# (p. x) List of Figures

(p. x) List of Figures

3.1 Efficient frontiers for EAE portfolios with 100 securities. 47

4.1 Predicted and realized active risk for optimized solutions of varying quality. 56

4.3 Optimized and heuristic realized efficient frontiers — Example 1. 58

4.4 Optimized and heuristic realized efficient frontiers — Example 2. 59

7.1 Box plots of out-of-sample log excess returns: Idealistic setup. 129

7.2 Box plots of out-of-sample log excess returns: Realistic setup. 130

8.1 Cumulative returns of five replication products, S&P 500, and HFRI Composite Index. 149

8.2 Scatter plot of the risk (S.D.) and annualized return (Mean) of replication products from Table 8.1. 150

9.2 Optimal centralized allocation. 169

9.3 Optimal decentralized allocation without benchmarks. 170

9.4 Required levels of managerial ability to justify decentralization. 171

(p. xi) 10.2 Portfolio manager’s payoff as a function of realized return under a fulcrum fee compensation structure. 181

10.3 Active efficient frontiers for portfolios with and without long-only investment constraints. 184

10.5 Active risk decisions at different investment stages under an asset-based fee structure. 190

10.7 Active risk decisions at different investment stages under an asymmetric incentive fee structure. 192

10.9 Active risk decisions at different investment stages under a fulcrum fee structure. 195

10.10 The effects of a knockout barrier on active risk decisions with a fulcrum fee structure. 197

11.1 Optimal robust P and ψ for three normal distribution efficiencies. 207

11.2 OLS and robust beta estimates for four different outlier configurations. 209

11.6 OLS betas. 215

11.7 Robust betas. 216

11.10 Distribution of paired differences between OLS and robust betas. 220

11.11 OLS beta standard errors. 221

11.13 OLS beta

*t*-statistics. 22311.14 Robust beta

*t*-statistics. 224(p. xii) 11.15 Percentage of observations rejected with 99% efficiency. 225

11.16 Ratio of systematic risk to total risk for OLS betas. 228

11.17 Ratios of systematic risk to total risk for robust betas. 228

11.18 Paired differences between systematic and total risk ratios. 229

11.C1 Initial and final robust beta estimates for firm with ticker DD. 235

11.D1 Relative changes in market capitalization median and quartiles. 236

11.D2 Size (log of market capitalization in $M) percentiles for the liquid stocks. 236

11.D3 Annualized mean excess market returns. 237

11.E1 Jarque—Bera tests of normality of excess stock returns. 238

11.E2 Jarque—Bera tests without 1987 Black Monday outlier. 239

11.E3 Skewness percentages of JB statistic without 1987 Black Monday outlier. 239

11.E4 Normalized skewness without 1987 Black Monday outlier. 240

13.A1 Several normal densities, and one uniform density that could be used as priors for

*μ*. 28815.1 Public and private debt. 309

15.3 U.S. Treasury actives (par) and spot curves, November 2009. 314

15.4 Constant maturity U.S. Treasury 10-year rates, 1962—2009. 320

15.5 First differences of constant maturity U.S. Treasury 10-year rates. 321

15.6 10 year minus 1 year U.S. Treasury slope, 1962—2009. 322

15.7 Rate/slope correlations, 1963—2009. 323

15.9 U.S. Treasury/Japanese Government bond correlations, 1976—2009. 327

15.10 Moody’s default rates, 1920—2009. 330

15.11 Differences between IG corporate bond yields and comparable U.S. Treasurys, 1920—2009. 331

16.2 Equation (16.3):

*P*(*L*(*T*)/*S*(*T*)*〈 r*),*r*= 1,*T*= 1,*ρ*= 6, GBM per Table 16.1. 344(p. xiii) 16.3 (a) Equation (16.4),

*r*= 1,*T*= 1,*λ*= 6, GBM per Table 16.1; (b) Equations (16.3) and (16.4),*r*= 1,*T*= 1,*λ*= 6, GBM per Table 16.1. 34616.4 Equation (16.6)

*P*(*L*(*T*) —*S*(*T*)*〈 k*),*k*= 0.5,*T*= 1,*λ*= 6, GBM per Table 16.1. 34816.6 Equations (16.6) and (16.7),

*k*= 0.5,*T*= 1,*λ*= 2,*ρ*= 0.8, GBM per Table 16.1. 35116.7 Equations (16.6) and (16.7),

*k*= 0.5,*T*= 1,*λ*= 2,*ρ*= —0.5, GBM per Table 16.1. 35116.18 Incremental success probability,

*k*= 1,*T*= 1,*λ*= 6,*ρ*= 0.8, GBM per Table 16.1. 36316.A.1 Exact and approximate paths of

*S*(*T*),*α*= 2%,_{S}*σ*= 20%,_{S}*K*= 5. 36517.1 Idealized market impact model showing sell of 200 shares. 373

17.2 Idealized market impact model showing two sells of 100 shares each. 374

18.1 Daily market-impact costs for U.S. indices trade lists up to $5 billion. 400

18.2 Optimal turnover rates for different levels of assets under management. 402

(p. xiv) 18.3 Turnover optimality. 402

18.6 Return vs. realized turnover for different portfolio wealth. 408

18.7 Median trading volume, % of ADDV vs. realized turnover, $1Bn portfolio. 410

18.8 Optimal turnover fora given

*r*and portfolio wealth. 41018.10 Monthly return vs. realized turnover. 412

18.11 Net return vs. realized turnover. 415

18.12 Net return vs. realized turnover. 416

19.3 Money supply measures. 444

19.4 Footnote overview of economic framework — Description of four quadrants. 445

20.1 Employer guarantee option for a 50—50 equity-bond mix. 459

20.2 Employer guarantee option suface. 459

20.3 Indexation option surface. 461

20.4 Employer share in total risk. 462

20.5 Option values and risk exposure under different investment strategies. 465

21.1 Stylized commodity fund. 471

21.2 Stylized excess reserve fund. 472

21.5 Balance of payments for sovereign wealth fund countries (1997—2007 average, % of GNI). 485

21.6 Ratio of reserves to M2 for developing economies (%). 487