Quantitative Investment Analysis

CFA Institute is the global association of investment professionals that sets the standard for professional excellence and credentials. The organization is a champion for ethical behavior in investment markets and a respected source of knowledge in the global financial community. The end goal: to create an environment where investors’ interests come first, markets function at their best, and economies grow. CFA Institute has more than 155,000 members in 165 countries and territories, including 150,000 CFA® charterholders, and 148 member societies. For more information, visit www.cfainstitute.org.

• Preface xvAcknowledgments xviiAbout the CFA Institute Investment Series xixChapter 1 The Time Value of Money 1Learning Outcomes 11. Introduction 12. Interest Rates: Interpretation 23. The Future Value of a Single Cash Flow 43.1. The Frequency of Compounding 93.2. Continuous Compounding 113.3. Stated and Effective Rates 124. The Future Value of a Series of Cash Flows 134.1. Equal Cash Flows—Ordinary Annuity 144.2. Unequal Cash Flows 155. The Present Value of a Single Cash Flow 165.1. Finding the Present Value of a Single Cash Flow 165.2. The Frequency of Compounding 186. The Present Value of a Series of Cash Flows 206.1. The Present Value of a Series of Equal Cash Flows 206.2. The Present Value of an Infinite Series of Equal Cash Flows—Perpetuity 246.3. Present Values Indexed at Times Other than t = 0 256.4. The Present Value of a Series of Unequal Cash Flows 277. Solving for Rates, Number of Periods, or Size of Annuity Payments 277.1. Solving for Interest Rates and Growth Rates 287.2. Solving for the Number of Periods 307.3. Solving for the Size of Annuity Payments 317.4. Review of Present and Future Value Equivalence 357.5. The Cash Flow Additivity Principle 378. Summary 38Practice Problems 39Chapter 2 Organizing, Visualizing, and Describing Data 45Learning Outcomes 451. Introduction 452. Data Types 462.1. Numerical versus Categorical Data 462.2. Cross-Sectional versus Time-Series versus Panel Data 492.3. Structured versus Unstructured Data 503. Data Summarization 543.1. Organizing Data for Quantitative Analysis 543.2. Summarizing Data Using Frequency Distributions 573.3. Summarizing Data Using a Contingency Table 634. Data Visualization 684.1. Histogram and Frequency Polygon 684.2. Bar Chart 694.3. Tree-Map 734.4. Word Cloud 734.5. Line Chart 754.6. Scatter Plot 774.7. Heat Map 814.8. Guide to Selecting among Visualization Types 825. Measures of Central Tendency 855.1. The Arithmetic Mean 855.2. The Median 905.3. The Mode 925.4. Other Concepts of Mean 926. Other Measures of Location: Quantiles 1026.1. Quartiles, Quintiles, Deciles, and Percentiles 1036.2. Quantiles in Investment Practice 1087. Measures of Dispersion 1097.1. The Range 1097.2. The Mean Absolute Deviation 1097.3. Sample Variance and Sample Standard Deviation 1117.4. Target Downside Deviation 1147.5. Coefficient of Variation 1178. The Shape of the Distributions: Skewness 1199. The Shape of the Distributions: Kurtosis 12110. Correlation between Two Variables 12510.1. Properties of Correlation 12610.2. Limitations of Correlation Analysis 12911. Summary 132Practice Problems 135Chapter 3 Probability Concepts 147Learning Outcomes 1471. Introduction 1482. Probability, Expected Value, and Variance 1483. Portfolio Expected Return and Variance of Return 1714. Topics in Probability 1804.1. Bayes’ Formula 1804.2. Principles of Counting 1845. Summary 188References 190Practice Problem 190Chapter 4 Common Probability Distributions 195Learning Outcomes 1951. Introduction to Common Probability Distributions 1962. Discrete Random Variables 1962.1. The Discrete Uniform Distribution 1982.2. The Binomial Distribution 2003. Continuous Random Variables 2103.1. Continuous Uniform Distribution 2103.2. The Normal Distribution 2143.3. Applications of the Normal Distribution 2203.4. The Lognormal Distribution 2224. Introduction to Monte Carlo Simulation 2285. Summary 231References 233Practice Problems 234Chapter 5 Sampling and Estimation 241Learning Outcomes 2411. Introduction 2422. Sampling 2422.1. Simple Random Sampling 2422.2. Stratified Random Sampling 2442.3. Time-Series and Cross-Sectional Data 2453. Distribution of the Sample Mean 2483.1. The Central Limit Theorem 2484. Point and Interval Estimates of the Population Mean 2514.1. Point Estimators 2524.2. Confidence Intervals for the Population Mean 2534.3. Selection of Sample Size 2595. More on Sampling 2615.1. Data-Mining Bias 2615.2. Sample Selection Bias 2645.3. Look-Ahead Bias 2655.4. Time-Period Bias 2666. Summary 267References 269Practice Problems 270Chapter 6 Hypothesis Testing 275Learning Outcomes 2751. Introduction 2762. Hypothesis Testing 2773. Hypothesis Tests Concerning the Mean 2873.1. Tests Concerning a Single Mean 2873.2. Tests Concerning Differences between Means 2943.3. Tests Concerning Mean Differences 2994. Hypothesis Tests Concerning Variance and Correlation 3034.1. Tests Concerning a Single Variance 3034.2. Tests Concerning the Equality (Inequality) of Two Variances 3054.3. Tests Concerning Correlation 3085. Other Issues: Nonparametric Inference 3105.1. Nonparametric Tests Concerning Correlation: The Spearman Rank Correlation Coefficient 3125.2. Nonparametric Inference: Summary 3136. Summary 314References 317Practice Problems 317Chapter 7 Introduction to Linear Regression 327Learning Outcomes 3271. Introduction 3282. Linear Regression 3282.1. Linear Regression with One Independent Variable 3283. Assumptions of the Linear Regression Model 3324. The Standard Error of Estimate 3355. The Coefficient of Determination 3376. Hypothesis Testing 3397. Analysis of Variance in a Regression with One Independent Variable 3478. Prediction Intervals 3509. Summary 353References 354Practice Problems 354Chapter 8 Multiple Regression 365Learning Outcomes 3651. Introduction 3662. Multiple Linear Regression 3662.1. Assumptions of the Multiple Linear Regression Model 3722.2. Predicting the Dependent Variable in a Multiple Regression Model 3762.3. Testing Whether All Population Regression Coefficients Equal Zero 3782.4. Adjusted R2 3803. Using Dummy Variables in Regressions 3813.1. Defining a Dummy Variable 3813.2. Visualizing and Interpreting Dummy Variables 3823.3. Testing for Statistical Significance 3844. Violations of Regression Assumptions 3874.1. Heteroskedasticity 3884.2. Serial Correlation 3944.3. Multicollinearity 3984.4. Heteroskedasticity, Serial Correlation, Multicollinearity: Summarizing the Issues 4015. Model Specification and Errors in Specification 4015.1. Principles of Model Specification 4025.2. Misspecified Functional Form 4025.3. Time-Series Misspecification (Independent Variables Correlated with Errors) 4105.4. Other Types of Time-Series Misspecification 4146. Models with Qualitative Dependent Variables 4146.1. Models with Qualitative Dependent Variables 4147. Summary 422References 425Practice Problems 426Chapter 9 Time-Series Analysis 451Learning Outcomes 4511. Introduction to Time-Series Analysis 4522. Challenges of Working with Time Series 4543. Trend Models 4543.1. Linear Trend Models 4553.2. Log-Linear Trend Models 4583.3. Trend Models and Testing for Correlated Errors 4634. Autoregressive (AR) Time-Series Models 4644.1. Covariance-Stationary Series 4654.2. Detecting Serially Correlated Errors in an Autoregressive Model 4664.3. Mean Reversion 4694.4. Multiperiod Forecasts and the Chain Rule of Forecasting 4704.5. Comparing Forecast Model Performance 4734.6. Instability of Regression Coefficients 4755. Random Walks and Unit Roots 4785.1. Random Walks 4785.2. The Unit Root Test of Nonstationarity 4826. Moving-Average Time-Series Models 4866.1. Smoothing Past Values with an n-Period Moving Average 4866.2. Moving-Average Time-Series Models for Forecasting 4897. Seasonality in Time-Series Models 4918. Autoregressive Moving-Average Models 4969. Autoregressive Conditional Heteroskedasticity Models 49710. Regressions with More than One Time Series 50011. Other Issues in Time Series 50412. Suggested Steps in Time-Series Forecasting 50513. Summary 507References 508Practice Problems 509Chapter 10 Machine Learning 527Learning Outcomes 5271. Introduction 5272. Machine Learning and Investment Management 5283. What is Machine Learning? 5293.1. Defining Machine Learning 5293.2. Supervised Learning 5293.3. Unsupervised Learning 5313.4. Deep Learning and Reinforcement Learning 5313.5. Summary of ML Algorithms and How to Choose among Them 5324. Overview of Evaluating ML Algorithm Performance 5334.1. Generalization and Overfitting 5344.2. Errors and Overfitting 5344.3. Preventing Overfitting in Supervised Machine Learning 5375. Supervised Machine Learning Algorithms 5395.1. Penalized Regression 5395.2. Support Vector Machine 5415.3. K-Nearest Neighbor 5425.4. Classification and Regression Tree 5445.5. Ensemble Learning and Random Forest 5476. Unsupervised Machine Learning Algorithms 5596.1. Principal Components Analysis 5606.2. Clustering 5637. Neural Networks, Deep Learning Nets, and Reinforcement Learning 5757.1. Neural Networks 5757.2. Deep Learning Neural Networks 5787.3. Reinforcement Learning 5798. Choosing an Appropriate ML Algorithm 5899. Summary 590References 593Practice Problems 593Chapter 11 Big Data Projects 597Learning Outcomes 5971. Introduction 5972. Big Data in Investment Management 5983. Steps in Executing a Data Analysis Project: Financial Forecasting with Big Data 5994. Data Preparation and Wrangling 6034.1. Structured Data 6044.2. Unstructured (Text) Data 6105. Data Exploration Objectives and Methods 6175.1. Structured Data 6185.2. Unstructured Data: Text Exploration 6226. Model Training 6296.1. Structured and Unstructured Data 6307. Financial Forecasting Project: Classifying and Predicting Sentiment for Stocks 6397.1. Text Curation, Preparation, and Wrangling 6407.2. Data Exploration 6447.3. Model Training 6547.4. Results and Interpretation 6588. Summary 664Practice Problems 665Chapter 12 Using Multifactor Models 675Learning Outcomes 6751. Introduction 6752. Multifactor Models and Modern Portfolio Theory 6763. Arbitrage Pricing Theory 6774. Multifactor Models: Types 6834.1. Factors and Types of Multifactor Models 6834.2. The Structure of Macroeconomic Factor Models 6844.3. The Structure of Fundamental Factor Models 6874.4. Fixed-Income Multifactor Models 6915. Multifactor Models: Selected Applications 6955.1. Factor Models in Return Attribution 6965.2. Factor Models in Risk Attribution 6985.3. Factor Models in Portfolio Construction 7035.4. How Factor Considerations Can Be Useful in Strategic Portfolio Decisions 7056. Summary 706References 707Practice Problems 708Chapter 13 Measuring and Managing Market Risk 713Learning Outcomes 7131. Introduction 7142. Understanding Value at Risk 7142.1. Value at Risk: Formal Definition 7152.2. Estimating VaR 7182.3. Advantages and Limitations of VaR 7302.4. Extensions of VaR 7333. Other Key Risk Measures—Sensitivity and Scenario Measures 7353.1. Sensitivity Risk Measures 7363.2. Scenario Risk Measures 7403.3. Sensitivity and Scenario Risk Measures and VaR 7464. Using Constraints in Market Risk Management 7504.1. Risk Budgeting 7514.2. Position Limits 7524.3. Scenario Limits 7524.4. Stop-Loss Limits 7534.5. Risk Measures and Capital Allocation 7535. Applications of Risk Measures 7555.1. Market Participants and the Different Risk Measures They Use 7556. Summary 764References 766Practice Problems 766Chapter 14 Backtesting and Simulation 775Learning Outcomes 7751. Introduction 7752. The Objectives of Backtesting 7763. The Backtesting Process 7763.1. Strategy Design 7773.2. Rolling Window Backtesting 7783.3. Key Parameters in Backtesting 7793.4. Long/Short Hedged Portfolio Approach 7813.5. Pearson and Spearman Rank IC 7853.6. Univariate Regression 7893.7. Do Different Backtesting Methodologies Tell the Same Story? 7894. Metrics and Visuals Used in Backtesting 7924.1. Coverage 7924.2. Distribution 7944.3. Performance Decay, Structural Breaks, and Downside Risk 7974.4. Factor Turnover and Decay 7975. Common Problems in Backtesting 8015.1. Survivorship Bias 8015.2. Look-Ahead Bias 8046. Backtesting Factor Allocation Strategies 8076.1. Setting the Scene 8086.2. Backtesting the Benchmark and Risk Parity Strategies 8087. Comparing Methods of Modeling Randomness 8137.1. Factor Portfolios and BM and RP Allocation Strategies 8147.2. Factor Return Statistical Properties 8157.3. Performance Measurement and Downside Risk 8197.4. Methods to Account for Randomness 8218. Scenario Analysis 8249. Historical Simulation versus Monte Carlo Simulation 82810. Historical Simulation 83011. Monte Carlo Simulation 83512. Sensitivity Analysis 84013. Summary 848References 849Practice Problems 849Appendices 855Glossary 865About the Authors 883About the CFA Program 885Index 887