1. © Brammertz Consulting, 20091Date: 20.10.2015 Unified Financial Analysis Risk & Finance Lab Chapter 11: Risk Willi Brammertz / Ioannis Akkizidis

2. © Brammertz Consulting, 20092Date: 20.10.2015 Risk

3. © Brammertz Consulting, 20093Date: 20.10.2015 Risk The 2 main dimensions of interest rate risk are: Rate Time tLtL VLVL tAtA VAVA  σr σr σr σr  Δ t Δ t Risk intuitively explained

4. © Brammertz Consulting, 20094Date: 20.10.2015 1 2 3 4 5 6 Gap measures Δ T (Sensitivity gap) Liabilities Assets t0t0 Time Interest rate gap

5. © Brammertz Consulting, 20095Date: 20.10.2015 Risk and sensitivity > General definition > Example: Interest rate risk Risk per unit of asset = Sensitivity * Risk factor volatility Δ NPV = NPV · Dur · Δ r = $DUR · Δ r σ NPV = NPV · Dur · σ r = $DUR · σ r

6. © Brammertz Consulting, 20096Date: 20.10.2015 Is risk = VaR? > No, VaR is subset of risk measures > Alternative measures: e.g. > Expected shortfall > Regulatory measures > Alternative techniques: e.g. Stress scenarios

7. © Brammertz Consulting, 20097Date: 20.10.2015 Critique on VaR > Losses beyond the confidence interval not taken into account > No sub-additivity > Focus on market value only > Sensitivity only linear approximation (parametric VaR)

8. © Brammertz Consulting, 20098Date: 20.10.2015 Critical voices > Taleb: “… VAR is charlatanism, a dangerously misleading tool – like much of modern mathematised academic finance” > Turner report: “… misplaced reliance on sophisticated mathematics, which, once irrational exuberance disappeared, contributed to a collapse …” and “Mathematical sophistication ended up not containing risk, but providing false assurance that other prima facie indicators of increasing risk (e.g. rapid credit extension and balance sheet growth) could be safely ignored”

9. © Brammertz Consulting, 20099Date: 20.10.2015 Critical voices > Keynes: “Too large a proportion of recent “mathematical” economics are mere concoctions, as imprecise as the initial assumptions they rest on, which allow the author to lose sight of the complexities and interdependencies of the real world in a maze of pretentious and unhelpful symbols” (General Theory, p.298)

10. © Brammertz Consulting, 200910Date: 20.10.2015 Definition of (market) VaR

11. © Brammertz Consulting, 200911Date: 20.10.2015 Expected shortfall and VaR

12. © Brammertz Consulting, 200912Date: 20.10.2015 CreditRisk+, assumptions > 1 year horizon > Net exposure per obligor (LGD i ) > Expected long term default ~p i > Variance of default σ i = p i * σ > States of sectors S k > Risk allocation Θ ik

13. © Brammertz Consulting, 200913Date: 20.10.2015 CreditRisk+, easy explanation > This is a Monte Carlo like explanation (However CreditRisk+ is analytic)

14. © Brammertz Consulting, 200914Date: 20.10.2015 CreditRisk+, interpretation Risk-marginRisk-capital

15. © Brammertz Consulting, 200915Date: 20.10.2015 CreditMetrics (Numerical method) Migration matrix

16. © Brammertz Consulting, 200916Date: 20.10.2015 CreditMetrics Correlation > Helper variable X i (for obligor i) > ε k is ideally a sector index (market correlated) > Weights

17. © Brammertz Consulting, 200917Date: 20.10.2015 CreditMetrics Simulation steps

18. © Brammertz Consulting, 200918Date: 20.10.2015 TodayLoss Valuation date Maturity date Principal Interest Bucket 1Bucket 2Bucket 3 PD 1PD 2PD 3 Discounted loss Valuation under Default and for Derivatives Exposure Impairment II Discounted recovery expected loss = discounted loss – discounted recovery

19. © Brammertz Consulting, 200919Date: 20.10.2015 Solvency II (~Basel II) credit risk formula

20. © Brammertz Consulting, 200920Date: 20.10.2015 Solvency II credit riks charge

21. © Brammertz Consulting, 200921Date: 20.10.2015 Liquidity and liquidity risk > Funding (structural, idiosyncratic) liquidity > Problem: Cash outflow > inflow > Risk incurred due to internal factors > Needs cash flow control (chapter 8) > Liquidity Gap analysis for basic analysis > Static analysis combined with behavioral stresses (ch 11.5) > Market liquidity: External factors affecting liquidity > Problem: Money stops flowing between actors > Risk incurred due to external factors > Related to credit risk > Dynamic analysis (chapter 14.4) Liquidity Risk Funding (structural, idiosyncratic) Market

22. © Brammertz Consulting, 200922Date: 20.10.2015 FSA Liquidity risk requirements Funding liquidity Market liquidity > Funding > Behaviour > Sales > Prepayments > Market liquidity > Spreads and Liquidity > Sales and Repos > Target variable: Survival period 22

23. © Brammertz Consulting, 200923Date: 20.10.2015 Other risks > Earning at risk: > Focus on earning instead of value > Makes no sense in a static environment > Insurance risk: Static makes little sense (although some method proposed by Solvency II) > Operational risk: The other animal (Chapter 12)

24. © Brammertz Consulting, 200924Date: 20.10.2015 Stress scenarios

25. © Brammertz Consulting, 200925Date: 20.10.2015 > A stress test is a shift in one or more of the risk factors > Market stress > Credit stress > Liquidity stress Static stress testing Time to Maturity Yield AAA AA A... A BBB BB... 1M 10% 3M 10% 6M 15% 1Y 25% >1Y 40% 20% 40% 30% 10%

26. © Brammertz Consulting, 200926Date: 20.10.2015 Interest rate stress scenario (Solvency II)

27. © Brammertz Consulting, 200927Date: 20.10.2015 Backtesting: Alpha and beta errors

28. © Brammertz Consulting, 200928Date: 20.10.2015 Backtesting: VaR (99%)

29. © Brammertz Consulting, 200929Date: 20.10.2015 Backtesting: Credit rating, Gini index

30. © Brammertz Consulting, 200930Date: 20.10.2015 Rating and collateral > Credit ratings are often a combination of probability of default, collateral and recovery > Each of these categories has different „statistical qualtiy“ > Therefore they should not be confounded into a single measure > Rating should only reflect probability of default = uncollateralized rating

31. © Brammertz Consulting, 200931Date: 20.10.2015 Spreads and collateral > Same problem applies to spreads > How much collateral is assumed? -> Not known > Better: Strict uncollateralized spreads