Risk & Portfolio

Even-money bets you win 55% of the time: Kelly says bet 10%. Expected log growth per bet is 0.00501 at full Kelly and 0.00375 at half Kelly — three-quarters of the growth for half the risk. At double Kelly growth is −0.00014, already shrinking, and at 2.5× it is clearly negative. Betting too little only slows growth; betting more than about twice Kelly turns a winning edge into a losing strategy.

• Kelly assumes you know p and b. With an estimated edge, an overestimate pushes you past the peak, which is why practitioners use half Kelly or less (Thorp 2006).
• Full Kelly has deep drawdowns: there is a 50% chance of halving your capital at some point.
• It maximizes long-run growth, which is not the same as what an investor with a horizon or liabilities wants.

p, b = 0.55, 1.0                                           # win 55% of even-money bets
kelly = (p * b - (1 - p)) / b

def growth(f):                                             # expected log growth per bet
    return p * np.log(1 + b * f) + (1 - p) * np.log(1 - f)

rates = {m: growth(m * kelly) for m in (0.5, 1, 2, 2.5)}

Assumes import numpy as np and import pandas as pd. Each snippet carries its own example numbers; the comments say which are made up or simulated.