Kelly Formula
What is the Kelly criterion (or formula)? It is a formula for calculating how much to bet. It assumes that your objective is long term capital growth (getting rich). The handicapper's choice of money management strategy is similar to the stock market choice between growth stocks and income stocks. Growth stocks tend to be more volatile, but in the long term return more profit. That is because the profits from growth stocks are reinvested rather than skimmed off. Every reinvestment is a calculated risk. Therefore, income stocks tend to fluctuate in value less, but also return less profit in the long term. Kelly betting is for growth. It reinvests profits, and thus puts them at risk. If your objective is to make small but consistent profits, it may be too aggressive a money management scheme.
The Kelly's formula is : Kelly % = W - (1-W)/R where:
Kelly % = percentage of capital to be put into a single trade.
W = Historical winning percentage of a trading system.
R = Historical Average Win/Loss ratio.
Kelly's seminal paper, A New Interpretation of Information Rate, 1956, examines ways to send data over telephone lines. One part of his work, The Kelly Formula, also applies to trading, to optimize bet size.
In reality, I think Kelly's formula is too risky for real money management. One reason is, your trading size will affect both market price and your own feelings. Another reason is, historical data may underestimate risk a lot as what happened in LTCM's blowup. The optimal trading size should be less than half of what Kelly's formula tells you and should be less than 30% of your portfolio for short term trading.
|
Kelly's formula
http://www.trader-soft.com/money-management/kelly.html
--------------------------------------------------------------------------------
This method defines the optimal percent of risk. Relatively to gambling and further, to stock trading was developed by professor Edward Thorpe. Kelly's method defines the percent of risk as Kelly% = %win – %loss / (Avg_profit / Avg_loss ) Let's look at how the Kelly Criterion might work. Suppose you have a system that has a winning percentage 60%. Your system also has average profits that are twice as large as the size of your average loss. Thus, %win = 60%, %loss = 40% and Avg_profit / Avg_loss = 2. Kelly % = 60 - 40/2 = 40% Thus, the percentage of equity bet that would provide a maximum rate of return is 40%. Number_of_shares = (Kelly% * Current_Capital / starting_risk_per_unity_of_assets)/Security_Price where starting risk = maximal loss at trade(in %). Example: Current Capital - 25000$ Security Price - 50$ Kelly - 0.20 (it's calculated on the basis of the historical data) Maximal Loss at trade - 25% (it's calculated on the basis of the historical data) In this case you can buy (0.2 * 25000/0.25)/50 = 20000/50 = 400 shares During his record-breaking trading Larry Williams used the Kelly's formula where the starting risk was defined by the size of the margin per futures fontract. Thorpe recommends using % of risk within 0.5 * Kelly <= % risk < Kelly bounds. |
