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

- 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
- 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,

## Stay connected