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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 5 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 6 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 7 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 8 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 9 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 10 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 11 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 12 FIXED-INCOME INTEGRATED MULTI-FACTOR RISK MANAGEMENT Ron D'Vari, Ph.D. State Street Research 13 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 State Street Research 14 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 15 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 16 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 18 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 21 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