This post continue on the calculations from part 2 of this TFSA
trading cost analysis series. Part 1 is an introduction outlining the
rationale for this work. Let's pick up where we left off. I was just
about to figure out what is my *expected profit* using probability
theory. To do that, I use my historical performance data to calculate my
probability of profitable trades. I've been calculating my trading
statistics in my monthly reviews, so it's just a matter of
aggregating all the monthly data to a single number. After a few
keystrokes, I find that my win/loss percentages are roughly 40%/60%.
Given my known reward/risk ratio (discussed in part 2) and
probability of win (40% as noted above), we can calculate a net return
expectancy. This is a simple formula if you know statistics and
confusing if you don't. So I'll just write it out as is but do refer to
the Wikipedia onstatistical expectancy if you'd like to know more
about how I derived this. Expected net return per trade = (Average
Reward from Step 1 - Commission) * (Probability of Win from Step 2) -
[(Risked Amount + Commission) * (1 - Probability of Win)] This formula
is the result we seek. We apply the forumula to extend the cost-benefit
table presented last time. Here's a complete cost-benefit table using
the parameters of a \$5000 principal balance, \$5 commission, capital
gain tax of 17.5% (half of marginal tax rate), reward/win ratio of 2.0,
and a 40% winning rate. It likely that you'll have different parameters
than me. So I am sharing my spreadsheet here so that you can use
your own parameters for your own set of results. Download it in your
preferred format and then edit the values under the Parameters column.
Contact me if you have any problem using it. I will discuss the
result and make [my conclusion in the next and final post in this TFSA
trading cost-benefit analysis series][]. Hint: Short answer to the
title's question is NO. [caption id="" align="aligncenter" width="570"
caption="TFSA Trading Cost-Benefit for Reward/Risk = 2.0 and 40% win
rate"][][][/caption]

## Calculation Example

For anyone interested, let's calculate one data point of the table above
using all the the steps discussed so far in this series. Using \$10 risk
(0.2% of \$5000) as an example. Known data: risk = \$10, commission
(comm) = \$5, reward/risk = 2.0, probability of win = 40% Round-trip
commission = \$5 x 2 = \$10 Average Reward = risk * (reward/risk) =
\$20 x (2.0) = \$20 Expected net profit = (Average Reward from Step 1 -
Commission) * (Probability of Win from Step 2) - [(Risked Amount +
Commission) * (1 - Probability of Win)] = (\$20 - \$10) * (40%) -
[(\$10 + \$10) * (1 - 40%)] = 10 * 0.4 - [\$20 * 0.6] = -\$8 If I
risk only \$10 on a trade, it is expected that I would **lose** \$8 on
average based on my historical trading performance statistics.

[my conclusion in the next and final post in this TFSA trading cost-benefit analysis series]: http://www.quantisan.com/is-a-5000-questrade-tfsa-trading-account-cost-effective-%e2%80%93-part-4/