{"product_id":"the-handbook-of-portfolio-mathematics-9780471757689","title":"The Handbook of Portfolio Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cb\u003e\u003ci\u003eThe Handbook of Portfolio Mathematics\u003c\/i\u003e\u003c\/b\u003e  \u003cp\u003eFor the serious investor, trader, or money manager, this book takes a rewarding look into modern portfolio theory. Vince introduces a leverage-space portfolio model, tweaks it for the drawdown probability, and delivers a superior model. He even provides equations to maximize returns for a chosen level of risk. So if you''re serious about making money in today''s markets, buy this book. Read it. Profit from it.\u003cbr\u003e Thomas N. Bulkowski, author, \u003ci\u003eEncyclopedia of Chart Patterns\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003eThis is an important book. Though traders routinely speak of their ''edge'' in the marketplace and ways of handling ''risk,'' few can define and measure these accurately. In this book, Ralph Vince takes readers step by step through an understanding of the mathematical foundations of trading, significantly extending his earlier work and breaking important new ground. His lucid writing style and liberal use of practical examples make this book must\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003ePreface xiii\u003c\/p\u003e \u003cp\u003eIntroduction xvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Theory 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 1 The Random Process and Gambling Theory 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIndependent versus Dependent Trials Processes 5\u003c\/p\u003e \u003cp\u003eMathematical Expectation 6\u003c\/p\u003e \u003cp\u003eExact Sequences, Possible Outcomes, and the Normal Distribution 8\u003c\/p\u003e \u003cp\u003ePossible Outcomes and Standard Deviations 11\u003c\/p\u003e \u003cp\u003eThe House Advantage 15\u003c\/p\u003e \u003cp\u003eMathematical Expectation Less than Zero Spells Disaster 18\u003c\/p\u003e \u003cp\u003eBaccarat 19\u003c\/p\u003e \u003cp\u003eNumbers 20\u003c\/p\u003e \u003cp\u003ePari-Mutuel Betting 21\u003c\/p\u003e \u003cp\u003eWinning and Losing Streaks in the Random Process 24\u003c\/p\u003e \u003cp\u003eDetermining Dependency 25\u003c\/p\u003e \u003cp\u003eThe Runs Test, Z Scores, and Confidence Limits 27\u003c\/p\u003e \u003cp\u003eThe Linear Correlation Coefficient 32\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 2 Probability Distributions 43\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe Basics of Probability Distributions 43\u003c\/p\u003e \u003cp\u003eDescriptive Measures of Distributions 45\u003c\/p\u003e \u003cp\u003eMoments of a Distribution 47\u003c\/p\u003e \u003cp\u003eThe Normal Distribution 52\u003c\/p\u003e \u003cp\u003eThe Central Limit Theorem 52\u003c\/p\u003e \u003cp\u003eWorking with the Normal Distribution 54\u003c\/p\u003e \u003cp\u003eNormal Probabilities 59\u003c\/p\u003e \u003cp\u003eFurther Derivatives of the Normal 65\u003c\/p\u003e \u003cp\u003eThe Lognormal Distribution 67\u003c\/p\u003e \u003cp\u003eThe Uniform Distribution 69\u003c\/p\u003e \u003cp\u003eThe Bernoulli Distribution 71\u003c\/p\u003e \u003cp\u003eThe Binomial Distribution 72\u003c\/p\u003e \u003cp\u003eThe Geometric Distribution 78\u003c\/p\u003e \u003cp\u003eThe Hypergeometric Distribution 80\u003c\/p\u003e \u003cp\u003eThe Poisson Distribution 81\u003c\/p\u003e \u003cp\u003eThe Exponential Distribution 85\u003c\/p\u003e \u003cp\u003eThe Chi-Square Distribution 87\u003c\/p\u003e \u003cp\u003eThe Chi-Square “Test” 88\u003c\/p\u003e \u003cp\u003eThe Student’s Distribution 92\u003c\/p\u003e \u003cp\u003eThe Multinomial Distribution 95\u003c\/p\u003e \u003cp\u003eThe Stable Paretian Distribution 96\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 3 Reinvestment of Returns and Geometric Growth Concepts 99\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eTo Reinvest Trading Profits or Not 99\u003c\/p\u003e \u003cp\u003eMeasuring a Good System for Reinvestment—The Geometric Mean 103\u003c\/p\u003e \u003cp\u003eEstimating the Geometric Mean 107\u003c\/p\u003e \u003cp\u003eHow Best to Reinvest 109\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 4 Optimal \u003ci\u003ef\u003c\/i\u003e 117\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eOptimal Fixed Fraction 117\u003c\/p\u003e \u003cp\u003eAsymmetrical Leverage 118\u003c\/p\u003e \u003cp\u003eKelly 120\u003c\/p\u003e \u003cp\u003eFinding the Optimal \u003ci\u003ef\u003c\/i\u003e by the Geometric Mean 122\u003c\/p\u003e \u003cp\u003eTo Summarize Thus Far 125\u003c\/p\u003e \u003cp\u003eHow to Figure the Geometric Mean Using Spreadsheet Logic 127\u003c\/p\u003e \u003cp\u003eGeometric Average Trade 127\u003c\/p\u003e \u003cp\u003eA Simpler Method for Finding the Optimal \u003ci\u003ef\u003c\/i\u003e 128\u003c\/p\u003e \u003cp\u003eThe Virtues of the Optimal \u003ci\u003ef\u003c\/i\u003e 130\u003c\/p\u003e \u003cp\u003eWhy You Must Know Your Optimal \u003ci\u003ef\u003c\/i\u003e 132\u003c\/p\u003e \u003cp\u003eDrawdown and Largest Loss with \u003ci\u003ef \u003c\/i\u003e141\u003c\/p\u003e \u003cp\u003eConsequences of Straying Too Far from the Optimal \u003ci\u003ef\u003c\/i\u003e 145\u003c\/p\u003e \u003cp\u003eEqualizing Optimal \u003ci\u003ef\u003c\/i\u003e 151\u003c\/p\u003e \u003cp\u003eFinding Optimal \u003ci\u003ef\u003c\/i\u003e via Parabolic Interpolation 157\u003c\/p\u003e \u003cp\u003eThe Next Step 161\u003c\/p\u003e \u003cp\u003eScenario Planning 162\u003c\/p\u003e \u003cp\u003eScenario Spectrums 173\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 5 Characteristics of Optimal \u003ci\u003ef\u003c\/i\u003e 175\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eOptimal \u003ci\u003ef\u003c\/i\u003e for Small Traders Just Starting Out 175\u003c\/p\u003e \u003cp\u003eThreshold to Geometric 177\u003c\/p\u003e \u003cp\u003eOne Combined Bankroll versus Separate Bankrolls 180\u003c\/p\u003e \u003cp\u003eTreat Each Play as If Infinitely Repeated 182\u003c\/p\u003e \u003cp\u003eEfficiency Loss in Simultaneous Wagering or Portfolio Trading 185\u003c\/p\u003e \u003cp\u003eTime Required to Reach a Specified Goal and the Trouble with Fractional \u003ci\u003ef\u003c\/i\u003e 188\u003c\/p\u003e \u003cp\u003eComparing Trading Systems 192\u003c\/p\u003e \u003cp\u003eToo Much Sensitivity to the Biggest Loss 193\u003c\/p\u003e \u003cp\u003eThe Arc Sine Laws and Random Walks 194\u003c\/p\u003e \u003cp\u003eTime Spent in a Drawdown 197\u003c\/p\u003e \u003cp\u003eThe Estimated Geometric Mean (or How the Dispersion of Outcomes Affects Geometric Growth) 198\u003c\/p\u003e \u003cp\u003eThe Fundamental Equation of Trading 202\u003c\/p\u003e \u003cp\u003eWhy Is \u003ci\u003ef \u003c\/i\u003eOptimal? 203\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 6 Laws of Growth, Utility, and Finite Streams 207\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eMaximizing Expected Average Compound Growth 209\u003c\/p\u003e \u003cp\u003eUtility Theory 217\u003c\/p\u003e \u003cp\u003eThe Expected Utility Theorem 218\u003c\/p\u003e \u003cp\u003eCharacteristics of Utility Preference Functions 218\u003c\/p\u003e \u003cp\u003eAlternate Arguments to Classical Utility Theory 221\u003c\/p\u003e \u003cp\u003eFinding Your Utility Preference Curve 222\u003c\/p\u003e \u003cp\u003eUtility and the New Framework 226\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 7 Classical Portfolio Construction 231\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eModern Portfolio Theory 231\u003c\/p\u003e \u003cp\u003eThe Markowitz Model 232\u003c\/p\u003e \u003cp\u003eDefinition of the Problem 235\u003c\/p\u003e \u003cp\u003eSolutions of Linear Systems Using Row-Equivalent Matrices 246\u003c\/p\u003e \u003cp\u003eInterpreting the Results 252\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 8 The Geometry of Mean Variance Portfolios 261\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe Capital Market Lines (CMLs) 261\u003c\/p\u003e \u003cp\u003eThe Geometric Efficient Frontier 266\u003c\/p\u003e \u003cp\u003eUnconstrained Portfolios 273\u003c\/p\u003e \u003cp\u003eHow Optimal \u003ci\u003ef\u003c\/i\u003e Fits In 277\u003c\/p\u003e \u003cp\u003eCompleting the Loop 281\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 9 The Leverage Space Model 287\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eWhy This New Framework Is Better 288\u003c\/p\u003e \u003cp\u003eMultiple Simultaneous Plays 299\u003c\/p\u003e \u003cp\u003eA Comparison to the Old Frameworks 302\u003c\/p\u003e \u003cp\u003eMathematical Optimization 303\u003c\/p\u003e \u003cp\u003eThe Objective Function 305\u003c\/p\u003e \u003cp\u003eMathematical Optimization versus Root Finding 312\u003c\/p\u003e \u003cp\u003eOptimization Techniques 313\u003c\/p\u003e \u003cp\u003eThe Genetic Algorithm 317\u003c\/p\u003e \u003cp\u003eImportant Notes 321\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 10 The Geometry of Leverage Space Portfolios 323\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eDilution 323\u003c\/p\u003e \u003cp\u003eReallocation 333\u003c\/p\u003e \u003cp\u003ePortfolio Insurance and Optimal \u003ci\u003ef\u003c\/i\u003e 335\u003c\/p\u003e \u003cp\u003eUpside Limit on Active Equity and the Margin Constraint 341\u003c\/p\u003e \u003cp\u003e\u003ci\u003ef\u003c\/i\u003e Shift and Constructing a Robust Portfolio 342\u003c\/p\u003e \u003cp\u003eTailoring a Trading Program through Reallocation 343\u003c\/p\u003e \u003cp\u003eGradient Trading and Continuous Dominance 345\u003c\/p\u003e \u003cp\u003eImportant Points to the Left of the Peak in the \u003ci\u003en\u003c\/i\u003e + 1 Dimensional Landscape 351\u003c\/p\u003e \u003cp\u003eDrawdown Management and the New Framework 359\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Practice 365\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 11 What the Professionals Have Done 367\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eCommonalities 368\u003c\/p\u003e \u003cp\u003eDifferences 368\u003c\/p\u003e \u003cp\u003eFurther Characteristics of Long-Term Trend Followers 369\u003c\/p\u003e \u003cp\u003e\u003cb\u003eChapter 12 The Leverage Space Portfolio Model in the Real World 377\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003ePostscript 415\u003c\/p\u003e \u003cp\u003eIndex 417\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402669924695,"sku":"9780471757689","price":51.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471757689.jpg?v=1730481178","url":"https:\/\/bookcurl.com\/products\/the-handbook-of-portfolio-mathematics-9780471757689","provider":"Book Curl","version":"1.0","type":"link"}