Internet And Money

Money Management
Martin Sewell
Department of Computer Science
University College London
May 2007, updated July 2008

1 Introduction
For a speculative investor, there are two aspects to optimizing a trading strategy.
The first and most important goal of a trader is to achieve a positive expected
risk-adjusted return. Once this has been achieved, the trader needs to know
what percentage of his capital to risk on each trade. The underlying principals
of money management apply to both gambling and trading, and were originally
developed for the former.
2 History of Money Management
• In a paper on the measurement of risk that launched ‘expected utility
theory’, Bernoulli (1738) proposed that people have a logarithmic utility
function. He noted that, as a consequence of this, when profits are
reinvested, in order to measure the value of risky propositions one should
calculate the geometric mean. The paper was later translated into English
(Bernoulli 1954).
• In an article on ‘Speculation and the carryover’ that focuses on cotton
trading, Williams (1936) states that a speculator should bet on a representative
future price, and points out that if his profits and losses are
reinvested the method of calculating such a price is to choose the geometric
mean of all the possible prices.
• In 1944 the mathematician John von Neumann and economist Oskar Morgenstern
wrote Theory of Games and Economic Behavior (von Neumann
and Morgenstern 1944). Now a classic book, this is the work upon which
modern-day game theory is based.
• In 1948 Claud Shannon published an article entitled ‘A mathematical theory
of communication’ in two parts (Shannon 1948). The paper established
the discipline of information theory and became a classic. In short, he developed
the concepts of information entropy and redundancy. Shannon