Carl R. Bacon - Practical Risk-Adjusted Performance Measurement

1 Cover

2 Title Page Practical Risk-Adjusted Performance Measurement CARL R. BACON Second Edition

3 Copyright

4 Dedication

5 Preface Note

6 Acknowledgements

7 About the Companion Website

8 CHAPTER 1: Introduction DEFINITION OF RISK RISK TYPES RISK MANAGEMENT VERSUS RISK CONTROL RISK AVERSION EX POST AND EX ANTE DISPERSION NOTES

9 CHAPTER 2: Descriptive Statistics MEAN (OR ARITHMETIC MEAN) ANNUALISED RETURN CONTINUOUSLY COMPOUNDED RETURNS (OR LOG RETURNS) WINSORISED MEAN MEAN ABSOLUTE DEVIATION (OR MEAN DEVIATION) VARIANCE MEAN DIFFERENCE (ABSOLUTE MEAN DIFFERENCE OR GINI MEAN DIFFERENCE) RELATIVE MEAN DIFFERENCE BESSEL'S CORRECTION (POPULATION OR SAMPLE, N OR N − 1) SAMPLE VARIANCE STANDARD DEVIATION (VARIABILITY OR VOLATILITY) ANNUALISED RISK (OR TIME AGGREGATION) THE CENTRAL LIMIT THEOREM FREQUENCY AND NUMBER OF DATA POINTS ALTERNATIVE RISK ANNUALISATION METHODS NORMAL (OR GAUSSIAN) DISTRIBUTION HISTOGRAMS SKEWNESS (FISHER'S OR MOMENT SKEWNESS) SAMPLE SKEWNESS KURTOSIS (PEARSON'S KURTOSIS) EXCESS KURTOSIS (OR FISHER'S KURTOSIS) SAMPLE KURTOSIS BERA–JARQUE STATISTIC (OR JARQUE–BERA) COVARIANCE SAMPLE COVARIANCE CORRELATION ( ρ ) SAMPLE CORRELATION AUTOCOVARIANCE AUTOCORRELATION (OR SERIAL CORRELATION) ANNUALISED VARIABILITY IF RETURNS ARE AUTOCORRELATED NOTES

10 CHAPTER 3: Performance Appraisal Measures PERFORMANCE APPRAISAL SHARPE RATIO (REWARD TO VARIABILITY, SHARPE INDEX) ROY RATIO RISK-FREE RATE ALTERNATIVE SHARPE RATIO REVISED SHARPE RATIO ADJUSTED SHARPE RATIO SKEW-ADJUSTED SHARPE RATIO SKEWNESS–KURTOSIS RATIO ALTERNATIVE ADJUSTED SHARPE RATIOS SMOOTHING-ADJUSTED SHARPE RATIO MAD RATIO GINI RATIO RELATIVE RISK TRACKING ERROR (OR TRACKING RISK, RELATIVE RISK, ACTIVE RISK) RELATIVE SKEWNESS RELATIVE KURTOSIS INFORMATION RATIO GEOMETRIC INFORMATION RATIO MODIFIED INFORMATION RATIO ADJUSTED INFORMATION RATIO SKEW-ADJUSTED INFORMATION RATIO NOTES

11 CHAPTER 4: Regression Analysis REGRESSION EQUATION REGRESSION ALPHA REGRESSION BETA REGRESSION EPSILON CAPITAL ASSET PRICING MODEL (CAPM) BETA (β) (SYSTEMATIC RISK OR VOLATILITY) JENSEN'S ALPHA (JENSEN'S MEASURE OR JENSEN'S DIFFERENTIAL RETURN OR EX-POST ALPHA ) ANNUALISED ALPHA BULL BETA ( β+ ) BEAR BETA ( β− ) BETA TIMING RATIO MARKET TIMING SYSTEMATIC RISK CORRELATION R2 (OR COEFFICIENT OF DETERMINATION) SPECIFIC (OR RESIDUAL) RISK THE GEOMETRY OF RISK TREYNOR RATIO (REWARD TO VOLATILITY) MODIFIED TREYNOR RATIO APPRAISAL RATIO (OR TREYNOR–BLACK RATIO) MODIFIED JENSEN FAMA DECOMPOSITION SELECTIVITY DIVERSIFICATION NET SELECTIVITY FAMA–FRENCH THREE-FACTOR MODEL THREE-FACTOR ALPHA (OR FAMA–FRENCH ALPHA ) CARHART FOUR-FACTOR MODEL FOUR-FACTOR ALPHA (OR CARHART'S ALPHA ) TYPES OF ALPHA MULTI-FACTOR MODELS NOTES

12 CHAPTER 5: Drawdown AVERAGE DRAWDOWN MAXIMUM DRAWDOWN LARGEST INDIVIDUAL DRAWDOWN RECOVERY TIME (OR DRAWDOWN DURATION) DRAWDOWN DEVIATION ULCER INDEX PAIN INDEX CALMAR RATIO (OR DRAWDOWN RATIO) MAR RATIO STERLING RATIO STERLING−CALMAR RATIO BURKE RATIO MODIFIED BURKE RATIO MARTIN RATIO (OR ULCER PERFORMANCE INDEX) PAIN RATIO ACTIVE (OR RELATIVE) DRAWDOWN NOTES

13 CHAPTER 6: Partial Moments DOWNSIDE RISK (OR SEMI-STANDARD DEVIATION) DOWNSIDE POTENTIAL PURE DOWNSIDE RISK HALF VARIANCE (OR SEMI-VARIANCE) UPSIDE RISK (OR UPSIDE UNCERTAINTY) MEAN ABSOLUTE MOMENT OMEGA RATIO (Ω) BERNARDO AND LEDOIT (OR GAIN–LOSS) RATIO d RATIO OMEGA –SHARPE RATIO SORTINO RATIO REWARD TO HALF-VARIANCE DOWNSIDE RISK SHARPE RATIO DOWNSIDE INFORMATION RATIO SORTINO–SATCHELL RATIO KAPPA RATIO UPSIDE POTENTIAL RATIO VOLATILITY SKEWNESS VARIABILITY SKEWNESS FARINELLI–TIBILETTI RATIO GAIN–LOSS SKEWNESS DOWNSIDE SKEWNESS AND KURTOSIS SORTINO RATIO WITH HIGHER ORDER MOMENTS NOTES

14 CHAPTER 7: Prospect Theory PROSPECT RATIO NEW PROSPECT RATIO OMEGA –PROSPECT RATIO NOTES

15 CHAPTER 8: Extreme Risk EXTREME EVENTS EXTREME VALUE THEORY VALUE AT RISK (VaR) RELATIVE VaR EX-POST VaR POTENTIAL UPSIDE (GAIN AT RISK) PERCENTILE RANK VaR CALCULATION METHODOLOGY PARAMETRIC VaR MODIFIED VaR HISTORICAL SIMULATION (OR NON-PARAMETRIC) MONTE CARLO SIMULATION WHICH METHODOLOGY FOR CALCULATING VaR SHOULD BE USED? VaR INTERPRETATION FREQUENCY AND TIME AGGREGATION TIME HORIZON WINDOW LENGTH REWARD TO VaR REWARD TO RELATIVE VaR DOUBLE VaR RATIO CONDITIONAL VaR (EXPECTED SHORTFALL, TAIL LOSS, TAIL VaR OR AVERAGE VaR) UPPER CVaR OR CVaR + LOWER CVaR OR CVaR− TAIL GAIN (EXPECTED GAIN OR EXPECTED UPSIDE) CONDITIONAL SHARPE RATIO (STARR RATIO OR REWARD TO CONDITIONAL VaR) MODIFIED SHARPE RATIO (REWARD TO MODIFIED VaR) TAIL RISK TAIL RATIO RACHEV RATIO (OR R RATIO) GENERALISED RACHEV RATIO DRAWDOWN AT RISK CONDITIONAL DRAWDOWN AT RISK REWARD TO CONDITIONAL DRAWDOWN GENERALISED Z RATIO NOTES

16 CHAPTER 9: Fixed Income Risk PRICING FIXED INCOME INSTRUMENTS REDEMPTION YIELD (YIELD TO MATURITY) WEIGHTED AVERAGE CASH FLOW DURATION (EFFECTIVE MEAN TERM, DISCOUNTED MEAN TERM OR VOLATILITY) MACAULAY DURATION MACAULAY–WEIL DURATION MODIFIED DURATION PORTFOLIO DURATION EFFECTIVE DURATION (OR OPTION-ADJUSTED DURATION) DURATION TO WORST CONVEXITY MODIFIED CONVEXITY EFFECTIVE CONVEXITY PORTFOLIO CONVEXITY BOND RETURNS DURATION BETA REWARD TO DURATION NOTES

17 CHAPTER 10: Miscellaneous Risk Measures UPSIDE CAPTURE RATIO (OR UP CAPTURE INDICATOR) DOWNSIDE CAPTURE RATIO (OR DOWN CAPTURE INDICATOR) UP/DOWN CAPTURE (OR CAPTURE RATIO) UP NUMBER RATIO DOWN NUMBER RATIO UP PERCENTAGE RATIO DOWN PERCENTAGE RATIO PERCENTAGE GAIN RATIO BATTING AVERAGE (OR RELATIVE BATTING AVERAGE) HURST INDEX (OR HURST EXPONENT) RELATIVE HURST INDEX (OR ACTIVE HURST) BIAS RATIO ACTIVE SHARE K RATIO NOTES

18 CHAPTER 11: Risk-Adjusted Return M2 M2 EXCESS RETURN DIFFERENTIAL RETURN GH1 (GRAHAM AND HARVEY 1) GH2 (GRAHAM AND HARVEY 2) CORRELATION AND RISK-ADJUSTED RETURN M3 RETURN ADJUSTED FOR DOWNSIDE RISK ADJUSTED M2 SKEW-ADJUSTED M2 OMEGA EXCESS RETURN NOTES

19 CHAPTER 12: A Periodic Table of Risk Measures PERIODIC TABLE DESIGN FILLING THE PERIODIC TABLE NOTATION NOTES

20 CHAPTER 13: Risk-Adjusted Performance Fees PERFORMANCE FEES ASYMMETRIC OR SYMMETRIC PERFORMANCE FEES IN PRACTICE NOTES

21 CHAPTER 14: Performance Dashboards EFFECTIVE DASHBOARDS DATA VISUALISATION TOOLS NOTES

22 CHAPTER 15: Manager Selection ASSET MANAGER SELECTION MANAGER EVALUATION PORTFOLIO EVALUATION MONITORING AND CONTROL NOTES

23 CHAPTER 16: The Four Dimensions of Performance EX-POST RETURN (THE TRADITIONAL DIMENSION) EX-POST RISK (THE NEGLECTED DIMENSION) EX-ANTE RETURN (THE UNKNOWN DIMENSION) EX-ANTE RISK (THE “SEXY” DIMENSION) RISK EFFICIENCY RATIO PERFORMANCE EFFICIENCY EX-ANTE RISK STANDARDS CONSISTENCY IN CALCULATIONS AND COMPARISON DISCLOSURE RECOGNITION OF ADHERENCE TO BEST PRACTICE MORE ROBUST INTERNAL PROCESS AND CONTROL NOTES

24 CHAPTER 17: Which Risk Measure to Use? WHY MEASURE EX-POST RISK? WHICH RISK MEASURES TO USE? HEDGE FUNDS SMOOTHING OUTLIERS DATA MINING RISK MEASURES AND THE GLOBAL INVESTMENT PERFORMANCE STANDARDS (GIPS ®) FUND RATING SYSTEMS WHICH MEASURES ARE ACTUALLY USED? WHICH RISK MEASURES SHOULD REALLY BE USED? COMMON ERRORS TO AVOID NOTES

25 CHAPTER 18: Risk Control REGULATIONS IN THE INVESTMENT RISK AREA RISK CONTROL STRUCTURE RISK MANAGEMENT

26 Glossary of Key Terms

27 APPENDIX A: Composite Internal Risk Measures

28 Bibliography

29 Index

30 End User License Agreement

1 Chapter 2 TABLE 2.1 Portfolio variability TABLE 2.2 Benchmark variability TABLE 2.3 Bessel's correctionTABLE 2.4 Portfolio skewness and kurtosisTABLE 2.5 Benchmark skewness and kurtosisTABLE 2.6 Covariance and correlationTABLE 2.7 Autocovariance and autocorrelation