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OVERVIEW OF AN INTEGRATED QUANTITATIVE FRAMEWORK IN FIXED-INCOME PORTFOLIO MANAGEMENT February 17, 1999 Global Association of Risk Professional Boston Ron D’Vari, Ph.D., CFA. The Three Pillars of Fixed-Income Portfolio Management. Ex Ante Market Expectations and Risk/Exposure - PowerPoint PPT Presentation
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Ron D'Vari 1
OVERVIEW OF AN INTEGRATED QUANTITATIVE FRAMEWORK IN
FIXED-INCOME PORTFOLIO MANAGEMENT
February 17, 1999 Global Association of Risk Professional
Boston
Ron D’Vari, Ph.D., CFA
Ron D'Vari 2
The Three Pillars of
Fixed-Income Portfolio Management
Relative Valuation and
Process Honing
Ex Post MarketMonitoring
andPerformance Attribution
Ex AnteMarket Expectations
andRisk/ExposureMeasurement
Portfolio Synthesis &Optimization
Ron D'Vari 3
• Uniform and Consistent Implementation of Market Views on Risk/Return
Multiple accounts Distinct investment guidelines Varied benchmarks
• Proper Integration of Sector views in portfolio synthesis Changing view of risk environment Performance attribution in process improvement
• Uniform Framework for Portfolio Positioning • Standardized Multivariate Risk Reports
Transparent and frequent (daily) Comprehensive yet easy to understand Address multidimensionality of risk
• Separation of Trading from Portfolio Management
ROLE OF MULTI-FACTOR MODELS IN FIXED-INCOME PORTFOLIO MANAGEMENT
Ron D'Vari 4
FACTORIDENTIFICATION
EXPOSUREDECOMPOSITION
- Intuitive
- High Explanatory
Power
- Ranked
- All Portfolios
- All Benchmarks
Control
- Benchmark Comparison
- Benchmark Variance
and Decomposition
- VAR Analysis
Absolute and Relative
- VAR Decomposition
- Forecast Returns
and Volatilities
- Scenario Analysis
SYNTHESIS/OPTIMIZATION
- Comprehensive
Scenario Sets
- Scenario
Optimization
- Scenario Return
Decomposition
- Overlay Strategies
FORWARD-LOOKINGANALYSIS
Ex Ante Risk/Exposure Measurement
• Uniform and Integrated Across All Portfolios/Business Units
• Reveals Intended and Implied Bets
Ron D'Vari 5
Factor Move Estimation and Monitoring
Factor Return Attribution Consistent with Risk Measurement
Portfolio Re-optimization
Sector/Quality Relative Valuation
Tactical SectorAllocation
Strategic Asset Allocation
Overlay Risk Hedges
Investment Process Honing
Evaluation of Asset Mix Policy
Ex-Post Market Move Monitoring and Decomposition
Feedback Into The Investment Process
Ron D'Vari 6
Elementary Risk Models
1 . S i n g l e F a c t o r f o r S t o c k s , e . g . C A P M
R R R R
C o v C o v Ri F i M F i
i j i i i
( )
( , ) , ( , ) ,0 0 0
2 . S i n g l e F a c t o r F o r F i x e d I n c o m e
R Y R Yi i M M i E f f D u r
E f f D u ri
M( )
I n i t i a l Y i e l d f o r i - t h B o n d a n d M a r k e t Y Yi M,M a r k e t R e t u r n = R M
3 . H i s t o r i c a l V a r i a n c e s A n d C o v a r i a n c e s A m o n g A l lS e c u r i t i e s - I m p r a c t i c a l
Ron D'Vari 7
Multi-Factor Risk Models
1 . N o n l i n e a r : R t f b b b ti n i( ) ( , , . . . , ) 1 2
2 . L i n e a r : R t R X t R b ti F j F jj
N
i
F
( ) ( ) ( )
1
j - t h F a c t o r E x p o s u r e = b tj ( )
j - t h F a c t o r P r e m i u m = X t Rj F( )
3 . C h o i c e o f F a c t o r s E x t e r n a l , S t a t i s t i c a l , o r I n t u i t i v e
Ron D'Vari 8
Traditional Approaches
Decoupled Macro (overall plan) vs. Micro (Portfolio) Macro: Highest risk-adjusted return via asset allocation Micro: Focus on highest return but often ignore incremental risk (stock/bond picking)
No Integrated Risk Management
Static Approach Using Forecast ReturnsRelies on historical volatilities and correlationsNeglects short horizon riskIgnores risk premium fluctuations
Does not take advantage of short term mispricing
Ron D'Vari 9
Breaks up risk in to its lowest common denominators
Integrates risk management with active management strategies
Use forward-looking view of expected returns, volatilities and correlations
Dynamic Approach Forecast both expected returns and volatilityFocus on forecast risk-adjusted returnsConsiders environment where expected returns are constant
but volatility might have risen Portfolio risk/return characteristics vs. Benchmark
State-of-the-Art Approach
Ron D'Vari 10
FIXED INCOME RISKS
CURVE SHAPE
- Parallel
- Twist
- Butterfly
- Higher Principal
Components
- Residual
VOLATILITY
- Short End
- Long End
- Volatility
Correlations
- Historical vs. Implied
CREDIT
- Spread Term
Structure
- Spread Volatilities
and Correlations
- Per Sector/Quality
- Residual Per Issuer
OTHERS
- Prepayment
- Currency (V/C)
- Sovereign
- Liquidity Premium
- Model
- Legal
- Political
- Taxes
Ron D'Vari 11
EQUITY RISKS
MARKET
- Domestic Equities
- Foreign Equities
- Beta Risk
- Correlations Risk
- Return Momentum
- Size
- Earnings: P/E
- Value: B/P
- Growth
- Dividend Yield
- Leverage [D/(D+E)]
- Liquidity
- Foreign Exposure
- Technology
- Financial
- Services
- Telecommunications
- Transportation
- Utilities
- Energy
- Healthcare
- etc.
VOLATILITY FUNDAMENTALS SECTORS
- Domestic
- Foreign
- Volatility
Correlations
- Historical and
Option-Implied
Ron D'Vari 12
HARD TO QUANTIFY RISKS
EMERGING MARKETS
- Insufficient Data/
Information
- Insufficient Credit
Legal/Political
Risk Methodology
- Data Incomparability
- Convertibility
- Expropriation
- Tradability
STRUCTURED PRODUCTS
- All Other Risks
- Basis Risk
- Liquidity Risk
- Counterparty Risk
CUSTODIAL
- Accurate Accounting
- Settlement & Disposition
- Discrepancy Reporting
- Information Accuracy
- Timely Monitoring
- Tradable Pricing
- Securities Lending,
Cash Management, etc.
- Credit
- Administration Errors
MODEL
- Insufficient Basis
- Oversimplification
- Missing Significant
Factors
- Implementation
Errors
- Insufficient Data
- Unaccounted
Structural Changes
Ron D'Vari 13
ADDED-VALUE FINANCIALRISK MANAGEMENT
FORWARD VIEW
REAR VIEW SYNTHESIS
RISK MODELS
• BENCHMARK COMPARISON
• BENCHMARK VARIANCE
• SCENARIO ANALYSIS (STRESS TESTING)
• VAR (NONLINEAR)
• PERFORMANCE ATTRIBUTION
• RISK ADJUSTED RETURN • RELATIVE VALUATION
• STRATEGIC/TACTICAL ASSET ALLOCATION
• SCENARIO OPTIMIZATION • RELATIVE VALUE ANALYSIS
Ron D'Vari 14
INTEGRATED
FIXED-INCOME
MULTI-FACTOR
MODEL
Ron D'Vari 15
Interest Rate Risk =Yield Curve = Term Structure Measured and Managed By
Curve Reshaping OA Durations (Elasticities) and Scenario Analysis
Curve
Reshaping Move
Option Adjusted Measure
Parallel Effective Duration (Edur) Twist Effective Twist Duration (Edur2)
Butterfly Effective Butterfly Duration (Edur3) Long-end Hump Effective Long-end Hump Duration (Edur4)
Residual Scenario Analysis and Key Rate Durations
MARKET
Ron D'Vari 16
Spot Curve Factor Shapes for Q1 = 7 and Q2 = 7
0
25
50
75
100
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
Tenor - Years
Sp
ot C
urv
e S
hif
t -
bp
Normalized D1 Shape
Normalized D2 Shape
Normalized D3 Shape
Wilshire Proposed Normalized D4 Shape
D1
D2D3
D4
Ron D'Vari 17
Spot Curve Factor Shapes for Q1 = 7 and Q2 = 12
0
25
50
75
100
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
Tenor - Years
Sp
ot C
urv
e S
hif
t -
bp
Normalized D1 Shape
Normalized D2 Shape
Normalized D3 Shape
Wilshire Proposed Normalized D4 Shape
D1
D2D3D4
Ron D'Vari 18
VOLATILITY
• Volatility Risk Volatility Sensitivity
• Prepayment and Call Risk Function of Interest Rates and Volatility Can be measured and managed by
Prepayment Elasticities and Convexity
Ron D'Vari 19
CREDIT
• Default Spread Measured and Managed by Effective Spread
Duration (Sprdur)
OTHERS
• Currency, Liquidity, Model, Operational, Counterparty, etc.
Ron D'Vari 20
SECTOR QUALITYTreasury Moody AaaAgency Moody Aa
Industrial Moody AUtility -Communications Moody Baa
Utility - Electric OtherUtility - Other COUPON
Finance Low Corporate (price < 95)GNMA Mortgage Current Corporate
FHLMC Mortgage High Corporate (price > 105)FNMA Mortgage Low Mortgage (price < 95)Other Mortgage Current Mortgage
High Mortgage (price > 102)
VOLATILITY
FACTORS
Ron D'Vari 21
ANALYTICREQUIREMENTS
FACTOR ANALYSIS
RISK DISSECTION
• FULL VALUATION
• SENSITIVITY ANALYSIS
• STOCHASTIC TS MODELS
• TS & Vol. FITTING
• PREPAYMENT
• INSTRUMENT & DERIVATIVES STRUCTURING
• FACTOR IDENTIFICATION
• DAILY/PERIODIC FACTOR CHANGE ESTIMATION
• FACTOR VARIANCE/ COVARIANCE EST.
• FACTOR EXPOSURE CALCULATION
• LINEAR ANALYSIS NORMAL DIST. LINEAR SENSITIVITIES LINEAR VAR
• NONLINEAR MONTE CARLO ANAL. FULL VALUATION ARBITRARY DIST.
• MULTI-FACTOR RISK DECOMPOSITION
VALUATIONENGINE
Ron D'Vari 22
FIXED-INCOME ANALYTIC
• Accurate Stochastic Interest Rate Term Structure Models Arbitrage Free One-Factor Models
Arbitrage Free Lognormal with Mean Reversion Term Structure of Volatility Stable Forward Curve Efficient and Accurate Implementation
Arbitrage Free Two-Factor Models Term Structure of Volatility
Mortgage Passthroughs, CMO’s, Special Securities Monte Carlo Simulation
Yield Curve Estimation Methodology (Fitting) Volatility Forecasting Methodology
Ron D'Vari 23
FIXED-INCOME ANALYTIC, cont.
• Option Adjusted Sensitivity AnalysisCurve ReshapingSpreadVolatility
• Prepayment Models for Agency and Non-agency Mortgages• Extensive Security Modeling Tools Call, Put, Conversion, Sinking Fund Structures, Make-Whole Calls CMO’s, Asset-backed Securities, Floating Instruments with Caps/Floors/Collars, Multi-index Floating• Derivative’s Structuring Tools Exchange and OTC Traded Fixed for Floating, CMT, and Fixed-for-Fixed Swaps Forward Swaps and Swaptions Credit Derivatives
Ron D'Vari 24
Option Adjusted Risk FactorsAbsolute, Relative, Target Relative
• Curve Sensitivities by SectorEffective Duration to Parallel Shift of Spot curveEffective Twist Duration (yield curve steepenning)Effective Barbell Duration (yield curve bulging)Effective Convexity
• Sensitivity to Key Rates• Sensitivity to Prepayment Factors• Sensitivity to Volatility• Spread Duration Risk• Sensitivity to Currencies• Sensitivity to Country Correlation Assumptions (for
tracking error)
Ron D'Vari 25
ALGORITHM FOR OPTION ADJUSTED INTEREST RATE SENSITIVITIES
ASSUME OA SPREAD
(E.G. PREVIOUS DAY VALUE)
Security Market Price
• RUN OAS• CALCULATE THEORETICAL PRICE• REVISE OAS UNTIL OAS PRICE = MARKET PRICE
SHOCK THE OAS ANALYSIS WITH• D1 CURVE MOVEMENT• D2 CURVE MOVEMENT• D3, D4 CURVE MOVEMENTS
EFF. DURATION, EffD2, EffD3, EffD4, EffCONVEXITY
Ron D'Vari 26
DAILY RISK REPORTS
• Relative Curve Exposures, Yield, OAS, Convexity• Absolute Curve Exposures• Absolute and Relative Sector Exposures
% Invested and Duration Contribution• Duration/Sector/Quality Bucket Exposure• Full-Valuation Scenario Returns by Sector
Absolute and Relative
Factor Returns
Ron D'Vari 27
FIXED-INCOME PERFORMANCE ATTRIBUTIONS
Two Approaches:• Periodic Performance Attribution
For selected accounts with special benchmarks Division to sub-periods (portfolio & benchmark)
• Portfolio action
• Market moves
• Cash Flows
• Daily Performance Attribution For all portfolios and composites
Ron D'Vari 28
GENERAL METHODOLOGY
• Detailed sub-period return attribution to: Yield, roll-down, convexity, curve,
sector/quality, selection, and trading
• Bottom-Up Approach
• Geometric Linking
• Accounts for Cash Flows at sub-period levels
Ron D'Vari 29
TOTALSUB-PERIOD RETURN
YIELD/AGING
- Yield
- Rolldown
CURVE
- Duration
- Twist
- Butterfly
- Long-end Hump
- Curve Residual
NON-CURVE
- Sector Spread
- Volatility
- Selection
OTHERS
- Currency
Hedge
- Currency
Exposure
- Trading
Ron D'Vari 30
YIELD/AGING
• Beginning portfolio return under unchanged yield curve, OAS, and volatility scenario• Includes accrued as well as accretion (aging)
CURVE
• Beginning portfolio return with end period curve and volatility under OAS unchanged scenario less yield• Decomposed to convexity, duration, twist, and butterfly • Curve residual/selection component for periodic attribution
Ron D'Vari 31
NONCURVE(OAS+VOL)
• Beginning Portfolio’s Buy-and-hold Total Return Minus [(Yield+Aging)+Curve Returns]
• Attributed to
• Credit
• Sector factor move (OAS)
• Security specific OAS move
• Selection/Residual
Ron D'Vari 32
INTRA-PERIODTRADING
• Calculated only for periodic approach
• Difference of the actual return of the portfolio from the buy-and-hold
• Portfolio’s actual total return (accounting) includes the effect of client-directed cash flows
Ron D'Vari 33
PERFORMANCE ATTRIBUTION PITFALLS
Plain bad pricing Non-contemporaneous pricing
Benchmark and PortfolioSectorsCurve calculation
Coarse generic pricing Insensitive to sector specific factors, e.g.WAM, WAC, seasoning, age, volatility
Ron D'Vari 34
PERFORMANCE ATTRIBUTION PITFALLS, cont.
Client-directed actions & cash flows that affect performance Over Linking and Cross Factor Returns Benchmark Changes and Inaccuracies
Sponsor initiated changesBenchmark pricingForward benchmark vs. Backward benchmarkExclusion/Inclusion of new asset classes
Ron D'Vari 35
CONCLUSIONS
• Comprehensive Multi-Factor ModelIntuitive FactorsHigh Fidelity Yield Curve Sensitivity ModelDetailed Sector/Benchmark Comparison Analysis
(BCA) Scenario Analysis (SA) and Optimization (SO)
• Uniform Measurement of Risk and Implementation of Market ViewsAcross Hundreds of Portfolios with Different
Benchmarks and Investment ObjectivesConsistent Reporting
Ron D'Vari 36
CONCLUSIONS (Cont’D)
• Other BenefitsPerformance Attribution
• Multi-factor
• Accurate
• Consistent with Risk Model
Quantitative Security and Sector Valuation Framework
• Multi-factor valuation
• Accurate
• Consistent with risk and performance attribution models