Every futures, options, and stock markets trader operates under a set of highly suspect rules and assumptions. Are you risking your career on yours? Exceptionally clear and easy to use, The Mathematics of Money Management substitutes precise mathematical modeling for the subjective decision-making processes many traders and serious investors depend on. Step-by-step, it unveils powerful strategies for creating and using key money management formulas--based on the rules of probability and modern portfolio theory--that maximizes the potential gains for the level of risk you are assuming. With them, you'll determine the payoffs and consequences of any potential trading decision and obtain the highest potential growth for your specified level of risk. You'll quickly decide: What markets to trade in and at what quantities When to add or subtract funds from an account How to reinvest trading profits for maximum yield The Mathematics of Money Management provides the missing element in modern portfolio theory that weds optimal f to the optimal portfolio.
Author(s): Ralph Vince
Edition: 1
Publisher: Wiley
Year: 1992
Language: English
Pages: 109
BookmarkTitle:......Page 3
SCOPE OF THIS BOOK......Page 5
WORST-CASE SCENARIOS AND STATEGY......Page 6
SYNTHETIC CONSTRUCTS IN THIS TEXT......Page 7
BookmarkTitle:......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
BookmarkTitle:......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
BookmarkTitle:......Page 73
DEFINITION OF THE PROBLEM......Page 74
SOLUTIONS OF LINEAR SYSTEMS USING ROW-EQUIVALENT MATRICES......Page 77
INTERPRETING THE RESULTS......Page 78
BookmarkTitle:......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
