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