4 INTRODUCTION THE INVESTMENT PROCESS Target asset allocation(Exante)Forecasts (active)OptimizationRe-balancingMarket movementsPerformance evaluation(Expost)
5 INTRODUCTION PERFORMANCE MONITORING PROCESS Production / ReportingPortfolio Analytics / Risk Control(quantitative aspect)(qualitative aspect)Considering of output (ex-post) and input (ex ante)PerformancePerformancePerformancePerformancePerformancePortfolioPerformancemeasurementaccountingReportingAnalysisWatch ListAnalyticsReviewFeed Forward and Feed BackEfficient monitoring of of Investment process
6 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.
7 INTRODUCTION RETURN MEASUREMENT Different source of return (Currency return, local market return, return from high yield investment, etc.)Computation ideally dailyInput data are criticalReturn is measured either absolute or relative to a reference portfolio (Benchmark)Return measurement is conceptually easier to understand than risk measurement
8 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 sufficientIn portfolio analytics we mostly consider variance or covariance as risk measuresDifferentiation between forward and backward looking riskComputation of absolute and relative risk measuresTracking Error is relative Risk Measure
9 DEFINITION PERFORMANCE ATTRIBUTION INTRODUCTIONDEFINITION PERFORMANCE ATTRIBUTIONReturn attribution mathematically: Decompose a real number into a sumRisk attribution mathematically: Consider generalisation of theorem of Pythagorasb.ac
10 DEFINITION PERFORMANCE ATTRIBUTION INTRODUCTIONDEFINITION PERFORMANCE ATTRIBUTIONMore 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.
12 THE WILSHIRE APPLICATION AXIOM RETURN OF A PORTFOLIO (relative) return rp of a portfolioThe arithmetic (relative return) of a portfolio is the (relative) weighted average (wi), (wi - bi), of the arithmetic return (ri) of the individual securities.On the right hand side and the left hand side is the same (no model)
13 THE WILSHIRE APPLICATION AXIOM ABSOLUTE DECOMPOSITION Consider portfolio of 3 securitiesMac DonaldsIBMCS GroupUSASwitzerlandCountryPortfolio returnw: weightr: returnrP = w1 r w2 r w3 r3SectorFoodTMTBank
14 THE WILSHIRE APPLICATION AXIOM SLICING THE INVESTMENT UNIVERSE Country (Subgroup)Sector (Subgroup)Multi step decisionUniverse
16 THE WILSHIRE APPLICATION AXIOM PROGRAM GLOBAL PERFORMANCE ATTRIBUTION Universe: Bond Markets of JP Morgan Global Bond IndexThe Application computes 3 different Model Returns (‘ Format ’) for 3 different return attributionallows the measurement of 3 different investment processesModel 1 and 2 are based on a form of the capital asset pricing model.leverage factor is ratio of Bond duration and Benchmark DurationModel 1 uses short term rate, Model 2 uses yield of a bond
17 THE WILSHIRE APPLICATION AXIOM PROGRAM GLOBAL PERFORMANCE ATTRIBUTION Model computes the Model return of a BondThe Application computes Buy and Hold return in USA Dollars:Example: U.S. Treasury BondPrice 07/01/2002: %Price 07/31/2002: %local return = ((end_price + end_accrued)/(begin_price + begin_accrued) -1)*100 = 3.29%
18 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 effectThe currency effect examines the impact of active currency exposure of the portfolio versus the benchmarkReturn in Swiss Francs with currency return -0.47%: base currency return = ((1 + local_return/100) * ( currency_return/100) - 1)*100 = 2.80%
19 THE WILSHIRE APPLICATION AXIOM FORMAT 1: DURATION/COUNTRY This format measures the following decisions:Duration effectValue 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.
20 THE WILSHIRE APPLICATION AXIOM FORMAT 1: DURATION/COUNTRY Country effectThe 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
21 THE WILSHIRE APPLICATION AXIOM FORMAT 2: YIELD/EXPOSURE This format measures the following decisions:Yield effectThe yield component measures the return contribution in the portfolio relative to the benchmark by being invested in higher yielding securities (e.g. corporate bonds).
22 THE WILSHIRE APPLICATION AXIOM FORMAT 2: YIELD/EXPOSURE Market effectIs 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
24 THE WILSHIRE APPLICATION AXIOM FORMAT 3: FACTOR EXPOSURE The Format measuresthe 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 curveConsistent with Risk modelBest explanatory power of the three formatsIt is regression based and represents a detailed description of returns in terms of a common set of risk factors
25 THE WILSHIRE APPLICATION AXIOM EFFECTIVE DURATION shift(d1)term structure100bpsspot rateshift(d1)time
26 THE WILSHIRE APPLICATION AXIOM EFFECTIVE DURATION Extension of flat yield conceptIn Wilshire the spot rates are held in cubic spline formsTakes shape of the spot rate curve into accountEffective duration and option adjusted duration is the sameTakes into account change of the bonds with different cash flows (callable bonds)Defined as price sensitivity of bond to shift in actual yield curve
27 CHANGES OF THE YIELD CURVE WILSHIRE SHIFT SLOPE AND CURVATURE term structurespot rateslope (d2)curvature (d3)shift(d1)time
29 FIXED INCOME RISK MODEL FACTOR ANALYSIS Historical DataSpecify factorsPrincipal components analysisRegression analysisProblem: Interpretation of factorsProblem: Goodness of the fit
30 FIXED INCOME RISK MODEL COMPARISON BarraShiftTwistButterflyWilshire ShiftSlopeCurvaturePrespecified by yield curve shapes with few parametersEstimated byhistorical data
31 FIXED INCOME RISK MODEL BARRA SHIFT TWIST AND BUTTERFLY
32 FIXED INCOME RISK MODEL BENCHMARK BOND EXPOSURES Step 1: Compute by regression analysis the Risk Matrix giventhe risk factors d1,d2,d3, country and currencies.Different length of time periods (90, 180, 360 days,exponential weightings)Independent of PortfolioStep 2: Compute the breakdown of the relative Risk (Tracking error)given the Portfolio Holdings and the Benchmark holdings.
34 THE RISK MODELS OF WILSHIRE DIFFERENT MODELS Wilshire Global Risk ModelWilshire Global Credit Risk Model
35 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, d3Currency
36 THE RISK MODELS OF WILSHIRE CHARACTERISTICS Factors in Credit Risk Model Total (16 countries, approx factor)d1, d2, d3CurrencySectorsQuality Rating (Three Groups: Moody Aa, A, Baa)Other spreadsEuro country spreadspecial Instrument in USA (e.g. GNMA prepay)