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P2.T6.416. Credit default swaps (CDS) and credit spread curve

Nicole Seaman

Director of FRM Operations
Staff member
Subscriber
AIMs: Describe credit default swaps (CDS) and their general underlying mechanics. Describe the credit spread curve and explain the motivation for curve mapping. Describe types of portfolio credit derivatives. Describe index tranches, super senior risk, and collateralized debt obligations (CDO).

Questions:

416.1. Gregory explains, "A (short) CDS protection position is equivalent to a position in an underlying fixed-rate bond and a payer interest rate swap. 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." (Source: Jon Gregory, Counterparty Credit Risk and Credit Value Adjustment: A Continuing Challenge for Global Financial Markets, 2nd Edition (West Sussex, UK: John Wiley & Sons, 2012))

Which of the following contributes to a DECREASE (i.e., a tendency toward a negative basis) in the CDS-bond basis?

a. Lower funding cost for the bond; e.g., sub-LIBOR
b. Strong market demand from CDS protection buyers; e.g., banks buying protection for their loan books
c. Significant wrong-way counterparty risk
d. A broad definition of the credit event, such that technical credit events may cause CDS protection to pay out on an event that is not considered a default by bondholders


416.2. Each of the following is true about the credit spread curve and curve mapping EXCEPT for which is not necessarily true?

a. The fundamental aim of credit curve mapping is to use some relevant points to achieve a general curve based on observable market data
b. Motivation for curve mapping includes Basel III capital rules
c. Motivation for curve mapping includes the hedging of credit value adjustment (CVA), in which case credit indices represent a better choice for data points than bond spreads
d. If a credit spread can only be defined for a single maturity, for example at the five-year point due to a single-maturity CDS, it is improper to attempt to to map (to extend) the curve to other maturities; this would be "highly subjective"


416.3. The two most common credit indices are DJ iTraxx Europe (which contains 125 equally-weighted European corporate investment-grade reference entities) and DJ CDX NA IG (which contains 125 equally-weighted North American, NA, corporate investment-grade reference entities). Their standard index tranches are illustrated below (Gregory's Figure 10.16):


(Source: Jon Gregory, Counterparty Credit Risk and Credit Value Adjustment: A Continuing Challenge for Global Financial Markets, 2nd Edition (West Sussex, UK: John Wiley & Sons, 2012))

If the weighted average recovery rate for defaults that occur is 25.0%, how many defaults can the super senior tranche of the DJ CDX NA credit index withstand before experiencing a loss?

a. Zero
b. 50
c. 78
d. 105

Answers here:
 
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David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
I changed 416.1.a to read: "Lower funding cost for the bond; e.g., sub-LIBOR," (this is meant to NOT be the correct answer, so its intended as a FALSE, which implies my intent for the TRUE statement to be: lower funding cost increases the CDS-bond basis).

So I do think lower funding cost tends to increase the basis (just as increased funding cost explained the persistent negative basis during the crisis) but this appears to superficially contradict Gregory (the associated reading) . I am confused in particular by Gregory's statement (which has survived intact the 2nd edition errata, suggesting I may not understand his meaning), emphasis mine:
"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 [dharper: sic?], as CDSs do not require funding." -- Gregory, Jon (2012-09-07). Counterparty Credit Risk and Credit Value Adjustment: A Continuing Challenge for Global Financial Markets (The Wiley Finance Series) (Kindle Locations 5906-5907). John Wiley and Sons. Kindle Edition.

Any insights would be greatly appreciated? Thanks,
 
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ohad999

New Member
Hi David,

I have a theory, which ironically I got from a video you posted a few years ago regarding the positive/negative basis trade: (its a way to test my understanding as well)


Maybe the funding cost is the repo rate (which is Libor equivalent per the example), and the spread is based on the Net bond spread - lets say cash spread 5% , repo 2% , bond yield is 3%.

Lets suppose that the protection payment is 3% as well. (CDS-Bond basis =0)


If the repo rate increases (excess of LIBOR, 3% for example) then the bond yield decreases to 2% , and then CDS-Bond basis = 1% (positive).

Anyway, I hope what I wrote here, if not correct, at least in the right direction....
 

ohad999

New Member
Hi David,
I have a theory, which ironically I got from a video you posted a few years ago regarding the positive/negative basis trade: (its a way to test my understanding as well)




Maybe the funding cost is the repo rate (which is Libor equivalent per the example), and the spread is based on the Net bond spread - lets say cash spread 5% , repo 2% , bond yield is 3%.

Lets suppose that the protection payment is 3% as well. (CDS-Bond basis =0)


If the repo rate increases (excess of LIBOR, 3% for example) then the bond yield decreases to 2% , and then CDS-Bond basis = 1% (positive).

Anyway, I hope what I wrote here, if not correct, at least in the right direction....
 

slacknoise

New Member
thanks for pointing it out David. I was confused by the funding cost answer as well and i am still confused, but could not find additional input.
 

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
Thank you @slacknoise This was a few years ago, I maybe did not think to refer to Choudhry (who I since uploaded here at https://www.bionicturtle.com/forum/resources/the-credit-default-swap-basis-by-moorad-choudhry.130/ ) and notice below what he says on page 70. Of course, the definition of the CDS-bond basis matters. I assume Gregory defines it like Choudhry: CDS-bond basis = CDS spread - [cash bond spread]; aka, CDS spread - [asset-swap spread]. That's every definition I've ever read, and not the other way around (i.e., not cash spread - CDS).

With that definition (basis = CDS Δ - cash Δ), Choudhry parses the factors into fundamental versus market, and within fundamental he says (emphasis mine):
"Funding versus Libor [footnote 3]: 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 [footnote 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."

—————
Footnote 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.
Footnote 4. This being market practice, even if the investor is a fund manager who has bought the bond outright: as the bondholder, he can repo out the bond, for which he will pay the repo rate on the borrowed funds. So the funding rate is always the bond’s repo rate for purposes of analysis.
 
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