© brammertz consulting, 20091date: 20.10.2015 unified financial analysis risk & finance lab...
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© Brammertz Consulting, 2009 1Date: 20.04.23
Unified Financial AnalysisRisk & Finance Lab
Chapter 11: Risk
Willi Brammertz / Ioannis Akkizidis
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Risk
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Risk
The 2 main dimensions of interest rate risk are:
Rate
TimetL
VL
tA
VA
σr
σr
Δ t
Δ t
Risk intuitively explained
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1 2 3 4 5 6
Gap measures Δ T (Sensitivity gap)
Liabilities
Assets
t0Time
Interest rate gap
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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 · σr = $DUR · σr
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Is risk = VaR?
> No, VaR is subset of risk measures
> Alternative measures: e.g. > Expected shortfall
> Regulatory measures
> Alternative techniques: e.g. Stress scenarios
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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)
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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”
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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)
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Definition of (market) VaR
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Expected shortfall and VaR
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CreditRisk+, assumptions
>1 year horizon
>Net exposure per obligor (LGDi)
>Expected long term default ~pi
>Variance of default σi = pi *σ
>States of sectors Sk
>Risk allocation Θik
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CreditRisk+, easy explanation
> This is a Monte Carlo like explanation (However CreditRisk+ is analytic)
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CreditRisk+, interpretation
Risk-margin Risk-capital
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CreditMetrics (Numerical method)Migration matrix
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CreditMetricsCorrelation
>Helper variable Xi (for obligor i)
>εk is ideally a sector index (market correlated)
>Weights
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CreditMetricsSimulation steps
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Today Loss Valuation date
Maturity date Principal
Interest
Bucket 1 Bucket 2 Bucket 3
PD 1 PD 2 PD 3
Discounted loss
Valuation under Default and for Derivatives
Exposure
Impairment II
Discounted recovery
expected loss = discounted loss
– discounted recovery
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Solvency II (~Basel II) credit risk formula
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Solvency II credit riks charge
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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)
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FSA Liquidity risk requirements
Funding liquidity
Ma
rke
t liq
uid
ity
> Funding
> Behaviour
> Sales
> Prepayments
> Market liquidity
> Spreads and Liquidity
> Sales and Repos
> Target variable: Survival period
22
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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)
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Stress scenarios
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> 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
AAAAAA...
ABBBBB...
1M 10%3M 10%6M 15%1Y 25%>1Y 40%
20%40%30%10%
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Interest rate stress scenario (Solvency II)
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Backtesting: Alpha and beta errors
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Backtesting: VaR (99%)
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Backtesting: Credit rating, Gini index
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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
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Spreads and collateral
> Same problem applies to spreads
> How much collateral is assumed? -> Not known
> Better: Strict uncollateralized spreads