**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.

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