The Mathematics of Money Management Risk Analysis Techniques for Traders,9780471547389

The Mathematics of Money Management Risk Analysis Techniques for Traders

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Edition: 1st
ISBN13: 9780471547389
ISBN10: 0471547387
Format: Hardcover
Pub. Date: 1992-08-04
Publisher(s): Wiley
List Price: $115.00

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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

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