Expectancy examples

In several blog posts I have referred to expectancy and how a lot of systems (especially short-term ones) eventually lead to losses. Below I will go through a couple of examples of how a high win rate may not necessarily lead you on the path to success.



This first example was given to me by another trader I know, who used to trade such a system on the forex majors on an intra-day basis. The system had specified price targets of only a few pips worth of profit. Against that, stops were placed five times the distance away from entry compared to the price target. This is typical of such systems, with the hook being that such a system can get a very high win percentage.

So, if we work on the basis of a win rate of say 80%, then the overall expectancy (expressed in terms of R) would be calculated as follows:

(Win %age x win size) - (Loss %age x loss size) =

(80% x 1R) - (20% x 5R) = 0.8 - 1 = -0.2R

In this example, despite being right on 4 out of every 5 trades, the overall system expectancy is negative. To even get into breakeven/small profit territory you would need to win at least 85% of the time.

The high win rate is achieved by potentially allowing the position to go against the trader significantly before a stop is hit. Some trades will quickly hit their profit target, others may go the other way.

In this scenario, if you made on average one trade per day, you could easily make profits the first four days of the week, and then that one losing trade on the Friday could wipe out of all those profits and leave you in deficit.

Even worse, if the stops are overriden, or some form of averaging down is done, or the trader encounters a run of losing trades, then the subsequent losses could be huge resulting in a major drawdown or even a blow-up of the account.

With this system the potential upside on trades is limited, whereas potential downside is unlimited (or at least not as limited as it should be). In the long term, that is not going to work.

Now, compare that to this example, which could be a typical trend following system. This will automatically have a much lower win rate, but losses would be contained and kept as small as possible. However, the winning positions are left to run as far as they can until an exit is triggered. So, with this type of system, the potential downside on any trade is limited, whereas there is no such restriction on the upside.

A typical system might have its expectancy calculated as follows:

40% win rate;
Average win 2.5R
Average loss 1R

(40% x 2.5R) - (60% x 1R) = 1 - 0.6 = 0.4R

The expectancy shows the average return gained over the whole sample of trades (winners and losers). So, in the two examples above, on a sample size of 100 trades, system 1 will lose a cumulative 20R, whereas system 2 will show an overall gain of 40R.

Having a limited downside on any trade means you can control the size of your losses. Having no such restriction of your profitable trades means that you can occasionally get into a small number of big winners, which help generate the overall positive expectancy. Get into a few decent winners at once, then that is when you can get the huge moves up in equity (refer to this post for such an example).

Remember though that having a good system with a positive expectancy is only part of the jigsaw. To make it work, you also need strong risk controls, and have the psychological skills to stick to the system rules. If you have all three, then you can make money over the long-term.