# Dependence between Credit Default Risk and Credit Spread Risk

I am trying to understand the difference and similarities between Credit Spread Risk and Credit Default Risk.

Here is brief (and not all too precise) definition.

• Credit Spread Risk: Losses due to changes in credit spreads - measured using a Value-at-Risk (VaR) approach.
• Credit Default Risk: Losses due to changes in PD and LGD - measured using an Unexpected Loss (UL) approach.

For simplicity sake, lets consider a portfolio which consists of a single zero-coupon bond.

Credit Spread Risk deals with changes in credit spreads. One of the main reasons why the Credit Spread of our bond might change is that market participants believe that the available information on potential future losses has changed. But this risk is also included in the definition of credit default risk.

I was wondering if to a certain degree these two risk definitions overlap and whether there are methods to quantify this overlap. So for example assume that for this particular bond we have that

• Credit Default UL = 100

Do you know any methods on how to quantify the overlap? Or put differently, do you know any methods to analyse if these figures include any kind of double counting of risks?

The way I see it (as of now) Credit Default Risk should to a large extend be included in Credit Spread Risk.

Thank you.

• To my understanding, this double counting takes place when you do not carefully prepare the input data that underlies your credit spread risk calculation. For example, if you use a (credit spread) risk factor time series that contained historical defaults, you would have default (risk) included in your credit spread risk. Jun 10, 2021 at 17:24
• What exactly would be a credit spread risk factor time series containing default? I think as long as there is a credit spread means that there was no default, no? Jun 10, 2021 at 21:31
• You are right; I was thinking of rating downgrades tbh, sorry. Say you use a spread index as risk factor. Then you should make sure that it’s time series is not ‘polluted’ by addresses that had a downgrade or a credit event. Fun fact: Here in Germany, you can try estimate the double counting and deduct it from your economic risk capital requirements - IF you manage to convince the supervisory body. None of the shops I visited managed to do that… Jun 11, 2021 at 5:00

Commonly, the definition of credit risk is the risk that, over a given time horizon, at a certain confidence level, names in our credit portfolio deteriorate or even default, leading to a (present value) loss. Commonly, this risk is not marked-to-market (most of our credit is not tradeable) and the risk horizon is 1 year. As you already noted, the risk is $$UL$$-$$EL$$; and the expected loss plus a tail risk provision has already been factored into the credit conditions / margin requirements.

The overlap between credit spread risk and credit risk is driven by the model(s) you use:

Disregarding interest rate risk, the effects of interim cash flows and time effects, an integrated risk model would consider the following:

1. gains / losses due to credit migration, with a revaluation of the position at 'new', corresponding credit spreads
2. gains / losses due to credit spread movements (given non-default).

Commonly, the credit risk model only covers 1 + 3, whereas the credit spread risk model covers 2 and parts of 1.

## Where is the overlap?

The magic is in the calibration of the credit spread risk factor you use in either of these models. Without going too much into the details:

• credit spread risk factors must be calibrated somehow, commonly using observed spread series; e.g. thru credit spread index series, rating/sector series, single name series - whatever is available (in your shop's terminals) and liquid. Some places even calculate their own credit spread series (...the horror!)
• observed series may be polluted by credit effects, e.g. there may be jumps in spreads that were induced by a true credit event (imminent or 'pre-visible' rating downgrade) - and these jumps will directly enter your credit spread risk components.

In a textbook world, we would calibrate the credit spread risk components in either model (credit,credit spread, integrated risk) based on a series of credit spreads that does not contain jumps due to credit events. Then, there would be no overlap between the two risks; in an integrated risk model, at least.

HTH?

Credit spread risk is a risk-neutral probability of default. That is, it includes the expected loss plus a systemic risk premium if one ignores factors like liquidity, counterparty risk, and tax effects. Other posts in this page show how one can calculate a risk-neutral probability of default given CDS spreads.

CDS Spread = EL + RP

Credit risk is a real-world probability normally calculated using something like Merton’s distance to default probability. As long as investors are risk-averse, your risk-neutral default probability will always be greater than your real world default probability, because it only captures the EL component of credit spread risk and your RP is positive.

By quantifying distance to default probability, you have already quantified the overlap between credit spread risk and credit risk.

• Thank you for your answer: that is also what I thought. However, I think it is rather difficult to convince the supervisor (as already Kermitttfrog mentioned). Is there any literature which discusses this issue? Jun 11, 2021 at 18:54
• people.stern.nyu.edu/eelton/working_papers/… --Just to quote the abstract, "We show that expected default accounts for a surprisingly small fraction of the premium in corporate rates over treasuries. While state taxes explain a substantial portion of the difference, the remaining portion of the spread is closely related to the factors that we commonly accept as explaining risk premiums for common stocks." Jun 11, 2021 at 19:41
• Thank you for the article. If I understood correctly the authors show that there is almost no overlap between those two risks, right? Jun 11, 2021 at 20:41
• It is more accurate to say that, by definition, there is FULL overlap between these two risks. A component of credit spread risk is credit default risk. Look at formula 11. It's in the definition of the risk premium: "we are dealing with that part of the spread on corporate bonds that is not explained by expected default loss and taxes" So like I said, ignoring taxes, CDS Spread = EL + RP. Jun 11, 2021 at 21:20
• I think that the term Credit Spread Risk pertains to the risk of mtm losses due to credit trading at different spreads. It is not the default risk, per se. Jun 12, 2021 at 13:21