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Practical Portfolio Performance Measurement and Attribution
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Acknowledgements xv 1 Introduction 1 Why measure portfolio performance? 1 The performance measurement process 2 The purpose of this book 2 Role of performance measurers 2 Book structure 3 2 The Mathematics of Portfolio Return 5 Simple return 5 Money-weighted returns 7 Internal rate of return (IRR) 7 Simple internal rate of return 7 Modified internal rate of return 8 Simple Dietz 10 ICAA method 11 Modified Dietz 12 Time-weighted returns 13 True time-weighted 13 Unit price method 14 Time-weighted versus money-weighted rates of return 16 Approximations to the time-weighted return 18 Index substitution 18 Regression method (or method) 19 Analyst's test 19 Hybrid methodologies 20 Linked modified Dietz 21 BAI method (or linked IRR) 21 Which method to use? 21 Self-selection 22 Annualised returns 27 Return hiatus 28 Continuously compounded returns 28 Gross- and net-of-fee calculations 29 Estimating gross- and net-of-fee returns 30 Initial fees 32 Portfolio component returns 32 Component weight 32 Short positions 34 Overlay strategies 34 Carve-outs 34 Multi-period component returns 35 Base currency and local returns 35 3 Benchmarks 39 Benchmarks 39 Benchmark attributes 39 Commercial indexes 39 Calculation methodologies 40 Aggregate price index (price-weighted index) 40 Geometric (or Jevons-type) index 41 Market capitalisation index 41 Laspeyres index 41 Paasche index 42 Marshall-edgeworth index 42 Fisher index 42 Equal-weighted indexes 42 Fundamental indexes 43 Currency effects in benchmark 43 Hedged indexes 43 Customised (or composite) indexes 44 Fixed weight and dynamised benchmarks 45 Capped indexes 45 Blended (or spliced) indexes 46 Money-weighted benchmarks 47 Benchmark statistics 47 Index turnover 47 Up capture indicator 47 Down capture indicator 47 Up number ratio 48 Down number ratio 48 Up percentage ratio 48 Down percentage ratio 48 Percentage gain ratio 48 Peer groups and universes 48 Percentile rank 49 Random portfolios 50 Notional funds 50 Normal portfolio 51 Growth and value 51 Excess return 51 Arithmetic excess return 51 Geometric excess return 52 Performance fees 55 Symmetrical performance fees (or fulcrum fees) 55 Asymmetrical performance fees 56 Performance fee structures 57 Sliding scale 57 Performance fee caps 57 Hurdle rate 58 Crystallisation 58 High water mark 58 Equalisation 58 4 Risk 61 Definition of risk 61 Risk management versus risk control 61 Risk aversion 62 Risk measures 62 Ex post and ex ante 62 Variability 62 Mean absolute deviation 62 Variance 63 Standard deviation 63 Frequency and number of data points 64 Sharpe ratio (reward to variability) 64 Risk-adjusted return: M2 67 M2 excess return 68 Differential return 68 GH1 (Graham and Harvey 1) 69 GH2 (Graham and Harvey 2) 70 Regression analysis 70 Regression equation 71 Regression alpha ( R ) 71 Regression beta ( R ) 71 Regression epsilon ( R ) 71 Capital asset pricing model (CAPM) 72 Beta ( ) (systematic risk or volatility) 72 Jensen's alpha (or Jensen's measure or Jensen's differential return or ex post alpha) 72 Bull beta ( +) 72 Bear beta ( ) 73 Beta timing ratio 73 Covariance 73 Correlation ( ) 73 Correlation and risk-adjusted return: M3 74 R2 (or coefficient of determination) 75 Systematic risk 75 Specific or residual risk 75 Treynor ratio (reward to volatility) 75 Modified Treynor ratio 77 Appraisal ratio (or Treynor-Black ratio) 77 Modified Jensen 77 Fama decomposition 77 Selectivity 78 Diversification 78 Net selectivity 78 Relative risk 78 Tracking error 78 Information ratio 80 Return distributions 81 Normal (or Gaussian) distribution 81 The central limit theorem 81 Skewness (Fisher's or moment skewness) 83 Sample skewness 84 Kurtosis (Pearson's kurtosis) 84 Sample kurtosis 84 Bera-Jarque statistic 85 Risk-adjusted performance measures for hedge funds 85 Drawdown 87 Average drawdown 87 Maximum drawdown 87 Largest individual drawdown 87 Recovery time (or drawdown duration) 87 Drawdown deviation 88 Ulcer index 88 Pain index 89 Calmar ratio 89 Sterling ratio 89 Sterling-Calmar ratio 90 Burke ratio 90 Modified Burke ratio 91 Martin ratio (or ulcer performance index) 91 Pain ratio 91 Lake ratio 91 Peak ratio 92 Downside risk (or semi-standard deviation) 92 Upside risk 92 Shortfall risk (or downside frequency) 94 Omega ratio (?) 94 Bernardo and Ledoit (or gain-loss) ratio 95 d ratio 95 Omega-Sharpe ratio 95 Sortino ratio 96 Kappa ( l ) 96 Upside potential ratio 97 Volatility skewness 97 Variability skewness 98 Adjusted Sharpe ratio 99 Skewness-kurtosis ratio 99 Prospect ratio 100 Value at risk (VaR) 100 Variance-covariance (or parametric) 100 Historical simulation (or non-parametric) 100 Monte Carlo simulation 101 VaR ratio 101 Reward to VaR ratio 101 Conditional VaR (or expected shortfall) 101 Conditional Sharpe ratio 101 Modified VaR 102 Modified Sharpe ratio 102 Return adjusted for downside risk 102 M2 for Sortino 102 Omega excess return 103 Hurst index 104 Fixed Income Risk 104 Duration (or volatility) 104 Macaulay duration 104 Modified duration 105 Macaulay-Weil duration 105 Portfolio duration 105 Effective duration (or option-adjusted duration) 107 Duration to worst 107 Convexity 108 Modified convexity 108 Effective convexity 108 Duration beta 108 Reward to duration 108 Which risk measures to use? 108 Risk efficiency ratio 109 Fund rating systems 109 Risk control structure 114 5 Performance Attribution 117 Arithmetic attribution 117 Brinson, Hood and Beebower 118 Asset allocation 118 Security (or stock) selection 119 Interaction 120 Brinson and Fachler 125 Interaction 126 Geometric excess return attribution 129 Asset allocation 130 Stock selection 130 Sector weights 133 6 Multi-currency Attribution 135 Ankrim and Hensel 135 Karnosky and Singer 140 Geometric multi-currency attribution 146 Naive currency attribution 146 Compounding effects 148 Geometric currency allocation 153 Currency timing 154 Interest rate differentials 155 Revised currency allocation 160 Revised country allocation 161 Incorporating forward currency contracts 163 Other currency issues 170 7 Fixed Income Attribution 171 The yield curve 171 Yield to maturity (or gross redemption yield) 171 Coupon yield curve 171 Par yield curve 171 Zero-coupon (or spot) curve 172 Wagner and Tito 172 Weighted duration attribution 173 Geometric fixed income attribution 178 Campisi framework 181 Yield curve analysis 187 Shift 187 Twist (or slope) 188 Curvature (or butterfly) 188 Carry 188 Credit (or spread) 189 Yield curve decomposition 189 8 Multi-period Attribution 191 Smoothing algorithms 191 Carino 191 Menchero 194 GRAP method 196 Frongello 199 Davies and Laker 201 Multi-period geometric attribution 204 Annualisation of excess return 206 Attribution annualisation 207 9 Further Attribution Issues 209 Attribution variations 209 Contribution analysis (or absolute return attribution) 209 Return (or regression)-based attribution 209 Holding-based (or buy/hold) attribution 209 Transaction-based attribution 210 Security-level attribution 210 Transaction costs 212 Off-benchmark (or zero-weight sector) attribution 213 Multi-level attribution 215 Balanced attribution 221 Lookthrough attribution (or fund of funds attribution) 221 Attribution standards 221 Evolution of performance attribution methodologies 222 Risk-adjusted attribution 223 Selectivity 224 10 Performance Measurement for Derivatives 227 Futures 227 Equity index future 227 Libor (London interbank offered rate) 228 Attribution including equity index futures 228 Leverage (or gearing) 232 Forward foreign exchange (FFX) contract (or currency forward) 235 Swaps 235 Interest rate swaps 236 Total return swap 236 Credit default swap 236 Equity index swaps 236 Contracts for difference (CFD) 237 Options 237 Option price sensitivity (the Greeks) 238 Warrants 239 Convertible bonds 239 Attribution analysis using options, warrants and convertible bonds 240 Market neutral attribution 241 Attribution for 130/30 funds (or extended short funds) 243 11 Performance Presentation Standards 247 Why do we need performance presentation standards? 247 Global Investment Performance Standards (GIPS (R))248 Advantages for asset managers 248 The standards 250 Composites 250 Presentation 251 Calculation 251 Claim of compliance 252 Structure of the standards 252 Verification 253 Verification/practitioners subcommittee 254 Interpretations subcommittee 254 Guidance statements 254 Definition of firm 255 Carve-outs 255 Significant cash flows 256 Portability 256 Supplemental information 257 Error correction 257 Measures of dispersion 258 Equal-weighted standard deviation 258 Asset-weighted dispersion 258 High-low 258 Interquartile range 258 Achieving compliance 259 Maintaining compliance 259 Appendix A Simple Attribution 261 Appendix B Multi-currency Attribution Methodology 264 Appendix C EIPC Guidance for Users of Attribution Analysis 271 Appendix D European Investment Performance Committee - Guidance on Performance Attribution Presentation 275 Appendix E The Global Investment Performance Standards 287 Appendix F Guidance Statement on Composite Definition 324 Appendix G Sample Global Investment Performance Standards Presentation 334 Appendix H Calculation Methodology Guidance Statement 336 Appendix I Definition of Firm Guidance Statements 345 Appendix J Treatment of Carve-outs Guidance Statement 351 Appendix K Significant Cash Flow Guidance Statement 356 Appendix L Guidance Statement on Performance Record Portability 361 Appendix M Guidance Statement on the Use of Supplemental Information 365 Appendix N Guidance Statement on Recordkeeping Requirements of the GIPS Standards 369 Appendix O Useful Websites 376 Bibliography 377 Index 381

About the Author

CARL BACON CIPM, is Chairman of StatPro, a data and software development specialist providing services for the asset management industry. He also runs his own consultancy business providing advice to asset managers on various risk and performance measurement issues. Prior to joining StatPro, Carl was Director of Risk Control and Performance at Foreign & Colonial Management Ltd., Vice President Head of Performance (Europe) for J P Morgan Investment Management Inc., and Head of Performance for Royal Insurance Asset Management. Carl holds a B.Sc. Hons. in Mathematics from Manchester University, is an executive committee member of Investment-Performance.com and also an associate tutor for 7city Learning. A founder member of both the Investment Performance Council and GIPS (r) , Carl is ex-chair of the IPC Interpretations & IPC Verification Sub-Committees, and is a member of the Advisory Board of the Journal of Performance Measurement. Author of the first edition of Practical Portfolio Performance Measurement & Attribution published in 2004 as part of the Wiley Finance Series, Carl is also Editor of Advanced Portfolio Attribution Analysis.

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