January 31st, 2005, 5:48 am
quantie:In the presence of "perfect" positive (+1) or negative (-1) serial correlation, you would know exactly what the next result would be, and your optimum bet would be to "bet it all". You are correct. However, what I am referring to, is when serial correlation between bets or trades is between 0 and +1, or 0 and -1. When serial correlation is zero, the optimum betting strategies are the Kelley or Optimal f formulas. Intuitively, as serial correlation approaches +1 or -1, the optimal betting percentage should increase above the Kelley percentage. But the big question is, how much more? For example, if the Kelley bet is 5% of capital, and serial correlation between your trades or bets is +.70, what is your optimum betting percentage? Intuitively, my guess is something greater than 5%, but less than 100%(since the serial correlation is not "perfect"(+1,-1),there is "risk of ruin" by betting 100%). However, that is not a very precise guess. What I would like to find is an optimal betting formula that takes into account not only the probability of winning and losing, and the payoff structure, but also the "amount" of serial correlation between trades(bets). I leave this problem to all the brilliant minds on this website.