The Mathematics Of Money Managment

The Mathematics Of Money Managment

Автор(ы): Vince Ralph

06.10.2007
Год изд.: 1992
Описание: «The favorable reception of Portfolio Management Formulas exceeded even the greatest expectation I ever had for the book. I had written it to promote the concept of optimal f and begin to immerse readers in portfolio theory and its missing relationship with optimal f. Besides finding friends out there, Portfolio Management Formulas was surprisingly met by quite an appetite for the math concerning money management. Hence this book. I am indebted to Karl Weber, Wendy Grau, and others at John Wiley & Sons who allowed me the necessary latitude this book required. There are many others with whom I have corresponded in one sort or another, or who in one way or another have contributed to, helped me with, or influenced the material in this book. Among them are Florence Bobeck, Hugo Rourdssa, Joe Bristor, Simon Davis, Richard Firestone, Fred Gehm (whom I had the good fortune of working with for awhile), Monique Mason, Gordon Nichols, and Mike Pascaul. I also wish to thank Fran Bartlett of G & H Soho, whose masterful work has once again transformed my little mountain of chaos, my little truckload of kindling, into the finished product that you now hold in your hands. This list is nowhere near complete as there are many others who, to varying degrees, influenced this book in one form or another. This book has left me utterly drained, and I intend it to be my last. Considering this, I’d like to dedicate it to the three people who have influenced me the most. To Rejeanne, my mother, for teaching me to appreciate a vivid imagination; to Larry, my father, for showing me at an early age how to squeeze numbers to make them jump; to Arlene, my wife, partner, and best friend. This book is for all three of you. Your influences resonate throughout it.»
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Introduction [5]
Scope of this book [5]
Some prevalent misconceptions [6]
Worst-case scenarios and stategy [6]
Mathematics notation [7]
Synthetic constructs in this text [7]
Optimal trading quantities and optimal f [8]
Chapter 1. The Empirical Techniques [9]
Deciding on quantity [9]
Basic concepts [9]
The runs test [10]
Serial correlation [11]
Common dependency errors [12]
Mathematical Expectation [13]
To reinvest trading profits or not [14]
Measuring a good system for reinvestment the Geometric Mean [14]
How best to reinvest [15]
Optimal fixed fractional trading [15]
Kelly formulas [16]
Finding the optimal f by the Geometric Mean [16]
To summarize thus far [17]
Geometric Average Trade [17]
Why you must know your optimal f [18]
The severity of drawdown [18]
Modern portfolio theory [19]
The Markovitz model [19]
The Geometric Mean portfolio strategy [21]
Daily procedures for using optimal portfolios [21]
Allocations greater than 100% [22]
How the dispersion of outcomes affects geometric growth [23]
The Fundamental Equation of trading [24]
Chapter 2. Characteristics of Fixed Fractional Trading and Salutary Techniques [26]
Optimal f for small traders just starting out [26]
Threshold to geometric [26]
One combined bankroll versus separate bankrolls [27]
Threat each play as if infinitely repeated [28]
Efficiency loss in simultaneous wagering or portfolio trading [28]
Time required to reach a specified goal and the trouble with fractional f [29]
Comparing trading systems [30]
Too much sensivity to the biggest loss [30]
Equalizing optimal f [31]
Dollar averaging and share averaging ideas [32]
The Arc Sine Laws and random walks [33]
Time spent in a drawdown [34]
Chapter 3. Parametric Optimal f on the Normal Distribution [35]
The basics of probability distributions [35]
Descriptive measures of distributions [35]
Moments of a distribution [36]
The Normal Distribution [37]
The Central Limit Theorem [38]
Working with the Normal Distribution [38]
Normal Probabilities [39]
Further Derivatives of the Normal [41]
The Lognormal Distribution [41]
The parametric optimal f [42]
The distribution of trade P&L’s [43]
Finding optimal f on the Normal Distribution [44]
The mechanics of the procedure [45]
Chapter 4. Parametric Techniques on Other Distributions [49]
The Kolmogorov-Smirnov (K-S) Test [49]
Creating our own Characteristic Distribution Function [50]
Fitting the Parameters of the distribution [52]
Using the Parameters to find optimal f [54]
Performing «What Ifs» [56]
Equalizing f [56]
Optimal f on other distributions and fitted curves [57]
Scenario planning [57]
Optimal f on binned data [60]
Which is the best optimal f? [60]
Chapter 5. Introduction to Multiple Simultaneous Positions under the Parametric Approach [62]
Estimating Volatility [62]
Ruin, Risk and Reality [63]
Option pricing models [63]
A European options pricing model for all distributions [66]
The single long option and optimal f [67]
The single short option [70]
The single position in The Underlying Instrument [71]
Multiple simultaneous positions with a causal relationship [71]
Multiple simultaneous positions with a random relationship [73]
Chapter 6. Correlative Relationships and the Derivation of the Efficient Frontier [74]
Definition of The Problem [74]
Solutions of Linear Systems using Row-Equivalent Matrices [77]
Interpreting The Results [78]
Chapter 7. The Geometry of Portfolios [81]
The Capital Market Lines (CMLs) [81]
The Geometric Efficient Frontier [82]
Unconstrained portfolios [84]
How optimal f fits with optimal portfolios [85]
Threshold to The Geometric for Portfolios [86]
Completing The Loop [86]
Chapter 8. Risk Management [89]
Asset Allocation [89]
Reallocation: Four Methods [91]
Why reallocate? [93]
Portfolio Insurance – The Fourth Reallocation Technique [93]
The Margin Constraint [96]
Rotating Markets [97]
To summarize [97]
Application to Stock Trading [98]
A Closing Comment [98]
APPENDIX A. The Chi-Square Test [100]
APPENDIX B. Other Common Distributions [101]
The Uniform Distribution [101]
The Bernouli Distribution [101]
The Binomial Distribution [102]
The Geometric Distribution [103]
The Hypergeometric Distribution [104]
The Poisson Distribution [104]
The Exponential Distribution [105]
The Chi-Square Distribution [105]
The Student’s Distribution [106]
The Multinomial Distribution [107]
The stable Paretian Distribution [107]
APPENDIX C. Further on Dependency: The Turning Points and Phase Length Tests [109]

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