Suppose I assume an index fund will unfold an asymmetric, binomial monte carlo (?), where it is either twice as likley to jump up as down, or to jump up twice as far the half the time when it does. And this property holds true for the finest, infinitesimal time increment. If I invest in this index fund, my risk is simply the maximum amount of time, and the maximum amount it can move, before I can hit the bid. But since this amount never changes as it falls, I will always renew my bet rather than sell. But suppose there is some price condition under which I would sell, like if a 20% drop signals there are no buyers, and the drift is invalid. Meaning, if your profit and loss rises and falls with your information, kelly might make more sense. >>If I understand you correctly, you are saying that this index fund offers you a series of bets, it can go up one tick with a probability of 2/3 or down one tick with a probability of 1/3 (or, in your alternative, the probabilities are 50/50 but it goes up two ticks and down one). However, you are not sure your model is correct. If the fund goes down enough you will believe that "the drift is invalid" meaning that the probabilities are 50/50 and the up and down amounts are the same.I think this is a reasonable description of trading. You make a series of bets whose outcome not only generates profits and losses, but gives you information about the distribution. If you specified it precisely enough, including a precise objective function and set of constraints, you could solve for an optimal strategy. Kelly might be a reasonable approximation to that strategy.But I say that's thinking like a gambler. I prefer to divide the problem into outcome distribution and betting amounts. The first is done by the risk manager, and does not depend on probabilities. You (the trader or portfolio manager) tell me (the risk manager) your view, that the fund has either 2/3 or 1/2 chance of upticks. Clearly this uncertainty dominates any tick-by-tick results (that is, if I know the probability is 2/3 I want to invest, whether I get 196 or 207 upticks out of 300; if I know the probability is 1/2 then I don't want to invest, whether I end up with 147 or 152 upticks out of 300). Therefore there are two main outcomes, 1/2 or 2/3.Since there are only two outcomes, I only have to pick how much I want to lose if the outcome is 1/2 and how much I want to make if the outcome is 2/3. I base this on the other opportunities and capital available, how many other opportunities capitalize on the same side of this bet and your record. I can't worry about the probability of 1/2 versus 2/3, that's your job. Of course, for a real strategy, there are more than two outcomes, so the limits and goals are more complex.Once I give you these two numbers, you can solve for the optimal strategy. In practice, you're not going to solve a mathmatical equation, but raise and lower your exposure as the fund ticks up and down; and other information comes in. As you near your loss limit or gain goal, you will get more mechanical (or you'll be fired). Also as a practical matter you will be doing other things than this one strategy, such as handling customer orders or running other strategies. You may have the ability to shift limits among these strategies.