Practical Portfolio Performance Measurement and Attribution

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®, 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 SeriesCarl is also Editor of Advanced Portfolio Attribution Analysis.

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 β 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 (αR ) 71

Regression beta (βR ) 71

Regression epsilon (εR ) 71

Capital asset pricing model (CAPM) 72

Beta (β) (systematic risk or volatility) 72

Jensen’s alpha (or Jensen’s measure or Jensen’s differential return or ex post alpha) 72

Bull beta (β+) 72

Bear beta (β−) 73

Beta timing ratio 73

Covariance 73

Correlation (ρ) 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 (Ω) 94

Bernardo and Ledoit (or gain–loss) ratio 95

d ratio 95

Omega–Sharpe ratio 95

Sortino ratio 96

Kappa (κl ) 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®)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