ANALYTICAL TOOLBOX: The Kelly Bet Fraction
August 10, 2006
The Kelly Bet Fraction is a value used to identify trade sizes for aggressive trading styles and was developed by John Kelly, a former Bell Laboratories physicist and computer scientist, for The Bell Systems Technical Journal (J.L. Kelly, Jr. “A New Interpretation of Information Rate”, 1956). Kelly used portions of Claude Shannon’s (another Bell Lab employee) information theory to identify a means to maximize returns. Initial widespread application of the theory was for sizing gambling bets using expected gains and game odds. Check out home.williampoundstone.net/Kelly.htm for some interesting biographical notes about John Kelly.
The reason why systems using the Kelly Bet Fraction are considered aggressive is because it uses relatively high trade level percentages in an attempt to maximize the bankroll (or account) size as quickly as possible. It absolutely relies on accurate outcome probabilities for any given wager (trade). As a result, if the profitability probability is estimated too high, the system will lose money over time.
Optionetics Platinum
The Optionetics Platinum website includes a variety of tools to find trades given an underlying symbol or stock list, bias for the security, volatility environment and sort criteria. Given the user inputs, Platinum will provide a list of trades that fit the trader’s outlook provided. The resulting list provides an initial view of option data that include cost and time to expiration, along with Max Risk, Probability of Profits, Trade Odds and the Kelly Bet Fraction. A variety of other position calculations are available including greeks, volatility and breakeven data.
Using detail from the Platinum web site, the formula to obtain the Kelly Bet Fraction [KBF] is as follows:
KBF = | 100 * | {[Probability of Profit * (Odds + 1) – 1] | / | Odds ]} |
The Odds are calculated by: “… dividing the predicted average profits by the predicted average losses.” These values are determined by projecting the stock price randomly into the future using the SV (statistical volatility). Average profits are obtained when the future stock price lands in the option trade''s profit regions and average losses are obtained when the future stock price lands in the option trade''s loss regions are computed also.
The Probability of Profit is: “the probability that the predicted stock price falls within the option trade''s profit regions. The predicted stock price distribution is computed by projecting the stock price randomly into the future using the SV.”
Statistical volatility [SV] plays a key role when determining both variables in the equation: probability of profit and odds. It’s important to refer to the specific definition of SV used by the system, which is the following: “The amount the stock has fluctuated over a given time period in the past and expressed as a percent change in price over one year.” Although the number of projections were not mentioned, it is very reasonable to assume there are a statistically significant number of iterations to obtain reliable distributions and present a statistically based result.
A sudden drop in SV levels could lead to more aggressive KBF calculations while a recent rise may make the calculations slightly more conservative. However, the impact of this “sudden” change is SV is dampened in the odds calculation since both profits and losses are projected. Recall that inaccurately high KBF calculations result in a system losing value, not gaining value, over time.
Rather than using the raw number provided in KBF, the glossary suggests using the value as a trade ranker—the higher the calculated percentage “bet” obtained the higher rank the trade receives. You’ll find that the KBF value is zero for a variety of trade searches. Trade Adjuster and Strategy Maker are two tools within Platinum that may generate KBF ranked trades.
If you are more interested in a pure use of KBF, you must research the tool beyond a ranker application by learning the math behind the system. To get started, the Platinum glossary points to the following thread on KBF: www.jimgeary.com/poker/letters/KELLY.HTM. Some variations of bet sizing include reducing the KBF value by a specific factor and/or using the values for simultaneous non-correlated trades. You must thoroughly understand the basis of any trade approach prior to using it and can always benefit by backtesting and paper trading new strategies.
Risk Management
As always, risk management is the most important part of your trading plan. Identifying reasonably sized trades and maximum risk allows the new trader to gain the experience needed to remain in the markets. This approach to risk management saves the intermediate trader from become too self-assured and sustaining large losses. The experienced trader recognizes it is as simple habit.
To see the other articles by this author, please click here.
Clare White, CMT
Contributing Writer and Options Strategist
Optionetics.com ~ Your Options Education Site
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