The Mathematics of Money Management Risk Analysis Techniques for Traders

by Vince, Ralph

• ISBN13: 9780471547389
• ISBN10: 0471547387
• Edition: 1st
• Format: Hardcover
• Copyright: 1992-08-04
• Publisher: Wiley

Summary

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 Biography

About the author RALPH VINCE is a computer trading systems consultant who develops computerized futures, options, and stock markets trading strategies for traders, advisors, and software vendors. He is the author of the widely hailed Portfolio Management Formulas: Mathematical Trading Methods for the Futures, Options, and Stock Markets (Wiley).

Table of Contents

Preface	v
Introduction	xi
Scope of This Book	xi
Some Prevalent Misconceptions	xv
Worst-Case Scenarios and Strategy	xvi
Mathematics Notation	xviii
Synthetic Constructs in This Text	xviii
Optimal Trading Quantities and Optimal f	xxi
The Empirical Techniques	1	(62)
Deciding on Quantity	1	(3)
Basic Concepts	4	(1)
The Runs Test	5	(4)
Serial Correlation	9	(5)
Common Dependency Errors	14	(2)
Mathematical Expectation	16	(4)
To Reinvest Trading Profits or Not	20	(1)
Measuring a Good System for Reinvestment: The Geometric Mean	21	(4)
How Best to Reinvest	25	(1)
Optimal Fixed Fractional Trading	26	(1)
Kelly Formulas	27	(3)
Finding the Optimal f by the Geometric Mean	30	(2)
To Summarize Thus Far	32	(2)
Geometric Average Trade	34	(1)
Why You Must Know Your Optimal f	35	(3)
The Severity of Drawdown	38	(1)
Modern Portfolio Theory	39	(1)
The Markowitz Model	40	(5)
The Geometric Mean Portfolio Strategy	45	(1)
Daily Procedures for Using Optimal Portfolios	46	(3)
Allocations Greater Than 100%	49	(4)
How the Dispersion of Outcomes Affects Geometric Growth	53	(5)
The Fundamental Equation of Trading	58	(5)
Characteristics of Fixed Fractional Trading and Salutary Techniques	63	(35)
Optimal f for Small Traders Just Starting Out	63	(2)
Threshold to Geometric	65	(3)
One Combined Bankroll versus Separate Bankrolls	68	(3)
Treat Each Play As If Infinitely Repeated	71	(2)
Efficiency Loss in Simultaneous Wagering or Portfolio Trading	73	(3)
Time Required to Reach a Specified Goal and the Trouble with Fractional f	76	(4)
Comparing Trading Systems	80	(2)
Too Much Sensitivity to the Biggest Loss	82	(1)
Equalizing Optimal f	83	(6)
Dollar Averaging and Share Averaging Ideas	89	(3)
The Arc Sine Laws and Random Walks	92	(3)
Time Spent in a Drawdown	95	(3)
Parametric Optimal f on the Normal Distribution	98	(51)
The Basics of Probability Distributions	98	(2)
Descriptive Measures of Distributions	100	(3)
Moments of a Distribution	103	(5)
The Normal Distribution	108	(1)
The Central Limit Theorem	109	(2)
Working with the Normal Distribution	111	(4)
Normal Probabilities	115	(9)
The Lognormal Distribution	124	(1)
The Parametric Optimal f	125	(7)
Finding the Optimal f on the Normal Distribution	132	(17)
Parametric Techniques on Other Distributions	149	(44)
The Kolmogorov--Smirnov (K-S) Test	149	(4)
Creating Our Own Characteristic Distribution Function	153	(7)
Fitting the Parameters of the Distribution	160	(8)
Using the Parameters to Find the Optimal f	168	(7)
Performing ``What Ifs''	175	(1)
Equalizing f	176	(1)
Optimal f on Other Distributions and Fitted Curves	177	(1)
Scenario Planning	178	(12)
Optimal f on Binned Data	190	(2)
Which is the Best Optimal f?	192	(1)
Introduction to Multiple Simultaneous Positions under the Parametric Approach	193	(44)
Estimating Volatility	194	(3)
Ruin, Risk, and Reality	197	(2)
Option Pricing Models	199	(9)
A European Options Pricing Model for All Distributions	208	(5)
The Single Long Option and Optimal f	213	(11)
The Single Short Option	224	(1)
The Single Position in the Underlying Instrument	225	(3)
Multiple Simultaneous Positions with a Causal Relationship	228	(5)
Multiple Simultaneous Positions with a Random Relationship	233	(4)
Correlative Relationships and the Derivation of the Efficient Frontier	237	(29)
Definition of the Problem	238	(12)
Solutions of Linear Systems Using Row-Equivalent Matrices	250	(8)
Interpreting the Results	258	(8)
The Geometry of Portfolios	266	(28)
The Capital Market Lines (CMLs)	266	(5)
The Geometric Efficient Frontier	271	(7)
Unconstrained Portfolios	278	(5)
How Optimal f Fits with Optimal Portfolios	283	(4)
Threshold to the Geometric for Portfolios	287	(1)
Completing the Loop	287	(7)
Risk Management	294	(75)
Asset Allocation	294	(8)
Reallocation: Four Methods	302	(9)
Why Reallocate?	311	(1)
Portfolio Insurance--The Fourth Reallocation Technique	312	(8)
The Margin Constraint	320	(4)
Rotating Markets	324	(2)
To Summarize	326	(1)
Application to Stock Trading	327	(1)
A Closing Comment	328	(3)
Appendixes
A The Chi-Square Test	331	(5)
B Other Common Distributions	336	(28)
The Uniform Distribution	337	(2)
The Bernoulli Distribution	339	(2)
The Binomial Distribution	341	(4)
The Geometric Distribution	345	(2)
The Hypergeometric Distribution	347	(1)
The Poisson Distribution	348	(4)
The Exponential Distribution	352	(2)
The Chi-Square Distribution	354	(2)
The Student's Distribution	356	(2)
The Multinomial Distribution	358	(1)
The Stable Paretian Distribution	359	(5)
C Further on Dependency: The Turning Points and Phase Length Tests	364	(5)
Bibliography and Suggested Reading	369	(4)
Index	373