Banking Tutorial 8 and 9 – Credit risk, Market risk Magda Pečená Institute of Economic Studies, Faculty of Social Science, Charles University in Prague, Czech Republic November 28, 2012

Slide 2 Excursus (related to Tutorial 6 – capital structure Tier 1 capital – „the capital“

Slide 3 Credit risk (in terms of capital requirement) – recap Source: CNB, Financial market supervision report, 2010

Slide 4 Credit risk management models, Credit risk assessment Scoring Altman Z-score Rating Credit risk models Credit Monitor Model (KMV Moody´s) Credit Margin Models CreditMetrics (based on VaR methodology) RAROC

Slide 5 Credit scoring Original Altman Z-score : Revised several times, but the ratios used are more or less the same/similar

Slide 6 Credit risk – KMV model

Slide 7 Loss distribution of credit risk with certain weight of fat tails

Slide 8 Loss distribution of market risk with zero weight of fat tails ?

Slide 9 Credit risk – CreditMetrics Example of a migration matrix

Slide 10 Credit risk – CreditMetrics

Slide 11 Loan princing, Traditional approach (Cost-plus-profit approach) RAROC (Risk-adjusted return on capital (risk adjusted profitability measure where the volatility of losses is taken into account)

Slide 12 Loan pricing – traditional approach, example

Slide 13 Loan pricing 5,184

Slide 14 Value at risk - Interpretation VaR = CZK 1 million at a confidence level of 99% over a 1-day holding period. (VaR is expressed in absolute numbers, amounts). Interpretation: In 99% of cases, i.e. on an average of 99 out of 100 trading days, a maximum loss of CZK 1 million is expected. The second largest loss to occur in 100 trading days is expected to be a maxi­mum of CZK 1 million. The CZK 1 million is the minimum loss to be expected for the worst 1% of days.

Slide 15 Value at risk Historical simulation Monte Carlo simulation Variance-covariance method (analytical method, delta normal method) VaR = (z-value)* σ *P VaR t-days =t 1/2 *VaR 1-day Numbers to be remembered : 95 % confidence level – 1,65 standard deviations 99 % confidence level – 2,33 standard deviations Portfolio VaR ! Risk factors vs. positions weights !

Slide 16 VaR - example A US investor is holding a position of CZK 1 million (which translates into USD at the exchange rate of 25 CZK/1USD). The standard deviation (daily volatility) of the CZK/USD exchange rate is 0.7%. a) What is the daily VaR at a 95% confidence level? b) Determine the 10-day VaR on the same confidence level.

Slide 17 VaR – example (solution)  σ = 0,7 %  t = 1 day  P =  95 % confidence level → 1,65 standard deviations a) 1 day VaR = * 0,007 * 1,65 = USD 462 nebo/ or CZK or equivalently the value of the position will not fall with a probability of 95% under USD (P - 1,65*σ ) b) 10 day VaR = CZK * 10 1/2 = CZK

Slide 18 Value at risk - examples 1. We have a position worth CZK 15 mil in ČEZ shares. Calculate the VaR at a confidence level of 99 %, the holding period is 10 days. The daily volatility of ČEZ shares is 0,5 %. 2. Now, determine the VaR from the point of view of an German investor (so VaR in EUR). The CZK/EUR expected FX rate is 24,6, the daily volatility of the FX rate is 0,8 % and the correlation between FX risk and Czech equity risk is 0,2. 3. Assume, the German investor made a portfolio of his ČEZ shares (in CZK) and EUR 2 mil of German government bonds, with a daily volatility of 0,2 %. Determine (all on the confidence level of 99 %) the total VaR his portfolio is exposed to. The correlation between the i.r. of the government bond and his position in Czech shares is -0,1.

Slide 19 VaR – interest rate risk Present value of a basis point - Unlike the modified duration, the PVBP measures the absolute – and not the percentage – change in the current market price of a fixed-yield security when the market interest rate has changed by one basis point (0.01%), so the size and value of the position is already taken into account.

Slide 20 VaR – interest rate risk There is a zero coupon bond with a PVBP of EUR 47,500 and a 1-day volatility estimate of 0.02% (2 bps). Calculate the daily VaR at a confidence level of 95%. VaR = * 2 * 1,65 = EUR

Slide 21 RAROC Risk adjusted return on capital (RAROC ) is the risk-adjusted profitability measure where the volatility of losses is taken into account. RAROC provides a consistent view of profitability across businesses (business units, divisions). It allows the comparison of two businesses with different risk profiles, and with different volatility of returns. The pricing of a loan/product is derived from the fact that the manager must meet certain RAROC requirements (benchmark RAROC). RAROC is based on Value at risk methodology

Slide 22 RAROC Net Expected Income = interest income + fee income Economic capital = Change in a loan value when the interest rate changes by 1% / credit quality decreases (this is only an arbitrary setting, other institutions may model a 2% increase in interest rates as the corresponding economic capital requirement). The capital requirement may be calculated as follows: dL –change in a loan value D –duration of the loan L –the face (par) value of the loan i –interest rate di –change in the interest rate