Introduction
When people think about gambling strategies and bet size management, the ‘doubling up’ strategy comes to mind. Officially, this bet size method is known as the ‘Martingale Gambling Strategy’.
The key principle is to bet a fixed size amount consistently every time you win, but when you take a loss, double the bet size on the next bet and so on until you win. This strategy is supposed to work itself out eventually on the belief that it is unlikely to have a continuous losing streak.
Now, there are actually a few problems with that, especially when it comes to trading.
Firstly, this doubling up strategy works best the more times you are able to double up. Therefore, it means you will likely start off with a small base trade size relative to your capital. If your base trade size is small, how can one expect to make reasonable returns each trade?
Secondly, you actually run the risk of bankrupting your capital. Imagine this: With a base bet of $1, all it takes is 11 bad runs for you to quickly get to $1,024. Imagine you start with $100 as a base; that would mean $102,400 on the 11th attempt! Take a look at the doubling sequence below.
| 1st | 2nd | 3rd | 4th | 5th | 6th | 7th | 8th | 9th | 10th | 11th |
|---|---|---|---|---|---|---|---|---|---|---|
|
$1 |
$2 |
$4 |
$8 |
$16 |
$32 |
$64 |
$128 |
$256 |
$512 |
$1024 |
Next, you really have to think about the risk and reward here. Do you know that if your full capital was $2,047 which allows 11 doubling attempts assuming $1 base bet, at the 11th attempt and once again assuming you’ve won, you would only have made $1? Is it worth it eventually to risk your entire capital just to win $1 at the end of the losing streak?
Also, any belief that it is impossible to have a bad 11 streak run is actually quite misplaced. When it comes to the laws of probability, there is no such rule that says you can’t lose continuously in a streak!
Lastly, unfortunately in the stock market, unlike casinos, there are commissions and interest fees associated with every trade which need to be factored in as well.
Needless to say, most professional gamblers do not use the Martingale approach and neither do we at AlgoMerchant.
TAKEAWAY
- The Kelly Criterion helps investors and gamblers determine what proportion of their capital they should allocate to each investment or bet.
- It has been proven to work mathematically, and has many more advantages compared to the Doubling up money management strategy (Martingale approach)
Our Approach
Instead, we adopt the Kelly Criterion, which is a bet size strategy used by many professional gamblers. In fact, famous investors such as Warren Buffet, Charlie Munger and Bill Gross have been known to use this strategy as well!
The key concept of how the Kelly Criterion works is this – increase your bet size when you are winning, and have an edge. When there is more uncertainty or you are losing, decrease your bet size.
This approach is actually the opposite of the Martingale strategy where bet sizes are increased every time you lose. What is most important to know is that the Kelly Criterion is actually based on math (with proof) substantiating how it can deliver higher long term returns compared to other strategies!
Also, what every reader of this article will be pleased to know is that the Kelly Criterion is designed such that you will never bankrupt your capital, because the bet size each trade has is dynamic and the more you lose, the lesser (% of your remaining capital) you will bet!
This is the Kelly Criterion formula:
K = W/A – (1-W)/B
Where:
K = Kelly bet size (% of portfolio)
W = Win rate
A = expected loss % (per trade)
B = expected profit % (per trade)
Example:
Assume your strategy’s winning ratio (W) is 60%, with a historical expected profit (B) of 1.5% per trade in the event of a win and expected loss (A) of 1% per trade in the event of a loss.
If the initial capital is $10,000, what is the amount you need to allocate initially?
Plugging the numbers:
K = 60/1 – (100 – 60)/1.5 = 33.33%
Kelly Criterion tells us to allocate 33.33% of our capital or $3,333!
From the formula, it shows that if you win the trade, the subsequent trade allocation will be bigger since your capital and win rate will be larger after the first trade.
If you lose the first trade, the subsequent trade allocation will be smaller since your capital and win rate will be reduced after the first trade.
Also note that as this formula hinges on the winning ratio and take-profit/stop-loss ratio as inputs, these numbers are typically obtained via backtesting/ simulation, which is why only data and statistical driven strategies can apply the Kelly Criterion!
Conclusion
To summarise how the Kelly Criterion works, this explanation from Edward Thorp is spot on:
“If we lost 5 percent, we would shrink our positions. If we lost another few percent, we would shrink our positions more. The program would therefore gradually shut itself down, as we got deeper in the hole, and then it had to earn its way out.”
Edward Thorp
