What is Kelly Fraction
What is Kelly Fraction? Explain.
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The Kelly criterion is to bet a specific fraction of your wealth in order to maximize your expected growth of wealth. We utilize φ to denote the random variable taking value 1 along with probability p and −1 along with probability 1 − p and f to signify the fraction of our wealth which we bet. The growth of wealth after every toss of the coin is then the random amount ln(1 + fφ).Therefore expected growth rate is p ln(1 + f ) + (1 − p ) ln(1 − f ).That function is plotted in figure for p = 0.55.
Figure: Expected return versus betting fraction.
This expected growth rate is maximized through the choicef = 2p − 1.It is the Kelly fraction.
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