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 Breuer 1 cka 1 Gerald Krenn 2 Martin Jandaˇ Klaus Rheinberger 1 Martin Summer 2 1 Research Centre PPE, Dornbirn, Austria 2 Oesterreichische 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 The Model 1 Risk Analysis of FX Loans 2 Interaction of Market and Credit Risk 3 Macro Stress Testing 4 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 Analyse risk profiles of foreign and home currency 1 portfolios Analyse interaction of market and credit risk 2 Propose systematic method to perform macro stress tests 3 on 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 The Model 1 Risk Analysis of FX Loans 2 Interaction of Market and Credit Risk 3 Macro Stress Testing 4 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 + r f ) / e ( 0 ) on interbank market costumer pays bank EUR amount PO f := l ( 1 + r f ) e ( 1 ) / e ( 0 ) + s l e ( 1 ) / e ( 0 ) , where r f is average CHF LIBOR interest rate, s is spread over LIBOR paid by obligor. Compare: For EUR loan costumer pays back PO h = l ( 1 + r h + 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 of 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 ( 0 ) · m · GDP ( t ) PA ( t ) = GDP ( 0 ) · ǫ, χ 2 ǫ ∼ k / k where χ 2 -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 ( 0 ) · m · GDP ( t ) PA ( 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 p i from rating. p i : conditional prob of default on the expected PO under condition that macro/market risk factors (GDP , e , r f ) 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 ) , r f ( 1 ) = E ( r f )] = p i . 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 , r f , 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 Y t which is assumed to obey the VECM ∆ Y t = Π Y t − 1 + Γ 1 ∆ Y t − 1 + ǫ t (1) with ǫ t ∼ 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 The Model 1 Risk Analysis of FX Loans 2 Interaction of Market and Credit Risk 3 Macro Stress Testing 4 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+: p i = 2 % rating class BBB+: p i = 0 . 1 % safety margin: PA ( 0 ) = 1 . 1 · 10 , 000 EUR spread over LIBOR: s = 100 bp . 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 Estimate parameters of log-normal dist of macro/market 1 risk factors from yearly data 1989–2005. 100,000 scenario draws from macro/market distribution 2 For each scenario draws 100 draws from PA distribution. 3 Calculate mean and Expected Shortfall (ES) 4 from resulting profit/loss distribution. Risk capital = mean – ES 5 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 The Model 1 Risk Analysis of FX Loans 2 Interaction of Market and Credit Risk 3 Macro Stress Testing 4 Breuer, Jandaˇ cka, Krenn, Rheinberger, Summer Market and Credit Risk in FX Loan Portfolios