1
Q
Features of Equity Returns
A
- Rarely IID
- Heteroscedasticity
- Volatility Clustering
- Leptokurtic
Less Pronounced over Long Periods (over-optimism/pessimism corrections however)
2
Q
Features of Portfolio Returns
A
- Correlations Between Series at Given Time
- Correlations Vary Over Time
- No Cross-correlation (t and t+1)
- Cross-correlation between squared/absolute value returns
- Increased dependence during high volatility periods
Less Pronounced over Long Periods (over-optimism/pessimism corrections however)
3
Q
Modelling Market Returns
A
- Historical Simulations (Boostrapping)
- Forward Looking
- Data (multi-variate normal, other joint distribution or copula - 6-step)
- Factor (PCA 10-step)
4
Q
6 Step Forward Looking Data Approach Market Risk
A
- Decide Frequency (daily, weekly, monthly)
- Time frame for historical data (volume vs relevance)
- Choose Return Index
- Evaluate log returns
- Calculate average returns, variances and covariances
- Simulate Series of Returns
5
Q
10 Step Forward Looking Factor Approach Market Risk
A
Dim Red, Assumes Normal Distribution,
- Decide Frequency (daily, weekly, monthly)
- Time frame for historical data (volume vs relevance)
- Choose Return Index
- Evaluate log returns
- Calculate average returns, variances and covariances
- Derive Matrix of Deviations From Average
- Derive Principle Components Sufficient To Explain Deviation
- - Power method (V1* = SigmaV, then V = V1/maxval)
- - Normalise dividing by V’V
- - Subtract eigenvalue*VV’ from Sigma
- - Repeat - Create i.i.d. random variables using eigenvalues as variance (X = VLZ + u)
- Weight by elements of eigenvectors.
- Add weighted projected deviances to expected returns.
6
Q
Market Risk Under Basal II
A
Internal model 10-day 99% VaR
7
Q
Credit Spread Reflects …
A
- Expected probability of, and loss given default
- Uncertainty of Above (risk premium)
- Liquidity Premium
8
Q
Three ways of measuring credit spread
A
- Nominal Spread (GRY risky less risk free)
- Static Spread (addition to risk free spot rates to have discounted cashflows equate to price)
- Option adjusted spread (stochastic models to adjust for embedded options)
9
Q
Expected Return on Other Asset Classes
A
Consider:
- Historical Risk Premiums
- Alter allowing for expected future changes
- Subjective
- Based on fundamental structural changes in asset class
- Consistent Approach with CAPM
10
Q
Properties of Good Benchmark (6, 7)
A
- Unambiguous
- Investable and Trackable
- Frequently measurable
- Appropriate to Objectives
- Reflects current sentiment
- Specified in advance
Optional, - Contains portion of assets in portfolio
- Similar investment style to portfolio
- Low constituent turnover
- Investable portion sizes
- p(rx - rm, rb - rm)»_space; 0
- p(rx - rb, rb - ru)»_space; 0
- Variability of portfolio returns relative to benchmark should be lower than variability relative to market return.
11
Q
Benchmark Risk Types
A
- Strategic Risk: Poor performance of benchmark
- Active Risk: Poor performance of portfolio relative to benchmark
- Active return: Return relative to benchmark
12
Q
Steps in PCA approach of interest rate risk
A
- Decide on frequency
- Decide on time frame
- Take GRYs for bonds of different durations and calculate average interest rate for series
- Deduct average interest rate (derive deviation)
- Set of factors chosen and weighted, then projected using independent random normal varaibles to produce expected interest rates for each term.
13
Q
Exchange Rate Equation
A
e_0(1 + Ry,T)/e_T = 1 + Rx,T
Where Ry,T is return in foreign currency.
e_0 is amount in foreign currency for 1 unit of domestic.
14
Q
Assessing Contagion Risk
A
- Suitably parameterised copula to model interaction between series’, particularly at extreme negative values.
- T-Copula with situation-dependent correlation parameter
- Sealer correlation effects ignored due to arbitrageurs.
15
Q
Brennan-Schwartz Model
A
r1,t = (a_1 + b(r2 - r1))deltaT + rE r2,t = ((a2 + b2r1 + cr2)r2)DeltaT + r2E
16
Q
Types of Credit Risk
A
- Default Risk (loss due to missed payment)
2. Credit Spread (changes in value due to change sin credit spread)
17
Q
Components of Default Risk
A
- Probability of Default
- Loss on Default
- Level and Nature of interactions between various credit exposures and other non-credit risks
18
Q
Sources of Information To Assess Credit Risk
A
- Credit Issuer (cost/benifit info)
- Counterparty (questionaire)
- Publicly available data (Basal disclosure, stock exchange)
- Proprietary Databases (experian)
19
Q
Difficulties of Credit Risk Assessment
A
- Lack of publicly available data
- Skewness of Loss Distribution
- Complex, uncertain interdependencies
- Model Risk
20
Q
Factors in Qualitative Credit Models
A
- Nature of Borrower
- Financial Ratios
- Economic Indicators
- Nature and Level of Security
- Seniority of Debt
- Face to Face Meetings
21
Q
Pros/Cons of Qualitative Credit Models
A
Pros:
- Wide range of features considered
Cons:
- Excessive Subjectivity
- Lack consistency between ratings
- Meanings of ratings change over economic cycle
- Ratings may not change in response to economic changes or counterparty changes (anchoring bias)
22
Q
Types of Quantitative Credit Models
A
- Credit-Scoring Models
- Empirical or expert models using fundamental information to assess default probability. - Structural Models
- Based on share price of volatility rather than “fundamental” attributes. - Reduced-Form Models
- Model as a statistical process rather than mechanism that could depend on economic variables (e.g. credit migration models) - Credit-Portfolio Models
- Estimate credit exposure, taking into account diversification effects - Credit Exposure Models
- Estimation of expected/maximum credit exposure using monte-carlo simulation where there are options/derivatives or guarantees
23
Q
Types of Credit Portfolio Models
A
- Multivariate Structural Models
- Multi-variate Credit Migration Models
- Models Movements in equity value
- Corresponding change in asset value
- Associated change in credit rating
- Implied change in bond value
(via monte-carlo simulation of index and specific asset volatility) - Economietric/Actuarial Models
- Don’t model asset value going forwards, but estimate default rate of firms from external or empirical data.
- Average default rates and volatility of portfolio, with broad brush estimate of future losses. - Common Shock Models
- Poisson process of shocks which impact one or more of the portfolio bonds. - Time-until-default Models
- Uses survival CDFs based on hazard rate, linking the CDF by a copula.
24
Q
Modelling Recoveries
A
- Price After Default
- Ultimate Recovery
Depends on:
- Availablitliy/marketability/liquidity of collateral
- Seniority of debt
- Rights of Other creditors
Estimated based on historical recovery rates.
25
Nature of Operational Risk (5 main points)
Data Insights (3 points)
1. No inherent upside
2. Main driver behind many recent major financial disasters
3. Interlinked with credit and market risk
4. Exacerbated by being treated differently accros parts of single organisation
5. Managed carefully to reduce impact on reputational risk.
Data Shows:
1. Skewed to large number of small losses.
2. Heavy tailed
3. Frequency can vary significantly over time, losses occur randomly.
4. Can be cyclical and/or depend on economic conditions.
26
Bottom Up Operational Risk Modelling Considerations
- Starts from low level of detail and aggregates up:
1. Small day to day losses modelled using statistical distribution.
2. Infrequency large events modelled using EVT.
3. Scenario Analysis reflect linkages between operational and other risks where data is limited.
27
Benefits of Scenario Analysis in Operational Risk
1. Captures opinions and concerns of management.
2. Not relying heavily on historical data.
3. Opportunity to identify hard to predict, high impact events.
4. Increased understanding of cause and effect
28
Top Down Operational Risk Models
1. Implied Capital Model
- Not straight forward to estimate risk capital
- Interdependence between risks ignored
- +ve: Simple, forward looking
2. Implied Volatility Model
- Better data for volatility than for capital.
- Not forward looking (e..g. if company is rapidly evolving)
- Doesn't account for softer risk (reputational)
3. Economic Pricing Models (CAPM)
- No info on specific risks
- Operational risk independent on controls
- Less account of tail risk
- Doesn't help to identify risk to avoid
4. Analogue Models (using data from similar companies)
Don't capture successfully low probability, high consequence risk events.
29
Operational risk Approach in Basal Accords
1. Advanced Measurement Approach:
- Internal models
- Scenario Analysis (approval and continually checked by supervisors)
- 1-year holding period 99.9% confidence interval
- Internal data for repeated, high frequency events, external data for low frequency losses, suitable stress scenarios.
2. Factor Based
- Basel Indicator
- Standardised Approach
30
Operational Risk Policy Requirements
1. Risk Policy and Organisation:
Principles, definitions, objectives, processes and tools, organisational structure, roles and responsibilities.
2. Risk Identification and Assessment:
Loss incident database, control self-assessment, risk mapping, key risk indicators, minimum performance triggers.
3. Capital allocation and performance measurement
4. Risk mitigation and control
5. Risk transfer and finance.
31
Demographic Risk Features and Assessment
1. Level Risk
- Combine experience rating (portfolio) and risk rating (GLM) with suitable creditiblity weighting
2. Reserving Risk
a. Volatility
- Stochastically assuming underlying statistical process
b. Catastrophe
- Scenario analysis, with complex dependencies via copulas
c. Trend Risk
- Conservative Assumptions
32
Non-life Demographic Risk Differences
1. Intensity of claim modelling
2. Multiple claims possible
3. Many states of policy
4. Trend risk less significant
5. Trend more likely with economic cycle
33
What is spectral theorem
Eigenvalue = eigenvector' x Sigma * eigenvector
ERM
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