Different profit/loss values with Position Sizing and PIP Value calculators, what am I doing wrong?

NajatiAlBukhari · May 3, 2020, 4:22am

Hello,

I am trying to wrap my head around PIP values and position sizing, but I am having trouble getting an exact P/L value as I’m getting different results when calculating them using the two methods. I’ve spent hours trying to figure out what I’m doing wrong to no avail.

For example, I’m trying to find the P/L of a hypothetical losing trade:

Account Value: CAD
Pair: USD/JPY (Long)
USD/CAD rate: 1.40873
CAD/JPY rate: 75.863
Units: 151,726 ((Calculated using the position value calculator - see screenshot)
Entry price: 106.85
Exit price: 106.35
(50 pips loss from a stop-loss)

As you can see below, the position value calculator set the loss as $1,000 as that’s 1% of my hypothetical account balance. When I input that exact same output to the PIP value calculator, I get a slightly different value.

tradeforex077 · May 3, 2020, 8:28am

Try the babypips calculator for position size:

Clint · May 3, 2020, 11:31am

I don’t know whose calculators you are using, but your results do not match the results generated by the Babypips calculators.

Let’s run the Babypips calculators first, and then try to sort out the results you’ve gotten from your calculators.

We have to run the Position Size Calculator first, because the Pip Value Calculator will ask for the calculated position size.

Here’s the Babypips Position Size Calculator, with your inputs —

Notice that the Position Size Calculator asks for only one price — the price of CAD/JPY — because your account is denominated in CAD, and pips (in your USD/JPY pair) will be denominated in JPY.

And here is the Babypips Pip Value Calculator, with your inputs —

Notice that this calculator asks for two prices — USD/JPY (the pair you are trading) and CAD/JPY. You will probably not believe me when I tell you this, but the USD/JPY price is unnecessary in this pip value calculation. You’ll have to prove it to yourself. Substitute ANY price, even a ridiculous price, like 500, in place of the actual USD/JPY price in the ASK box, and you will get the same result — pip value = 20.

So, the way the Babypips calculators work, there is no disagreement in any of the metrics of your trade. But, these calculators do not display P/L at stop-out, which is where the confusion arises.

Next, let’s use your calculators.

Your position size calculator displays more of the metrics of your trade, than the Babypips calculator does. But, none of the metrics displayed contradict the Babypips calculator. The important result — the position size corresponding to your specified risk percentage and stop-loss — is the same in both calculators: 151,726 units of USD/JPY.

In your position size calculator, as in the Babypips position size calculator, the only price which enters into the calculation is the CAD/JPY price. The USD/JPY prices at entry (106.850) and at stop-out (106.350) are simply an alternative way of specifying the 50 pips you are risking. But, other than that, the USD/JPY prices do not affect the position size calculation.

Your pip value calculator is very different from the Babypips pip value calculator, in that it calculates P/L at exit (where you were stopped out) the way your platform would do the accounting, using all three prices — CAD/JPY (implied in the calculated position size), plus USD/JPY, and USD/CAD.

At exit (stop-out), you have lost 50 JPY-pips in a USD/JPY trade. Those 50 JPY-pips have a value in USD which is calculated, based on the USD/JPY price at exit (106.350). Finally, that USD-value has to be converted to CAD, your account currency.

The math works out this way:

one JPY-pip = 0.01 JPY

[one JPY-pip] ÷ [USD/JPY at exit] x [USD/CAD] x [position size] x [SL in pips] = P/L

[0.01] ÷ [106.35] x [1.40873] x [151,726] x [-50] = - C$1,004.89 (loss)

So, why does your position size calculator indicate exactly C$20 per pip, and a total loss of exactly C$1,000, whereas your pip value calculator indicates C$20.09788 per pip, and a total loss of C$1,004.89 ?

The answer lies in the fact that the three prices (CAD/JPY, USD/JPY, and USD/CAD), as factored into your calculations, were not perfectly related mathematically.

In theory, CAD/JPY should be equal to USD/JPY ÷ USD/CAD. This can be seen more clearly if we write those prices as algebraic fractions, as follows:

C/J = U/J ÷ U/C

which can be rewritten as C/J = U/J x C/U

which simplifies to the identity C/J = C/J

If we use the three prices in your trade in the theoretical equation above, we get

C/J = U/J ÷ U/C

75.8630 = 106.350 ÷ 1.40873 = 75.4935 and the equality clearly fails.

If the three prices in your trade had satisfied the equation exactly, then your pip value calculator would have rendered the results you expected: C$20 per pip, and C$1,000 total loss at stop-out.

You can prove this to yourself by adjusting either the USD/JPY or USD/CAD price to satisfy the equation. Note that the CAD/JPY price must be maintained as it was when entered into the position size calculator, because that price determined the position size imported into the pip value calculator.

If you choose to adjust the USD/JPY price, then it becomes 106.870

Alternatively, if you choose to adjust the USD/CAD price, then it becomes 1.40187

Plug these adjusted prices (one at a time) into the calculations in your pip value calculator, and you will get the values you were expecting.

Currency prices are fluctuating constantly. All combinations of three related pairs (such as the CAD/JPY, USD/JPY, and USD/CAD pairs above) fluctuate around an equality similar to the one given above. But, the equality is very seldom exact. A difference, such as you have experienced in your example, is typical. But, such a difference can never become large, because if it did, computer trading algorithms would quickly arbitrage it back toward equality.

Finally, the metrics you enter into your position size calculator represent your plan. In your example, your plan was for C$20 pips, and a 50-pip stop loss that equated exactly to a loss of C$1,000.

The results from your pip value calculator represent the real-world result of your trade, where your loss in pips — which was exactly 50 pips — did not equate exactly to a dollar-loss of C$1,000.

Welcome to the real world.

And welcome to this forum.

NajatiAlBukhari · May 3, 2020, 1:17pm

Aha, got it!

Thank you so much for the detailed answer.

Follow up question: So whenever my account’s currency is not the counter currency in the pair, the real-world P/L would be the value I get from my PIP value P/L calculation. Do I understand this correctly?

Clint · May 4, 2020, 5:23am

Yes, you understand it correctly.

(1) If you trade USD/CAD (or any pair of the form XXX/CAD) in your CAD-denominated account, then when you enter your trade, one pip will be worth C$10 per standard lot, and when you exit your trade, one pip will still be worth C$10 per standard lot, regardless of how much prices have moved, and regardless of how long you have held your trade.

(2) On the other hand, if you trade CAD/JPY in your CAD-denominated account, then there are potentially two different pip values – one at the time of entry, and one at the time of exit. Let’s assume a huge change in the price of CAD/JPY, and see how these two pip values might differ in an extreme case.

Suppose CAD/JPY = 75.000 when your trade is entered, and CAD/JPY = 95.000 when your trade is closed. That’s a 2,000-pip price move in CAD/JPY. The Babypips Pip Value Calculator tells us that the pip value would be C$13.33 per standard lot at the time of entry, and C$10.53 at the time of exit. Obviously, this was a position trade, and you were LONG.

At the beginning of your trade, you were expecting to earn C$13.33 per pip. But, as those pips rolled into your account, the value of each one declined proportionally. When you closed your trade, your P/L was C$21,060 per standard lot (2,000 pips x C$10.53, rounding the pip value to the nearest cent).

In the final P/L accounting, only one variable currency pair (CAD/JPY) was involved. But, it had two influences on your P/L — a gain (or loss) in pips, and a changing pip value.

At the beginning of this trade, you might have thought, “If I earn 2,000 pips on one standard lot, I’ll make C$26,660.” At the end of your trade, when you compared that to your actual P/L, you might have been sorely disappointed.

But, consider this: If you had traded this CAD/JPY pair SHORT for a 2,000-pip ride, you would have earned a much bigger P/L than initial conditions (the pip value at time of entry) would have indicated. Again, welcome to the real world.

In forex trading, there are so many ways that final outcomes can differ from initial plans.

Most retail traders do not hold large positions for 2,000-pip runs, and they never see “discrepancies” of C$5,600 between expected profit and actual profit. Therefore, most retail traders don’t even think about the things we are discussing here.

(3) Lastly, when neither the base currency nor the quote currency matches your account currency, there are not two variable currency pairs in the final P/L calculation, but three – as discussed in your original example.