1. Banking Seminar 4 – Risk management Magda Pečená Institute of Economic Studies, Faculty of Social Science, Charles University in Prague, Czech Republic October 24, 2012

2. Slide 2 Content 1.Recap of Lecture 4 (Risk management, ALM) 2.GAP analysis (Example 1) 3. Duration and convexity (Example 2, 3, 4, 5) 4. Overview of credit risk management models 5. Overview of market risk management models

3. Slide 3 Definition of risk and risk management Risk management is … (different sources) Measurement/evaluation and monitoring of risks and, where appropriate, the taking of action to limit the risks undertaken. A process involving the identification of the exposures to risk, the establishment of appropriate ranges for exposures, the continuous measurement of these exposures, and their execution. Structured asset and liability management as well as the management of off-balance sheet items (ALM). But usually we concentrate on the management of specific risks (specific stage of ALM).

4. Slide 4 Asset and liability management ALM - coordinated management of the balance sheet using various development scenarios of interest rates, liquidity and payments. ALM is managed through special banking units and/or Assets and Liabilities Committee (ALCO). The objective of ALM is to assure a banks’ liquidity, solvency and efficiency concerning: capital and liabilities structure in term of the management of capital and external sources; most of the external sources come from small depositors, but their influence on a bank is minimal, and on the other hand, the influence of management and big creditors is substantial, assets structure, their liquidity, return and risks, assets and liabilities and off-balance sheet item relations. At this point liquidity risk and insolvency risk shall be mentioned especially because they might be in mutual contradiction when achieving an optimal assets and liabilities structure.

5. Slide 5 A three stage view of ALM General stage Specific stage P/L stage (the areas to be managed are e.g. spread management, fee income management, non-interest rate costs control, tax optimisation etc.)

6. Slide 6 Categorization of risks Financial risks credit risk market risk (interest rate risk, FX risk, equity risk, commodity risk) liquidity risk Non-financial risks operational model settlement legal taxes regulation political reputational……

7. Slide 7 Content 1.Recap of Lecture 4 (Risk management, ALM) 2.GAP analysis (Example 1) 3. Duration and convexity (Example 2, 3, 4, 5) 4. Overview of credit risk management models 5. Overview of market risk management models

8. Slide 8 GAP Analysis – Basic risk management model GAP analysis for measuring liquidity risk - incremental GAP An incremental GAP analysis divides all institutions’ assets and liabilities into different time buckets. The periodic (relative) incremental GAP is defined as the difference between assets and liabilities in each time bucket.

9. Slide 9 GAP Analysis – Basic risk management model GAP analysis for measuring interest rate risk The interest rate GAP analysis divides an institution’s interest rate sensitive assets (RSA) and liabilities (RSL) into different time buckets. It measures the risk that arises from interest rate mismatch between the different time buckets. GAP analysis measures the effect of potential interest rate changes on net interest income/capital.

10. Slide 10 GAP Analysis – Basic risk management model general division of interest rate sensitive and non-sensitive assets and liabilities Assets and liabilities are assigned buckets, when repriced (revaluated).

11. Slide 11 GAP Analysis – Example Calculate: the respective periodic GAPs for all individual time buckets for interest rate sensitive assets and liabilities the cumulative interest rate GAP for interest rate sensitive assets and liabilities cumulative incremental GAP for all assets and liabilities

12. Slide 12 GAP Analysis – Example Please note that the cumulative interest rate GAP does not have to equal zero because the sum of interest rate sensitive assets usually does not equal the sum of interest rate sensitive liabilities, only the cumulative incremental GAP has to add up to 0, as assets always equal liabilities.

13. Slide 13 GAP Analysis – Example 1 Here we have a simple bank having assets and equity and liabilities in its balance sheet as of 1.2. 2012. The 6M Pribor rate is 0,6 % 1.Determine the missing asset items 2.Determine the „Registered capital“ item 3.Determine the amounts in respective time buckets.

14. Slide 14 Example 1

15. Slide 15 Content 1.Recap of Lecture 4 (Risk management, ALM) 2.GAP analysis (Example 1) 3. Duration and convexity (Example 2, 3, 4, 5) 4. Overview of credit risk management models 5. Overview of market risk management models

16. Slide 16 Traditional risk measures Volatility is a basic measurement tool of a market risk (Lecture 4). Another instrument for measuring risk is the sensitivity to adverse movements in the value of a key variable. First-order risk measures: Beta (β), Duration (D), Delta (δ) Second-order risk measures (changes in sensitivities): Convexity, Gamma, Vega and other

17. Slide 17 Traditional risk measures - Duration Interpretation is important ! Technically, duration is the time-weighted, present value of a financial instrument’s cash flows. The Macaulay duration measures the “average” life of an asset in years. It measures how long in years it takes for the price of a bond to be repaid by its internal cash flows (coupons).

18. Slide 18 Traditional risk measures - Duration Macaulay duration (  P/P)/(  i/(1+i)) Modified duration – Price sensitivity (  P/P)/  i Effective duration is the same as modified duration, but can be applied to callable bonds also, i.e. bonds with option features (it takes into account changes in cash flows when the call feature becomes effective)

19. Slide 19 Duration Important features of duration Duration can never be greater than the remaining time to maturity of a fixed-interest bearing instrument when repaid at maturity. The duration of a zero-coupon bond is exactly equivalent to the bond’s remaining time to maturity. The higher (lower) the market interest rate, the smaller (greater) the duration since the invested capital will be paid back earlier (later). The longer the time to maturity of a fixed-interest bearing security, the greater the duration.

20. Slide 20 Duration - Interpretation

21. Slide 21 Portfolio Duration Portfolio duration (D P ) is a weighted average of individual asset durations.,

22. Slide 22 Duration and convexity effects, The change in bond price is given by the sum of duration effect and convexity effect. Duration effect

23. Slide 23 Effective duration P - = the price of the bond, when interest rate decrease P + = the price of the bond, when interest rate decrease P 0 = current price di = change in the interest rate

24. Slide 24 Effective duration, Example 2 A portfolio manager wants to estimate the interest rate risk of a bond using duration. The current price of the bond is 82. A valuation model found that if interest rates decline by 30 basis points, the price will increase to 83,5 and if interest rates increase by 30 basis points, the price will decline to 80,75. What is the duration of this bond ? CFA Program, Level 1, Volume 5

25. Slide 25 Comparison calculations, Example 3 Duration determined by effective duration calculation and by Modified duration calculation – for comparison see the excel sheet 6-year loan (2007-2013), repayment in 6 annual instalments, coupon of 5 %. Now (31.12.2010), three years to go for the final repayment.

26. Slide 26 Duration and convexity, Example 4, Assume the current price of the bond is 108, the modified duration is 4.5 and convexity 87. Interpret this information in the case of a 0.8% decrease in the general level of interest rates.

27. Slide 27 Duration and convexity, Example 4, Assume the current price of the bond is 108, the modified duration is 4.5 and convexity 87. Interpret this information in the case of a 0.8% decrease in the general level of interest rates. Price change (in %) due to duration = (–4.5) * (–0.8%) = 3.6% Interest rates decreased => price due to duration increased New price due to duration only = 108* (1 + 0.036) = 111.89 Price change due to convexity only = 0,5 * 87 * 108 * 0.008 2 = 0.300672 New price (due to duration and convexity) = 111.89 + 0.30 = 112.19

28. Slide 28 Duration, Example 5 A bond portfolio manager gathered teh following information about a bond issue: Par valueUSD 10 mil. Current market valueUSD 9,85 mil. Duration4,8 If yields are expected to decline by 75 basis points, which of the following would provide the most appropriate estimate of the price change for the bond issue: A.3,6 % of USD 9,85 mil. B.3,6 % of USD 10 mil. C.4,8% of USD 9,85 mil. CFA Program, Level I, Volume 5

29. Slide 29 Content 1.Recap of Lecture 4 (Risk management, ALM) 2.GAP analysis (Example 1) 3. Duration and convexity (Example 2, 3, 4, 5) 4. Overview of credit risk management models 5. Overview of market risk management models

30. Slide 30 Credit risk management models, Credit risk assessment Rating Scoring Altman Z-score Credit risk models Credit Monitor Model (KMV Moody´s) Credit Margin Models CreditMetrics (based on VaR methodology) RAROC

31. Slide 31 Content 1.Recap of Lecture 4 (Risk management, ALM, GAP analysis) 2.GAP analysis (Example 1) 3. Duration and convexity (Example 2, 3, 4, 5) 4. Overview of credit risk management models 5. Overview of market risk management models

32. Slide 32 Market risk management models, Portfolio immunization (application of information contained in duration) Value at risk

33. Slide 33 Portfolio immunization, Immunization is a process by which a bond portfolio is created to have an assured return for a specific time horizon irrespective of interest rate changes. Conditions that must be met in order to have the portfolio immunized: portfolio’s (assets) duration is equal to the liability’s (effective) duration, initial present value of the projected cash flows from the asset portfolio equals the present value of the future liabilities. (To immunize is to match the durations of assets and liabilities within a portfolio for the purpose of minimizing/eliminating the impact of interest rate changes on the net worth., i.e. under each interest rate change scenario the reinvestment risk and the price risk compensate each other.)

34. Slide 34 Source