Friday, December 18, 2009

part -2

asserted that binary digits could be transmitted over a noisy channel with
an arbitrary small probability of error if the binary digits were suitably
encoded.
• In 1956 a scientist working for Bell Labs, John Larry Kelly, Jr., brought
together game theory and information theory when he published ‘A new
interpretation of information rate’1 (Kelly 1956). He showed that in order
to achieve maximum growth of wealth, at every bet a gambler should
maximize the expected value of the logarithm of his capital, because it is
the logarithm which is additive in repeated bets and to which the law of
large numbers applies. The assumptions are that the gambler’s capital
is infinitely divisible and all profits are reinvested. Money management
systems which maximize the expected value of the capital are said to
employ the Kelly criterion.
• Bellman and Kalaba (1957) considered the role of dynamic programming
in statistical communication theory and generalized and extended (Kelly
1956)’s results.
• The first to introduce the Kelly criterion in an economic context, Latan´e
(1959) showed that investors should maximize the geometric mean of their
portfolios.
• Breiman (1961) proved that using the Kelly criterion is asymptotically
optimal under two criteria: (1) minimal expected time to achieve a fixed
level of resources and (2) maximal rate of increase of wealth. It is only in
continuous time that the results are exact.
• In 1962, Edward O. Thorp, an American maths professor, author and
blackjack player wrote Beat the Dealer (Thorp 1962), which became a
classic and was the first book to prove mathematically that blackjack
could be beaten by card counting.
• Thorp and Walden (1966) developed a winning strategy for a side bet in
Nevada Baccarat and used the Kelly criterion to determine bet sizes.
• Thorp (1969) concluded that the Kelly criterion should replace theMarkowitz
criterion (Markowitz 1959) as the guide to portfolio selection.
• Hakansson (1970) consider the optimal investment and consumption strategies
under risk for a class of utility functions and also give the necessary
and sufficient conditions for long-run capital growth.
• Radner (1971) was the first to employ a balanced investment strategy in
the context of stochastic generalizations of the von Neumann model of
economic growth.
1The original title was ‘Information theory and gambling’, but Kelly changed it to appease
his employer.

Money Management

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

Budget Guidelines

Housing – Spend no more than 35% of net income on housing. Depending on whether you rent or own, that
can include: mortgage/rent, utilities, insurance, taxes, and home maintenance.
Savings – Save at least 10% of income throughout your working
life. Make sure you have 3–6 months income in an emergency fund
before you start saving for other goals.
Transportation – Spend no more than 15% of net income on
transportation. That includes: car payment, auto insurance, tag or license,
maintenance, gasoline, and parking.
Debt – Spend no more than 15% of net income on all other consumer
debt: student loans, retail installment contracts, credit cards, personal
loans, tax debts, and medical debts.
Other – Spend no more than 25% of net income on all other expenses:
food, clothing, entertainment, childcare, medical expenses, tithing/charity,
and vacations.

If you don’t know where your money is going, it’s time to start tracking your spending. Different methods of
tracking work for different people—some like to save receipts while others prefer to jot down all purchases
in a small notebook they carry with them. Remember, tracking is only effective if you count every expense,
including the morning newspaper and the 75 cents you put in the office vending machine. Use the sheets on
the next two pages to record weekly and monthly spending totals. (We suggest you make copies of the charts
so that you can track for longer than one week.)

The Money Management Planner is a guide to help you take control of your finances. It will help you determine your net worth, set goals, monitor
your cash flow and track expenses. A sound spending and savings plan is the foundation for
your long-term financial success.
Examine your past finances to create a plan for all future spending and savings. In other words, a review of your expenses and spending habits will enable you to design a realistic monthly budget.
Be prepared to make some changes, though, if those habits have kept you from achieving your
financial goals.
If your expenses exceed your income, call BALANCE to schedule a money management session.
One of our professional counselors can help you design a realistic spending and savings plan that will help you get back on track and achieve your financial goals.

;;