Finally, a book that presents modeling formulas to maximize returns and manage risk for serious traders using empirical, statistical techniques. Specific topics covered include the importance of understanding investing as a statistical process. From there traditional concepts of money management are explored and many myths debunked. Formulas are given for the probability that a stop loss or stop profit will be executed. The impact of stops on the average return, probability of success, variance, skew, and kurtosis are examined. The formulas for these mutations in investment outcome have never before appeared in print. In many cases, readers may be shocked at the implications of stop loss techniques. A comprehensive set of optimal investment size formulas are developed which include cases of a single investment at a time and multiple investments both with and without correlations between them.In addition, the book explains how to extend these formulas to both the case of standard distributions as well as empirical distributions. The goal of the optimal investment size formulas is to both maximize long term compounded return while reducing risk. Individual and professional money managers will also learn how to allocate portfolio assets to mathematically maximize their Sharpe ratio. The book also offers a unique new investment goal designed to maximize the compounded utility of wealth on a compounded basis.
Ch. 1 Modeling Market Microstructure - Randomness in Markets 1
Ch. 2 Distribution of Price Changes 13
Ch. 3 Investment Objectives 29
Ch. 4 Modeling Risk Management and Stop-loss Myths 51
Ch. 5 Maximal Compounded Return Model 67
Ch. 6 Utility Models - Preferences Toward Risk and Return 79
Ch. 7 Money Management Formulas Using the Joint Multiasset Distribution 93
Ch. 8 Proper Backtesting for Portfolio Models 101
Ch. 9 The Combined Optimal Portfolio Model 113
App. 1 Table of Values of the Normal Distribution
App. 2 Installing R
App. 3 Introduction to R
App. 4 R Language Definition
Index