The Mathematics

I got to spend the day studying my past trades. Here's what they look like. I'll break this thing down nice and slow, because I learned a lot. 1st off, notice all the negatives in the Profit column? Yeah, it's been rough.

• Next thing to notice is the Type column. I've been pretty even with my buys and sells.  
• Alright, next is the Volume column.  I was really random.  When I lost or gained a lot, I would drop down, up, and all around, so there's no rhyme or reason to the volumes, but they came in handy when I was doing the math.
• Next are the stop loss (S/L) and target profit (T/P) columns.  Most of my trades were automatically executed at the S/L (negative profits) and T/P (positive profits).  You can see this in the far right Price column - the closing price - as it matches the respective S/L for negative profits and T/P for positive returns.
• Take the 2nd trade down: .07 lots of the USDCHF pair sold at .97933.  The position is closed at .97963.  This matches with the S/L price.  It's pretty consistent all the way down the list, unless it's a trade with nothing in the S/L and T/P columns because I didn't even want to take the time to figure it out. (never again).

Les équations

The fun stuff. Ok, skipping all the trouble getting here, I give the conclusions.  Let's calculate the profit for a few of these.  In particular, I'll do one for each currency pair I'm working with. 

Note: 1E5 = 1*10⁵= 100,000, 4E-4 = 4*10^(-4) = .0004, etc.

Second Trade: Sell .07 lots of USDCHF at .97933.

profit = [(lot size)*(1E5)*(start price - close price)]/(close price)
= [(.07)(1E5)(.97933-.97963)]/.97963
= [(7000)(-.00030)]/.97963 = -$2.14 

 Notice that it's (start price - close price). This is because we're selling.  Buying, it's reversed to (close price - start price).  I'm not going into how I got this formula finally, but it makes sense when you try to figure it out for yourself. 

 Also note that we had to divide by the closing price. That's because USD is not the base currency position, CHF is. You'll see the same thing in this next trade. 

 .00030 is how many pips I wanted to risk (3 pips).  The risk reward should be 1:2 or 1:3 meaning S/L:T/P pip spreads of 3:6 or 3:9 for example.  I didn't strictly follow this, but I will.

Fourth Trade: Sell .4 lots of USDJPY at 106.557.

profit = [(lot size)(1E5)(start price - close price)]/(close price)
= [(.4)(1E5)(106.554-106.574)]/106.574
= (4E4)(-2E-2)/106.574 = -$7.51

• Note that JPY pips are .01, while all others are .0001, so this trade was "down 2 pips"

Seventh Trade: Buy 1.00 lot of GBPUSD at 1.22583.

profit = (lot size)(1E5)(close price - start price)
= (1E5)(1.22812-1.22583)
= (1E5)(22.9E-4)= $229

• Note that we didn't have to divide by anything because the base currency is USD.
• That was a 22.9 pip spread. 1 pip is $10, hence $229. Making sense? I'm feeling it.  Alright last one...

Twelfth trade down: Buy 1.0 lot of EURUSD at 1.10928.

profit = (lot size)(1E5)(close price - start price) 

= (1E5)(1.10750 - 1.10928)

= (1E5)(-17.8E-4) = -$178.00

Important Note: There were no commission or swaps (time sensitive fees) using this broker. Most have fees associated with the bid/ask spread as well as how long you hold the position. I'm not looking forward to that part either.

Sizing it Up

After doing the exercises through all the trades, I was able to work backwards and put more together. Here's the end result.  First, you find the S/L and T/P, then you can calculate the lot size.  Here's an example using my current paper money portfolio.  

Balance: $3500

Leverage: 1:200

I want to expose about 40% of my account at a max.  That's .4(3500) = 1400.  My 1:200 leverage means 1 lot is covered with 100,000/200 = 500.  So, I can have 1400/500 = 2.8 lots in total trades at once.

That's something I can look at and add up really quick, and that deals with not getting into trouble with my margin. For position sizing, let's say I only want to risk 4% of my account in each trade.  Well, that's .04(3500) = 140.

Working backwards from all those exercises, 140 takes the place of my profit (really it's the S/L), and I'm solving for lot size using the same equation!  When looking at graphs, I've been setting my stop loss based on indicators.  For instance, if the EMA 36 is 20 pips underneath EMA 12, that's what my stop loss is.  So, we get the pips, then use:

lot size = profit/(1E5)(pipsE-4)

=140/(1E5)(pipsE-4)

=140/[(10)(pips)]

=14/pips

Note: For XXXJPY trades, (pipsE-4) changes to (pipsE-2).

This is easy enough for me to change whenever my account balance changes.  140 = (risk percentage)(account balance).  I'm hoping typing all this out helps me remember it.  I'll probably hold off until next week and open some positions when I see an entrance.

Tomorrow, I'm back onto options.