© brammertz consulting, 20091date: 20.10.2015 unified financial analysis risk & finance lab...

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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