Aij(τ) and Ci(τ), i = c, d, j = λ, r are functions of τ .

Lemma 2: Aij(τ) are solved as:

Acλ(τ) = {−αc(τ)|zc(τ)|zc(τ)

+ L− γL2∫ T0

[zc(τ) + zd(τ)]dτ}1− e−κλτ

κλ

Adλ(τ) = {−αd(τ)|zd(τ)|zd(τ)

+ L− γL2∫ T0

[zc(τ) + zd(τ)]dτ}1− e−κλτ

κλ

Acr(τ) =1− e−κrτ

κr

Adr(τ) =1− e−κrτ

κr(18)

Proof. see Appendix.

Prices on the two markets have the same coefficients for the short rate. When local investors’demand on the two markets are in the same direction, then prices on the two markets havethe different coefficients for the default intensity risk if funding costs on the two markets havedifferent sensitivity to the default intensity risk, i.e. αc(τ) 6= αd(τ); when local investors’demand on the two markets are in opposite directions, i.e. sign[zc(τ)] = −sign[zd(τ)], theprices on the two markets have different coefficients for λt even if the funding costs havethe same sensitivities to λt. Before deriving more results on Aiλ in later subsections on yieldcurve implications, I first calculate the expected excess returns of basis trading.

Proposition 1: The expected excess returns are:

EERnbt = σλ[αc(τ)|zc(τ)|zc(τ)

− αd(τ) |zd(τ)|zd(τ)

]1− e−κλτ

κλΦλ,t (19)

EERpbt = σλ[αd(τ)|zd(τ)|zd(τ)

− αc(τ) |zc(τ)|zc(τ)

]1− e−κλτ

κλΦλ,t (20)

Φλ,t = γσλ∫ T0

[zc(τ)Acλ(τ) + zd(τ)Adλ(τ)]dτ (21)

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Proof. see Appendix.

Corollary 1: The expected excess return of basis trading

• Under the following three scenarios, basis trading doesn’t earn non-zero expected excessreturn: 1) αc(τ) = αd(τ) = 0; 2) αc(τ) = αd(τ) 6= 0 and sign[zc(τ)] = sign[zd(τ)]; 3)zc(τ) = zd(τ) = 0.

• When capital is flowing away from both markets, or only moderate amount of capital isflowing into both markets, basis trading is profitable by buying the asset whose fundingcost has higher sensitivity to default intensity risk and selling the other.

• When huge amount of capital is flowing into both markets such that prices have positivesensitivities to default intensity, basis trading is profitable by buying the asset whosefunding cost is less sensitive to default intensity and selling the other.

• When sign(zc) = sign(zd), risk exposure of basis trading is increasing in |αc − αd|.

• When sign(zc) = −sign(zd), risk exposure of basis trading is increasing in (αc +αd).

• Size of basis trading EER is increasing in the volatility of default intensity.

The first point suggests that basis trading is a risky arbitrage that earns non-zero EERonly when both funding cost friction and market liquidity friction are present. Under sce-nario 1) and 2), either funding costs on the two markets have no sensitivities to λt or theyhave the same sensitivities and arbitrageur takes the same side of trade on the two markets,then the two assets carry the same exposures to the default intensity risk factor, whichresults in them carrying the same risk premia. Therefore, buying on one market and sellingon the other results in zero aggregate exposure to risk factors and basis trading earns zeroEER. In scenario 3), even if assets on the two markets may have different risk exposures todefault intensity risk, the market prices of risks are all zeros because the arbitrageur doesn’thave to provide liquidity in equilibrium and all EERs should be zero. Other than the abovementioned three scenarios, basis trading is expected to earn non-zero expected return inexcess of the funding costs, i.e. earning non-zero EER.

The second and third points concern the sign of basis trading EERs. When local investorson the two markets are all selling, bonds on both markets carry positive risk premia whichcompensates the arbitrageurs who are buying to provide liquidity. The arbitageur is ex-posed to more default intensity risk on the market with higher funding cost sensitivity toλt, therefore earns more defautl intensity risk premium on this market. So buying bond onthis market and selling on the other generates positive expected excess return. For instance,if there’s funding cost on corporate bond market but not on CDS market, i.e. αc > 0 andαd = 0, then if local investors are selling on both markets, the model predicts negative basistrading to be profitable even after deducting the funding costs. In contrary, when localinvestors on the two markets are all buying moderate amount, bonds on both markets carry

12

negative risk premium. The market whose funding cost has higher sensitivity to λt haslower sensitivity to the default intensity risk, therefore earns less negative risk premium. Sobuying bond on this market and selling on the other is expected to be profitable.

However, if local investors are buying too much on both markets, bonds also carry nega-tive default intensity risk premium but the market whose funding cost has lower sensitivityto λt now has lower sensitivity to the default intensity risk, therefore earns less negativerisk premium. So buying bond on this market and selling on the other is expected to beprofitable. The difference here with the moderately positive local investor demand case isthat when local investors are buying too much, bond prices become increasing in defaultintensity. This is true because of the assumption that bond holders retain (1−L) fraction ofbond’s market value upon default. The compensation to arbitrageur for providing liquidityin this case is for price to be increasing in default intensity so that she’s expected to gainmore upon default when default intensity is higher.

As mentioned above, the net exposure to default intensity risk depends on the fundingcosts’ sensitivities to λt. When the local demands on the two markets are in the samedirection, like in the three cases discussed above, the net exposure is determined by thedifference of αc and αd. But when the local investors’ demand are in opposite directions,the net exposure depends on the sum of αc and αd. The size of EER of basis trading is alsoincreasing in σλ, which is not surprising as σλ is positively priced in both the basis trading’sabsolute net exposure to default intensity risk and the market price of default intensity risk.

3.2.2 Implications on Credit Spread Term structure and the Predictability ofCredit Spread

Earlier empirical works such as Bedendo et.al.(2007) found that the slope of the creditspread term structure positively predicts future changes in credit spread. Such a resultwould still hold under my model when friction is low, but may not hold when there’s highlevel of market friction. To see this point in detail, I first make the following definitions.

Definition 2: Credit spread is the difference between the yield to maturity of a defaultablebond and the yield to maturity of a default-free bond of the same maturity. Denote yields tomaturity of the defaultable bond with time to maturity τ in by Y ct (τ), and the credit spreadby CSct (τ).

Y ct (τ) = −logP ct (τ)

τ(22)

There’s no default-free bond market in my model, but it is safe to conjecture that default-freebond prices are DFt(τ) = e−[Ar(τ)rt+C

df (τ)],5 so that yield to maturity of default-free bondcan be denoted by Y dft (τ) = −logDFt(τ)/τ . Because the defaultable bond and default-free

5for example, this can be derived from Vayanos and Vila (2009) by assuming arbitrageurs in their modelare risk-neutral.

13

bond have the same coefficient to short rate rt, therefore the credit spread term structureCSt(τ) has λt as the only time-varying risk factor.

CSt(τ) = Yt(τ)− Y dft (τ) =Acλ(τ)τ

λt +Cc(τ)τ

− Cdf (τ)τ

(23)

Bedendo et.al.(2007) run the following regression for credit spread of a certain maturityτ and found coefficient psi to be significantly positive, which suggests the slope of creditspread term structure positively predicts future credit spread changes.

CSt+∆τ (τ −∆τ)− CSt(τ) = ψ0 + ψ[CSt(τ)− CSt(τ −∆τ)] + �t+∆τ (24)

Proposition 2: Denote F (τ) = −αc(τ) |zc(τ)|

zc(τ) +L−γL2∫ T0 [z

c(τ)+zd(τ)]dτ , when ∆τ → 0,the regression coefficient ψ(τ) = F (τ)

1−F (τ)e−κλτ

• When there’s no friction, i.e. αc(τ) = 0 and zc(τ) = zd(τ) = 0, then ψ > 0 for sure.

• When local investors are selling large quantities and funding cost is very sensitive toλt, i.e. zc(τ) > 0 αc(τ) > 0 and both large, it is possible to have ψ < 0.

• ψ < 0 is more likely to happen to bonds with short time-to-maturity.

Proof. see Appendix.

Under standard set-up without the funding cost and demand pressure frictions, the conditionfor ψ > 0 simplifies to L < eκλτ , which is always satisfied as L < 1 by assumption. There-fore, the credit spread slope should always positively predict future credit spread changes,which has been documented by Bedendo et.al.(2007) among others. But new features inthis model suggests market frictions can distort this predictability. The coefficient ψ canbe either positive or negative depending on market conditions, so the positive predictabilitymay disappear under market conditions described in the second point of Proposition 2. Inthe empirical section, this point is supported by data during the crisis in 2008.

3.3 Equilibrium under Opposite Stochastic Demand Pressure

3.3.1 Solutions

To add more dynamics to the model, I make an additional assumption that the demand fromlocal investors on the cash and derivative markets are exactly the opposite, i.e. −zdt (τ) =zct (τ). This is equivalent to assuming:

6

zct (τ) = θ̄(τ) + θ(τ)zt (25)zdt (τ) = −θ̄(τ)− θ(τ)zt (26)

6If I assume the two demand pressures to be exactly the opposite and price-elastic, the equilibrium pricescan still be solved in closed-form, but takes very complicated forms that makes discussions on assets returnsunclear, so results for that case are not presented.

14

For the two scenarios: 1) θ̄(τ) very positive and 2) θ̄(τ) very negative, the model hasclosed-form solution. Similarly, conjecture that prices are exponential affine in risk factors:

P ct (τ) = e−[Acλ(τ)λt+A

cr(τ)rt+A

cz(τ)zt+C

c(τ)] (27)

P dt (τ) = e−[Adλ(τ)λt+A

dr(τ)rt+A

dz(τ)zt+C

d(τ)] (28)

Lemma 3a: For very negative θ̄(τ) and negative θ(τ):

Acλ(τ) = [αc(τ) + L]

1− e−κλτ

κλ

Adλ(τ) = [−αd(τ) + L]1− e−κλτ

κλ

Acr(τ) =1− e−κrτ

κr

Adr(τ) =1− e−κrτ

κr

Acz(τ) = −γσ2λAcλ(τ)∫ T0θ(τ)[αc(τ) + αd(τ)]

1− e−κλτ

κλdτ

1− e−κ∗zτ

κ∗z

Adz(τ) = −γσ2λAdλ(τ)∫ T0θ(τ)[αc(τ) + αd(τ)]

1− e−κλτ

κλdτ

1− e−κ∗zτ

κ∗z

where κ∗z is the unique solution to:

κ∗z = κz + γσ2z

∫ T0θ(τ)[Acz(τ)−Adz(τ)]dτ (29)

Lemma 3b: For very positive θ̄(τ), positive θ(τ) and very positive κz:

Acλ(τ) = [−αc(τ) + L]1− e−κλτ

κλ

Adλ(τ) = [αd(τ) + L]

1− e−κλτ

κλ

Acr(τ) =1− e−κrτ

κr

Adr(τ) =1− e−κrτ

κr

Acz(τ) = γσ2λA

cλ(τ)

∫ T0θ(τ)[αc(τ) + αd(τ)]

1− e−κλτ

κλdτ

1− e−κ∗zτ

κ∗z

Adz(τ) = γσ2λA

dλ(τ)

∫ T0θ(τ)[αc(τ) + αd(τ)]

1− e−κλτ

κλdτ

1− e−κ∗zτ

κ∗z

where κ∗z is the unique solution to:

κ∗z = κz + γσ2z

∫ T0θ(τ)[Acz(τ)−Adz(τ)]dτ (30)

15

Proof. see Appendix.

Once again, prices on the two markets have the same coefficients for the short rate. But sincelocal investors’ demand on the two markets are in opposite directions, the prices on the twomarkets have different coefficients for λt and zt even if the funding costs on the two marketshave same sensitivities to λt. The calculation of expected excess return is now complicatedby the inclusion of zt as the EER of basis trading has exposure to two sources of risk premia.

Proposition 3: The expected excess returns of basis trading:

EERnbt = −γσ2λGλ(τ)∫ T0Gλ(τ)zct (τ)dτ − γσ2zGz(τ)

∫ T0Gz(τ)zct (τ)dτ

EERpbt = −EERnbt (31)

Gλ(τ) = [αc(τ) + αd(τ)]1− e−κλτ

κλ

Gz(τ) = −γσ2λGλ(τ)∫ T0Gλ(τ)θ(τ)dτ

1− e−κ∗zτ

κ∗z(32)

• EER of basis trading is zero if αc(τ) = αd(τ) = 0.

• sign(EERnbt) = −sign(EERpbt) = −sign(zct ) The market on which local investorsare selling has higher EER, taking long position on this market and short position onthe other market is expected to earn profit in excess of funding costs.

• The size of expected excess return of basis trading is increasing in αi, σj and |zct (τ)|.

Proof. see Appendix.

The first point corresponds to the point made in the previous subsection. If the fund-ing costs are constants that have no sensitivities to risk factors such as λt, then the twoassets have exactly the same exposure to the same risk factor. Even in the presence ofmarket liquidity friction represented by zct (τ) = −zdt (τ) 6= 0, basis trading still earns zeroEER as the two assets will have the same EERs.

The sign of basis trading EER is completely determined by the sign of local investors’sdemand on the cash market. Under the assumption about local investors’ demand, thearbitrageur is always taking opposite positions on the two markets. Without funding costs,the two assets carry exactly the same exposure to risk factors. Then the arbitrageur is leftwith zero aggregate exposure to any risk factors, therefore all market prices of risk will bezero. In that case, bonds on both markets and basis trading will all earn zero risk premiaand hence zero EER. However, due to the existence of funding costs which are functionsof λt, the two assets carry different exposures to default intensity risk and demand shockrisk. The arbitrageur’s aggregate exposures to these two risks are non-zero, hence marketprices of risks for these two factors are non-zero. Therefore, basis trading is expected to earn

16

non-zero EER and the sign of the EER is determined by the sign of local investors’ demand.

Corollary 3: The expected excess return of bond is positive no matter if local investors arebuying or selling.

• When zct < 0: EERc > EERd > 0

• When zct > 0: EERd > EERc > 0

The result that if zit > 0 then sign(EERi) = sign(zit) is against conventional wisdom.

The usual conclusion on the pricing implication of demand shocks is that when there’s excessdemand, those who provide the liquidity will only agree to sell at a high price in equilibriumso as to earn something extra, which is the compensation for providing liquidity. Therefore,the instantaneous expected excess return should have the opposite sign of the local investorsdemand. However, with the presence of the other market, the arbitrageur in this model iswilling to provide liquidity at a loss on the market that she has to short because she canearn more on the other market. By doing so, the arbitrageur doesn’t correct but insteadmagnifies the price deviation, or in other words, creates a bubble.

3.3.2 Implications on Basis

Definition 3: Basis is the difference between the yield to maturity of bond on market Dminus the yield to maturity of bond on market C with the same time to maturity.

Basis(τ) = [− logPdt (τ)τ

]− [− logPct (τ)τ

]

= [Adλ(τ)τ

− Acλ(τ)τ

]λt + [Adz(τ)τ

− Acz(τ)τ

]zt +Cd(τ)τ

− Cc(τ)τ

(33)

Under conventional wisdom, the negative Basis implies negative basis trading is profitablewhile positive Basis implies positive basis trading is profitable. But the value of Basis is notvery meaningful in the presence of funding costs. As shown in the previous subsection, inthe presence of market frictions in the model, the sign of basis trading EER is determinedjust by the sign of local investors’ demand. The value of Basis depends on the values of λt,zt and τ . The solution of Ci(τ) also makes the discussion very complicated. However, thesensitivities of Basis to the risk factors can be derived clearly:

Proposition 4: The sensitivities of Basis to risk factors are:

• When zct < 0: ∂Basis∂λt < 0, and∂Basis

∂zt> 0.

• When zct > 0: ∂Basis∂λt > 0, and∂Basis

∂zt> 0.

Proof. see Appendix.

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3.3.3 Implications on Term Structure

The coefficients of λt and zt in bond prices are increasing in the bond’s time to maturityτ . If assume the funding cost’s sensitivity to λt is the same across τ , then basis trading onunderlyings of longer time to maturity has larger net exposure to the risk factors than basistrading on underlyings of short time to maturity. Therefore, the size of basis trading EERis increasing in τ . Together with the property of the sign of basis trading EER, I derive thefollowing Proposition:

Proposition 5: Assume αc(τ) = αc and αd(τ) = αc, then the term structures of expectedexcess returns are:

• When zct < 0: ∂EERnbt

∂τ > 0, and∂EERpbt

∂τ < 0.

• When zct > 0: ∂EERnbt

∂τ < 0, and∂EERpbt

∂τ > 0.

• The expected excess profit of basis trading is increasing in the time to maturity of basistrading instruments.

Proof. see Appendix.

As in the previous subsection, Yt(τ) denotes the time t yield to maturity of bond withtime to maturity τ . The collection of Yt(τ) gives the yield curve of corporate bonds. Asshown in the following Proposition 6, the slope of corporate bond yield curve ∂Yt(τ)/∂τ isdecreasing in λt, but the degree of the decreasing relationship depends on local investors’demand.

Proposition 6: The sensitivity of yield curve slope to default intensity risk is ∂2Yt(τ)/(∂τ∂λt) =[A

cλ(τ)

τ ]′ < 0.

• The slope of corporate bond yield curve is decreasing in λt.

• The decreasing effect is stronger when zct < 0 than when zct > 0.

Proof. see Appendix.

4 Empirical Study

I apply the theoretical results on CDS basis trading and credit spread to offer some empiricalevidence for the model. A main conclusion from the model is that the co-existence offrictions in funding cost and market liquidity turns basis trading into a risky arbitrage.To test this point, I run a set of regressions to test whether basis trading is exposed tosystematic factors. I also test whether certain parts of the EER formula from the modelhave any predictive power on abnormal basis trading profits after controlling for systematicfactors. I also test several comparative statics results from the model, such as the increasing

18

relationship between certain variable/parameters and the size/risk of basis trading profits,as well as the term structure of basis trading profits and the relationship between CDSbasis and corporate bond market trading volume. Moreover, I test the predictability ofcredit spread term structure on future credit spread changes to support the points made inProposition 2. I focus on data from 2007 to 2009, a period which has not only persistentlynegative CDS basis, but also high funding costs and poor market liquidity. In general, theempirical results are consistent with the model’s predictions.

4.1 Data and Variables

I collected various CDS and corporate bond indices data from Markit, individual CDS andcorporate bond data from Bloomberg and TRACE, various kinds of interest rates data fromthe Federal Reserve web-site and Fama-French three factor data from Kenneth French’s web-site. Daily observation starts as early as the beginning of 2007 and ends at the end of 2009.

I calculate the realized excess holding period return (RER) of negative basis trading as:

RERnbtt,t+k = ReturnCBondt,t+k −ReturnCDSt,t+k −NetHoldingCostt,t+k (34)

BasisTradingProfits = |RERnbtt,t+k| (35)

Since my main results are on the instantaneous expected excess return or expected returns,I mainly focus on k =1-day and 1-week. By definition, the realized excess return of doingpositive basis trading is the opposite of that of negative basis trading. The realized excessreturn of doing negative basis trading between time t and t+ k is calculated as the returnfrom holding corporate bond index minus the return from holding CDS index, and finallysubtract net funding costs. The model implies that the return of positive basis trading isthe opposite of negative basis trading, therefore the absolute value of negative basis tradingRER is used as the profits of basis trading. For the corporate bond index, I first collectthe 1-10yrs Markit iBoxx USD Domestic Corporates AAA, AA, A and BBB indices7, andthen create a value-weighted corporate bond index by taking the average return of thesefour indices weighted by their market values. Holding period return of the corporate bondindex is calculated as change of the corporate bond index for each holding period dividedby the index value at the beginning of the holding period. The CDS index return is calcu-lated from the Markit CDX North America Investment Grade Excess Return Index, whosecomponents have maturities of 5-year.

The net funding cost is the funding cost of corporate minus the funding cost of CDS. Iproxy the funding cost of corporate as:

BondHoldingCostt,t+k = Σt+k−1s=t [(1− haircut) ∗ Tbills + haircut ∗ LIBORs] (36)

This assumption implies investors can fund the one minus hair-cut fraction of their corpo-rate bond purchase at the collateralized rate, and the hair-cut fraction at uncollateralized

7average maturity around 5-year

19

rate. The funding cost is increasing in the hair-cut, the difference between collateralizedand uncollateralized rate. Ideally, the hair-cut input should be time-varying as well, how-ever, daily data on hair-cut is very difficult to get. Therefore, I applied different values ofhair-cut for different sub-periods in the sample based on the average hair-cut data describedin Gorton and Metrick (2010). The empirical evidence found in later part of the paper isnot very sensitive to different hair-cut assumptions. I calculate funding cost for each dayand sum up to get funding cost over a period.

The funding cost of CDS is approximated by the average CDS premium on financial in-stitutions. During the crisis, the main friction on CDS market is the counterparty risk,especially from the protection writers’ side. A protection buyer would suffer from the jointdefault of the underlying entity and the protection writer. In order for the protection buyerto be willing to trade at the CDS premium without counterparty risk, the protection buyerrequires the protection seller to buy a CDS on the seller herself for the buyer, so that in theevent of joint default, the protection buyer can at least get paid from the CDS on the pro-tection seller. Therefore, I calculated the average CDS premium on financial institutions,and divide this premium according to the holding periods to reflect the funding cost. It isnot surprising to see the funding cost of CDS being close to zero before the crisis, but verylarge during the crisis. After the Lehman collapse, the funding cost of CDS is even higherthan the funding cost of corporate bond, which is consistent with both empirical evidencefound by others and observation made by practitioners.

I also collect Markit iBoxx USD Domestic Corporate rating indices for 1-3 years, 3-5 years,1-5 years, 5-7 years, 7-10 years and 5-10 years of maturity and use the asset swap spread ofthese indices to build the credit spread term structure. To test the term structure propertyof basis trading profits, I further calculated RER of negative basis trading on 2 year, 5 yearand 9 year underlyings using individual CDS and corporate bond data.

As can be seen from the discussion of borrowing cost, the hair-cut in the borrowing costis multiplied by LIBOR-Tbill. Comparing with the model assumption, if hair-cut is linearin λt, then α is a multiple of LIBOR-Tbill, which is the TED spread. Therefore, α in themodel is empirically proxied by TED spread. The sign of local investors’ demand is difficultto measure, but the absolute value of local investors’ demand on the cash market can beproxied by the corporate bond market trading volume, hereafter TV, which is collected fromTRACE. I also use the contemporaneous volatility of asset swap spread (hereafter ASW)of Liquid Corporate Bond Index from Markit to proxy for the volatility of λt since it’s lessaffected by interest rate and market liquidity.

4.2 Time-series Tests on Basis Trading Profits

Hypothesis 1: Basis trading profit in excess of arbitrage costs contains systematic riskpremia

20

The model implies that the expected excess return of basis trading contains compensa-tion for the exposure to risk factors. Therefore, the realized excess return (or return) ofbasis trading might be explained by systematic risk factors. However, the model suggeststhat negative basis trading’s exposure to risk factors is time-varying. Depending on thesign of local investors demand and relative sensitivity of funding cost on λt, negative basistrading can have positive or negative loadings on the risk premia. Thus it is not appropriateto test the negative basis trading return on systematic factors directly. It is more reasonableto test the absolute negative basis trading excess return (in other words, the profit of doingbasis trading, which can come from either negative basis trading or positive basis trading)on the absolute values of systematic risk premia. The coefficient estimates obtained fromsuch a regression gives the absolute exposure of basis trading on systematic factors. If basistrading profit in excess of funding costs represents compensation from taking systematicrisk, then the regression results will have significant coefficient estimates for systematic riskfactors. I run the following two regressions to test the above Hypothesis 1:

Regression A

|RERnbtt,t+k| = β0 + β1(LIBOR− FFR)t,t+k + β2(TED ∗ASW )t,t+k + �A,t (37)

Regression B

|RERnbtt,t+k| = β0+Σ5i=1βi|FF5(i)t,t+k|+β6(LIBOR−FFR)t,t+k+β7(TED∗ASW )t,t+k+�B,t(38)

Because the funding costs in the calculation of basis trading profits may not be accurateenough, I include two terms to control for potential mis-measurement of funding costs inRegression A to see if funding costs can explain the realized profit of basis trading, whichis given by the absolute value of RER of negative basis trading. The two control terms areLibor-FFR summed up over the holding period, where FFR is the federal funds rate, andTED*ASW summed up over the holding periods, which accounts for the effect from the mis-measurement of the hair-cut. In Regression B, I added the absolute value of conventionalFama-French five factors FF5(i), i = 1, 2, 3, 4, 5, as explanatory variables. Apart from theusual Fama-French three factors, the DEF factor is the liquid corporate bond index returnminus the T-Note index return of similar maturity8, and the TERM factor is the T-Notereturn minus the T-Bill return from Kenneth French’s website.

Hypothesis 2: Interaction of funding liquidity and market liquidity predicts abnormalbasis trading profit

According to the formula in the model, the expected excess profit of basis trading con-tains two terms that can be proxied by TED2 ∗ TV and FFR2 ∗ TV . Moreover, the modelalso suggests that the absolute exposure of basis trading to risk factors is increasing in αc.In the model, αc captures the difference between uncollateralized and collateralized rates.

8calculated based on Markit iBoxx 1-10yrs USD Domestic Treasury Index

21

Empirically, αc can be proxied by the TED spread, so the realized excess return of basistrading might also be explained by TED spread times systematic risk factors. Therefore, Icarry out the following two regressions:

Regression C

|RERnbtt,t+k| = β0 + Σ5i=1βi|FF5(i)t,t+k|+ β6(LIBOR− FFR)t,t+k + β7(TED ∗ASW )t,t+k+β8TED2t ∗ TVt + β9FFR2t ∗ TVt + �C,t

(39)

Regression D

|RERnbtt,t+k| = β0 + Σ5i=1βi|FF5(i)t,t+k|+ β6(LIBOR− FFR)t,t+k + β7(TED ∗ASW )t,t+k+β8TED2t ∗ TVt + β9FFR2t ∗ TVt + Σ14j=10βjTEDt ∗ |FF5(j − 9)t,t+k|+ �D,t

(40)

The basis trading profits have very different levels of volatility in different sub-periods of2007-2009. Therefore, I performed the above mentioned four regressions on three sub-periods separately. The first period is from 07/2007 to 02/2008, the first stage of the crisis,before the collapse of Bear Stern. The second period is from 03/2008 to 03/2009, whichcorresponds to the period when the crisis is the most severe. The last period is from 04/2009to 09/2009, when markets start to recover. I run these regressions for 1-day and 1-weekholding periods respectively. Due to serial correlation, I report OLS regressions results withNewey-West adjusted t-stats in Table 1-3.

In general, regression results support both Hypothesis 1 and 2. Basis trading profits are notjust compensation for funding costs, but contains compensation for exposures to systematicrisk factors. Using factors representing potential mis-measurements of funding costs cannotfully explain basis trading profits. Adding systematic factors (Fama-French five factors) helpexplaining basis trading profits, which has significant exposures to some of these factors.However, in most cases, there’s still significant abnormal returns from Regression B whichhas funding cost factors plus Fama-French five factors as explanatory variables. Addingsome model explained factors, in the form of interaction of TED and FFR squared timescorporate bond market trading volume, the intercepts from Regression C is no longer sig-nificant. The significance of these interaction terms preserves in some cases even when theproducts of TED and Fama-French 5 factors are added. For some cases, adding those termsbetter explains basis trading profits, which is consistent with the idea that the absolute ex-posure to systematic factors are increasing in the difference between un-collateralized andcollateralized rates. The highest adjusted R-sqaureds are from Regression C or RegressionD.

22

4.3 Term Structure of Basis Trading Profit

Proposition 5 predicts that basis trading profit is increasing in the time to maturity of theunderlying bond. I compared the profits of basis trading on underlyings with 2 years, 5years and 9 years time to maturity. I list the average 1-day, 1-week and 1-month holdingperiod profits for these maturities in Table 4, which clearly shows that basis trading onlonger maturities earn higher profits. This result is also shown by the cumulative 1-weekprofits of basis trading on these maturities in Figure 2. Basis trading on longer maturitieshave higher cumulative profits, and the gaps between the lines are also increasing over time,which is consistent with the prediction that basis trading profit is increasing in the time tomaturity of the underlying bond.

4.4 Comparative Statics on Basis Trading and the CDS Basis

The model yields several testable comparative statics results. The purpose here is to showthat more severe market frictions make basis trading more risky, hence earning higher re-turn. To be specific, I tested the following predictions:

Hypothesis 3:

• The profit of basis trading is increasing in αc and σλ.

• Basis trading is risky, the profit of basis trading is increasing in the volatility of basistrading return.

• The volatility of basis trading return is increasing in αc, which is proxied by TEDspread.

The volatility of basis trading return is the next 90-day volatility of the negative basistrading RER. To test the comparative statics results, I sort the time-series of the abso-lute value and volatility of basis trading returns of different holding periods based on theircorresponding TED and default intensity volatility values. For instance, I assign each datein the sample period into 5 groups according to the TED spread value at each date, thefirst group contains dates with the lowest TED spread values, the 5th group contains dateswith the highest TED spread values. Then I calculate the median value of basis tradingprofit for each group, and report in a table to see if the group with higher TED spread alsohas larger basis trading profit. I also sort basis trading profit into negative basis tradingvolatility groups. Results are summarized in Table 5, in which each panel provides resultof each comparative statics. In general, the results support Hypothesis 3 very well.

Using the similar approach, I test the prediction from Proposition 4 that CDS basis isincreasing in the demand shock on corporate bond market. The results in Proposition 4are given conditional on the sign of local investors’ demand on cash market. Together withthe result on the sign of basis trading returns and the assumption that basis is more likelyto be negative when negative basis trading is profitable and vice versa, it is reasonable

23

to conjecture that the absolute value of CDS basis is increasing in the absolute value oflocal investors’ demand on corporate bond market, which is proxied by the corporate bondmarket trading volume. Table 6 shows that those dates with larger corporate bond markettrading volume has larger absolute basis. Therefore, the following hypothesis is also sup-ported by the data.

Hypothesis 4: The absolute value of CDS basis is increasing in corporate bond markettrading volume.

4.5 Predictability of Credit Spread Term Structure Slope on Future CreditSpread Changes

Hypothesis 5:

• Credit spread term structure slope positively predicts future credit spread changes whenfrictions are small.

• Credit spread term structure slope cannot predict future credit spread changes wheninvestors are selling corporate bonds and funding cost has high sensitivity to defaultintensity. This poor predictability is more likely to be seen on short maturities.

I carry out the following regressions to test this hypothesis:

CSt+k − CSt = ψ0 + ψSlopet + �t (41)

I used 4 sets of dependent variables and 4 sets of independent variables. For instance, for Set1, I use the 1-5 years grade A corporate bond index asset swap spread as the CS variable.For this dependent variable, I use the 3-5 years grade A corporate bond index asset swapspread minus the 1-3 years grade A corporate bond index asset swap spread as the Slopevariable. For this set, the dependent variable proxies the future change in credit spreadof a 3-year corporate bond, while the independent variable proxies the difference of creditspreads of a 4 year corporate bond and a 2 year corporate bond issued by the same entity asthe 3-year bond. The independent variable thus proxies the term structure of credit spreadat 3 year. A full list of variables for other Sets are listed in Table 7, which also reportsregression results. I test for k =5days and 15days respectively and run the regressions onthe three sub-periods defined in previous subsections.

The results are in favor of Hypothesis 5. For sub-periods 1 (07/2007 to 02/2008) andsub-periods 3 (04/2009-09/2009) which corresponds to periods with less market frictions,the positive predictability of the independent variable on dependent variable is found inmost cases, a result consistent with Bedendo et.al.(2007). But in sub-period 2 (03/2008-03/2009) when market frictions are high, the predictability is lost for Set 1 and Set 3, whichcorrespond to credit spread term structure at approximately 3 year, while the predictabil-ity is still significant for Set 2 and Set 4, which correspond to longer time to maturity at

24

approximately 7.5 year. Such findings support the predictions from Proposition 2, whichstates the regression coefficient ψ is positive when friction is low but can take negativevalues when friction is high. Therefore, it’s not surprising to find that the predictabilityis lost during sub-period 2, in which severe frictions can drive the coefficient negative attimes.

4.6 Robustness Checks

The main results are not affected when using alternative funding cost proxies. To test if theresults are sensitive to the construction of the Markit indices, I also construct alternativenegative basis trading returns using individual CDS and corporate bond data. Regressionresults using these returns as dependent variables are consistent with results in the previoussection. But individual CDS and corporate bond data are less reliable than the Markitindices, so I still report results using the Markit indices as the main results.

5 Conclusion

The theoretical part of this paper proposes a continuous-time limited arbitarge model toshow how time-varying funding costs and demand pressure jointly create risky arbitrageopportunities on markets with identical assets. The interaction of arbitrageurs’ risk aversion,funding illiquidity and market illiquidity results in one assets being more sensitive to riskfactors that have non-zero market prices of risk than another asset with identical cash-flowdoes. Taking opposite positions on the two markets therefore has non-zero risk exposureand hence non-zero expected excess return. The model is applied to analyze CDS basistrading in closed-form and generate a number of testable predictions. Empirically, I findevidence for the exposure of basis trading to systematic risks as the Fama-French MKT, DEFand TERM factors are significant in explaining realized basis trading profits. Factors in theform of TED spread (and Federal Fund Rate) sqaured times corporate bond market tradingvolume have some short-term predictive power on abnormal basis trading profits. The sizeand volatility of realized basis trading profit is increasing in the severity of market frictions,while basis trading profits are increasing in the time to maturity of the underlying bond. Aspredicted by the model, under high levels of market frictions, the positive predictability ofcredit spread term structure slope on future changes in credit spread is no longer existing.

25

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3. Berndt, Antje, Rohan Douglas, Darrell Duffie, Mark Ferguson, and David Schranz,2009, Measuring default risk premia from default swap rates and EDFs, Workingpaper.

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15. Ellul, Andrew, Chotibnak Jotikasthira, and Christian T. Lundblad, 2009, RegulatoryPressure and Fire Sales in the Corporate Bond Markets, working paper, IndianaUniversity and UNC.

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21. Garleanu, Nicolae and Lasse Heje Pedersen, 2009, Margin-based Asset Pricing andDeviation from the Law of One Price, 2009, Working Paper.

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24. Greenwood, Robin and Dimitri Vayanos, 2010, Bond Supply and Excess Bond Re-turns, working paper, Havard and LSE.

25. Gromb, Denis and Dimitri Vayanos, 2010, Limits of Arbitrage: The State of theTheory, Annual Review of Financial Economics, 2010, 2, 251-275.

26. Han, Song, and Hao Zhou, 2007, Effects of Bond Liquidity on the Non-default Compo-nent of Corporate Bond Spreads: Evidence from Intraday Transactions Data, Workingpaper, Federal Reserve Board.

27. Houweling, Patrick, and Ton Vorst, 2005, Pricing default swaps: Empirical evidence,Journal of International Money and Finance, 24, 1200-1225.

28. Houweling, Patrick, Albert Mentink, and Ton Vorst, 2005, Comparing possible proxiesof corporate bond liquidity, Journal of Banking and Finance, 29, 1331C1358.

29. Huang, Jing-zhi, and Ming Huang, 2003, How much of the corporate-Treasury yieldspread is due to credit risk? Working paper, Penn State University.

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30. Hull, John, Mirela Predescu, and Alan White, 2004, The relationship between creditdefault swap spreads, bond yields, and credit rating announcements, Journal of Bank-ing and Finance 28, 2789-2811.

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36. Longstaff, Francis A., Sanjay Mithal, and Eric Neis, 2005, Corporate yield spreads:Default risk or liquidity? New evidence from credit-default swap market, Journal ofFinance 60, 2213-2253.

37. Mitchell, Mark, and Todd Pulvino, 2011, Arbitrage Crashes and the Speed of Capital,Journal of Financial Economics, Forthcoming.

38. Naranjo, Lorenzo, 2008, Implied Interest Rates in a Market with Frictions, WorkingPaper. NYU Stern.

39. Nashikkar, Amrut, and Marti Subrahmanyam, 2006, Latent liquidity and corporatebond yield spreads, Working paper, NYU Stern.

40. Pan, Jun, and Kenneth J. Singleton, 2005, Default and recovery implicit in the termstructure of sovereign CDS spreads, Working paper, MIT and Stanford.

41. Tang, Dragon-Yongjun. and Hong Yan, 2007, Liquidity and Credit Default SwapSpreads. Working Paper. University of South Carolina and Kennesaw State Univer-sity.

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43. Vayanos, Dimitri and Jean-Luc Vila, 2009, A Preferred-Habitat Model of the TermStructure of Interest Rates. Working Paper, London School of Economics and MerrillLynch.

28

44. Vayanos, Dimitri and Jiang Wang, 2009, Liquidity and Asset Prices: A Unified Frame-work, working paper, LSE and MIT.

45. Yu, Fan, 2003, Dependent Default in Intensity-Based Models, Working Paper, Clare-mont Mckenna College.

46. Zhu, Haibin, 2006, An Empirical Comparison of Credit Spreads between the BondMarket and the Credit Default Swap Market, Journal of Financial Services Research29, 211-235.

29

6 Appendix A: Motivation for the Funding Costs Function

6.1 Borrowing Costs

Assume there’s a continuum of competitive cash lenders lends yt cash for 1-dollar worth ofbond.

maxyt

[Et(dwt)−γ̄

2V art(dwt)] (42)

dwt = (wt − yt)rtdt+ yt(rt + s)dt+ [(1− L)− yt]dN̄t (43)

where N̄t is counting process for the borrower’s default, the intensity of N̄t is f(λt) whichis increasing in λt. s > 0 is the exogenous rate above short-rate asked by the lender forlending using the risky bond as collateral.

y∗t = s/[γ̄f(λt)]− 1/γ̄ + (1− L) (44)

Therefore y∗t is decreasing in f(λt), thus decreasing in λt. The borrower borrows y∗t fraction

of her bond purchase at rt+s and 1−y∗t fraction at rt+u, where u > 0 reflects the differencebetween un-collateralized rate and risk-free short rate. So the borrow cost in excess of rt is:

ht = y∗t (rt + s) + (1− y∗t )(rt + u)− rt = u− (u− s)y∗t (45)

which is a decreasing function of y∗t . Since y∗t is decreasing in λt, the borrow cost ht is

increasing in λt. With careful choice of the exogenous f(λt), the borrow cost has the linearfunctional form of αλt + δ as in the model.

6.2 Short-selling Costs

Assume there’s a continuum of competitive bond lenders requires yt cash for 1-dollar worthof bond.

maxyt

[Et(dwt)−γ̃

2V art(dwt)] (46)

dwt = (wt + yt)rtdt+ yt(rt − s)dt+ (yt − 1)dÑt (47)

where Ñt is counting process for the short-seller’s default, the intensity of Ñt is g(λt) whichis decreasing in λt. s > 0 is the exogenous special repo rate offered by the bond lender onthe cash collateral.

y∗t = s/[γ̃g(λt)] + 1/γ̃ + 1 (48)

Therefore y∗t is decreasing in g(λt), thus increasing in λt. The short-seller lends y∗t fraction

of her bond sales at rt − s and 1− y∗t fraction at rt. So her short selling cost is:

ht = rt − [y∗t (rt − s) + (1− y∗t )rt] = sy∗t (49)

which is a increasing function of y∗t . Since y∗t is also increasing in λt, the short-selling cost

ht is increasing in λt. With careful choice of the exogenous g(λt), the short-selling cost hasthe linear functional form of αλt + δ as in the model.

30

7 Appendix B: Proofs of Lemma and Proposition

7.1 Proof of Lemma 1

In the most general set-up, there’re 4 sources of uncertainties, one is the jump at default,characterized by Nt, and three others as the Brownian Motions in the default intensity λt,short rate rt and local investors’ demand shock zt, i.e. Bλ,t, Br,t and Bz,t. The dynamicof Nt only enters into play through λt, so I can rewrite P dt (τ) as P

dt (τ, λ, r, z) and P

ct (τ) as

P ct (τ, λ, r, z). Assuming all three Brownian Motions Bλ,t, Br,t and Bz,t are independent, Iapply Ito’s lemma to write dP ct (τ, λ, z) and dP

dt (τ, λ, z) as:

dP ct (τ, λ, r, z) = µct(τ)P

ct dt+ σλ

∂P

∂λdBλ,t + σr

∂P

∂rdBr,t + σz

∂P

∂zdBz,t (50)

dP dt (τ, λ, r, z) = µdt (τ)P

dt dt+ σλ

∂V

∂λdBλ,t + σr

∂V

∂rdBr,t + σz

∂V

∂zdBz,t (51)

where µct and µdt are the expected returns of the bond C and bond D, conditional on

no default. Entering the above dynamic into the arbitrageur’s optimization problem anddropping τ , I derive the F.O.C. as in Lemma 1.

7.2 Proof of Lemma 2

Applying Ito’s lemma, the dP dt /Pdt and dP

ct /P

ct terms can be re-written as:

dP ct (τ)P ct (τ)

= µct(τ)dt−AcλσλdBλ,t −AcrσrdBr,t (52)

dP dt (τ)P dt (τ)

= µdt (τ)dt−AdλσλdBλ,t −AdrσrdBr,t (53)

where, omitting τ , the instantaneous expected returns conditional on no default are:

µct = −Acλκλ(λ̄− λt)−Aczκr(r̄ − rt) +Acλ′λt +Acr

′rt + Cc′ +12Acλ

2σ2λ +12Acr

2σ2r (54)

µdt = −Adλκλ(λ̄− λt)−Adrκr(r̄ − rt) +Adλ′λt +Adr

′rt + Cd

′+

12Adλ

2σ2λ +

12Adr

2σ2r (55)

Substitute the above into the dynamic budget constraint, the arbitrageur’s F.O.C.s are:

µct(τ)− rt − hct(τ)|xct(τ)|xct(τ)

− Lλt = LΦJ,t − σλAcλ(τ)Φλ,t − σrAcr(τ)Φr,t (56)

µdt (τ)− rt − hdt (τ)|xdt (τ)|xdt (τ)

− Lλt = LΦJ,t − σλAdλ(τ)Φλ,t − σrAdr(τ)Φr,t (57)

where

ΦJ,t = γL∫ T0

[xdt (τ) + xct(τ)]dτλt (58)

31

Φλ,t = γσλ∫ T0

[−xdt (τ)Adλ(τ)− xct(τ)Acλ(τ)]dτ (59)

Φr,t = γσr∫ T0

[−xdt (τ)Adr(τ)− xct(τ)Acr(τ)]dτ (60)

are the market prices of risks to the default jump, default intensity and short rate factors.

In equilibrium, markets clear. So xit + zi = 0, i = c, d. Replace xit(τ) by −zi(τ), and

replace hit by the functions defined in previous sections, then the F.O.C.s are affine equa-tions in the risk factors λt and rt. Setting the linear terms in λt and rt to zero implies thatAij(τ) are the solutions to the a system of ODEs with initial conditions A

ij(0) = 0, i = v, p

and j = λ, r:

Acλ′(τ) + κλAcλ(τ)− [−αc(τ)

|zc(τ)|zc(τ)

+ L] = −γL2∫ T0

[zd(τ) + zc(τ)]dτ (61)

Adλ′(τ) + κλAdλ(τ)− [−αd(τ)

|zd(τ)|zd(τ)

+ L] = −γL2∫ T0

[zd(τ) + zc(τ)]dτ (62)

Acr′(τ) + κrAcr(τ)− 1 = 0 (63)

Adr′(τ) + κrAdr(τ)− 1 = 0 (64)

7.3 Proof of Proposition 1

Replace ∂Pct

∂λ /Pct with −Acλ(τ) and replace

∂P dt∂λ /P

dt with −Adλ(τ) in Definition 1,

∂P ct∂r /P

ct

and ∂Pct

∂r /Pct are the same.

7.4 Proof of Proposition 2

The time-varying component in the dependent variable is: Acλ(τ−∆τ)τ−∆τ λt+∆τ −

Acλ(τ)

τ λt, the

time-varying componet in the independent variable is: Acλ(τ)

τ λt−Acλ(τ−∆τ)

τ−∆τ λt. So the regres-sion coefficient is:

ψ =cov[A

cλ(τ−∆τ)τ−∆τ λt+∆τ −

Acλ(τ)

τ λt,Acλ(τ)

τ λt −Acλ(τ−∆τ)

τ−∆τ λt]

var[Acλ(τ)

τ λt −Ac

λ(τ−∆τ)τ−∆τ λt]

(65)

=τAcλ(τ −∆τ)e−κλ∆τ − (τ −∆τ)Acλ(τ)

(τ −∆τ)Acλ(τ)− τAcλ(τ −∆τ)(66)

when ∆τ → 0,

ψ = −τ [Acλ(τ)

′ + κλAcλ(τ)]τ [Acλ(τ)

′ − 1](67)

=F (τ)

1− F (τ)e−κλτ(68)

32

where F (τ) = −αc(τ) |zc(τ)|

zc(τ) + L− γL2∫ T0 [z

c(τ) + zd(τ)]dτ .

ψ > 0 if F (τ) < eκλτ , and ψ < 0 if F (τ) > eκλτ .

7.5 Proof of Lemma 3

Lemma 3a: For very negative θ̄(τ) and negative θ(τ), the Arbitrageur’s F.O.C.s are:

µct(τ)− rt − hct(τ)− Lλt = LΦJ,t − σλAcλ(τ)Φλ,t − σrAcr(τ)Φr,t − σzAcz(τ)Φz,t (69)µdt (τ)− rt + hdt (τ)− Lλt = LΦJ,t − σλAdλ(τ)Φλ,t − σrAdr(τ)Φr,t − σzAdz(τ)Φz,t (70)

where

ΦJ,t = γL∫ T0

[xdt (τ) + xct(τ)]dτλt (71)

Φλ,t = γσλ∫ T0

[−xdt (τ)Adλ(τ)− xct(τ)Acλ(τ)]dτ (72)

Φr,t = γσr∫ T0

[−xdt (τ)Adr(τ)− xct(τ)Acr(τ)]dτ (73)

Φz,t = γσz∫ T0

[−xdt (τ)Adz(τ)− xct(τ)Acz(τ)]dτ (74)

are the market prices of risks to the default jump, default intensity, short rate and demandshock factors.

In equilibrium, markets clear. So xit + zit = 0. Then the F.O.C.s are affine equations

in the risk factors λt, rt and zt.9 Setting the linear terms in λt, rt and zt to zero impliesthat Aij(τ) are the solutions to the a system of ODEs with initial conditions A

ij(0) = 0,

i = v, p and j = λ, r, z:

Acλ′(τ) + κλAcλ(τ)− [αc(τ) + L] = 0 (75)

Adλ′(τ) + κλAdλ(τ)− [−αd(τ) + L] = 0 (76)

Acr′(τ) + κrAcr(τ)− 1 = 0 (77)

Adr′(τ) + κrAdr(τ)− 1 = 0 (78)

Acz′(τ) + κzAcz(τ) = −γσ2λAcλ(τ)

∫ T0θ(τ)[Acλ(τ)−Adλ(τ)]dτ − γσ2zAcz(τ)

∫ T0θ(τ)[Acz(τ)−Adz(τ)]dτ

(79)

Adz′(τ) + κzAdz(τ) = −γσ2λAdλ(τ)

∫ T0θ(τ)[Acλ(τ)−Adλ(τ)]dτ − γσ2zAdz(τ)

∫ T0θ(τ)[Acz(τ)−Adz(τ)]dτ

(80)

Lemma 3b: similar to Lemma 3a, but the unique positive solution of κ∗z is guaranteed onlywhen κz is large enough.

9By assuming that the two markets have exact opposite demand pressure, the market price of risk forthe default jump factor becomes zero as the arbitrageur’s aggregate positions are free of default jump risk.

33

7.6 Proof of Proposition 3

Replace ∂Pct

∂λ /Pct with −Acλ(τ), replace

∂P dt∂λ /P

dt with −Adλ(τ), replace

∂P ct∂z /P

ct with −Acz(τ),

replace ∂Pdt

∂z /Pdt with −Adz(τ) in Definition 1,

∂P ct∂r /P

ct and

∂P ct∂r /P

ct are the same.

7.7 Proof of Proposition 4

∂Basis

∂λt=

Adλ(τ)τ

− Acλ(τ)τ

(81)

∂Basis

∂zt=

Adz(τ)τ

− Acz(τ)τ

(82)

so sign(∂Basis∂λt ) = sign(Adλ −Acλ) and sign(

∂Basis∂zt

) = sign(Adz −Acz).

7.8 Proof of Proposition 5

Easily proved by taking the derivatives of Gλ(τ) and Gz(τ) on τ , then summarize resultsfor different signs of zct (τ).

7.9 Proof of Proposition 6

∂2Yt(τ)/∂τ = [Acλ(τ)

τ ]′λt + constants, where

Acλ(τ)

τ = [αc + L]1−e

−κλτ

κλτwhen zct < 0 and

Acλ(τ)

τ = [−αc + L]1−e

−κλτ

κλτwhen zct > 0.

1−e−κλτκλτ

is a decreasing function of τ , therefore

∂2Yt(τ)/(∂τ∂λt) = [Acλ(τ)

τ ]′ < 0. When zct < 0, [

Acλ(τ)

τ ]′ = [αc+L](1−e

−κλτ

κλτ)′ is more negative

than [Acλ(τ)

τ ]′ = [−αc + L](1−e−κλτκλτ )

′ when zct > 0.

34

Appendix C: Figures and Tables

Figure 1: CDS Basis and 1‐week Negative Basis Trading Returns 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

04/07 08/07 03/08 10/08 12/08 04/09 12/09-500

0

500Basis vs Negative Basis Trading Return (1-week holding period)

04/07 08/07 03/08 10/08 12/08 04/09 12/09-5%

0%

5%Basis (cds price - credit spread)Negative Basis Trading Return

35

 

Figure 2: Cumulative Profit of Basis Trading on Underlyings of Different Maturities 

 

 

 

01/01/2007 01/01/2008 01/01/2009 01/01/20100

0.5

1

1.5

2

2.5

3

3.5

4Cumulative Profit of Basis Trading on Underlyings of Different Maturities

cumulative basis trading profit on 2yr underlyingcumulative basis trading profit on 5yr underlyingcumulative basis trading profit on 10yr underlying

36

Table 1 Regression Tests of Hypothesis 1 and 2 (Sub‐period 1)Time‐series Regression of Realized Profit of Basis Trading |RER_nbt| on Explanatory and Predictive VariablesSub‐period 1: 07/2007‐02/2008k=1 day holding period

Regression A Regression B Regression C Regression Dcoefficient NWtstat coefficient NWtstat coefficient NWtstat coefficient NWtstat

constant 0.21 (6.82) 0.23 (3.68) 0.07 (0.65) ‐0.05 (‐0.39)|RMRF_t,t+k| ‐0.04 (‐2.74) ‐0.05 (‐2.79) ‐0.11 (‐2.03)|SMB_t,t+k| 0.03 (0.69) 0.03 (0.62) 0.06 (0.50)|HML_t,t+k| 0.10 (1.66) 0.09 (1.55) 0.18 (0.94)|DEF_t,t+k| 0.26 (3.26) 0.29 (3.45) 0.65 (3.37)|TERM_t,t+k| ‐0.04 (‐0.98) ‐0.04 (‐0.96) 0.04 (0.51)(Libor‐FFR)_t,t+k ‐9.20 (‐0.52) 10.86 (0.64) 25.56 (1.47) 34.29 (1.88)(TED*lambda)_t,t+k 13.12 (1.57) 1.88 (0.24) 31.99 (1.65) 49.20 (2.48)(TED^2*TV)_t ‐0.03 (‐1.48) ‐0.02 (‐0.81)(FFR^2*TV)_t 0.00 (1.68) 0.00 (1.58)TED_t*|RMRF_t,t+k| 0.04 (1.30)TED_t*|SMB_t,t+k| ‐0.02 (‐0.29)TED_t*|HML_t,t+k| ‐0.09 (‐0.66)TED_t*|DEF_t,t+k| ‐0.28 (‐2.40)TED_t*|TERM_t,t+k| ‐0.05 (‐1.07)Rsquared 0.01 0.13 0.15 0.18Adjusted Rsquared 0.00 0.09 0.10 0.10k=1 week holding period

Regression A Regression B Regression C Regression Dcoefficient NWtstat coefficient NWtstat coefficient NWtstat coefficient NWtstat

constant 0.46 (5.19) 0.70 (3.13) 0.52 (2.26) 0.51 (2.07)|RMRF_t,t+k| 0.06 (2.36) 0.05 (2.03) 0.18 (3.19)|SMB_t,t+k| ‐0.11 (‐1.71) ‐0.12 (‐2.03) ‐0.27 (‐1.58)|HML_t,t+k| 0.03 (0.42) ‐0.02 (‐0.31) 0.18 (1.42)|DEF_t,t+k| ‐0.15 (‐0.85) ‐0.17 (‐0.95) ‐0.33 (‐0.76)|TERM_t,t+k| ‐0.03 (‐1.36) ‐0.03 (‐1.13) ‐0.03 (‐0.86)(Libor‐FFR)_t,t+k ‐17.02 (‐1.27) ‐3.82 (‐0.30) 1.16 (0.11) ‐3.77 (‐0.34)(TED*lambda)_t,t+k 9.41 (1.48) 4.09 (0.64) 17.26 (1.55) 21.24 (1.95)(TED^2*TV)_t ‐0.07 (‐2.04) ‐0.06 (‐1.59)(FFR^2*TV)_t 0.01 (1.17) 0.00 (0.48)TED_t*|RMRF_t,t+k| ‐0.11 (‐2.49)TED_t*|SMB_t,t+k| 0.10 (1.18)TED_t*|HML_t,t+k| ‐0.19 (‐1.70)TED_t*|DEF_t,t+k| 0