《资金管理数学mathematicsofmoneymanagementvinceralph》由会员分享，可在线阅读，更多相关《资金管理数学mathematicsofmoneymanagementvinceralph（753页珍藏版）》请在金锄头文库上搜索。
1、THE MATHEMATICS OF MONEY MANAGEMENT: RISK ANALYSIS TECHNIQUES FOR TRADERS by Ralph Vince - 2 - Published by John Wiley 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 i
2、nfluences resonate throughout it. Chagrin Falls, OhioR. V. March 1992 - 5 - Index Introduction5 Scope of this book5 Some prevalent misconceptions6 Worst-case scenarios and stategy 6 Mathematics notation.7 Synthetic constructs in this text7 Optimal trading quantities and optimal f8 Chapter 1-The Empi
3、rical Techniques9 Deciding on quantity9 Basic concepts9 The runs test.10 Serial correlation11 Common dependency errors.12 Mathematical Expectation13 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 t
4、rading15 Kelly formulas16 Finding the optimal f by the Geometric Mean 16 - 6 - To summarize thus far17 Geometric Average Trade17 Why you must know your optimal f18 The severity of drawdown18 Modern portfolio theory.19 The Markovitz model.19 The Geometric Mean portfolio strategy21 Daily procedures fo
5、r using optimal portfolios21 Allocations greater than 100%22 How the dispersion of outcomes affects geometric growth23 The Fundamental Equation of trading 24 Chapter 2 - Characteristics of Fixed Fractional Trading and Salutary Techniques.26 Optimal f for small traders just starting out26 Threshold t
6、o geometric.26 One combined bankroll versus separate bankrolls27 Threat each play as if infinitely repeated28 Efficiency loss in simultaneous wagering or portfolio trading 28 Time required to reach a specified goal and the trouble with fractional f29 Comparing trading systems30 - 7 - Too much sensiv
7、ity to the biggest loss30 Equalizing optimal f.31 Dollar averaging and share averaging ideas32 The Arc Sine Laws and random walks33 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 distributi
8、ons 35 Moments of a distribution36 The Normal Distribution37 The Central Limit Theorem38 Working with the Normal Distribution38 Normal Probabilities 39 Further Derivatives of the Normal41 The Lognormal Distribution.41 The parametric optimal f42 The distribution of trade P the other defines 1 unit as
9、 100 shares and can trade the fractional unit. Suppose the optimal quantity to trade in today for the first trader is to trade 61 units (i.e., 61 shares) and for the second trader for the same day it is to trade 0.61 units (again 61 shares). - 32 - I have been told by others that, in order to be a b
10、etter teacher, I must bring the material to a level which the reader can understand. Often these other peoples suggestions have to do with creating analogies between the concept I am trying to convey and something they already are familiar with. Therefore, for the sake of instruction you will find n
11、umerous analogies in this text. But I abhor analogies. Whereas analogies may be an effective tool for instruction as well as arguments, I dont like them because they take something foreign to people and (often quite deceptively) force fit it to a template of logic of something people already know is
12、 true. Here is an example: The square root of 6 is 3 because the square root of 4 is 2 and 2+2 = 4. Therefore, since 3+3 = 6, then the square root of 6 must be 3. Analogies explain, but they do not solve. Rather, an analogy makes the a priori assumption that something is true, and this “explanation“
13、 then masquerades as the proof. You have my apologies in advance for the use of the analogies in this text. I have opted for them only for the purpose of instruction. OPTIMAL TRADING QUANTITIES AND OPTIMAL F Modern portfolio theory, perhaps the pinnacle of money management concepts from the stock tr
14、ading arena, has not been - 33 - embraced by the rest of the trading world. Futures traders, whose technical trading ideas are usually adopted by their stock trading cousins, have been reluctant to accept ideas from the stock trading world. As a consequence, modern portfolio theory has never really
15、been embraced by futures traders. Whereas modern portfolio theory will determine optimal weightings of the components within a portfolio (so as to give the least variance to a prespecified return or vice versa), it does not address the notion of optimal quantities. That is, for a given market system
16、, there is an optimal amount to trade in for a given level of account equity so as to maximize geometric growth. This we will refer to as the optimal f. This book proposes that modern portfolio theory can and should be used by traders in any markets, not just the stock markets. However, we must marry modern portfolio theory (which gives us optimal weights) with the notion of optimal quantity (optimal f) to arrive at a truly optimal portfolio. It is this truly optimal portfolio that can and sho
