Wrong-way risk · RiskAtoms Academy

By the end you will be able to

1Recognise wrong-way and right-way risk in a counterparty's trades and collateral.
2Tell general wrong-way risk (shared market drivers) from specific wrong-way risk (a structural link), with examples.
3Use a correlation between default and a market driver to compute the expected exposure given default, and the CVA it implies.
4State how the Basel rules treat wrong-way risk, and what a risk manager does about it.

Why it matters

In February 2008, a Federal Reserve official told the US Congress that banks holding the safest tranches of mortgage-backed CDOs had bought protection on them from financial guarantors, and warned: “These hedges lose value when the financial condition of the guarantors deteriorates.” The guarantors were weakening for the same reason the CDOs were falling. In RiskAtoms Bank's book, Saltney Capital sold the bank a put on the equity index. The put is worth most after a crash. A hedge fund is most likely to fail after a crash.

Core explanation

When exposure and default arrive together

Illustrative dataRiskAtoms Bank plc's derivatives book

The module's OTC book: eight trades (swaps, FX forwards, a bought index put) with four invented counterparties, each one netting set: Halvergate Manufacturing (BBB, no CSA), Corriemoor Bank (A), Saltney Capital (a hedge fund) and Ebbsworth Pension Trustees (AA). Exposures come from 2,000 seeded Monte Carlo paths of a flat GBP rate, GBPUSD and an equity index, half a month apart, out to ten years. Every firm and figure is made up for teaching, in pounds, on one valuation day; none is market data.

The correlated-default illustration is an extra: it links Saltney's default to the index with a chosen correlation and reweights the book's 2,000 paths. With no correlation it gives the book's CVA of £958k exactly.

The CVA formula of L3.4.10: CVA basics multiplies expected exposure by the probability of default, date by date. That treats them as independent: the exposure on the day of default is assumed to be the same, on average, as on any other day. Wrong-way risk is what happens when it is not. L2.2.03: Credit and counterparty risk named it and L3.3.12: Collateral, guarantees and credit risk mitigation met it in guarantees; here we measure it.

General and specific

General wrong-way risk comes from shared market drivers. Saltney's put is the book's example: an index fall raises the exposure and weakens a fund that, like many, makes money selling insurance against falls. A bank receiving dollars forward from a bank in a country whose currency would collapse in a sovereign crisis has the same problem: the exposure grows as the currency falls, which is when the local bank is most likely to fail.

Specific wrong-way risk comes from a direct link. A counterparty that posts its own shares or bonds as collateral: on default they are worth little. If Corriemoor posted £10m face of its own senior bonds with a 2% haircut, they would count as £9.8m today and be worth about £4.0m at a 40% recovery: £5.8m of the “secured” exposure vanishes at the worst moment. Buying CDS protection from a seller closely tied to the reference name, and the monoline insurers below, are the classic cases.

The opposite also exists. Right-way risk: Halvergate earns dollars and sells them forward to the bank. A stronger dollar raises the bank's exposure on the forward and also makes Halvergate richer. Linking Halvergate's default to a weaker dollar with a correlation of 0.3 cuts its CVA from £211k to £168k. Banks rarely take credit for right-way risk; they worry about the wrong way.

Sort itWrong way, specific or general? Or right way?

A hedge fund that sells equity puts has sold the bank a put on the index.
A counterparty posts its own shares as initial margin.
An oil producer sells oil forward to the bank to lock in its revenue.
The bank buys protection on a sovereign from a bank headquartered in that country.
The bank receives dollars against a local currency from an emerging-market bank.

The monolines, 2007–08

ExploreHow a hedge turned into a loss

Click a box to see what happens there.

Banks hold super-senior CDO tranches

Banks that structured CDOs of asset-backed securities kept large amounts of the top, super-senior tranches, which were rated AAA.

The formal version

The link uses correlation (M-C10: Covariance and correlation). Let $Y$ be the counterparty's credit variable and $X$ the standardised market move, with $\operatorname{corr}(X,Y) = -\rho$ . Write $X$ as its regression on $Y$ plus an independent part, and condition on default at $t$ :

\begin{aligned} X &= -\rho\,Y + \sqrt{1-\rho^2}\,Z, \qquad Y, Z \sim N(0,1) \text{ independent} \\ \mathbb{E}[X \mid Y = y_t] &= -\rho\,y_t, \qquad \operatorname{var}(X \mid Y = y_t) = 1 - \rho^2 \\ y_t &= \Phi^{-1}\big(1 - e^{-\lambda t}\big) \\ \text{Saltney, } t = 1:\quad y_1 &= \Phi^{-1}(0.0408) = -1.741 \\ \rho = 0.4:\quad X \mid \text{default} &\sim N\big(0.697,\; 0.917^2\big) \end{aligned}

This is a Gaussian copula, the same device as the one-factor model of L3.3.11: Unexpected loss and default correlation: each variable keeps its own distribution, and the correlation decides how they move together. Saltney's default probability does not change, and neither do the simulated market paths. Only which paths count when Saltney defaults changes. The model is deliberately simple: it says nothing about why the fund fails, and real defaults can arrive with a jump in the market that no correlation of this kind captures. Richer models, such as hazard rates that depend on the exposure, are in M6.6: Counterparty risk and XVA.

Try it

Move the correlation from right-way (negative) to strongly wrong-way. The dashed line is the ordinary EE; the red line is the EE the bank can expect on the day Saltney defaults.

Try itLink Saltney's default to the market

Correlation ρ between Saltney's default and an index fall0.3

Collateral

CVA with this correlation£1,437k

CVA if independent (ρ = 0)£958k

Wrong-way multiplier×1.50

Directionwrong way

EE at 1 year, given default then£31.60m

EE at 1 year, unconditional£19.92m

EE, independentEE given default, ρ = 0.3

Basel scales exposure by an alpha of 1.4, and supervisors may ask for more where general wrong-way risk is high. Find the correlation at which this multiplier passes 1.4. Then switch on the CSA: margin shrinks the CVA, but not the multiplier.

Worked example

Saltney's put, given that Saltney defaults

One date, one correlation: one year, ρ = 0.4

Step 1 of 5

1
Saltney's default threshold
Saltney's spread of 250bp gives λ = 4.17% and a one-year PD of $1 - e^{-0.0417} = 4.08\%$ . The credit variable's threshold is $y_1 = \Phi^{-1}(0.0408) = -1.74$ .

What the risk team notes

Saltney: put sold to us by a fund that is short volatility. Independent CVA £958k; at ρ = 0.2 it is £1,266k, at 0.6 £2,016k. Keep the CSA (it cuts CVA to £35k–£100k), raise Saltney's initial margin, and stress the exposure under a crash scenario rather than trusting the average profile.

Regulatory lens

The Basel counterparty rules (CRE53) ask banks to identify exposures with high general wrong-way risk and to stress-test for it, looking for risk factors positively correlated with a counterparty's creditworthiness. Exposure under the internal model is scaled by an alpha of 1.4, and supervisors may require a higher alpha for banks with high general wrong-way risk. Specific wrong-way risk gets a blunt treatment (CRE53.48): the trades are taken out of the counterparty's netting set, and their exposure is set as if the underlying issuer had defaulted at once (jump to default). For collateral, the credit risk mitigation rules (CRE22.15) require that the counterparty's credit quality and the collateral's value have no material positive correlation, so securities issued by the counterparty or its group are not eligible. Capital for counterparty risk is in M4.4: Counterparty, operational and large exposures, CVA capital in M4.3: Market risk capital (FRTB) and CVA, and wrong-way risk models in M6.6: Counterparty risk and XVA.

Spark Atoms

Spark AtomAAA, until it mattered

Financial guarantors sold banks protection backed by their AAA ratings. A guarantee is only as good as the guarantor in the state of the world where it pays, and here that state was a nationwide mortgage crisis that hit the guarantors too. The same lesson is in L1.7.12: Derivatives disasters and their lessons: AIG's credit protection triggered collateral calls just as AIG itself was downgraded.

Spark AtomDefault that depends on the value

John Hull and Alan White proposed in 2012 a simple way to build wrong-way risk into CVA: let the counterparty's hazard rate depend on variables the exposure simulation already produces, such as the value of the bank's portfolio with it. They found that wrong-way and right-way risk can change CVA significantly, and that the size of the effect, in percentage terms, depends on the collateral arrangements.

Key takeaways

Wrong-way risk: exposure tends to be high when the counterparty is likely to default; the plain CVA formula assumes they are independent.
General wrong-way risk comes from shared market drivers; specific wrong-way risk from a direct link (own shares or bonds, related protection sellers).
Linking Saltney's default to an index fall with ρ = 0.4 lifts its CVA from £958k to £1,618k; collateral shrinks the CVA but not the multiplier.
The monolines in 2007–08 showed a hedge losing value just as it was needed.
Basel: stress-test general wrong-way risk, take specific wrong-way trades out of netting sets with jump-to-default exposure, and refuse collateral correlated with the counterparty.

Reaction

Check what stuck

Glossary

Wrong-way risk: Wrong-way risk: the exposure to a counterparty tends to be large when its chance of default is high.
General wrong-way risk: General wrong-way risk: exposure and the counterparty's credit quality are both driven by the same market factors (an index, rates, a currency), so they move together.
Specific wrong-way risk: Specific wrong-way risk: a direct, structural link between the counterparty and the exposure or collateral, such as its own shares or bonds, or protection on a closely related name.
Right-way risk: Right-way risk: the exposure tends to be large when the counterparty is strong, so default is least likely when the bank is owed most.
Monoline insurer: Monoline insurer (financial guarantor): an insurer whose only business is guaranteeing timely payment on bonds, originally US municipal bonds, later also structured credit.
Gaussian copula: Gaussian copula: a way to link two random events (here, default and a market move) through correlated standard normal variables, keeping each one's own distribution.
Jump to default: Jump to default: valuing a position as if the issuer of the underlying defaulted at once.

Deep Dives & Origins

Deep Dives

J. Gregory, The xVA Challenge: Counterparty Credit Risk, Funding, Collateral, and Capital, 3rd edition, Wiley, 2015 (the chapter on wrong-way risk). Intermediate.
J. Hull and A. White, “CVA and wrong-way risk”, Financial Analysts Journal 68(5), 2012, pp. 58–69. Advanced.

Origins

P. M. Parkinson, Federal Reserve Board, testimony on financial guarantors before the House Financial Services Subcommittee on Capital Markets, Insurance, and Government Sponsored Enterprises, 14 February 2008.
Basel Committee on Banking Supervision, Basel Framework, CRE53 Internal models method for counterparty credit risk (paragraphs 53.14, 53.15, 53.47 and 53.48).
Basel Committee on Banking Supervision, Basel Framework, CRE22 Standardised approach: credit risk mitigation (paragraph 22.15).

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