Mathematics of money management

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......Page 3 SCOPE OF THIS BOOK ......Page 5 WORST-CASE SCENARIOS AND STATEGY ......Page 6 SYNTHETIC CONSTRUCTS IN THIS TEXT ......Page 7 ......Page 8 BASIC CONCEPTS ......Page 9 THE RUNS TEST ......Page 10 SERIAL CORRELATION ......Page 11 COMMON DEPENDENCY ERRORS ......Page 12 MATHEMATICAL EXPECTATION ......Page 13 MEASURING A GOOD SYSTEM FOR REINVESTMENT THE GEOMETRIC MEAN ......Page 14 OPTIMAL FIXED FRACTIONAL TRADING ......Page 15 FINDING THE OPTIMAL F BY THE GEOMETRIC MEAN ......Page 16 GEOMETRIC AVERAGE TRADE ......Page 17 THE SEVERITY OF DRAWDOWN ......Page 18 THE MARKOVITZ MODEL ......Page 19 DAILY PROCEDURES FOR USING OPTIMAL PORTFOLIOS ......Page 21 ALLOCATIONS GREATER THAN 100% ......Page 22 HOW THE DISPERSION OF OUTCOMES AFFECTS GEOMETRIC GROWTH ......Page 23 THE FUNDAMENTAL EQUATION OF TRADING ......Page 24 THRESHOLD TO GEOMETRIC ......Page 26 ONE COMBINED BANKROLL VERSUS SEPARATE BANKROLLS ......Page 27 EFFICIENCY LOSS IN SIMULTANEOUS WAGERING OR PORTFOLIO TRADING ......Page 28 TIME REQUIRED TO REACH A SPECIFIED GOAL AND THE TROUBLE WITH FRACTIONAL F ......Page 29 TOO MUCH SENSIVITY TO THE BIGGEST LOSS ......Page 30 EQUALIZING OPTIMAL F ......Page 31 DOLLAR AVERAGING AND SHARE AVERAGING IDEAS ......Page 32 THE ARC SINE LAWS AND RANDOM WALKS ......Page 33 TIME SPENT IN A DRAWDOWN ......Page 34 DESCRIPTIVE MEASURES OF DISTRIBUTIONS ......Page 35 MOMENTS OF A DISTRIBUTION ......Page 36 THE NORMAL DISTRIBUTION ......Page 37 WORKING WITH THE NORMAL DISTRIBUTION ......Page 38 NORMAL PROBABILITIES ......Page 39 THE LOGNORMAL DISTRIBUTION ......Page 41 THE PARAMETRIC OPTIMAL F ......Page 42 THE DISTRIBUTION OF TRADE P&L'S ......Page 43 FINDING OPTIMAL F ON THE NORMAL DISTRIBUTION ......Page 44 THE MECHANICS OF THE PROCEDURE ......Page 45 THE KOLMOGOROV-SMIRNOV (K-S) TEST ......Page 49 CREATING OUR OWN CHARACTERISTIC DISTRIBUTION FUNCTION ......Page 50 FITTING THE PARAMETERS OF THE DISTRIBUTION ......Page 52 USING THE PARAMETERS TO FIND OPTIMAL F ......Page 54 EQUALIZING F ......Page 56 SCENARIO PLANNING ......Page 57 WHICH IS THE BEST OPTIMAL F? ......Page 60 ......Page 61 ESTIMATING VOLATILITY ......Page 62 OPTION PRICING MODELS ......Page 63 A EUROPEAN OPTIONS PRICING MODEL FOR ALL DISTRIBUTIONS ......Page 66 THE SINGLE LONG OPTION AND OPTIMAL F ......Page 67 THE SINGLE SHORT OPTION ......Page 70 MULTIPLE SIMULTANEOUS POSITIONS WITH A CAUSAL RELATIONSHIP ......Page 71 ......Page 73 DEFINITION OF THE PROBLEM ......Page 74 SOLUTIONS OF LINEAR SYSTEMS USING ROW-EQUIVALENT MATRICES ......Page 77 INTERPRETING THE RESULTS ......Page 78 ......Page 80 THE CAPITAL MARKET LINES (CMLS) ......Page 81 THE GEOMETRIC EFFICIENT FRONTIER ......Page 82 UNCONSTRAINED PORTFOLIOS ......Page 84 HOW OPTIMAL F FITS WITH OPTIMAL PORTFOLIOS ......Page 85 COMPLETING THE LOOP ......Page 86 ASSET ALLOCATION ......Page 89 REALLOCATION: FOUR METHODS ......Page 91 PORTFOLIO INSURANCE – THE FOURTH REALLOCATION TECHNIQUE ......Page 93 THE MARGIN CONSTRAINT ......Page 96 TO SUMMARIZE ......Page 97 A CLOSING COMMENT ......Page 98 APPENDIX A - The Chi-Square Test ......Page 100 THE BERNOULI DISTRIBUTION ......Page 101 THE BINOMIAL DISTRIBUTION ......Page 102 THE GEOMETRIC DISTRIBUTION ......Page 103 THE POISSON DISTRIBUTION ......Page 104 THE CHI-SQUARE DISTRIBUTION ......Page 105 THE STUDENT'S DISTRIBUTION ......Page 106 THE STABLE PARETIAN DISTRIBUTION ......Page 107 APPENDIX C - Further on Dependency: The Turning Points and Phase Length Tests ......Page 109