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# CDS - Bond basis factors : confusing impact

#### rajeshtr

##### Member
Hi David,
I am getting very confused with the impact of the factors on CDS minus Bond basis (especially positive basis and negative basis as described below).
I feel like i am missing something extremely basic causing all the factors influence to be illogical in sign.. I would sincerely appreciate if you can kindly spend some time explaining how to think through this.

eg., Cheapest to Deliver option : CDS value should improve --> CDS Spread should decrease (-ve basis would be my logical derivation).. Gone Wrong..

Bond Trading Above Par : CDS is indexed to Bonds at Par. So if the Bond price increases, Bond Yields decrease. --> +ve spread would be my logical derivation --> gone wrong..

So fundamentally i am missing something.. Kindly spend time how you think though each of these factors ..

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
@rajeshtr Can I refer you to my absolutely favorite book on this topic: The Credit Default Swap Basis by Moorad Choudhry https://www.bionicturtle.com/forum/resources/the-credit-default-swap-basis-by-moorad-choudhry.130/

Below I copied the key section on the factors. I think it's more helpful than Gregory's section on CDS-Bond basis precisely because of your point: Choudry does give a framework. He starts at the very beginning which is to distinguish the unfunded CDS from the funded asset swap. The, of course, the definition of CDS-bond basis is important, which Choudry defines as:

Then this sets up viewing the basis as a function of fundamental and market factors (see long text below), which I find very useful. Hopefully this is helpful as a start, but let me know if you want to discuss any of the particulars further? Thanks!

Factors Behind the Basis
The basis arises from a combination of factors, which we may group into:
• Technical factors
• Market factors
Technical factors, which are also referred to in the market variously as fundamental or contractual factors, are issues related to the definition or specification of the reference asset and of the CDS contract. Market factors, which are also referred to
as trading factors, relate to issues connected with the state of the market in which contracts and reference assets are traded. Each factor exerts an influence on the basis, forcing it wider or tighter; the actual market basis at any one time will reflect the impact of all these factors together. We consider them in detail next.

Technical Factors
Technical factors that will influence the size and direction of the basis include the following:
• CDS premiums are above zero: the price of a CDS represents the premium paid by the protection buyer to the protection seller—in effect an insurance premium. As such, it is always positive. Certain bonds rated AAA (such as U.S. agency securities, World Bank bonds, or German Pfandbriefe) frequently trade below Libor in the asset-swap market; this reflects the market view of credit risk associated with these names as being very low and also better than bank quality. A bank writing protection on such a bond, however, will expect a premium (positive spread over Libor) for selling protection on the bond. This will lead to a positive basis.
• Greater protection level of the CDS contract: credit default swaps are frequently required to pay out on credit events that are technical defaults, and not the full default that impacts a cash bondholder. Protection sellers will therefore demand a premium for this additional risk, which makes the CDS trade above the ASW spread.
• Bond identity and the delivery option: many CDS contracts that are physically settled name a reference entity rather than a specific reference asset. On occurrence of a credit event, the protection buyer often has a choice of deliverable assets with which to effect settlement. The looser the definition of deliverable asset is in the CDS contract documents, the larger the potential delivery basket: as long as the bond meets prespecified requirements for seniority and maturity, it may be delivered. Contrast this with the position of the bondholder in the cash market, who is aware of the exact issue that he is holding in the event of default. Default swap sellers, on the other hand, may receive potentially any bond from the basket of deliverable instruments that rank pari passu with the cash asset—this is the delivery option afforded the long swap holder. In practice therefore, the protection buyer will deliver the cheapest-to-deliver bond from the delivery basket, exactly as he would for an exchange-traded futures contract. This delivery option has debatable value in theory, but can have significant value in practice. For instance, the bonds of a specific obligor that might be trading cheaper in the market include:
• The bond with the lowest coupon
• A convertible bond
• An illiquid bond
• An asset-backed security (ABS) bond compared to a conventional fixed-coupon bond
• A very-long-dated bond
....
• Accrued coupon: this factor may be associated with cash- or physically settled contracts. In certain cases, the reference bond accrued coupon is also delivered to the protection buyer in the event of default. This has the effect of driving the CDS premium (and hence the basis) higher. Assets trading above or below par: unlike a long cash bond position, a CDS contract provides protection on the entire par value of the reference asset. On occurrence of a credit event, the CDS payout will be par minus the recovery value (or minus the asset price at the time of default). If the asset is not trading at par, this payout will either over- or undercompensate the protection buyer, depending on whether the asset is trading at a premium or discount to par. So if the bond is trading at a discount, the pro tection seller will experience a greater loss than that suffered by an investor who is holding the cash bond. For instance, an investor who pays $90 per$100 nominal to buy a cash bond has less value at risk than an investor who has written CDS protection on the same bond. If the bond obligor defaults, and a recovery value for the bond is set at $30, the cash investor will have lost$60 while the CDS seller will have lost \$70. As a result, the CDS price will trade at a higher level than the asset-swap price for the same asset where this is trading below par, leading to a larger basis. The reverse applies for assets trading above par. If the reference asset is trading at a premium, the loss suffered by a CDS seller will be lower than that of the cash bondholder. This has the effect of driving the basis lower.
• Funding versus Libor: the funding cost of a bond plays a significant part in any trading strategy associated with it in the cash market. As such, it is a key driver of the ASW spread. A cash bond investor will need to fund the position, and we take the bond’s repo rate as its funding rate.4 The funding rate, or the bond’s cost-of-carry, will determine if it is worthwhile for the investor to buy and hold the bond. A CDS contract, however, is an unfunded credit derivative that assumes a Libor funding cost. So an investor who has a funding cost of Libor plus 25 basis points will view the following two investments as theoretically identical:

❑ Buying a floating-rate note priced at par and paying Libor plus 125 bps
❑ Selling a CDS contract on the same FRN at a premium of 100 bps

Thus, the funding cost in the market will influence the basis. If it did not, the above two strategies would no longer be identical and arbitrage opportunities would result. Hence a Libor-plus funding cost will drive the basis lower. Equally, the reverse applies if the funding cost of an asset is below Libor (or if the investor can fund the asset at sub-Libor), which factor was discussed earlier. Another factor to consider is the extent of any “specialness” in the repo market.5 The borrowing rate for a cash bond in the repo market will differ from Libor if the bond is to any extent special; this does not impact the default swap price, which is fixed at inception. This is more a market factor, however, which we consider in the next section.
• Counterparty risk: the protection buyer in a CDS contract takes on the counterparty risk of the protection seller, which does not occur in the cash market. This exposure lasts for the life of the contract, and will be significant if, on occurrence of credit event, the protection seller is unable to fulfill his commitments. This feature has the effect of driving down the basis, because to offset against this risk, the buyer will look to a CDS premium that is below the cash asset-swap spread. In addition, the protection buyer will wish to look for protection seller counterparties that have a low default correlation to the reference assets being protected, to further reduce counterparty risk exposure. For instance, the counterparty risk exposure of a protection buyer in a CDS contract is increased when the contract has been written by an investment bank on a bank that is also a CDS market maker.
On the other side, the protection seller is exposed to counterparty risk of the protection buyer. Should the latter default, the CDS contract will terminate. The protection seller will suffer a mark-to-market loss if the CDS premium has widened since trade inception.
• Legal risk associated with CDS contract documentation: this risk has been highlighted in a number of high-profile cases, where an unintendedly broad definition of “credit event,” as stated in the contract documents, has exposed the protection seller to unexpected risks. Typically, this will be where a “credit event” has been deemed to occur beyond what might be termed a default or technical default. This occurred, for instance, with Conseco in the United States, as first discussed in Tolk (2001). Associated with legal risk is documentation risk, the general risk that credit events and other terms of trade, as defined in the CDS documentation, may be open to dispute or arguments over interpretation. We can expect documentation risk to decrease as legal documentation is standardized across a larger number of shares. The 2003 International Swaps and Derivatives Association (ISDA) definitions also seek to address this issue.
Market Factors
Market factors that will influence the size and direction of the basis include the following:
• Market demand: strong demand from protection buyers such as commercial banks protecting loan books, or insurance companies undertaking synthetic short selling trades, will drive the basis wider. Equally, strong market demand from protection sellers will drive the basis tighter.
• Liquidity premium: the CDS for a particular reference asset may reflect a liquidity premium for that name. An investor seeking to gain exposure to that name can buy the bond in the cash market or sell protection on it in the CDS market. For illiquid maturities or terms, the protection seller may charge a premium. At the 2- to 5-year maturities, the CDS market is very liquid (as is the cash market). For some corporate names, however, cash market liquidity dries up toward the 10-year area. In addition, depending on the precise reference credit, the default swap may be more liquid than the cash bond, resulting in a lower default swap price, or less liquid than the bond, resulting in a higher price.
Liquidity in the cash market can be quite restricted for below-investment-grade names, and secondary market trading is usually confined to “current” issues. Similarly, to the repo market, the relationship flows both ways, and liquid names in the cash market are usually liquid names in the CDS market. For corporate names for whom no bonds exist, however, CDS contracts are the only way for investors to gain an exposure (see below).
Relative liquidity is also related to the next item on our list.
• Shortage of cash assets: in some markets, it is easier to source a particular reference name or reference asset in the CDS market than in the cash market. This has always been the case in the loan market; although there has been a secondary market in loans in the United States for some time, it is relatively illiquid in Europe. In the bond market, it can be difficult to short some corporate bonds due to problems in covering the position in repo, and also the risk that the bonds go special in repo. When cash assets are difficult to short, traders and speculators can buy protection in the CDS market. This does not involve any short covering or repo risk, and also fixes the cost of “funding” (the CDS premium) at trade inception. The demand for undertaking this in CDS will have a positive impact on the basis.
• The structured finance market: the rapid growth of the market in synthetic CDOs has both arisen out of, and driven, the liquidity of the CDS market. These products are considered in detail in Choudhry (2002) and Anson et al. (2004). Synthetic CDOs use CDS contracts to source reference credits in the market, and frequently make use of basket CDSs and a portfolio of credits. As investment vehicles, they sell protection on reference names. The counterparty to the CDO vehicle will hedge out its exposure in the CDS market. Large demand in the CDS market, arising from hedging requirements of CDO counterparties, impacts the basis and frequently drives it lower.
• New market issuance: the impact of new bond and loan is sues on the CDS basis illustrates the rapid acceptance of this instrument in the market, and its high level of liquidity. Where previously market participants would hedge new issues using interest-rate derivatives and/or government bonds, they now use CDSs as a more exact hedge against credit risk. The impact on the basis flows both ways, however, and may increase or decrease it, depending on specific factors. For example, new issues of corporate bonds enlarge the delivery basket for physically settled CDS contracts. This should widen the basis, but the cash market may also widen as well, as investors move into the new bonds. For loans, a new issue by banks is often hedged in the CDS market, and this should cause the basis to widen. Convertible bond issuance also tends to widen the basis; we noted earlier the impact of the issue of an exchangeable bond by Fiat on the CDS basis for that name.

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#### [email protected]

##### Active Member
Hi David,
In which category would the bond squeeze go? I don’t see it mentioned?
The closest is perhaps shortage in cash market, but this suggests positive basis? I thought Gregory says this is negative?
Thanks for clarifying!

#### theapplecrispguy

##### New Member
Hello David. Based on my reading of Choudry and the study notes, there seems to be a discrepancy on the basis for "Funding". The study notes indicate that funding levels in excess of LIBOR in the cash market with make the basis positive. Choudry indicates that LIBOR plus funding costs will drive the basis lower. Could you please clarify. Also is "Delivery Squeeze" in the study notes referring to a shortage of cash assets when it indicates that this would tend to make the basis negative? Again, this appears to be the opposite of Choudry's view.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @theapplecrispguy When you say "study notes," I don't know what you mean in this context (and it's time-consuming for me to search through our notes to try and figure out to what you are referring. It would be helpful if you can be more specific in the future. I can't find the reference to which you refer in the "study notes."). With respect to 2018 (and 2019), the only FRM assignment for Moorad Choudhry is Chapter 12 (i.e., An Introduction to Securitization [CR–20]) of his Credit Derivatives & Synthetic Securitization, 2nd Edition. And this chapter, as far as I can tell, makes direct no reference to the CDS-bond basis (aka, CDS basis).

To my knowledge, Choudry (who I've read extensively) has always classified "funding cost" as technical factor in the CDS-bond basis which is an decreasing function of the basis: a higher funding cost lowers the CDS basis. This is by almost by definition of the CDS-bond basis, per Choudry which is: CDS-bond basis = Credit Default Spread - Asset-swap Spread; i.e., B = D - S. In this context, funding cost is the cost of buying the bond (as the funded short position) as an alternative to synthetically shorting the reference via an writing an unfunded CDS. As the cost of funding the bond increases, per B = D - S, a higher S implies a lower B.

... oh, okay, now I see the problem based on the above at https://www.bionicturtle.com/forum/threads/cds-bond-basis-factors-confusing-impact.10284/post-48598 ... that's based not on Choudry but on Jon Gregory. per his (2nd version) Chapter 10.2.4:
"10.2.4 The CDS– Bond Basis It is possible to show theoretically (Duffie, 1999) that, under certain assumptions, a (short) CDS protection position is equivalent to a position in an underlying fixed-rate bond and a payer interest rate swap. 15 This combination of a bond and interest rate swap corresponds to what is known as an asset swap. This implies that spreads, as calculated from the CDS and bond markets, should be similar. However, a variety of technical and fundamental factors means that this relationship will be imperfect. The difference between CDS and bond spreads is known as the CDS– bond basis. A positive (negative) basis is characterised by CDS spreads being higher (lower) than the equivalent bond spreads. 16

Factors that drive the CDS– bond basis are:
• Counterparty risk. CDSs have significant wrong-way counterparty risk (Chapter 15), which tends to make the basis negative.
• Funding. The theoretical link between bonds and CDSs supposes that LIBOR funding is possible. Funding at levels in excess of LIBOR will tend to make the basis positive, as CDSs do not require funding. Contributing further to this effect is that shorting cash bonds tends to be difficult, as the bond needs to be sourced in a fairly illiquid and short-dated repo market in which bonds additionally might trade on special, making it expensive to borrow the bond." -- Gregory, Jon. Counterparty Credit Risk and Credit Value Adjustment: A Continuing Challenge for Global Financial Markets (The Wiley Finance Series) (Kindle Locations 5897-5909). John Wiley and Sons. Kindle Edition.

Notice Gregory (correctly) defines the CDS basis as CDS_spread - bond_spread. I don't know why he says that higher funding cost "makes the basis positive." @Nicole Seaman can we write Jon Gregory and ask if he is mistaken please? (i don't see this on errata at https://cvacentral.com/books/credit-value-adjustment/errata/ ). I think it should be (10.2.4):
"[bullet]Funding. The theoretical link between bonds and CDSs supposes that LIBOR funding is possible. Funding at levels in excess of LIBOR will tend to make the basis negative, as CDSs do not require funding [i.e., higher funding cost tighten the spread between the unfunded CDS and the funded bond]. Contributing further to this effect is that shorting cash bonds tends to be difficult, as the bond needs to be sourced in a fairly illiquid and short-dated repo market in which bonds additionally might trade on special, making it expensive to borrow the bond." -- Gregory, Jon. Counterparty Credit Risk and Credit Value Adjustment: A Continuing Challenge for Global Financial Markets (The Wiley Finance Series) (Kindle Locations 5906-5909). John Wiley and Sons. Kindle Edition

... We'll update when we hear back from Jon Gregory. Thanks,

#### JonGregory

##### New Member
Sorry - this was just drawn to my attention and I agree that the basis should be negative for funding costs. Have added in to the Errata on my website.

#### tom87

##### Member
Hi David,

I am still struggling with the explanation provided. Would it be possible to zoom on the following assertion?

"As the cost of funding the bond increases, per B = D - S, a higher S implies a lower B. "

Since S = Asset Swap Spread = Yield of the bond - funding cost,
if funding cost increases then Asset Swap Spread decreases,
therefore B=D-S should increase.

Did I miss something?

Thanks,

Thomas

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @tom87 But isn't it a fallacy to hold the Yield constant in the expression "S = Asset Swap Spread = Yield of the bond - funding cost" in order to draw such an inference? If the funding costs goes up, the bond's yield (as it includes a funding component) should go up. And, sorry, where are you getting that formula?

#### tom87

##### Member
Hi David,

Agreed the bond yield is an increasing function of funding cost, but that does not explain why the asset swap spread is an increasing function of funding cost. How can we prove that when the funding cost increases by dx, bond yield increases by more than dx?

You are right to come back to the definition I think that's where the confusion lies on my side. I have found several definitions of asset swap spread and cds basis. I got the above formula from Google (agreed it is not the most appropriate reference )

Asset swap spread: I understand it is the spread over libor in a fixed vs floating interest rate swap where the fixed rate of the swap is equal to the coupon rate of a bond priced at par. It represents the credit spread of the bond.

CDS Basis:
- In the following video the CDS basis is defined as the difference between CDS spread and (Cash Spread - funding cost), where Cash Spread = bond fixed coupon - Risk free rate.
According to that definition i still struggle to see how CDS basis would decrease when funding cost increases.
- In the text from Choudry that you have copied, we can read the following:

In the example given, my understanding is that
funding cost = LIBOR + 25 bps
ASW spread = FRN coupon - funding cost = LIBOR+125 bps - (LIBOR+25bps)=100 bps
cds basis = 100 bps - 100bps=0

If funding cost increases to LIBOR + 50 bps,

ASW spread (new) = FRN coupon (NEW) - (LIBOR+50 bps)
ASW spread (new) - ASW spread = FRN coupon (NEW) - FRN coupon -50bps
Again how can we prove this last quantity is positive?

Thanks,

Thomas

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi Thomas (@tom87) Right, that's good analysis. (and yes, earlier in the FRM, a less sophisticated definition of CDS Basis was employed per the video; Choudry in his book actually has more than one definition simply because there are multiples spreads that can be compared to the CDS spread)

Re: how can we prove this last quantity is positive? I am currently thinking that we cannot prove it. I am not sure, I find this very difficult, but I think I started the fallacy by saying that given CDS-Bond basis (B) = CDS_spread - ASW(S), a higher funding cost increases S which decreases the basis. I think it's the same sort of fallacy to which I referred in your expression: these relationships are valid as residuals, but there is a fallacy when we hold the CDS_spread constant, or for that matter the bond yield.

In other words, let's just presume momentarily that theoretically the CDS-bond basis should be equal to zero. Then in your example, when the funding cost increases by + 25 bps, how would a zero CDS-bond basis be maintained? I see two ways to maintain zero basis
1. If the FRN coupon increased by + 25 bps to (L + 150 bps) such that ASW spread is maintained at 100 bps, equal to the CDS spread; or
2. if the FRN coupon did not change such that the ASW spread reduced to 75 bps, but the CDS spread reduced to 75 bps.
To me, either actually seems plausible! In case (1), the bond coupon increases appropriately because the bond should reflect funding cost; but even (2) is plausible when we consider that the CDS is an unfunded position and its pricing should reflect this advantage, just like a swap spread's pricing should reflect its "carry-cost" advantage.

So yea, I reversed into this from the conclusion, but the more i look at it, the more that I think it's a fallacy to look at C = A - B, in this context and to hold (A) constant when referring to the impact of ΔB on C given that A and B are not independent. I just re-read Choudry's Chapter 3 and noticed this footnote in regard to the the technical factor of Funding (versus Libor) that you have quoted above:
3. It is a moot point whether this is a technical factor or a market factor. Funding risk exists in the cash market, and does not exist in the CDS market: the risk that, having bought a bond for cash, the funding rate at which the cost of funds is renewed rises above the bond’s cost-of-carry. This risk, if it is to be compensated in the cash (ASW) market, would demand a higher ASW spread, and hence would drive the basis lower

... and I do admit that I missed this before. He has funding classified as a fundamental factor (very confusingly labelled technical factor) but as I re-read this chapter, I think it really deserves to be a technical factor and this footnote almost justifies this (he confusingly refers to technical factors as market factors).

What i mean is: if funding cost were a truly fundamental factor, then we should be able to show how its increase has a direct impact on the CDS-bond basis; like credit risk is a fundamental factor that drives the CDS spread. But, in fact, I do not perceive there to be any obvious fundamental factors. The CDS spread fundamentally measures unfunded credit risk (but may be distorted by technical factors) and, I *think*, Choudhry's measure of the CDS-bond basis might be a measure that fundamentally should measure to zero (but we still do expect some distortions due to technical factors); i.e., perhaps the CDS-bond basis, when exactly defined, has zero fundamental factors. Now, there are alternative CDS-basis measures such that we could define a CDS-basis that explicitly "gaps" the funding cost, but I don't see that here ....

So i think that way above when I wrote that a higher (S) implies a lower (B) given B = D - S, I think I made a literal mistake even as Choudhry does say that higher funding costs puts downward pressure on the CDS basis, because it's not a "fundamental factor" relationship" but rather (perhaps) a merely technical issue of, as he writes in the footnote, the fact that "funding risk exists in the cash market, and does not exist in the CDS market." In other words, arbitrage should enforce approximately a zero CDS-bond basis (wherein the CDS spread is priced accurately according to its unfunded property) per fundamental factors, but technically speaking, an increase in the funding cost impacts the equation by explicitly acting on one side such that, just technically, we can expect an increased funding cost to exhibit upward pressure on basis (but fundamentally we would not expect it too persist because the basis itself does not include funding cost, or really any other fundamental factor). Thanks,

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Hi David,