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Ralph Vince - Portfolio Mathematics

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    • PART I Theory Introduction xvii

    • CHAPTER 1 The Random Process and Gambling Theory

    • Independent versus Dependent Trials Processes

    • Mathematical Expectation

      • Normal Distribution Exact Sequences, Possible Outcomes, and the



    • Possible Outcomes and Standard Deviations

    • The House Advantage

    • Mathematical Expectation Less than Zero Spells Disaster

    • Baccarat

    • Numbers

    • Pari-Mutuel Betting

    • Winning and Losing Streaks in the Random Process

    • Determining Dependency

    • The Runs Test, Z Scores, and Confidence Limits

    • The Linear Correlation Coefficient

    • CHAPTER 2 Probability Distributions

    • The Basics of Probability Distributions

    • Descriptive Measures of Distributions

    • Moments of a Distribution

    • The Normal Distribution



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    • The Central Limit Theorem viii THE HANDBOOK OF PORTFOLIO MATHEMATICS

    • Working with the Normal Distribution

    • Normal Probabilities

    • Further Derivatives of the Normal

    • The Lognormal Distribution

    • The Uniform Distribution

    • The Bernoulli Distribution

    • The Binomial Distribution

    • The Geometric Distribution

    • The Hypergeometric Distribution

    • The Poisson Distribution

    • The Exponential Distribution

    • The Chi-Square Distribution

    • The Chi-Square “Test”

    • The Student’s Distribution

    • The Multinomial Distribution

    • The Stable Paretian Distribution

      • Growth Concepts CHAPTER 3 Reinvestment of Returns and Geometric



    • To Reinvest Trading Profits or Not

      • Geometric Mean Measuring a Good System for Reinvestment—The



    • Estimating the Geometric Mean

    • How Best to Reinvest

    • CHAPTER 4 Optimalf

    • Optimal Fixed Fraction

    • Asymmetrical Leverage

    • Kelly

    • Finding the Optimalfby the Geometric Mean

    • To Summarize Thus Far

      • Spreadsheet Logic How to Figure the Geometric Mean Using



    • Geometric Average Trade



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    • A Simpler Method for Finding the Optimalf CONTENTS ix

    • The Virtues of the Optimalf

    • Why You Must Know Your Optimalf

    • Drawdown and Largest Loss withf

      • from the Optimalf Consequences of Straying Too Far



    • Equalizing Optimalf

    • Finding Optimalfvia Parabolic Interpolation

    • The Next Step

    • Scenario Planning

    • Scenario Spectrums

    • CHAPTER 5 Characteristics of Optimalf

    • Optimalffor Small Traders Just Starting Out

    • Threshold to Geometric

    • One Combined Bankroll versus Separate Bankrolls

    • Treat Each Play as If Infinitely Repeated

      • Portfolio Trading Efficiency Loss in Simultaneous Wagering or

      • Trouble with Fractionalf Time Required to Reach a Specified Goal and the



    • Comparing Trading Systems

    • Too Much Sensitivity to the Biggest Loss

    • The Arc Sine Laws and Random Walks

    • Time Spent in a Drawdown

      • of Outcomes Affects Geometric Growth) The Estimated Geometric Mean (or How the Dispersion



    • The Fundamental Equation of Trading

    • Why IsfOptimal?

      • Streams CHAPTER 6 Laws of Growth, Utility, and Finite



    • Maximizing Expected Average Compound Growth

    • Utility Theory

    • The Expected Utility Theorem

    • Characteristics of Utility Preference Functions



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    • Alternate Arguments to Classical Utility Theory x THE HANDBOOK OF PORTFOLIO MATHEMATICS

    • Finding Your Utility Preference Curve

    • Utility and the New Framework

    • CHAPTER 7 Classical Portfolio Construction

    • Modern Portfolio Theory

    • The Markowitz Model

    • Definition of the Problem

    • Solutions of Linear Systems Using Row-Equivalent Matrices

    • Interpreting the Results

    • CHAPTER 8 The Geometry of Mean Variance Portfolios

    • The Capital Market Lines (CMLs)

    • The Geometric Efficient Frontier

    • Unconstrained Portfolios

    • How OptimalfFits In

    • Completing the Loop

    • CHAPTER 9 The Leverage Space Model

    • Why This New Framework Is Better

    • Multiple Simultaneous Plays

    • A Comparison to the Old Frameworks

    • Mathematical Optimization

    • The Objective Function

    • Mathematical Optimization versus Root Finding

    • Optimization Techniques

    • The Genetic Algorithm

    • Important Notes

      • Space Portfolios CHAPTER 10 The Geometry of Leverage



    • Dilution

    • Reallocation

    • Portfolio Insurance and Optimalf

    • Upside Limit on Active Equity and the Margin Constraint



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    • fShift and Constructing a Robust Portfolio CONTENTS xi

    • Tailoring a Trading Program through Reallocation

    • Gradient Trading and Continuous Dominance

    • Important Points to the Left of the Peak in then+

      • Dimensional Landscape



    • Drawdown Management and the New Framework

    • PART II Practice

    • CHAPTER 11 What the Professionals Have Done

    • Commonalities

    • Differences

    • Further Characteristics of Long-Term Trend Followers

      • the Real World CHAPTER 12 The Leverage Space Portfolio Model in

      • Postscript

      • Index





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