LogFAQs > #942112966

https://www.oldschoolvalue.com/investing-strategy/kelly-criterion-investing-portfolio-sizing/

Here is an article on the Kelly Criterion which I find to be very useful in helping with bet sizing. The Kelly Criterion tells you what percentage of your capital to bet given the odds and your expected edge. Roughly speaking, an optimally sized Kelly bet is:

Percentage of Capital = Edge / Payoff

So, let's say stock A is trading at $10. You think it has a 50% chance of going to $30 and a 50% chance of going to $0 (bankruptcy). How much do you bet?

Applying Kelly, we first calculate your edge. The expected value of the stock price is $15 (1/2*0 + 1/2*30). You can buy it now for $10. Therefore, your edge is 50%.

Next you divide your edge by the payoff (+200%). So 50/200 = 25%. Thus, an optimal Kelly bet for this situation would be 25% of your capital.

As the article says, in practice a full Kelly bet is very risky and humans are likely to feel extreme psychological pressure when a full Kelly bet goes bad. Thus, in practice, it's probably better to do a half-Kelly bet. So in the above situation, bet 12.5% of your portfolio instead of 25%. According to the article, a half-Kelly bet captures 75% of the edge of the full-Kelly bet with only half the risk.

Once you increase your bet beyond full-Kelly, your expected bankroll growth actually starts going down because your risk is increasing much faster than your edge. Thus, betting substantially more than full Kelly is likely to lead to portfolio ruin even if you have an edge because the volatility will be so high that when a downswing comes it will wipe you out. For an extreme example, imagine playing Powerball when the prize has reached $1 billion. Your EV is majorly positive, your edge may be something like +400%, but if you invest your life savings in Powerball tickets, there is still a 99.999999% or something chance you go broke. If you have enough money to buy every single combination of numbers, you would do that for $200 million or whatever it cost and pick up your free $800 million. But since you don't, even though the edge doesn't change, the risk does.

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September 1, 2003; November 4, 2007; September 2, 2013
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