Eureka! The secret to identifying a winning strategy

I always wanted to know “How do I know if my strategy is a winner?” … I keep seeing in my FX research something that really bugs me, and it is this magical risk/reward ratio of 2. There’s so much information out there that says that you should trade with a risk/reward ratio of at least 2, or you’ll end up burning your account.

Well, I’ve come up with many strategies that are very profitable for a certain period of time, but not profitable in other periods of time. Some of them have risk rewards greater than 2, some of them half a risk reward of 0.5… but they all made money.

So how do I know what is good and what isn’t? How can I actually compare them properly?

Today I wanted to test out two very important things all traders should know about

  • Risk Reward Ratios and their significance
  • Variable Amounts vs Fixed Amounts (Position Sizing)

To do this, I wanted to test some very basic systems that we all understand like flipping a coin, or rolling a dice. So, if I had a system that won 50% of the time, or 1/6 times, what risk reward ratio should I use to ensure in the long run I will be profitable? Also, how will position sizing impact my PnL.

So I put together a simple spreadsheet to test these. It takes the following inputs

  • Risk Reward
  • Win Rate (%)
  • Initial Balance
  • Fixed Trade Amount
  • Variable Trade Amount (%)

…and that’s it! I then generated 1000 “trades”, or rather guesses, to determine if it would win or not according to the probability defined in Win Rate. If a trade lost, the amount bet was deducted from the balance. If a trade won, the amount * risk reward was added to the balance.

I also generated curves of the balance so I could easily compare the curve for fixed amount positions versus the variable amount positions.

So here’s a couple of output charts

Win Rate 40% Risk/Reward 1:2

Win Rate 50% Risk/Reward 1:1

Win Rate 90% Risk/Reward 3:1

Win Rate 50% Risk/Reward 1:1

So, as confirmed by the charts, I want to make my first point here: Variable Position Sizing is always better. Regardless if this is a winning strategy, or a losing strategy, if you use a variable position size it always eventually wins more, or loses less.

…But wait a minute, there’s two Win Rate 50s Risk/Reward 1:1s but one makes money and one loses money… that’s right. Everytime I calculate the spreadsheet there is a different 1000 trades so sometimes there may be a large draw down or luck is not in your favour.

It’s kind of like the example of flipping a coin. If you flip a coin and it is heads 500 times in a row, it should eventually be tails because we know in the long run it should be 50/50. Note that the probability of tails coming next does NOT increase (this is known as Gambler’s Fallacy: http://en.wikipedia.org/wiki/Gambler%27s_fallacy).

So, as I kept refreshing this chart, I could see that certain strategies mostly won, and certain strategies mostly lost, and some were mostly flat… I thought to myself, there has to be some way I can create a formula based off these inputs so I can always calculate it (like extrapolate out to millions of trades).

Well, there is. It’s called the Kelly Formula (http://en.wikipedia.org/wiki/Kelly_criterion). By using Risk Reward Ratio and Win Rate, we can determine in advance if this strategy is likely to be profitable or not. In simple terms, the formula is:

KELLY = WIN_RATE – [(1 – WIN_RATE) / RISK_REWARD_RATIO]

For visual ease, I have created this heat map of a range of Kelly Formula outputs.

Kelly Formula Output

So you can see, a risk reward of 1:2 and a win rate of 40% does make money in the long run… but it certainly isn’t the only winning combination. This brings me to my second point: If you want to use a risk reward of 1:5 or 5:1, do it… as long as you know your Kelly Formula output will indicate you should make money in the long run.

So that, I think, is the secret to identifying if you have a winner strategy. The challenge of course is that in FX the two inputs are inversely correlated… That is, if you want to a higher risk/reward ratio, your win rate will drop.

But we can backtest the strategy and see what our Kelly Formula would output. If the results of the backtest are much higher than the Kelly Formula would indicate, then maybe we just had luck on our side and the strategy isn’t as good as it looks.

If you would like a copy of the spreadsheet, please contact me.

Posted in Backtesting, Forex, Optimization, Research, Strategies and tagged , , , .

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