Integration of Market and Credit Risk in Foreign Currency Loan - - PowerPoint PPT Presentation

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Integration of Market and Credit Risk in Foreign Currency Loan Portfolios

Thomas Breuer1 Martin Jandaˇ cka1 Gerald Krenn2 Klaus Rheinberger1 Martin Summer2

1Research Centre PPE, Dornbirn, Austria 2Oesterreichische Nationalbank, Vienna, Austria

GOR AG "Finanzwirtschaft und Finanzinstitutionen" Augsburg, 16 May 2007

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Outline

1

The Model

2

Risk Analysis of FX Loans

3

Interaction of Market and Credit Risk

4

Macro Stress Testing

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

The Market Share of Foreign Currency Loans

Quelle: OeNB: Vortrag Christl, Innsbruck, 3. 10. 2005

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Goals

1

Analyse risk profiles of foreign and home currency portfolios

2

Analyse interaction of market and credit risk

3

Propose systematic method to perform macro stress tests

• n loan portfolios

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Outline

1

The Model

2

Risk Analysis of FX Loans

3

Interaction of Market and Credit Risk

4

Macro Stress Testing

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Portfolio

Obligors 1, . . . , N hold CHF loans maturing in one year CHF amount due: l/e(0) where e(0) is initial exchange rate, and l is loan amount in EUR. After one year:

bank pays back CHF amount l(1 + rf)/e(0) on interbank market costumer pays bank EUR amount POf := l (1 + rf) e(1)/e(0) + s l e(1)/e(0), where rf is average CHF LIBOR interest rate, s is spread over LIBOR paid by obligor.

Compare: For EUR loan costumer pays back POh = l (1 + rh + s).

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Assumption 1: Costumer default

Costumers default in case their payment ability PA at the expiry

• f the loan is smaller than their payment obligation PO.

In case of default the costumer pays PA. The profit or loss the bank makes with a costumer is min(PA, PO) − l(1 + r)e(1)/e(0).

Remarks: One-period structural model specifying default frequencies and losses given default endogeneously. We assume collaterals enter only indirectly via PA. LGD depends on macroeconomic situation only indirectly via PA. Even if costumer defaults bank might make a profit because PO includes the spread over the LIBOR.

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Assumption 2: Payment Ability

The payment ability of each costumer is distributed like PA(t) = PA(0)· m· GDP(t) GDP(0)· ǫ, ǫ ∼ χ2

k/k

where χ2-dist with k dof and expectation k, and m is a constant. For different costumers the realisations of ǫ are independent.

Remarks: m describes sensitivity of PA to GDP changes. PA(0) = 1.1· l: safety margin set by bank. The expectation of PA(t) is PA(0)· m times the expectation of GDP(t)/GDP(0).

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Assumption 2’: Payment Ability

The payment ability of each costumer is distributed like PA(t) = PA(0)· m· GDP(t) GDP(0)· ǫ, ǫ ∼ lognormal with expectation 1 m is a constant. For different costumers the realisations of ǫ are independent.

Remarks: m describes sensitivity of PA to GDP changes. PA(0) = 1.1· l: safety margin set by bank. The expectation of PA(t) is PA(0)· m times the expectation of GDP(t)/GDP(0).

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Calibration to rating

Bank determines "average" default probability pi from rating. pi: conditional prob of default on the expected PO under condition that macro/market risk factors (GDP , e, rf) at time 1 take their expected values. The only free parameter k (resp. σ) in the distribution ǫ is determined by the calibration condition P [PA < PO|GDP(1) = E(GDP), e(1) = E(e), rf(1) = E(rf)] = pi.

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Assumption 3: Lognormal Macro/Market Model

The logarithmic changes of the macro/market risk factors (GDP , rf, e) follow a joint normal distribution.

Assume all 4 time series are stationary

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Assumption 3’: VECM Macro/Market Model

The four risk factors GDP , home and foreign interest rate, and exchange rate are modelled jointly in the vector time series Yt which is assumed to obey the VECM ∆Yt = ΠYt−1 + Γ1∆Yt−1 + ǫt (1) with ǫt ∼ N(0, Ω). No deterministic trends are assumed in the VECM.

Allow for non-stationary time series: det(Π) = 0. Π = αβ′ with rank (α) = rank (β) = r ≤ 4. Allow for r co-integating relationships (stationary linear combinations.) Alternative: GVAR: include weakly exogenous variables from other economies.

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Outline

1

The Model

2

Risk Analysis of FX Loans

3

Interaction of Market and Credit Risk

4

Macro Stress Testing

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Sample Portfolio

100 CHF loans equivalent to 10,000 EUR each, maturing in 1 year rating class B+: pi = 2% rating class BBB+: pi = 0.1% safety margin: PA(0) = 1.1· 10, 000 EUR spread over LIBOR: s = 100bp. If no defaults: Bank Profits from spreads 10, 000· e(1)/e(0) EUR for FX loan portfolio, 10, 000 EUR from EUR loan portfolio.

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Estimation of Profit/Loss distribution

1

Estimate parameters of log-normal dist of macro/market risk factors from yearly data 1989–2005.

2

100,000 scenario draws from macro/market distribution

3

For each scenario draws 100 draws from PA distribution.

4

Calculate mean and Expected Shortfall (ES) from resulting profit/loss distribution.

5

Risk capital = mean – ES

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Risk and Return of home vs. FX loan portfolio

VECM for Macro Risk Factors

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Risk and Return of home vs. FX loan portfolio

Expected profits from the home currency loan portfolios are significantly higher than from foreign currency loan portfolios. To compensate for this banks should require 3 to 8 bp higher spreads over LIBOR for foreign currency loans than for home currency loans. Risk of foreign currency loan portfolios is far higher than for home currency loan portfolios. e.g. for lognormal model – in rating class B+ by a factor between 6 and 22, – in rating class BBB+ by a factor between 35 and 90.

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Outline

1

The Model

2

Risk Analysis of FX Loans

3

Interaction of Market and Credit Risk

4

Macro Stress Testing

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

How to Measure Interaction of Market and Credit Risk

(0) pure macro/market risk model: assume no defaults are possible (1) pure credit risk model: assume macro/market risk factors are constant (2) integrated macro and credit risk model: macro/market and credit risk factors move simultaneously integration effect indicator I = RC(integrated) RC(market&macro) + RC(credit). If I<1: "Diversification" between credit and market risk. If I>1: dangerous interaction of credit and market risk.

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Interaction of Macro/Market and Credit Risk

VECM Model for Macro Risk Factors

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Interaction of Market and Credit Risk

For the home currency loan portfolio Integrated risk capital is more or less the same as the sum

• f separate market and credit risk capital.

Pure credit risk is practically the same as integrated risk. Pure market risk is zero, because at the time horizon all loans mature and interest rate risk becomes irrelevant. For the foreign currency loan portfolio Integrated risk exceeds the sum of pure market and pure credit risk by a factor between 2.6 and 22, depending on the quantile and the rating class.

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Outline

1

The Model

2

Risk Analysis of FX Loans

3

Interaction of Market and Credit Risk

4

Macro Stress Testing

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Standard Stress Scenarios

Consider conditional profit/loss distributions if EUR rises against CHF by 20%, GDP falls by 3%.

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Standard Stress Scenarios

Lognormal Model for Macro Risk Factors

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Results of Standard Stress Tests

Lognormal Model for Macro Risk Factors

Both shocks affect the B+ portfolio more seriously than the BBB+ portfolio. This is true for both the home and the FX loan portfolios. The GDP shock affects both the home and the FX loan portfolio, but the foreign more seriously: It reduces expected profits of BBB+ home portfolio by 1/10,

• f BBB+ FX loan portfolio by 1/3.

The exchange rate shock has a dramatic effect on the mean and the quantiles of the P/L-distributions: Expected profits move from ca. +9,900 EUR to ca. −60, 000.

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Dangers of Standard Stress Tests

False illusion of safety: Perhaps we missed more dangerous scenarios Implausible scenarios: If our standard scenarios are implausible, should we act on alarming stress test results?

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Worst Case Scenarios

Search for worst case scenarios over admissibility domain of all plausible macro scenarios. Worst case: lowest expected profits. Plausible Macro Scenarios r:

• (r − µ)T · Σ−1 · (r − µ) ≤ k

All moves smaller than k standard deviations. Σ−1: covariance matrix of macro/market risk factor changes.

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Stochastic Optimisation Problem

Minimise expectation value of conditional profit/loss distribution given macro scenario

• ver macro scenarios in ellipsoid

n r : p (r − µ)T · Σ−1 · (r − µ) ≤ k

• Nonlinear, noisy objective function,

non-linear boundary of admissibility domain.

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Deterministic Optimisation Problem

Lemma The conditional expectation of the P/L distribution, given the values e := e(1)/e(0), g := GDP(1)/GDP(0), and rf is PA(0)g λ0 λρ(λ)dλ + les − le(1 + rf + s) λ0 ρ(λ)dλ, where ρ is the probability density of the distribution ǫ (1), and λ0 := e(1 + rf + s)/(PA(0)g). Thus: Expected profits conditional on macro scenario are a deterministic function of macro risk factors (e, GDP , r).

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Worst Case Scenarios

Key risk factors: Bold face Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Worst Case Scenario Analysis

Risk of FX loan portfolio much higher Key risk factor of FX loan portfolio: EUR/CHF rate Key risk factor of EUR loan portfolio: GDP

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Expected profits as a function of macro risk factors

Lognormal Model for Macro Risk Factors

−2 −1 1 2 80 85 90 95 100 Change of risk factors [stdevs]. Expected profit/loss gdp exchange ir −2 −1 1 2 80 85 90 95 100 Change of risk factors [stdevs]. Expected profit/loss gdp ir

FX loans EUR loans Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Expected profits as a function of macro risk factors

−4 −2 2 4 −600 −500 −400 −300 −200 −100 100 200 Change of risk factors [stdevs]. Expected profit/loss gdp exchange ir −4 −2 2 4 −600 −500 −400 −300 −200 −100 100 200 Change of risk factors [stdevs]. Expected profit/loss gdp ir

FX loans EUR loans Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

Expected profits as a function of macro risk factors

−2 −1 1 2 −2 −1 1 2 −50 50 100 Change of gdp [stdevs]. Change of exchange [stdevs]. Expected prtofit/loss

−2 2 −2 2 −50 50 100 Change of gdp [stdevs]. Change of ir [stdevs]. Expected prtofit/loss

FX loans EUR loans Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

And here are the main points again ...

1

Expected profits are lower for FX loan portfolios than for EUR loan portfolios, assuming same spread over LIBOR, same loan approval policy.

2

For bank, risk is dramatically higher for FX loan portfolios than for EUR loan portfolios, assuming same spread over LIBOR, same loan approval policy.

3

Only integrated credit and market risk models can capture the dangerous interaction effects between credit and market risk.

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios

The Model Risk Analysis of FX Loans Interaction of Market and Credit Risk Macro Stress Testing

And here are the main points again ...

1

For stress tests with standard scenarios: do not fill in values of risk factors you are not interested, instead analyse conditional P/L-distribution

2

Search systematically for worst case scenarios in a domain

• f plausible scenarios

so consider all scenarios which are sufficiently plausible

Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios