Download Multi-Factor Models of Risk for Fixed Income Portfolios

INTEGRATED MULTI-FACTOR
RISK MANAGEMENT AND
PERFORMANCE ATTRIBUTION
Ron D’Vari, Ph.D.
Vice President, Fixed Income
State Street Research & Management
Visiting Lecturer, Boston University
Presented At Risk ‘97 Seminar
June 4, 1997, Chicago, IL
Ron D'Vari, Ph.D.
State Street Research
1
The Three Pillars of Integrated Financial
Management and Performance Attribution
Ex Ante
Risk/Exposure
Measurement
Ex Post
Market
Monitoring/
Performance
Attribution
Ron D'Vari, Ph.D.
Relative
Valuation/
Process
Honing
State Street Research
2
Ex Ante Risk/Exposure Measurement
• Uniform and Integrated Across All Portfolios/Business Units
• Reveals Intended and Implied Bets
FACTOR
IDENTIFICATION
- Intuitive
EXPOSURE
DECOMPOSITION
- All Portfolios
FORWARD-LOOKING
ANALYSIS
- Forecast Returns
- Comprehensive
and Volatilities
Scenario Sets
- High Explanatory - All Benchmarks
Power
- Ranked
- Scenario Analysis
Control
SYNTHESIS/
OPTIMIZATION
- Benchmark Comparison
- Scenario
Optimization
- Benchmark Variance
- Scenario Return
and Decomposition
Decomposition
- Enterprise-wide
- VAR Analysis
Absolute and Relative
Overlay Strategies
- VAR Decomposition
Ron D'Vari, Ph.D.
State Street Research
3
Ex-Post Market Move Monitoring and Decomposition

Factor Move Estimation and Monitoring

Factor Return Attribution Consistent with Risk Measurement
Feedback Into The Investment Process

Relative Valuation

Investment Process Honing

Benchmark Setting/Improvement

Guideline/Mandate Improvements

Strategic Asset Allocation

Tactical Asset Allocation

Overlay Risk Hedges
Ron D'Vari, Ph.D.
State Street Research
4
Elementary Risk Models
1. Single Factor for Stocks, e.g. CAPM
Ri  RF  i ( R M  RF )  i
Cov (i ,  j )  0, Cov (i , Ri )  0, i  0
2. Single Factor For Fixed Income
EffDuri
Ri  Yi 
 ( R M  YM )  i
EffDurM
Initial Yield for i - th Bond and Market  Yi , YM
Market Return = R M
3. Historical Variances And Covariances Among All
Securities - Impractical
Ron D'Vari, Ph.D.
State Street Research
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Multi-Factor Risk Models
1. Nonlinear: Ri (t )  f (b1 , b2 ,...bn , t )  i
NF


2. Linear: Ri (t )  RF   X j (t )  RF  b j (t )  i
j 1
j- th Factor Exposure = b j (t )
j- th Factor Premium = X j (t )  RF


3. Choice of Factors
External, Statistical, or Intuitive
Ron D'Vari, Ph.D.
State Street Research
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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 Returns
Relies on historical volatilities and correlations
Neglects short horizon risk
Ignores risk premium fluctuations
 Ron
Does
not take advantage
of short term mispricing
D'Vari, Ph.D.
State Street Research
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State-of-the-Art Approach
 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 volatility
 Focus on forecast risk-adjusted returns
 Considers environment where expected returns are constant
but volatility might have risen
 Portfolio risk/return characteristics vs. Benchmark
Ron D'Vari, Ph.D.
State Street Research
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FIXED INCOME
RISKS
CURVE
SHAPE
VOLATILITY
CREDIT
- Spread Term
OTHERS
- Prepayment
- Parallel
- Short End
- Twist
- Long End
- Butterfly
- Per Country
- Higher Principal
- Volatility
Correlations
- Per Sector
- Model
- Historical vs.
- Per Security
- Legal
Components
- Residual
- Per Country
Structure
- Spread Volatilities
and Correlations
Implied
- Currency (V/C)
- Sovereign
- Liquidity Premium
- Political
- Taxes
- Factor Variance/
Covariance (V/C)
Sensitivity
Ron D'Vari, Ph.D.
State Street Research
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EQUITY RISKS
MARKET
VOLATILITY
- Domestic Equities - Domestic
FUNDAMENTALS
SECTORS
- Size
- Technology
- Foreign Equities
- Foreign
- Earnings: P/E
- Financial
- Beta Risk
- Volatility
- Value: B/P
- Services
- Growth
- Telecommunications
- Dividend Yield
- Transportation
- Leverage [D/(D+E)]
- Utilities
- Liquidity
- Energy
- Foreign Exposure
- Healthcare
- Correlations Risk
Correlations
- Return Momentum- Historical and
Option-Implied
- etc.
Ron D'Vari, Ph.D.
State Street Research
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SPECIAL RISKS
EMERGING
MARKETS
STRUCTURED
PRODUCTS
- Insufficient Data/ - All Other Risks
Information
CUSTODIAL
- Accurate Accounting
- Settlement & Disposition
- Basis Risk
- InsufficientCredit/ - Liquidity Risk
- Discrepancy Reporting
Legal/Political Risk- Counterparty Risk- Information Accuracy
Methodology
- Timely Monitoring
- Data Incomparability
- Tradable Pricing
- Convertibility
- Securities Lending,
- Expropriation
- Tradability
Cash Management, etc.
- Credit
- Administration Errors
Ron D'Vari, Ph.D.
State Street Research
MODEL
- Insufficient Basis
- Oversimplification
- Missing Significant
Factors
- Implementation
Errors
- Insufficient Data
- Unaccounted
Structural
Changes
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ADDED-VALUE FINANCIAL
RISK MANAGEMENT
FORWARD
VIEW
REAR
VIEW
RISK MODELS
• BENCHMARK
COMPARISON
• BENCHMARK
VARIANCE
• SCENARIO ANALYSIS
(STRESS TESTING)
SYNTHESIS
• PERFORMANCE
ATTRIBUTION
• STRATEGIC/TACTICAL
ASSET ALLOCATION
• RISK ADJUSTED
RETURN
•SCENARIO
OPTIMIZATION
• RELATIVE
VALUATION
• RELATIVE VALUE
ANALYSIS
• VAR (NONLINEAR)
Ron D'Vari, Ph.D.
State Street Research
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FIXED-INCOME
INTEGRATED
MULTI-FACTOR
RISK MANAGEMENT
Ron D'Vari, Ph.D.
State Street Research
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MARKET

Interest Rate Risk =Yield Curve = Term Structure
Measured and Managed By
Curve Reshaping OA Durations (Elasticities)
and Scenario Analysis
Curve
Reshaping Move
Parallel
Twist
Butterfly
Long-end Hump
Residual
Ron D'Vari, Ph.D.
Option Adjusted Measure
Effective Duration (Edur)
Effective Twist Duration (Edur2)
Effective Butterfly Duration (Edur3)
Effective Long-end Hump Duration (Edur4)
Scenario Analysis and Key Rate Durations
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Spot Curve Factor Shapes for Q1 = 7 and Q2 = 7
D1
Spot Curve Shift - bp
100
D3
75
D2
50
D4
Normalized D1 Shape
25
Normalized D2 Shape
Normalized D3 Shape
Wilshire Proposed Normalized D4 Shape
0
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
Tenor - Years
Ron D'Vari, Ph.D.
State Street Research
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Spot Curve Factor Shapes for Q1 = 7 and Q2 = 12
D1
Spot Curve Shift - bp
100
D4
D3
75
D2
50
Normalized D1 Shape
25
Normalized D2 Shape
Normalized D3 Shape
Wilshire Proposed Normalized D4 Shape
0
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
Tenor - Years
Ron D'Vari, Ph.D.
State Street Research
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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

Ron D'Vari, Ph.D.
State Street Research
17
CREDIT
• Default
Spread
 Measured and Managed by Effective Spread
Duration (Sprdur)

OTHERS
• Currency, Liquidity, Model, Operational,
Counterparty, etc.
Ron D'Vari, Ph.D.
State Street Research
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FACTORS
SECTOR
QUALITY
Treasury
Agency
Industrial
Utility -Communications
Utility - Electric
Utility - Other
Moody Aaa
Moody Aa
Moody A
Moody Baa
Other
Finance
GNMA Mortgage
FHLMC Mortgage
FNMA Mortgage
Other Mortgage
COUPON
Low Corporate (price < 95)
Current Corporate
High Corporate (price > 105)
Low Mortgage (price < 95)
Current Mortgage
High Mortgage (price > 102)
VOLATILITY
Ron D'Vari, Ph.D.
State Street Research
19
ANALYTIC
REQUIREMENTS
VALUATION
ENGINE
• FULL VALUATION
FACTOR
ANALYSIS
• FACTOR
IDENTIFICATION
• SENSITIVITY ANALYSIS
• STOCHASTIC TS MODELS
• TS & Vol. FITTING
• PREPAYMENT
• DAILY/PERIODIC
FACTOR CHANGE
ESTIMATION
RISK
DISSECTION
• LINEAR ANALYSIS
NORMAL DIST.
LINEAR SENSITIVITIES
LINEAR VAR
• NONLINEAR
MONTE CARLO ANAL.
• FACTOR VARIANCE/ FULL VALUATION
ARBITRARY DIST.
COVARIANCE EST.
• FACTOR EXPOSURE • MULTI-FACTOR
• INSTRUMENT &
RISK DECOMPOSITION
DERIVATIVES STRUCTURING CALCULATION
Ron D'Vari, Ph.D.
State Street Research
20
FIXED-INCOME ANALYTIC
I. Accurate Stochastic Interest Rate Term Structure Models
A. Arbitrage Free One-Factor Models
1. Arbitrage Free
2. Lognormal with Mean Reversion
3. Term Structure of Volatility
4. Stable Forward Curve
5. Efficient and Accurate Implementation
B. Arbitrage Free Two-Factor Models with Term Structure
of Volatility
1. Mortgage Passthroughs, CMO’s, Special Securities
2. Monte Carlo Simulation
II. Yield Curve Estimation Methodology (Fitting)
III. Volatility Forecasting Methodology
Ron D'Vari, Ph.D.
State Street Research
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FIXED-INCOME ANALYTIC, cont.
IV. Option Adjusted Sensitivity Analysis
 Curve Reshaping
 Spread
 Volatility
V. Prepayment Models for Agency and Non-agency Mortgages
VI. 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
VII. Derivative’s Structuring Tools
Exchange and OTC Traded
Fixed for Floating, CMT, and Fixed-for-Fixed Swaps
Forward Swaps and Swaptions
Ron D'Vari, Ph.D.
State Street Research
22
Option Adjusted Risk Factors
Absolute, Relative, Target Relative and Variance
• Curve Sensitivities by Sector
 Effective Duration to Parallel Shift of Spot curve
 Effective 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
Ron D'Vari, Ph.D.
State Street Research
23
ALGORITHM FOR OPTION ADJUSTED
INTEREST RATE SENSITIVITIES
Security
Market Price
ASSUME
OA SPREAD
(E.G. PREVIOUS DAY VALUE)
• 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, Ph.D.
State Street Research
24
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
Ron D'Vari, Ph.D.
State Street Research
25
OTHER
APPLICATIONS
ANALYTIC
REFINEMENT
STRUCTURED
PORTFOLIOS
SPECIAL
APPLICATIONS
• ASSET/LIAB
MANAGEMENT
• STRUCTURED
PRODUCTS
• REFINED
IMMUNIZATION
• STRATEGIC AND
TACTICAL ASSET
ALLOCATION
VALUATION MODELS
• STOCHASTIC TS
MODELS
• TS & Vol. FITTING
• PREPAYMENT
• INSTURMENT
STRUCTURING
• DERIVATIVES
STRUCTURING
Ron D'Vari, Ph.D.
• PERFORMANCE
ATTRIBUTION
State Street Research
DOMESTIC
GLOBAL
26
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, Ph.D.
State Street Research
27
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
Ron D'Vari, Ph.D.
State Street Research
28
TOTAL
SUB-PERIOD RETURN
YIELD/
AGING
CURVE
NONCURVE
OTHERS
- Yield
- Duration
- Sector Spread - Currency
- Rolldown
- Twist
- Volatility
- Butterfly
- Selection
- Long-end Hump
- Curve Residual
Ron D'Vari, Ph.D.
State Street Research
Hedge
- Currency
Exposure
- Trading
29
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, Ph.D.
State Street Research
30
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, Ph.D.
State Street Research
31
INTRA-PERIOD
TRADING
• 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, Ph.D.
State Street Research
32
SECURITY RETURN DECOMPOSITION
~
Ri
Tot
 Accrued Income  Price Change Under Curve & Spread Unchanged



Yield +Rolldown
 1 / 2  Ci  Yi2

Convexity
  ED1i * y D1  ED2i * y D2  ED3i * y D3  ED4i * y D4



Curve Factor Change
 Residual Curve
17

  y j * EDij 
j 1



Sector Spread Changes
Where:
Ron D'Vari, Ph.D.
 Selection Spread Change(i )
1 if security belongs to a factor group
Fj  
0 Otherwise
Dij   D1i * Fj
State Street Research
33
PORTFOLIO RETURN DECOMPOSITION
~
R p Due to J - th Factor 
All Securities in Portfolio
 % Weight 
i 1
* DijP * y j
i-th Security
BENCHMARK RETURN DECOMPOSITION
~
RB Due to J - th Factor 
Ron D'Vari, Ph.D.
All Securities in Benchmark.
 % Weight 
i 1
State Street Research
* DijB * y j
i-th Security
34
PERFORMANCE ATTRIBUTION
PITFALLS
 Plain bad pricing
 Non-contemporaneous pricing
 Benchmark
and Portfolio
 Sectors
 Curve
calculation
 Coarse generic pricing
 Insensitive
to sector specific factors, e.g.
 WAM, WAC, seasoning, age, volatility
Ron D'Vari, Ph.D.
State Street Research
35
PERFORMANCE ATTRIBUTION
PITFALLS, cont.




Inaccurate Analytic Tools
Mortgages and Asset-Backed Securities
Client-directed actions & cash flows that affect performance
Over Linking and Cross Factor Returns
Benchmark Changes and Inaccuracies
Sponsor initiated changes
Benchmark pricing
Forward benchmark vs. Backward benchmark
Exclusion/Inclusion of new asset classes
Ron D'Vari, Ph.D.
State Street Research
36
CONCLUSIONS
• Comprehensive Multi-Factor Model
Intuitive Factors
High Fidelity Yield Curve Sensitivity Model
Detailed Sector/Benchmark Comparison Analysis
(BCA)
Scenario Analysis (SA) and Optimization (SO)
• Uniform Measurement of Risk and
Implementation of Market Views
Across Hundreds of Portfolios with Different
Benchmarks and Investment Objectives
Consistent Reporting
Ron D'Vari, Ph.D.
State Street Research
37
CONCLUSIONS (Cont’D)
• Other Benefits
Performance 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
Ron D'Vari, Ph.D.
State Street Research
38