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<p><b>Chapter 1 Introduction 15</b></p> <p>Definition of risk 15</p> <p>Risk types 15</p> <p>Risk management v Risk control 18</p> <p>Risk aversion 19</p> <p>Ex-post and ex-ante 19</p> <p>Dispersion 20</p> <p><b>Chapter 2 Descriptive statistics 21</b></p> <p>Mean (or arithmetic mean) 21</p> <p>Annualised return 22</p> <p>Continuously compounded returns (or log returns) 22</p> <p>Winsorised mean 23</p> <p>Mean absolute deviation (or mean deviation) 24</p> <p>Variance 25</p> <p>Mean difference (absolute mean difference or Gini mean difference) 30</p> <p>Relative mean difference 31</p> <p>Bessel’s correction (population or sample, n or n-1) 31</p> <p>Sample variance 35</p> <p>Standard deviation (variability or volatility) 36</p> <p>Annualised risk (or time aggregation) 37</p> <p>The Central Limit Theorem 38</p> <p>Frequency and number of data points 38</p> <p>Alternative risk annualisation methods 39</p> <p>Normal (or Gaussian) distribution 40</p> <p>Histograms 42</p> <p>Skewness (Fisher’s or moment skewness) 43</p> <p>Sample skewness 44</p> <p>Kurtosis (Pearson’s kurtosis) 45</p> <p>Excess kurtosis (or Fisher’s kurtosis) 47</p> <p>Sample kurtosis 47</p> <p>Bera-Jarque statistic (or Jarque-Bera) 48</p> <p>Covariance 53</p> <p>Sample covariance 54</p> <p>Correlation (𝜌) 54</p> <p>Sample correlation 55</p> <p>Autocovariance 55</p> <p>Autocorrelation (or serial correlation) 57</p> <p>Annualised variability if returns are autocorrelated 60</p> <p><b>Chapter 3 APPRAISAL MEASURES 62</b></p> <p>Performance appraisal 62</p> <p>Sharpe ratio (reward to variability, Sharpe index) 63</p> <p>Roy ratio 65</p> <p>Risk-free rate 66</p> <p>Alternative Sharpe ratio 66</p> <p>Revised Sharpe ratio 67</p> <p>Adjusted Sharpe Ratio 68</p> <p>Skew-adjusted Sharpe Ratio 69</p> <p>Skewness-Kurtosis ratio 74</p> <p>Alternative adjusted Sharpe Ratios 74</p> <p>Smoothing-adjusted Sharpe Ratio 75</p> <p>MAD ratio 76</p> <p>Gini ratio 76</p> <p>Relative risk 77</p> <p>Tracking error (or tracking risk, relative risk, active risk) 77</p> <p>Relative skewness 78</p> <p>Relative kurtosis 79</p> <p>Information ratio 79</p> <p>Geometric information ratio 80</p> <p>Modified information ratio 87</p> <p>Adjusted information ratio 88</p> <p>Skew-adjusted information ratio 88</p> <p><b>Chapter 4: Regression Analysis 94</b></p> <p>Regression analysis 94</p> <p>Regression equation 95</p> <p>Regression alpha 95</p> <p>Regression beta 95</p> <p>Regression epsilon 95</p> <p>Capital Asset Pricing Model (CAPM) 96</p> <p>Beta (𝛽) (systematic risk or volatility) 97</p> <p>Jensen’s alpha (Jensen’s measure or Jensen’s differential return or ex-post alpha) 97</p> <p>Annualised alpha 98</p> <p>Bull beta (𝛽⁺) 106</p> <p>Bear beta (𝛽-) 106</p> <p>Beta timing ratio 106</p> <p>Market timing 107</p> <p>Systematic risk 115</p> <p>Correlation 115</p> <p>R2(or coefficient of determination) 116</p> <p>Specific (or residual) risk 117</p> <p>The Geometry of Risk 120</p> <p>Treynor ratio  (Reward to volatility) 124</p> <p>Modified Treynor ratio 124</p> <p>Appraisal ratio (or Treynor-Black ratio) 125</p> <p>Modified Jensen 126</p> <p>Fama decomposition 126</p> <p>Selectivity 127</p> <p>Diversification 127</p> <p>Net selectivity 127</p> <p>Fama-French three factor model 128</p> <p>Three factor alpha (or Fama-French alpha) 129</p> <p>Carhart four factor model 129</p> <p>Four factor alpha (or Carhart’s alpha) 130</p> <p>Types of Alpha 130</p> <p>Multi-factor Models 131</p> <p><b>Chapter 5 Drawdown 132</b></p> <p>Drawdown 132</p> <p>Average drawdown 132</p> <p>Maximum drawdown 133</p> <p>Largest individual drawdown 133</p> <p>Recovery time (or drawdown duration) 133</p> <p>Drawdown deviation 134</p> <p>Ulcer index 134</p> <p>Pain index 135</p> <p>Calmar ratio (or Drawdown ratio) 136</p> <p>MAR ratio 136</p> <p>Sterling ratio 136</p> <p>Sterling-Calmar ratio 137</p> <p>Burke ratio 138</p> <p>Modified Burke ratio 138</p> <p>Martin ratio (or Ulcer performance index) 138</p> <p>Pain ratio 138</p> <p>Active (or relative) Drawdown 143</p> <p><b>Chapter 6 Partial Moments 148</b></p> <p>Downside risk (or semi-standard deviation) 148</p> <p>Downside potential 149</p> <p>Pure downside risk 149</p> <p>Half variance (or semi-variance) 149</p> <p>Upside risk (or upside uncertainty) 150</p> <p>Mean absolute moment 150</p> <p>Omega ratio (Ω) 151</p> <p>Bernardo & Ledoit (or gain–loss) ratio 151</p> <p>d ratio 151</p> <p>Omega-Sharpe ratio 152</p> <p>Sortino ratio 153</p> <p>Reward to half-variance 153</p> <p>Downside risk Sharpe ratio 154</p> <p>Downside information ratio 154</p> <p>Sortino-Satchell ratio 155</p> <p>Kappa ratio 155</p> <p>Upside potential ratio 156</p> <p>Volatility skewness 156</p> <p>Variability skewness 157</p> <p>Farinelli- Tibiletti Ratio 160</p> <p>Gain-loss skewness 160</p> <p>Downside Skewness & Kurtosis 161</p> <p>Sortino Ratio with higher order moments 161</p> <p><b>Chapter 7 Prospect Theory 165</b></p> <p>Prospect ratio 165</p> <p>New Prospect ratio 166</p> <p>Omega-Prospect ratio 166</p> <p><b>Chapter 8 Extreme Risk 170</b></p> <p>Extreme events 170</p> <p>Extreme value theory 170</p> <p>Value at Risk (VaR) 170</p> <p>Relative VaR 171</p> <p>Ex-post VaR 171</p> <p>Potential upside (gain at risk) 172</p> <p>Percentile rank 172</p> <p>VaR calculation methodology 175</p> <p>Parametric VaR 175</p> <p>Modified VaR 176</p> <p>Historical simulation (or non-parametric) 177</p> <p>Monte Carlo simulation 177</p> <p>Which methodology for calculating VaR should be used? 178</p> <p>VaR Interpretation 178</p> <p>Frequency and time aggregation 180</p> <p>Time horizon 180</p> <p>Window length 181</p> <p>Reward to VaR 181</p> <p>Reward to relative VaR 182</p> <p>Double VaR ratio 183</p> <p>Conditional VaR (expected shortfall, tail loss, tail VaR or average VaR) 183</p> <p>Upper CVaR or CVaR⁺ 184</p> <p>Lower CVaR or CVaR^- 184</p> <p>Tail gain (expected gain or expected upside) 186</p> <p>Conditional Sharpe ratio (STARR ratio or reward to conditional VaR) 191</p> <p>Modified Sharpe ratio (reward to modified VaR) 191</p> <p>Tail risk 191</p> <p>Tail ratio 192</p> <p>Rachev ratio (or R ratio) 192</p> <p>Generalised Rachev ratio 194</p> <p>Drawdown at risk 194</p> <p>Conditional drawdown at risk 194</p> <p>Reward to conditional drawdown 195</p> <p>Generalised Z ratio 195</p> <p><b>Chapter 9 Fixed Income Risk 197</b></p> <p>Pricing fixed income instruments 197</p> <p>Redemption yield (yield to maturity) 197</p> <p>Weighted average cash flow 197</p> <p>Duration (effective mean term, discounted mean term or volatility) 198</p> <p>Macaulay duration 198</p> <p>Macaulay-Weil duration 199</p> <p>Modified duration 199</p> <p>Portfolio duration 200</p> <p>Effective duration (or option-adjusted duration) 202</p> <p>Duration to worst 204</p> <p>Convexity 204</p> <p>Modified convexity 205</p> <p>Effective convexity 205</p> <p>Portfolio convexity 207</p> <p>Bond returns 207</p> <p>Duration beta 209</p> <p>Reward to duration 209</p> <p><b>Chapter 10 miscellaneous Risk Measures 210</b></p> <p>Upside Capture Ratio (or up capture indicator) 210</p> <p>Downside capture ratio (or down capture indicator) 210</p> <p>Up/down capture (or Capture ratio) 211</p> <p>Up number ratio 216</p> <p>Down number ratio 216</p> <p>Up percentage ratio 217</p> <p>Down percentage ratio 217</p> <p>Percentage gain ratio 217</p> <p>Batting Average (or Relative Batting Average) 217</p> <p>Hurst index (or Hurst exponent) 218</p> <p>Relative Hurst Index (or Active Hurst) 225</p> <p>Bias ratio 231</p> <p>Active Share 237</p> <p>K ratio 239</p> <p><b>Chapter 11 Risk-adjusted Return 248</b></p> <p>Risk-adjusted return 248</p> <p>M² 248</p> <p>M² excess return 250</p> <p>Differential return 250</p> <p>GH1 (Graham & Harvey 1) 252</p> <p>GH2 (Graham & Harvey 2) 252</p> <p>Correlation and risk-adjusted return M³ 253</p> <p>Return adjusted for downside risk 253</p> <p>Adjusted M² 257</p> <p>Skew-adjusted M² 257</p> <p>Omega excess return 258</p> <p><b>Chapter 12: A Periodic Table of Risk Measures 259</b></p> <p>A Periodic Table of Risk Measures 259</p> <p>Periodic Table Design 260</p> <p>Filling the Periodic Table 261</p> <p>Notation 264</p> <p><b>Chapter 13: Risk-adjusted Performance Fees 269</b></p> <p>Performance Fees 269</p> <p>Asymmetric or Symmetric 269</p> <p>Performance Fees in Practice 273</p> <p><b>Chapter 14: Performance Dashboards 276</b></p> <p>Effective dashboards 276</p> <p>Data visualisation tools 277</p> <p><b>Chapter 15: Manager Selection 279</b></p> <p>Asset Manager Selection 279</p> <p>Manager Evaluation 280</p> <p>Portfolio Evaluation 281</p> <p>Monitoring and Control 282</p> <p><b>Chapter 16: The Four Dimensions of Performance 284</b></p> <p>Ex-post Return (The traditional dimension) 285</p> <p>Ex-post Risk (The neglected dimension) 285</p> <p>Ex-ante Return (The unknown dimension) 285</p> <p>Ex-ante Risk (The “sexy” dimension) 286</p> <p>Risk efficiency ratio 286</p> <p>Performance efficiency 287</p> <p>Ex-ante Risk Standards 287</p> <p>Consistency in calculations and comparison 288</p> <p>Disclosure 288</p> <p>Recognition of adherence to best practice 288</p> <p>More robust internal process and control 288</p> <p><b>Chapter 17: Which Risk Measure to Use? 291</b></p> <p>Why measure ex-post risk? 291</p> <p>Which risk measures to use? 291</p> <p>Hedge funds 295</p> <p>Smoothing 296</p> <p>Outliers 299</p> <p>Data mining 300</p> <p>Risk measures and the Global Investment Performance Standards (GIPS^®) 300</p> <p>Fund rating systems 303</p> <p>Which measures are actually used? 304</p> <p>Which risk measures should really be used? 309</p> <p>Common Errors to avoid 310</p> <p><b>Chapter 18: Risk Control 311</b></p> <p>Regulations in the investment risk area 311</p> <p>Risk control structure 312</p> <p>Risk management 313</p> <p>Glossary of Key Terms 318</p> <p>Appendix A – Composite Internal Risk Measures 321</p> <p>Bibliography 323</p>

<p><b>CARL R. BACON,</b> CIPM, is Chief Advisor to Confluence. He is a member of the Advisory Board of the <i>Journal of Performance Measurement</i> and Founder of The Freedom Index Company. He was formerly Chairman of StatPro Plc from 2000 to 2017.</p>

<p><b>PRACTICAL RISK-ADJUSTED PERFORMANCE MEASUREMENT</b></p> <p><b>An indispensable to ex-post risk measurement</b> <p>While many examinations of risk tend towards mathematical complexity, the latest edition of <i>Practical Risk-adjusted Performance Measurement </i>delivers a practical, insightful, and comprehensive discussion of ex-post risk measurement. Filled with implementable and user-friendly content, this book transforms the subject of risk into a straightforward and immensely useful resource. <p>The book is written from a buy-side, asset management perspective and includes a companion website that hosts supporting documents, worked examples, and a Periodic Table of Risk. In this new edition, readers will also find the most up-to-date measures accompanied by illustrative explanations. From the fundamentals of risk to regression measures, risk-adjusted returns, and the four dimensions of performance, Carl R. Bacon offers readers a roadmap to the selection and implementation of appropriate risk measures in a wide variety of different investment scenarios. <p><i>Practical Risk-adjusted Performance Measurement</i> remains the industry-leading guide to the application of risk measures in the real-world. It is ideal for portfolio managers, investment performance analysts, and others who need a one-stop resource to help build their understanding of risk-adjusted performance.

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