Lecture Notes in Investment: Investment Fundamentals

by Eliezer Prisman (Author)

About this Book

This is an introduction to an investment course that focuses on basic models used in the financial industry for investment and decision making. The course begins with an overview of the investment environment in developed markets, followed by a more in-depth analysis of key investment topics. These topics include modern portfolio theory, asset pricing models, term structure of interest rates, stock and bond portfolio management and evaluation of portfolio performance. Modern finance extensively uses the conceptof arbitrage, or rather the lack of it in financial markets, and the course highlights such uses in different circumstances. The course takes a hands-on approach with the aid of a software package, Maple™, the details of which willbe explained during the first lecture. Consequently, most lectures will be divided between a theoretical lecture and a lab — a practical implementation ofthe theoretical material of the lecture. The use of the Maple™ software in this course simulates, to a certain extent, a professional environment. It allows visualizations of different concepts, minimizes tedious algebraic calculations and the use of calculus while equipping students with intuitive understanding. This is facilitated by the symbolic power of Maple™ and its excellent graphic and animation capabilities. Institutional material is surveyed very concisely, so the reader gets an appreciation of the investment 'lay of the land'. It is enhanced by an eLearning unit, self-administrated quizzes as well as a stock market game, utilizing StockTrack™. StockTrack™ introduces students to trading in the real world by practicing different types of orders as well as introducing conventions common in the investment community.

Brief Contents

Chapter 1. Introduction 1

    Preface 1

    Investment: The Lay of the Land 2

    The Maple Software: A Preliminary 3

    Introduction and Review of Simple Concepts 4

    Examples 9

    Revisiting an Arbitrage Example 12

Chapter 2. A Basic Model of Bond Markets 15

    Introduction 15

    Setting the Framework 15

    Arbitrage in Bond Markets: Introduction 19

Chapter 3. No Arbitrage Condition and the Term Structure, its Estimation and Smoothing 29

    Introduction 29

    The Term Structureof Interest Rates and NA 29

        Zero-Coupon, Spot and Yield Curves 38

    Smoothing of the Term Structure 47

        Smoothing and Continuous Compounding 58

    Forward Rate: A Classical Approach 60

Chapter 4. Duration and Immunization 67

    Introduction 67

    Duration: A Sensitivity Measure of Bonds’ Prices to Changes in Interest Rates 67

           Immunization 77

Chapter 5. Portfolio Choice Under Uncertainty: The Mean–Variance Framework 81

    Introduction 81

    Risk and Return in an Uncertain Environment: A First Look 83

    Expected Value, Variance, and the Mean–Variance Framework 86

    The Feasible Setwith Two Assets: A Specific Case 90

    The Feasible Setwith Two Assets: The Generic Case 97

        A Useful Variance Property 98

        A Useful Covariance Property and Generalization of the Variance Formula for N Securities 100

    Appendix: Estimation of Expected Values Variances, Covariances and Regressions 111

        Estimation with Maple 113

        Regression with Maple 115

Chapter 6. The Feasible Set: A General Formulation 121

    Introduction 121

    The Efficient Frontier Without a Risk-Free Asset 122

        An Example 125

        Solving Numerically for the Efficient Frontier 133

    The Efficient Frontier with a Risk-Free Asset 138

        Hints for Solving the Maximization of the Slope 144

Chapter 7. The Capital Asset Pricing Model: CAPM 147

    Introduction 147

    Mean–Variance and Utility Representation 148

    Choosing the Optimal Portfolio 151

        Solving for the Optimal Portfolio 155

    The CAPM as an Equilibrium Model and the Security Market Line (SML) 158

    Another Way of Proving the SML 162

    Properties of the SML 166

    Concluding Remarks 169

    Appendix A: Utility and Uncertainty 170

    Appendix B: Safety First Models 174

        Roy’s Criterion 176

        Kataoka’s Criterion 182

        Tesler’s Criterion 189

Chapter 8. The Security Market Line, Estimations and Single Index Models 193

    Introduction 193

    Estimation of the SML and β 193

        Solving the Regression Algebraically 195

        The use of β in Corporate Finance 197

    The Single Index Model 198

        Explanation for the Covariance Formula 202

        Explanation for the Variance Formula 203

        Example: Implementing the SIM 204

    Practitioners’ Form of the CAPM 220

        A Visualized Example 221

    Appendix: SIM, Constant Correlation, and the Efficient Frontier 227

    Constant Correlation Coefficient 238

Chapter 9. Multi-Index Models and Arbitrage Pricing Theory 241

    Introduction 241

    The APT Model 242

        Why is sum(xiei) = 0, i = [1, N] not a Binding Constraint? 245

    The Intuition Behind the APT 246

    Examples 249

    APT and CAPM 252

    WLG the APT Factors can be Assumed to be Orthogonal 254

    Appendix: Linear Programming and Arbitrage 257

        The Lagrangian and the APT main result 260

Index 263

Series : World Scientific Lecture Notes in Finance Book 5

ASIN : B08QG9NGVW

Publisher : World Scientific Publishing Company (November 24, 2020)

Language : English

Pages : 279

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