|
If we assume that the outcome of each month's result is independent of the previous day's result (which is to a very large extent true), i.e. that the random numbers are not correlated then the expected value of the above growth rate will be (ignoring the constant term in the above formula):
If we expand the argument of the above expected value in Taylor series around the mean and the standard deviation and then take the first mathematical derivative of that expression and equate it to zero (a condition for maxima) you will get the value of the fraction that you should invest in the stock in each month. In our example with a mean of 0.2% and volatility of 7% we will get the value for that fraction equal to 0.408. Therefore, you need to bet an amount equal to 0.40 of your holdings every month, i.e., starting with $100,000, you will invest roughly $40,800 in the first month, $16,600 in the second month and so on.
The most important constraint on the above framework is that the mean of the outcomes should be really small and the volatility should be high. If that is not true then the mathematical formulation will break down. Secondly, and equally importantly, in the stock market no trader or fund manager will bet (invest) a constant fraction of his holding every period regardless of the movement of the market. In fact, this dynamic nature of adjustment would render the whole exercise quite futile as in that event, when the quantity q is dynamically adjusted according to market's movement one cannot apply the above.
Still, Kelly criterion is can give an important insight into portfolio trading and asset allocation problem and can expanded greatly from the above simplistic model.
Disclaimer
"Risk Latte uses proprietary and non-proprietary mathematical and empirical models to measure the volatility and estimate the direction of the market. There is no guarantee of any particular outcome happening and readers must exercise caution while interpreting the conclusions of this article. Risk Latte Company is not a registered stock broker or an SFC registered entity and readers must take advise from their financial advisors, stock brokers, research analysts and bankers while making any buying or selling decisions. Risk Latte Company is not in the business of making stock or asset forecasts whether explicitly or implicitly and shall not be responsible for and/or liable for any losses arising out of any trading decisions based on the above article."
  
Any comments and queries can be sent through our web-based form. |
a d v e r t i s e m e n t
