INTEGRATED MULTI-FACTOR RISK MANAGEMENT AND PERFORMANCE ATTRIBUTION

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


The Three Pillars of Integrated Financial Management and Performance Attribution

Relative Valuation/

ProcessHoning

Ex Post Market

Monitoring/Performance Attribution

Ex AnteRisk/ExposureMeasurement


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


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


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


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


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


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


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


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


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


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


FIXED-INCOME

INTEGRATED

MULTI-FACTOR

RISK MANAGEMENT


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


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


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


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


CREDIT

• Default Spread Measured and Managed by Effective Spread

Duration (Sprdur)

OTHERS

• Currency, Liquidity, Model, Operational, Counterparty, etc.


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


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


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


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.


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


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


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


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


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


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


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


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


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


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


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:


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


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


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


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


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

INTEGRATED MULTI-FACTOR RISK MANAGEMENT AND PERFORMANCE ATTRIBUTION

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