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

© Brammertz Consulting, 20092Date: Risk

© Brammertz Consulting, 20093Date: 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

© Brammertz Consulting, 20094Date: Gap measures Δ T (Sensitivity gap) Liabilities Assets t0t0 Time Interest rate gap

© Brammertz Consulting, 20095Date: 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

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

© Brammertz Consulting, 20097Date: 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)

© Brammertz Consulting, 20098Date: 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”

© Brammertz Consulting, 20099Date: 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)

© Brammertz Consulting, Date: Definition of (market) VaR

© Brammertz Consulting, Date: Expected shortfall and VaR

© Brammertz Consulting, Date: 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

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

© Brammertz Consulting, Date: CreditRisk+, interpretation Risk-marginRisk-capital

© Brammertz Consulting, Date: CreditMetrics (Numerical method) Migration matrix

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

© Brammertz Consulting, Date: CreditMetrics Simulation steps

© Brammertz Consulting, Date: 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

© Brammertz Consulting, Date: Solvency II (~Basel II) credit risk formula

© Brammertz Consulting, Date: Solvency II credit riks charge

© Brammertz Consulting, Date: 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

© Brammertz Consulting, Date: 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

© Brammertz Consulting, Date: 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)

© Brammertz Consulting, Date: Stress scenarios

© Brammertz Consulting, Date: > 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%

© Brammertz Consulting, Date: Interest rate stress scenario (Solvency II)

© Brammertz Consulting, Date: Backtesting: Alpha and beta errors

© Brammertz Consulting, Date: Backtesting: VaR (99%)

© Brammertz Consulting, Date: Backtesting: Credit rating, Gini index

© Brammertz Consulting, Date: 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

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