The Handbook of Portfolio Mathematics


  • Pages: 442
  • Format: PDF
  • Published Date: 2007


The Handbook of Portfolio Mathematics: Formulas for Optimal Allocation & Leverage 

In The Handbook of Portfolio Mathematics, Ralph Vince takes readers step by step through an understanding of the mathematical foundations of trading, significantly extending his earlier work and breaking important new ground. His lucid writing style and liberal use of practical examples make this book must reading.

Author’s Introduction:

This is a book in two distinct parts. Originally, my task was to distill the previous three books on this subject into one book. In effect, Part I comprises that text. It’s been reorganized, rehashed, and reworked to resemble the original texts while creating a contiguous path of reasoning, which takes us from the basic gambling theory and statistics, through the introduction of the Kelly criterion, optimal f , and finally onto the Leverage Space Portfolio Model for multiple-simultaneous positions.

The Leverage Space Portfolio Model addresses allocations and leverage. Often these are two distinct facets, but herein they refer to the same thing. Allocation is the relative leverage between multiple portfolio components. Thus, when we speak of leverage, we are also speaking of allocation, and vice versa.

Likewise, money management and portfolio construction, as practiced, don’t necessarily refer to the same exercise, yet in this text, they do. Collectively, whatever the endeavor of risk, be it a bond portfolio, a commodities fund, or a team of blackjack players invading a casino, the collective exercise will be herein referred to as allocation.

I have tried to keep the geometric perspective on these concepts, and keep those notions about them intact. The first section is necessarily heavy on math. The first section is purely conceptual. It is about allocation and leverage to maximize returns without respect to anything else.


  • The Random Process and Gambling Theory
  • Probability Distributions
  • Reinvestment of Returns and Geometric Growth Concepts
  • Optimal f
  • Characteristics of Optimal f
  • Laws of Growth, Utility, and Finite Streams
  • Classical Portfolio Construction
  • The Geometry of Mean Variance Portfolios
  • The Leverage Space Model
  • The Geometry of Leverage Space Portfolios
  • What the Professionals Have Done
  • The Leverage Space Portfolio Model in the Real World