Preparing for the Worst -- Contents -- List of Figures -- List of Tables -- Preface -- 1. Quantitative Measures of the Stock Market -- 1.1. Pricing Future Cash Flows -- 1.2. The Expected Return -- 1.3. Volatility -- 1.4. Modeling of Stock Price Diffusion -- 1.4.1. Continuous Time -- 1.4.2. Jump Diffusion -- 1.4.3. Mean Reversion in the Diffusion Context -- 1.4.4. Higher Order Lag Correlations -- 1.4.5. Time-Varying Variance -- 1.5. Efficient Market Hypothesis -- 1.5.1. Weak Form Efficiency -- 1.5.2. Semi-strong Form Efficiency -- 1.5.3. Strong Form Efficiency -- Appendix: Simple Regression Analysis -- 2. A Short Review of the Theory of Risk Measurement -- 2.1. Quantiles and Value at Risk -- 2.1.1. Pearson Family as a Generalization of the Normal Distribution -- 2.1.2. Pearson Type IV Distribution for Our Mutual Fund Data -- 2.1.3. Nonparametric Value at Risk (VaR) Calculation from Low Percentiles -- 2.1.4. Value at Risk for Portfolios with Several Assets -- 2.2. CAPM Beta, Sharpe, and Treynor Performance Measures -- 2.2.1. Using CAPM for Pricing of Securities -- 2.2.2. Using CAPM for Capital Investment Decisions -- 2.2.3. Assumptions of CAPM -- 2.3. When You Assume . . . -- 2.3.1. CAPM Testing Issues -- 2.4. Extensions of the CAPM -- 2.4.1. Observable Factors Model -- 2.4.2. Arbitrage Pricing Theory (APT) and Construction of Factors -- 2.4.3. Jensen, Sharpe, and Treynor Performance Measures -- Appendix: Estimating the Distribution from the Pearson Family of Distributions -- 3. Hedging to Avoid Market Risk -- 3.1. Derivative Securities: Futures, Options -- 3.1.1. A Market for Trading in Futures -- 3.1.2. How Smart Money Can Lose Big -- 3.1.3. Options Contracts -- 3.2. Valuing Derivative Securities -- 3.2.1. Binomial Option Pricing Model -- 3.2.2. Option Pricing from Diffusion Equations -- 3.3. Option Pricing Under Jump Diffusion.

3.4. Implied Volatility and the Greeks -- 3.4.1. The Role of D of an Option for Downside Risk -- 3.4.2. The Gamma (G) of an Option -- 3.4.3. The Omega, Theta, Vega, and Rho of an Option -- Appendix: Drift and Diffusion -- 4. Monkey Wrench in the Works: When the Theory Fails -- 4.1. Bubbles, Reversion, and Patterns -- 4.1.1. Calendar Effects -- 4.1.2. Mean Reversion -- 4.1.3. Bubbles -- 4.2. Modeling Volatility or Variance Explicitly -- 4.3. Testing for Normality -- 4.3.1. The Logistic Distribution Compared with the Normal -- 4.3.2. Empirical cdf and Quantile-Quantile (Q-Q) Plots -- 4.3.3. Kernel Density Estimation -- 4.4. Alternative Distributions -- 4.4.1. Pareto (Pareto-Levy, Stable Pareto) Distribution -- 4.4.2. Inverse Gaussian -- 4.4.3. Laplace (Double-Exponential) Distribution -- 4.4.4. Azzalini's Skew-Normal (SN) Distribution -- 4.4.5. Lognormal Distribution -- 4.4.6. Stable Pareto and Pareto-Levy Densities -- 5. Downside Risk -- 5.1. VaR and Downside Risk -- 5.1.1. VaR from General Parametric Densities -- 5.1.2. VaR from Nonparametric Empirical Densities -- 5.1.3. VaR for Longer Time Horizon (t > 1) and the IGARCH Assumption -- 5.1.4. VaR in International Setting -- 5.2. Lower Partial Moments (Standard Deviation, Beta, Sharpe, and Treynor) -- 5.2.1. Sharpe and Treynor Measures -- 5.3. Implied Volatility and Other Measures of Downside Risk -- 6. Portfolio Valuation and Utility Theory -- 6.1. Utility Theory -- 6.1.1. Expected Utility Theory (EUT) -- 6.1.2. A Digression: Derivation of Arrrow-Pratt Coefficient of Absolute Risk Aversion (CARA) -- 6.1.3. Size of the Risk Premium Needed to Encourage Risky Equity Investments -- 6.1.4. Taylor Series Links EUT, Moments of f(x), and Derivatives of U(x) -- 6.2. Nonexpected Utility Theory -- 6.2.1. A Digression: Lorenz Curve Scaling over the Unit Square.

6.2.2. Mapping from EUT to Non-EUT within the Unit Square -- 6.3. Incorporating Utility Theory into Risk Measurement and Stochastic Dominance -- 6.3.1. Class D1 of Utility Functions and Investors -- 6.3.2. Class D2 of Utility Functions and Investors -- 6.3.3. Explicit Utility Functions and Arrow-Pratt Measures of Risk Aversion -- 6.3.4. Class D3 of Utility Functions and Investors -- 6.3.5. Class D4 of Utility Functions and Investors -- 6.3.6. First-Order Stochastic Dominance (1SD) -- 6.3.7. Second-Order Stochastic Dominance (2SD) -- 6.3.8. Third-Order Stochastic Dominance (3SD) -- 6.3.9. Fourth-Order Stochastic Dominance (4SD) -- 6.3.10. Empirical Checking of Stochastic Dominance Using Matrix Multiplications and Incorporation of 4DPs of Non-EUT -- 6.4. Incorporating Utility Theory into Option Valuation -- 6.5. Forecasting Returns Using Nonlinear Structures and Neural Networks -- 6.5.1. Forecasting with Multiple Regression Models -- 6.5.2. Qualitative Dependent Variable Forecasting Models -- 6.5.3. Neural Network Models -- 7. Incorporating Downside Risk -- 7.1. Investor Reactions -- 7.1.1. Irrational Investor Reactions -- 7.1.2. Prospect Theory -- 7.1.3. Investor Reaction to Shocks -- 7.2. Patterns of Downside Risk -- 7.3. Downside Risk in Stock Valuations and Worldwide Investing -- 7.3.1. Detecting Potential Downturns from Growth Rates of Cash Flows -- 7.3.2. Overoptimistic Consensus Forecasts by Analysts -- 7.3.3. Further Evidence Regarding Overoptimism of Analysts -- 7.3.4. Downside Risk in International Investing -- 7.3.5. Legal Loophole in Russia -- 7.3.6. Currency Devaluation Risk -- 7.3.7. Forecast of Currency Devaluations -- 7.3.8. Time Lags and Data Revisions -- 7.3.9. Government Interventions Make Forecasting Currency Markets Difficult -- 7.4. Downside Risk Arising from Fraud, Corruption, and International Contagion.

7.4.1. Role of Periodic Portfolio Rebalancing -- 7.4.2. Role of International Financial Institutions in Fighting Contagions -- 7.4.3. Corruption and Slow Growth of Derivative Markets -- 7.4.4. Corruption and Private Credit Rating Agencies -- 7.4.5. Corruption and the Home Bias -- 7.4.6. Value at Risk (VaR) Calculations Worsen Effect of Corruption -- 8. Mathematical Techniques -- 8.1. Matrix Algebra -- 8.1.1. Sum, Product, and Transpose of Matrices -- 8.1.2. Determinant of a Square Matrix and Singularity -- 8.1.3. The Rank and Trace of a Matrix -- 8.1.4. Matrix Inverse, Partitioned Matrices, and Their Inverse -- 8.1.5. Characteristic Polynomial, Eigenvalues, and Eigenvectors -- 8.1.6. Orthogonal Vectors and Matrices -- 8.1.7. Idempotent Matrices -- 8.1.8. Quadratic and Bilinear Forms -- 8.1.9. Further Study of Eigenvalues and Eigenvectors -- 8.2. Matrix-Based Derivation of the Efficient Portfolio -- 8.3. Principal Components Analysis, Factor Analysis, and Singular Value Decomposition -- 8.4. Ito's Lemma -- 8.5. Creation of Risk-Free Nonrandom g(S, t) as a Hedge Portfolio -- 8.6. Derivation of Black-Scholes Partial Differential Equation -- 8.7. Risk-Neutral Case -- 9. Computational Issues -- 9.1. Sampling, Compounding, and Other Data Issues in Finance -- 9.1.1. Random Sampling Implicit in the Available Data -- 9.1.2. Sampling Distribution of the Sample Mean -- 9.1.3. Compounding of Returns and the Lognormal Distribution -- 9.1.4. Relevance of Geometric Mean of Returns in Compounding -- 9.1.5. Sampling Distribution of Average Compound Return -- 9.2. Numerical Procedures -- 9.2.1. Faulty Rounding Stony -- 9.2.2. Numerical Errors in Excel Software -- 9.2.3. Binary Arithmetic -- 9.2.4. Round-off and Cancellation Errors in Floating Point Arithmetic -- 9.2.5. Algorithms Matter -- 9.2.6. Benchmarks and Self-testing of Software Accuracy.

9.2.7. Value at Risk Implications -- 9.3. Simulations and Bootstrapping -- 9.3.1. Random Number Generation -- 9.3.2. An Elementary Description of Simulations -- 9.3.3. Simple iid Bootstrap in Finance -- 9.3.4. A Description of the iid Bootstrap for Regression -- Appendix A: Regression Specification, Estimation, and Software Issues -- Appendix B: Maximum Likelihood Estimation Issues -- Appendix C: Maximum Entropy (ME) Bootstrap for State-Dependent Time Series of Returns -- 10. What Does It All Mean? -- Glossary of Greek Symbols -- Glossary of Notations -- Glossary of Abbreviations -- References -- Name Index -- Index.