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Slide 1 10/4/03 Wolfgang Marty Date: Produced by: FIXED INCOME PERFORMANCE ATTRIBUTION Wolfgang Marty Portfolio Analytics CSAM Zürich A PRESENTATION TO THE EUROPEAN BOND COMMISSION

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Slide 2 10/4/03 Wolfgang Marty Date: Produced by: 1. INTRODUCTION 2. DECOMPOSING THE RETURN 3. FACTOR ANALYSIS 4. FIXED INCOME RISK MODELS 5. THE RISK MODELS OF WILSHIRE 6. EXAMPLES

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Slide 3 10/4/03 Wolfgang Marty Date: Produced by: 1. INTRODUCTION

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Slide 4 10/4/03 Wolfgang Marty Date: Produced by: INTRODUCTION THE INVESTMENT PROCESS Target asset allocation (Exante) Performance evaluation (Expost) Re-balancing Optimization Market movements Forecasts (active)

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Slide 5 10/4/03 Wolfgang Marty Date: Produced by: INTRODUCTION PERFORMANCE MONITORING PROCESS Portfolio Analytics / Risk Control (qualitative aspect) Performance Watch List Performance Reporting Considering of output (ex-post) and input (ex ante) Performance measurement Performance accounting Performance Analysis Portfolio Analytics Feed Forward and Feed Back Efficient monitoring of of Investment process Performance Review Production / Reporting (quantitative aspect)

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Slide 6 10/4/03 Wolfgang Marty Date: Produced by: INTRODUCTION DEFINITION PORTFOLIO ANALYTICS Portfolio analytics is concerned with quantifying the sources of the return and assessing the risk of a portfolio. It not only measures the evolution of the wealth over a certain time period but it provides a comprehensive discussion of the performance of specific portfolios.

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Slide 7 10/4/03 Wolfgang Marty Date: Produced by: INTRODUCTION RETURN MEASUREMENT Different source of return (Currency return, local market return, return from high yield investment, etc.) Computation ideally daily Input data are critical Return is measured either absolute or relative to a reference portfolio (Benchmark) Return measurement is conceptually easier to understand than risk measurement

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Slide 8 10/4/03 Wolfgang Marty Date: Produced by: INTRODUCTION RISK ASSESSMENT Different source of risk (Exchange rate risk, Interest rate risk, Credit risk, Sector risk, etc.) Computation based on historical data (time series) Updating once a month is sufficient In portfolio analytics we mostly consider variance or covariance as risk measures Differentiation between forward and backward looking risk Computation of absolute and relative risk measures Tracking Error is relative Risk Measure

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Slide 9 10/4/03 Wolfgang Marty Date: Produced by: INTRODUCTION DEFINITION PERFORMANCE ATTRIBUTION Return attribution mathematically: Decompose a real number into a sum b a c Risk attribution mathematically: Consider generalisation of theorem of Pythagoras.

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Slide 10 10/4/03 Wolfgang Marty Date: Produced by: INTRODUCTION DEFINITION PERFORMANCE ATTRIBUTION More precisely: Analyse the portfolio performance and the relative performance in terms of the decisions that generate returns. Conclusion: Need mapping from the decision making process to a performance attribution model.

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Slide 11 10/4/03 Wolfgang Marty Date: Produced by: 2. DECOMPOSING THE RETURN

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Slide 12 10/4/03 Wolfgang Marty Date: Produced by: THE WILSHIRE APPLICATION AXIOM RETURN OF A PORTFOLIO (relative) return r p of a portfolio The arithmetic (relative return) of a portfolio is the (relative) weighted average (w i ), (w i - b i ), of the arithmetic return (r i ) of the individual securities. On the right hand side and the left hand side is the same (no model)

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Slide 13 10/4/03 Wolfgang Marty Date: Produced by: THE WILSHIRE APPLICATION AXIOM ABSOLUTE DECOMPOSITION Consider portfolio of 3 securities Mac Donalds IBM CS Group r P = w 1 r 1 + w 2 r 2 + w 3 r 3 USA Switzerlan d Food TMTBank Country Sector Portfoli o return w: weight r: return

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Slide 14 10/4/03 Wolfgang Marty Date: Produced by: THE WILSHIRE APPLICATION AXIOM SLICING THE INVESTMENT UNIVERSE Sector (Subgroup) Country (Subgroup) Universe Multi step decision

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Slide 15 10/4/03 Wolfgang Marty Date: Produced by: Benchmark portfolio Starting point x y Interactio n Portfolio Ending point THE WILSHIRE APPLICATION AXIOM CROSS PRODUCT

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Slide 16 10/4/03 Wolfgang Marty Date: Produced by: THE WILSHIRE APPLICATION AXIOM PROGRAM GLOBAL PERFORMANCE ATTRIBUTION Universe: Bond Markets of JP Morgan Global Bond Index The Application computes 3 different Model Returns (‘ Format ’) for 3 different return attribution allows the measurement of 3 different investment processes Model 1 and 2 are based on a form of the capital asset pricing model. leverage factor is ratio of Bond duration and Benchmark Duration Model 1 uses short term rate, Model 2 uses yield of a bond

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Slide 17 10/4/03 Wolfgang Marty Date: Produced by: THE WILSHIRE APPLICATION AXIOM PROGRAM GLOBAL PERFORMANCE ATTRIBUTION Model computes the Model return of a Bond The Application computes Buy and Hold return in USA Dollars: Example: U.S. Treasury Bond Price 07/01/2002: % Price 07/31/2002: % local return = ((end_price + end_accrued)/(begin_price + begin_accrued) -1)*100 = 3.29%

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Slide 18 10/4/03 Wolfgang Marty Date: Produced by: THE WILSHIRE APPLICATION AXIOM PROGRAM GLOBAL PERFORMANCE ATTRIBUTION The difference between Model Return and Buy and Hold return is the selection effect. Illustration: Return due to Market Movement versus Return calculated by duration times yield change. Common in all Formats: Currency effect The currency effect examines the impact of active currency exposure of the portfolio versus the benchmark Return in Swiss Francs with currency return -0.47%: base currency return = ((1 + local_return/100) * (1 + currency_return/100) - 1)*100 = 2.80%

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Slide 19 10/4/03 Wolfgang Marty Date: Produced by: THE WILSHIRE APPLICATION AXIOM FORMAT 1: DURATION/COUNTRY Duration effect Value added by being longer than the benchmark in a country where interest rate fell and shorter than benchmark in a country where interest rose. It is only not zero if you have duration exposure in the benchmark and the portfolio. This format measures the following decisions:

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Slide 20 10/4/03 Wolfgang Marty Date: Produced by: THE WILSHIRE APPLICATION AXIOM FORMAT 1: DURATION/COUNTRY Country effect The country effect quantifies the effect of the managers active country bets on management performance by taking the difference between the portfolio weights and the benchmark weights for each country and then multiplying this bet by the relative return to that country (relative to the average local benchmark). Asset allocation approach as it incorporates cross - country decisions

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Slide 21 10/4/03 Wolfgang Marty Date: Produced by: THE WILSHIRE APPLICATION AXIOM FORMAT 2: YIELD/EXPOSURE Yield effect The yield component measures the return contribution in the portfolio relative to the benchmark by being invested in higher yielding securities (e.g. corporate bonds). This format measures the following decisions:

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Slide 22 10/4/03 Wolfgang Marty Date: Produced by: THE WILSHIRE APPLICATION AXIOM FORMAT 2: YIELD/EXPOSURE Market effect Is a combination of country-weighting and duration within country decisions. Thus a large country weighting offset by a short duration might result in a neutral or even negative net market exposure. In the duration/country format we would have a large country bet and a large negative duration bet. Suited for investment process that centres around yield curve shifts

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Slide 23 10/4/03 Wolfgang Marty Date: Produced by: 3. FACTOR ANALYSIS

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Slide 24 10/4/03 Wolfgang Marty Date: Produced by: THE WILSHIRE APPLICATION AXIOM FORMAT 3: FACTOR EXPOSURE The Format measures the decomposition the returns in multi-currency portfolios in terms of different types of yield curve movements and currency changes. Characteristics: Measures investment process that makes bets on different sections of the yield curve Consistent with Risk model Best explanatory power of the three formats It is regression based and represents a detailed description of returns in terms of a common set of risk factors

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Slide 25 10/4/03 Wolfgang Marty Date: Produced by: spot rate term structure time shift(d 1 ) THE WILSHIRE APPLICATION AXIOM EFFECTIVE DURATION shift(d 1 ) 100bps

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Slide 26 10/4/03 Wolfgang Marty Date: Produced by: THE WILSHIRE APPLICATION AXIOM EFFECTIVE DURATION Extension of flat yield concept In Wilshire the spot rates are held in cubic spline forms Takes shape of the spot rate curve into account Effective duration and option adjusted duration is the same Takes into account change of the bonds with different cash flows (callable bonds) Defined as price sensitivity of bond to shift in actual yield curve

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Slide 27 10/4/03 Wolfgang Marty Date: Produced by: CHANGES OF THE YIELD CURVE WILSHIRE SHIFT SLOPE AND CURVATURE spot rate term structure tim e shift(d 1 ) slope (d 2 ) curvature (d 3 )

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Slide 28 10/4/03 Wolfgang Marty Date: Produced by: 4. FIXED INCOME RISK MODEL

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Slide 29 10/4/03 Wolfgang Marty Date: Produced by: Problem: Goodness of the fit Specify factors Historical Data FIXED INCOME RISK MODEL FACTOR ANALYSIS Problem: Interpretation of factors Principal components analysis Regression analysis

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Slide 30 10/4/03 Wolfgang Marty Date: Produced by: FIXED INCOME RISK MODEL COMPARISON Prespecified by yield curve shapes with few parameters Estimated by historical data Wilshire Shift Slope Curvature Barra Shift Twist Butterfly

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Slide 31 10/4/03 Wolfgang Marty Date: Produced by: FIXED INCOME RISK MODEL BARRA SHIFT TWIST AND BUTTERFLY

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Slide 32 10/4/03 Wolfgang Marty Date: Produced by: FIXED INCOME RISK MODEL BENCHMARK BOND EXPOSURES Step 1: Compute by regression analysis the Risk Matrix given the risk factors d 1,d 2,d 3, country and currencies. Step 2: Compute the breakdown of the relative Risk (Tracking error) given the Portfolio Holdings and the Benchmark holdings. Different length of time periods (90, 180, 360 days, exponential weightings) Independent of Portfolio

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Slide 33 10/4/03 Wolfgang Marty Date: Produced by: 5. THE RISK MODELS OF WILSHIRE

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Slide 34 10/4/03 Wolfgang Marty Date: Produced by: Wilshire Global Risk Model Wilshire Global Credit Risk Model THE RISK MODELS OF WILSHIRE DIFFERENT MODELS

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Slide 35 10/4/03 Wolfgang Marty Date: Produced by: THE RISK MODELS OF WILSHIRE SOME CHARACTERISTICS Factors in Global Risk Model (based on 13 Countries of J.P. Morgan GBI, Total: 47 factors) d1, d2, d3 Currency

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Slide 36 10/4/03 Wolfgang Marty Date: Produced by: THE RISK MODELS OF WILSHIRE CHARACTERISTICS Factors in Credit Risk Model Total (16 countries, approx. 109 factor) d1, d2, d3 Currency Sectors Quality Rating (Three Groups: Moody Aa, A, Baa) Other spreads Euro country spread special Instrument in USA (e.g. GNMA prepay)

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Slide 37 10/4/03 Wolfgang Marty Date: Produced by: 6.EXAMPLES

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Slide 38 10/4/03 Wolfgang Marty Date: Produced by: EXAMPLE 1 ILLUSTRATION: BUCKETING APPROACH Benchmark: JPM EMU Index Portfolio: All Bonds with Duration > 8 Years (subset of Benchmark)

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Slide 39 10/4/03 Wolfgang Marty Date: Produced by: EXAMPLE 1 ILLUSTRATION: BUCKETING APPROACH Benchmark: JPM EMU Index Portfolio: All Bonds with Duration > 8 Years (subset of Benchmark)

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Slide 40 10/4/03 Wolfgang Marty Date: Produced by: EXAMPLE 1 ILLUSTRATION: DURATION /COUNTRY FORMAT

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Slide 41 10/4/03 Wolfgang Marty Date: Produced by: EXAMPLE 1 ILLUSTRATION: YIELD/EXPOSURE FORMAT

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Slide 42 10/4/03 Wolfgang Marty Date: Produced by: EXAMPLE 1 ILLUSTRATION: FACTOR FORMAT

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Slide 43 10/4/03 Wolfgang Marty Date: Produced by: EXAMPLE 2 SAMPLE REPORT

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Slide 44 10/4/03 Wolfgang Marty Date: Produced by: EXAMPLE 2 SAMPLE REPORT

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Slide 45 10/4/03 Wolfgang Marty Date: Produced by: EXAMPLE 2 SAMPLE REPORT

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Slide 46 10/4/03 Wolfgang Marty Date: Produced by: EXAMPLE 2 SAMPLE REPORT

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Slide 47 10/4/03 Wolfgang Marty Date: Produced by: EXAMPLE 2 SAMPLE REPORT

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Slide 48 10/4/03 Wolfgang Marty Date: Produced by: EXAMPLE 2 SAMPLE REPORT

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Slide 49 10/4/03 Wolfgang Marty Date: Produced by: EXAMPLE 2 SAMPLE REPORT

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Slide 50 10/4/03 Wolfgang Marty Date: Produced by: EXAMPLE 2 SAMPLE REPORT

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Slide 51 10/4/03 Wolfgang Marty Date: Produced by: EXAMPLE 2 SAMPLE REPORT

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