Ron D'Vari, Ph.D. State Street Research 1
INTEGRATED MULTI-FACTORRISK MANAGEMENT AND
PERFORMANCE ATTRIBUTION
Ron D’Vari, Ph.D.Vice President, Fixed Income
State Street Research & ManagementVisiting Lecturer, Boston University
Presented At Risk ‘97 SeminarJune 4, 1997, Chicago, IL
Ron D'Vari, Ph.D. State Street Research 2
The Three Pillars of Integrated Financial Management and Performance Attribution
Relative Valuation/
ProcessHoning
Ex Post Market
Monitoring/Performance Attribution
Ex AnteRisk/ExposureMeasurement
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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
- Enterprise-wide
Overlay Strategies
FORWARD-LOOKINGANALYSIS
Ex Ante Risk/Exposure Measurement
• Uniform and Integrated Across All Portfolios/Business Units
• Reveals Intended and Implied Bets
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Factor Move Estimation and Monitoring
Factor Return Attribution Consistent with Risk Measurement
Relative Valuation
Investment Process Honing
Benchmark Setting/Improvement
Guideline/Mandate Improvements
Strategic Asset Allocation
Tactical Asset Allocation
Overlay Risk Hedges
Ex-Post Market Move Monitoring and Decomposition
Feedback Into The Investment Process
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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
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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, Ph.D. State Street Research 7
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 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
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Breaks up risk to its lowest common denominator
Integrates risk management into active management strategies
Use forward-looking view of volatility 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
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FIXED INCOMERISKS
CURVE SHAPE
- Parallel
- Twist
- Butterfly
- Higher Principal
Components
- Residual
- Per Country
- Factor Variance/
Covariance (V/C)
Sensitivity
VOLATILITY
- Short End
- Long End
- Per Country
- VolatilityCorrelations
- Historical vs.
Implied
CREDIT
- Spread Term
Structure
- Spread Volatilities
and Correlations
- Per Sector
- Per Security
OTHERS
- Prepayment
- Currency (V/C)
- Sovereign
- Liquidity Premium
- Model
- Legal
- Political
- Taxes
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EQUITY RISKS
MARKET
- Domestic Equities
- Foreign Equities
- Beta Risk
- Correlations Risk
- Return Momentum
- Domestic
- Foreign
- Volatility
Correlations
- Historical and
Option-Implied
- 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
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SPECIAL RISKS
EMERGING MARKETS
- Insufficient Data/
Information
- InsufficientCredit/
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
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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
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FIXED-INCOME
INTEGRATED
MULTI-FACTOR
RISK MANAGEMENT
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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
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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
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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
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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
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CREDIT
• Default Spread Measured and Managed by Effective Spread
Duration (Sprdur)
OTHERS
• Currency, Liquidity, Model, Operational, Counterparty, etc.
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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
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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
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I. Accurate Stochastic Interest Rate Term Structure ModelsA. Arbitrage Free One-Factor Models
1. Arbitrage Free2. Lognormal with Mean Reversion3. Term Structure of Volatility4. Stable Forward Curve5. Efficient and Accurate Implementation
B. Arbitrage Free Two-Factor Models with Term Structureof Volatility1. Mortgage Passthroughs, CMO’s, Special Securities2. Monte Carlo Simulation
II. Yield Curve Estimation Methodology (Fitting)III. Volatility Forecasting Methodology
FIXED-INCOME ANALYTIC
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IV. Option Adjusted Sensitivity AnalysisCurve ReshapingSpreadVolatility
V. Prepayment Models for Agency and Non-agency MortgagesVI. Extensive Security Modeling Tools
Call, Put, Conversion, Sinking Fund Structures, Make-Whole CallsCMO’s, Asset-backed Securities, Floating Instruments
with Caps/Floors/Collars, Multi-index FloatingVII. Derivative’s Structuring Tools
Exchange and OTC TradedFixed for Floating, CMT, and Fixed-for-Fixed SwapsForward Swaps and Swaptions
FIXED-INCOME ANALYTIC, cont.
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Option Adjusted Risk FactorsAbsolute, Relative, Target Relative and Variance
• 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
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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
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RECOMMENDED DAILY REPORTS
• Relative Curve Exposures, Yield, OAS, Convexity• Absolute Curve Exposures• Absolute and Relative Sector Exposures
% Invested and Duration Contribution• Duration Bucket Exposure• Full-Valuation Scenario Returns by Sector
Absolute and Relative Factor Returns
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OTHER APPLICATIONS
STRUCTURED PORTFOLIOS
SPECIAL APPLICATIONS
VALUATION MODELS
• STOCHASTIC TS MODELS• TS & Vol. FITTING• PREPAYMENT• INSTURMENT STRUCTURING• DERIVATIVES STRUCTURING
• ASSET/LIAB MANAGEMENT
• REFINED IMMUNIZATION
• PERFORMANCE ATTRIBUTION
• STRUCTURED PRODUCTS
• STRATEGIC AND TACTICAL ASSET ALLOCATION DOMESTIC GLOBAL
ANALYTICREFINEMENT
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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
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GENERAL METHODOLOGY
• Detailed sub-period return attribution to: Yield, roll-down, convexity, curve, sector,
selection, and trading
• Bottom-Up Approach
• Geometric Linking
• Accounts for Cash Flows at sub-period levels
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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
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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
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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
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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
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SECURITY RETURN DECOMPOSITION
~
/
* * * *
*
RiTot
C Y
Convexity
ED yD ED yD ED yD ED yD
y ED
i i
i i i i
j ijj
Accrued Income Price Change Under Curve & Spread Unchanged
Yield+Rolldown
Residual Curve
Curve Factor Change
1 2
1 1 2 2 3 3 4 4
2
1
17
Sector Spread Changes
Selection Spread Change(
i )
D D Fij i j 1 * Fj
1
0
if security belongs to a factor group
OtherwiseWhere:
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PORTFOLIO RETURN DECOMPOSITION
~ * *R D ypi
ijP
j Due to J - th Factor % WeightAll Securities in Portfolio
i-th Security
1
BENCHMARK RETURN DECOMPOSITION
~ * *R D yBi
ijB
j Due to J - th Factor % WeightAll Securities in Benchmark.
i-th Security
1
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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
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PERFORMANCE ATTRIBUTION PITFALLS, cont.
Inaccurate Analytic ToolsMortgages and Asset-Backed Securities
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
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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
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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