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]
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/