1. 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

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

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

4. 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

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

6. Slide 6 Credit risk – KMV model

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

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

9. Slide 9 Credit risk – CreditMetrics Example of a migration matrix

10. Slide 10 Credit risk – CreditMetrics

11. 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)

12. Slide 12 Loan pricing – traditional approach, example

13. Slide 13 Loan pricing 5,184

14. 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.

15. 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 !

16. Slide 16 VaR - example A US investor is holding a position of CZK 1 million (which translates into USD 40 000 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.

17. Slide 17 VaR – example (solution)  σ = 0,7 %  t = 1 day  P = 40 000  95 % confidence level → 1,65 standard deviations a) 1 day VaR = 40 000 * 0,007 * 1,65 = USD 462 nebo/ or CZK 11 550 or equivalently the value of the position will not fall with a probability of 95% under USD 39 538 (P - 1,65*σ ) b) 10 day VaR = CZK 11 550 * 10 1/2 = CZK 36 524

18. 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.

19. 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.

20. 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 = 47 500 * 2 * 1,65 = EUR 156 750

21. 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

22. 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