Having a brain fart morning, so the question is, I'm trying to position size with KC the overnight SP trade, which I assume needs no explanation. Now in determining expectancy, do I use simple winning trades or trades where the win or loss was better than the win/loss during market hours, or just wins during market hours even?
Kelly Criterion question
- Thread starter dcwriter2
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Kelly Criterion is more of a rule of thumb than a specific risk management method. Generally speaking, if you think you have a slight edge, you start your bet at 2% of bankroll. Instead of trying to figure out your win/loss ratio, you should think about the win/loss on different trade types.
So you should categorize different types of trades you make and find your w/l for each, which will help you determine % bankroll for one of those trades.
For a rule of thumbs approach, start a position at 2% and scale up to 8-10% if you have high confidence and a strong w/l rate. The purpose of KC is to optimize the size of your bet given (and you should never bet if you don’t think you have an edge).
So you should categorize different types of trades you make and find your w/l for each, which will help you determine % bankroll for one of those trades.
For a rule of thumbs approach, start a position at 2% and scale up to 8-10% if you have high confidence and a strong w/l rate. The purpose of KC is to optimize the size of your bet given (and you should never bet if you don’t think you have an edge).
You take the expected value of the trade, the maximum risk of the trade, and your account value and you can calculate the size which will give you the highest geometric mean return. However if your figures are too optimistic following the KC will either give you suboptimal or even negative compounded returns. Which is why people back down off the true KC.
That and even if you have things right, KC gives you a very wide distribution of equity paths. That distribution has the highest mean return but the outcomes can greatly vary. However as time -> infinity all of those paths will eventually outpace any other risk control scheme. The time for that to occur is usually really long though, so if you want to fit a confidence interval like targeting 90% of all possible equity curves above your starting capital in 5 years, you are going to need to back down significantly from KC to lower your variance.
That being said if you have accurate forecasts of fed returns, a halfway decent edge and high enough trade frequency 10% is way too low to be risking if you are trying to maximize terminal wealth. Not many people can get the forecasting, discipline, and math correct so a lot of these random rules of thumb end up falling way short of the optimal leverage just to mitigate risk.
That and even if you have things right, KC gives you a very wide distribution of equity paths. That distribution has the highest mean return but the outcomes can greatly vary. However as time -> infinity all of those paths will eventually outpace any other risk control scheme. The time for that to occur is usually really long though, so if you want to fit a confidence interval like targeting 90% of all possible equity curves above your starting capital in 5 years, you are going to need to back down significantly from KC to lower your variance.
That being said if you have accurate forecasts of fed returns, a halfway decent edge and high enough trade frequency 10% is way too low to be risking if you are trying to maximize terminal wealth. Not many people can get the forecasting, discipline, and math correct so a lot of these random rules of thumb end up falling way short of the optimal leverage just to mitigate risk.
♣ Kelly Criterion
The Kelly criterion is the fraction of capital to wager to maximize compounded growth of capital. Even when there is an edge, beyond some threshold, larger bets will result in lower compounded return because of the adverse impact of volatility. The Kelly criterion defines this threshold. The Kelly criterion indicates that the fraction that should be wagered to maximize compounded return over the long run equals:
F = PW – (PL/W)
F = Kelly criterion fraction of capital to bet
W = Dollars won per dollar wagered (i.e., win size divided by loss size)
PW = Probability of winning
PL = Probability of losing
For example, if a trader loses $1,000 on losing trades and gains $1,000 on winning trades, and 60 percent of all trades are winning trades, the Kelly criterion indicates an optimal trade size equal to 20 percent (0.60 − 0.40 = 0.20).
As another example, if a trader wins $2,000 on winning trades and loses $1,000 on losing trades, and the probability of winning and losing are both equal to 50 percent, the Kelly criterion indicates an optimal trade size equal to 25 percent of capital: 0.50 − (0.50/2) = 0.25.
Proportional over betting is more harmful than under betting. For example, betting half the Kelly criterion will reduce compounded return by 25 percent, while betting double the Kelly criterion will eliminate 100 percent of the gain. Betting more than double the Kelly criterion will result in an expected negative compounded return, regardless of the edge on any individual bet.
"If you bet half the Kelly amount, you get about three-quarters of the return with half the volatility, it is much more comfortable to trade. I believe that betting half Kelly is psychologically much better." Edward Thorp
Something else to consider: This is using a volatility adjust loss exit
(Van Tharp - 5 year study of position sizing)
3% of our capital in each trade Profit: $231,121
1% of our capital in each trade Profit: $1,840,493
Limit losses to 0.5% of volatility (using ATR) Profit: $2,109,266
The Kelly criterion is the fraction of capital to wager to maximize compounded growth of capital. Even when there is an edge, beyond some threshold, larger bets will result in lower compounded return because of the adverse impact of volatility. The Kelly criterion defines this threshold. The Kelly criterion indicates that the fraction that should be wagered to maximize compounded return over the long run equals:
F = PW – (PL/W)
F = Kelly criterion fraction of capital to bet
W = Dollars won per dollar wagered (i.e., win size divided by loss size)
PW = Probability of winning
PL = Probability of losing
For example, if a trader loses $1,000 on losing trades and gains $1,000 on winning trades, and 60 percent of all trades are winning trades, the Kelly criterion indicates an optimal trade size equal to 20 percent (0.60 − 0.40 = 0.20).
As another example, if a trader wins $2,000 on winning trades and loses $1,000 on losing trades, and the probability of winning and losing are both equal to 50 percent, the Kelly criterion indicates an optimal trade size equal to 25 percent of capital: 0.50 − (0.50/2) = 0.25.
Proportional over betting is more harmful than under betting. For example, betting half the Kelly criterion will reduce compounded return by 25 percent, while betting double the Kelly criterion will eliminate 100 percent of the gain. Betting more than double the Kelly criterion will result in an expected negative compounded return, regardless of the edge on any individual bet.
"If you bet half the Kelly amount, you get about three-quarters of the return with half the volatility, it is much more comfortable to trade. I believe that betting half Kelly is psychologically much better." Edward Thorp
Something else to consider: This is using a volatility adjust loss exit
(Van Tharp - 5 year study of position sizing)
3% of our capital in each trade Profit: $231,121
1% of our capital in each trade Profit: $1,840,493
Limit losses to 0.5% of volatility (using ATR) Profit: $2,109,266
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