This month’s article closely relates some definitive mathematical calculations to a part of our trading psychology. And if you’ve already got the maths part of it understood, the psychology is still very interesting.

In technical analysis we can appreciate the use of mathematics. Our Ranges Resistance Cards, Highs Resistance Cards, Lows Resistance Cards, and Repeating Ranges all between them make use of the fundamental mathematical principles – addition, subtraction, multiplication and division. Soon after, we make use of the fractions and percentages for milestones and resistance levels. We use these extensively in our price forecasting, not to mention that our time analysis is also mathematically driven. So there is our analysis largely, if not completely done – all thanks to the maths.

But there is one other extremely important contribution by the mathematical world to our trading – and it is that of Compound Interest. And it’s a powerful contribution indeed. Some even call it the most powerful mathematical force in the universe. Well and good, but where is it relevant in our trading?

Have you ever opened the new month with an absolute cracker of a trade, soon after becoming cocky, overly excited or overconfident, then quickly giving back all of your profits and then some by overtrading? That first trade may have increased the trading account by a significant percentage of itself, but the series of losses that quickly followed put you in negative territory, ending the month with an overall percentage decrease. A sinking feeling indeed – many of us have been there.

So for some of us, after enjoying a good win, the message is to: chill out and pat yourself on the back. Even take a break if you need to. Let the excitement and emotion settle. And here is the reason: The effect of compound interest is so powerful that we only need a surprisingly small average percentage increase in our trading account each month to make a huge difference over the medium to long term. There is no need to overdo our trading.

Without further ado, let’s get into some facts:

To inflate an account by, for example 7%, we would do the following calculation:

Original Account Size x 1.07

To inflate the account size by 7% again, we would do the following calculation:

Original Account Size x 1.07 x 1.07

To inflate the account size by 7% once more, we would do the following calculation:

Original Account Size x 1.07 x 1.07 x 1.07

Get the pattern? Easy. And we can express the resulting account size in a more compressed way:

Final Account Size = Original Account size x 1.07³

Now let’s do a few examples (answers rounded to the nearest dollar).

Example #1: Initial account size $10,000, and growth of the trading account was 7% per month. Let’s do this for 3 months and have a close look at what happens each time. After one month, the account size would be calculated as follows:

New Account Size = $10,000 x 1.07 = $10,700

So $10700 – $10,000 = $700 has been made in the first month.

After another month:

New Account Size = $10,700 x 1.07 = $11,449

For a profit of $11449 – $10700 = $749 during the month.

And after the third month:

New Account Size = $11,449 x 1.07 = $12,250

For a profit of $12,250 – $11,449 = $801

Notice that although we kept the percentage increase each month fixed at 7%, the absolute individual profit levels from each month went up – from $700 to $749 to $801. So in other words the effect of the 7% became more and more each time – what we refer to as a compounding effect, hence the name Compound Interest.

And just to check our “formula”, we could compress all of the above calculations into one in order to directly calculate the final account balance after 3 months under the same conditions:

Final Account Size         = $10,000 x 1.07³

                                                   = $12,250

Example #2: Initial account size $10,000, and growth of the trading account was only 6% per month for 12 months, final account size would be calculated as follows:

Final Account Size = $10,000 x 1.06¹² = $20,122

Practice doing and therefore verifying the above calculations. Try them with different account sizes and percentage increases. Few traders will have the exact same starting account size or the same ability to increase their account each month.

Now let’s discuss the last result, the one where we traded in each of the 12 months of the year. Certainly not a bad result – more than doubling the account by a mere 6% increase in the account size each month. This doesn’t sound like much is required of us, especially considering that a well traded ABC off the daily chart can increase our account by 15% (assuming a reward to risk ratio of 3:1, and risk on the trade 5% of account size).

So what can we conclude here? That indeed compound interest is a powerful mathematical force and we can let it do its thing if we avoid over trading. Remember, one of the advantages of trading is that we don’t have to be in the market all the time.

Obviously the discussion so far has been very theoretical – there’s very little chance that we achieve the exact same percentage change in our account each month. How about in practice? How can we start to recognise these effects in our own trading? The answer is to start looking closely at your account each month, and get into a routine of doing the following: Work out the percentage change in your account size from month to month:

% change in account = (New Account size – Old Account Size)/Old Account Size x 100%

The same formula will of course work for when we have a negative month. And if you have a string of negative months, the book work is less exciting to do, but keep it up and aim for a smaller negative, if not a positive result in the next month.

Do this for a few months in a row, and get a feel for what your percentage change is each month. Then keep doing it every month. And remember this article doesn’t have to mean that we only ever aim for a 6% increase each month. A much higher reward to risk ratio is possible with regards to trades taken with the higher levels of course material, especially with the use of time analysis from the Ultimate Gann Course and beyond.

Work hard, work smart.

Andrew Baraniak