In my last post, I mentioned that if you control your downside, your upside will take care if itself. Some of you will be wondering how could that be! Then I believe it's time to explain trade expectancy. This is a concept most commonly used by the casinos, high frequency traders and forex traders.

Before we go on, (for those who have not yet read my previous post) , A Thing Called Risk is the first part of achieving profits with 50% win rate. If you do not understand or have not made it into a habit to set your maximum risk per trade, it is best to go to the link to read and re-read until it is second nature before continuing.

Let's play a game of coin flipping. If you win, I will pay you $1. If you lose, you will pay me $2, After >100 rounds, I would always be profitable. Why? Because the expectancy ratio is better for me. A coin has a near 50-50% chance of being either heads or tails given enough flips. If you try it only for 10 rounds, you may get 7-3 or 8-2. But try it for 100 rounds or even 1000 rounds and you may get around 50% (may not be exactly 50%).

Apply this game to your trades. Let's say you have a $100 account and by limiting the risk per trade mentioned in the link above, you set the maximum risk as $1. But your only enter trades which you have a possible reward of > $2. This is what we call a Risk-Reward Ratio of 1:2 where you risk $1 for a reward of $2.

Steps for developing expectancy

1. Calculate % of Winning trades and Losing trades

2. Calculate Average Win and Average Loss

3. Obtain Trade Expectancy = (% Win x Average Win) - (% Loss x Average Loss)

Lets determine a 50% win rate (either you decide by flipping a coin or base it on you gut feeling)

1. % Win : % Loss Ratio = 50% : 50%

2. Average Win : Average Loss Ratio = 2 : 1

3. Trade Expectancy = (50% x $2) - (50% x $1) = $0.5 per trade (0.5% of a $100 account )

Trade Expectancy Ratio means that you are expected to win $0.5/trade in the long run. Everything is just a numbers game in the world of trading. If you got a negative number, you need to review your numbers (Win : Loss %, Average Win or Average Loss) and concentrate on making your numbers better by limiting your losses while letting your profits run.

In fact, with a winning ratio of 34%, you can also be profitable. Because the Trade Expectancy = (34% x $2) - (66% x $1) = $0.02 per trade.

Although this has very little to do with investing and is more relevant to traders, it is important to limit your losses before your blow up your account.

Below is a chart to illustrate the effects of drawdowns on the account. As you will see, the more you lose, the more difficult it becomes to regain your original capital. So the important lesson is to Limit Losses before they take you out of the game.

Investing Wolf

Disclaimer: This is not a recommendation to buy or sell any mentioned stocks or securities in this blog.

Hi investing Wolf,

ReplyDeleteHaha, I take issue with the statement that you will always win after more than 100 rounds! It's not mathematically sound! I put out two blog posts on this to illustrate :

http://bullythebear.blogspot.sg/2015/02/that-statement-is-probably-improbable.html?m=1#.VPwVBSWwrqA and

http://bullythebear.blogspot.sg/2015/02/i-played-800-games-of-100-coin-toss.html?m=1#.VPweOiWwrqA

If you say you will have high chance of winning after more than 100 rounds, I will agree. But to say there's no chance of losing because you'll always win? Can't accept that, lol!

Hi La Papillion,

DeleteThank you for pointing that out, While I do agree that there is chance of loss (provided your luck super bad until the coin with a possibility of 50% head or tails becomes <33%), there are a couple of portions which are as critical.

1) Do note that the mentioned Average Loss is fixed yet the Average Win is not. If your Reward is always more than 2x your loss (and by that i mean sometimes you win 3x or 4x instead of just 2x)

2) The number of trades also matters. If 100 rounds does not work, move towards 200 or 300. The idea is that if you do a large enough rounds, the probability of winning will always go to the one with a reward of >2.

3) The whole idea of this post was link with the previous post on Risk Management and to advocate investors to limit losses to only a small percentage of your account and not to risk blowing up the account.

Thank you once again. Do share more on your thoughts.

Hi guys, I guess it's more accurate to say that the statements are more applicable the more we tend towards infinity for the number of rounds.

ReplyDeleteHi RetailTrader,

DeleteI believe it belongs to the Law of Large Numbers whereby it states that as a sample size grows, its' mean will get closer and closer to the average of the whole population - Investopedia

Hi investing wolf,

ReplyDeleteI've no issues with your article, just that line where you said "After >100 rounds, I would always be profitable" :) No matter how large the sample size is, the probability of having profitable games is still not going to be 100%. It's important to know that it's still possible to lose, rather than saying that it's impossible to lose.

In other words, we cannot make something risk-free by just playing more games!

There is always a probability in life. But whether it happens or not, is another story. In theory, it could happen as you say 0.043686% chance of loss but in reality, you would not even get a chance to receive less than 34 (if we really do a heck load of demonstrations, i doubt we could even achieve less than 34% win ratio in >100 rounds, not to mention with the average win of more than 2).

DeleteAlso, Risk is ever present. Do refer to my other post http://investingwolf.blogspot.sg/2015/03/a-thing-called-risk.html for more information.

Also, when you're using a theoretical case of coin tossing to simulate trades, it's likely not going to work well in reality. The expectancy of an average trade might be positive, but that doesn't take into account the fact that you could be having more than 1 open positions in one go. If that's the case, each trade is no longer independent and the probability are probably tied to one another i.e. dependent. In the event of an unexpected market event, all your 10 open trades might drop heavily at the same time. You might set your cut loss level and the sum of all your slippage will result in losses more than you would have normally accounted for. Or you could be trading one counter at a time, but these trades you undertook could all be dependent on each other. You'll likely see a string of losses and a string of profits, rather than a random scatter of gains and losses. All these things are not captured in a game of coin tosses and calculated mathematically in the form of expectancy. The stock market is just not so simply modeled.

ReplyDeleteI'll treat all these calculations of expectancy with a huge dose of skepticism. Good for academic discussion, no doubt, but probably not going to be of much use in real life :)

Well, it all count towards the entire number of trades involved (it doesn't matter if you have more than 1 position at any 1 time).

DeleteI highly oppose to having 10 trades (of the same nature) open at any time. Even if you set your stop losses at 1% of the account, you would be risking 10% of your account which will still be detrimental to your account. It will also be difficult to be monitoring news of all 10 positions. It would be more advisable to be having 3 - 6 position in either long or short the market (Hedging your positions). Putting all your trades in the same direction is asking for trouble when the market rises or tanks sharply.

This model is actually not meant for stocks investors. Notice it is more useful for casinos, high frequency traders and forex traders as they have not much slippage (I included slippage margin into my risk per trade as well. It means I do not lose any more than 2% of my account if it doesn't go well).