Practical Risk-Adjusted Performance Measurement -- Contents -- Preface -- Acknowledgements -- 1 Introduction -- Definition of risk -- Risk types -- Risk management v risk control -- Risk aversion -- Ex-post and ex-ante -- Dispersion -- 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 -- Janssen annualisation -- Frequency and number of data points -- 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 -- Up capture indicator -- Down capture indicator -- Up number ratio -- Down number ratio -- Up percentage ratio -- Down percentage ratio -- Percentage gain ratio -- Hurst index (or Hurst exponent) -- Bias ratio -- 3 Simple Risk Measures -- Performance appraisal -- Sharpe ratio (reward to variability, Sharpe index) -- Roy ratio -- Risk free rate -- Alternative Sharpe ratio -- Revised Sharpe ratio -- Adjusted Sharpe ratio -- Skewness-kurtosis 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 -- Relative Hurst.

4 Regression Analysis -- Regression equation -- Regression alpha (αR) -- Regression beta (βR) -- Regression epsilon (εR) -- 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 -- R2 (or coefficient of determination) -- Specific or residual 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) -- K ratio -- 5 Drawdown -- Drawdown -- Average drawdown -- Maximum drawdown (or peak to valley 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 -- Lake ratio -- Peak ratio -- 6 Partial Moments -- Downside risk (or semi-standard deviation) -- Pure downside risk -- Half variance (or semi-variance) -- Upside risk (or upside uncertainty) -- Mean absolute moment -- Omega ratio ( -- 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 -- Kappa (Kl) (or Sortino-Satchell ratio) -- Upside potential ratio -- Volatility skewness -- Variability skewness -- Farinelli-Tibiletti ratio -- Prospect ratio -- 7 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? -- 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 -- 8 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 -- 9 Risk-adjusted Return -- Risk-adjusted return -- M2 -- M2 excess return -- Differential return -- GH1 (Graham & Harvey 1) -- GH2 (Graham & Harvey 2) -- Correlation and risk-adjusted return M3 -- Return adjusted for downside risk -- Adjusted M2 -- Omega excess return -- 10 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 R ) -- Fund rating systems -- Risk efficiency ratio -- Which measures are actually used? -- Which risk measures should really be used? -- 11 Risk Control -- Regulations in the investment risk area -- Risk control structure -- Risk management -- Glossary of Key Terms -- Appendix A - Composite Internal Risk Measures -- Appendix B - Absolute Risk Dashboard -- Appendix C - Relative Risk Dashboard -- Bibliography -- Index.