Calculating Projected Annual Return of a Trading System

How to combine expectancy and compounding

Whether using an automated algorithm or a manual trading system, it is imperative that investors have some method of projecting the annual returns of their systems and portfolios. The human mind has a very difficult time grasping the concept of probability, and people often assume correlation or cause and effect where there is none. We search for patterns on a micro level and our brains supply them for us, happily falsifying the data to appease our desire for order and structure. Meanwhile what we really need in order to overcome this is to simply be shown the end results of our system over a long period of time. That way we will be able to see past the ups and downs and concentrate more objectively on macro results. Note; I’m not talking about back testing which traders love to do, rather I’m talking about combining individual results to create a smoothed projection in simple, relatable terms to show us where we are likely to end up after plying a system for a year. Put simply, if we could see ahead and estimate a 5 or 10 percent return, we could objectively determine the quality of the system and not make rash, unqualified adjustments.

So how do we combine all of our trading data into a single number? Basically it goes like this: First we need to know what the expectancy of our system is. What is the average net result of all our trades?

Here is the formula:

 EXPECTANCY = [(average win percentage * average win size)-(average loss percentage * average win size)]

OR

E=([%W*Wsize)-(%L*Lsize)]   Note: percentages are expressed like this: 40% gets entered as 0.40

Now we need to convert expectancy into a percentage. Simply divide expectancy by principle (principle being the starting account or portfolio amount at the beginning of the year):

EXPECTANCY/PRINCIPLE=EXPECTANCY% (again expressed as a decimal- 0.5% is entered as 0.005)

Next we need to calculate iteration; that is, how many times does the system repeat or generate a result in a year? This is pretty straightforward. Whether you’re marking individual trades or entire portfolios, simply divide the length of time the position remains open by the total available time for the period.

Example: if a portfolio gets opened on a Monday and is closed out on Friday, then ITERATION=52 (52 weeks in a year).

Now we need to plug our expectancy and iteration values into the compound interest formula and generate a total amount returned after one year.

Here is the formula:

RETURN AMOUNT= [principle*(1+expectancy%) ^ iteration]- principle

Finally, to arrive at our annual expected rate of return, simply divide RETURN AMOUNT by PRINCIPLE

RETURN AMOUNT/PRINCIPLE=RETURN%  

So there you have it; a clear and understandable value to show you objectively how your system is performing. One thing you will notice is that this approach highlights otherwise imperceptible individual results. A trade, fund, or portfolio with a profit of a quarter percent on its own doesn’t seem like much but compounded many times over will produce a healthy return. After all, the market is about the small, consistent advantage- if only most traders could see it. Hopefully now they will, armed with this tool.