How General Wrong-Way Risk Differs from Concentration Risk

# Is it possible to model general wrong way risk via concentration risk?


# Is it possible to model general wrong way risk via concentration risk?












General wrong way risk (GWWR) is defined as due to a positive correlation between the level of exposure and the default probability of the counterparty, due to general market factors. (Specific wrong way risk is when they are positively correlated anyway). According to the “Risk Concentration Principles” (bcbs63) “different entities within the conglomerate could be exposed to the same or similar risk factors or to apparently unrelated risk factors that may interact under some unusual stressful circumstances.”

Given that the different market factors tend have a stronger positive correlation when one is talking about the same country/region(mainly the base curves), the same industry (mainly the spreads), etc, should be the concentration risk (per region, industry,..) be used to model the general wrong way risk?

With 5 regions (Americas, UK, Europe(ex UK), Japan, Asia-Pacific(ex Japan) and 10 sectors (Energy, Basic Materials ,Industrails, consumer Cyclical, consumer Non-Cyclical, Health Care, Financials, Information Techniology, Telecomunication Services and Utilities), you should be able to get the GWWR from a sort of variance of the concentration from the average_of_sectors(ideally 10%) and average_of_regions (ideally 20%). When you have 40% of your exposure in Energy, 30% in Financials 20% in Telecomunication services and 10% in whatever else; well diversified. What I mean is, assuming that the rest of the parameters is all the same (same maturities, types of instruments=bonds -to simplify, pricipals, etc), the GWWR should be much larger for 40-10-40-10 than for 30-30-30-10.

Ex1: A Swiss company receives CHF, buys materials in EUR and takes a loan in EUR to pay them. In case the EUR increases with respect to CHF, both the probability of default of the company (raw materials increase in price) and its exposure in CHF increase. As the default is a statistical property, having 40% of your portfolio as loans provided to many of such companies will make you notice the default (which does not any longer behave idiosyncraticly, as when you would have one company). Assume the lender does not structure its business around the EUR/CHF exchange risk.

Ex2: You are a European lender 10 years ago. People buy houses and earn salaries in the local currency and take mortgages in CHF, as CHF had very low/the lowest interest rates. The CHF rises by 1.25, and the exposure rises by 25%. The probability of default rises, as the price of the house/collateral does not rise in the local currency and the monthly rate to pay goes well over the allowed indebtment percentage.If you are providing many of such mortgages, you are exposed to GWWR proportional to their concentration with respect to your portfolio.

My question is if general wrong way risk is not a form of double counting (Should'nt wrong way risk include only the specific wrong way risk?) Could someone,please, give an example of GWWR where concentration is not a factor?

I guess that one can regress credit risk/hazard rates on market factors and look for strong correlations, but this should already be accounted for by the stressed VaR.

## Answer by lehalle (score 3)

https://quant.stackexchange.com/a/14246

Let's try to summarize your question before answering it:

- on the one hand concentration risk comes from the fact your book is highly correlated to few factors, hence you cannot take profit of diversification, market moves will affect you a lot;

- on the other hand wrong way risk is about being exposed to a counterparty such a way that the more you have products from it in your book, the more risk you have in them. General risk of this kind stems from underlying market wide relationships, and not from a badly designed product specific to one counterpart (it would be specific wrong way risk). Hence having this product from any counterpart will embed GWWR.

All this seems to mean that GWWR increases when you concentrate your book on products that are wrong way, and concentration risk is about... well... concentrate your book on few market factors. Then: what is the difference?

I guess the difference stems from where the exposure to the risk come from:

- for concentration risk, it is direct exposure to market factors it more or less increases the volatility of your book;

- for GWWR is about counterparty risk, to cite an ISDA doc:

> [...] the credit quality of the counterparty may for non-specific reasons be held to be correlated with a macroeconomic factor which also affects the value of derivatives transactions.

Counterparty risk affects your book another way that increasing volatility: for instance it propagates a non linear way via CVA (Credit Valuation Adjustment) in your book. According to this US Interagency Supervisory Guidance on Counterparty Credit Risk Management document (p13 and beyond), counterparty risk management is not limited to CVA ; they list:

- counterparty limits, mainly via CVA;

- margin policies and practices, via haircuts, collateral and margining management;

- close-out policies and practices.

My answer thus will be: if you do not value GWWR via counterparty channels (like CVA), but only by increasing the volatility of your book, you are right, there is not that much difference between concentration risk and GWWR in your procedures. But it is not the right way: these two risks should propagate in your book different ways.