# Real-life slippage deductions from P/L per unit

Matthew,

The slippage mouseover text indicates that the slippage indicated is per side, yet the amount is only deducted from the P/L per unit once rather than twice.

It would seem either one or the other is incorrect, or I am missing something.

Also, the P/L per unit isn’t representative of a simple calculation (currently 152 contracts / \$17,537 profit =\$115.38 per contract versus the \$99.84 shown).

Is this intended, and if so what general factors help determine this figure?

Dustin,

I believe that what you describe about the P/L per unit is the phenomenon that I described already in a long closed thread, after it was previously pointed out to me by Hans Hansen. I will now take the liberty to describe it quite extensively, because confusion seems to arise easily in this topic.

There are two “reasonable” formulas to compute P/L per unit. These two formulas are

P/L per unit (1) = (total cumulative profit) / (total number of contracts traded)

P/L per unit (2) = SUM {profit trade of #i / number of contracts of trade #i} / (total number of trades)

To see what the difference is between these formulas, let’s first assume a shorthand notation: write p(i) = profit of trade #i, and s(i) = size of trade #i = number of contracts in trade #i, and N = number of trades. Furthermore, write y(i) = p(i) / s(i). Then

P/L per unit (1) = SUM {p(i)} / SUM {s(i)}

P/L per unit (2) = SUM {p(i) / s(i)} / N.

This is the same as what I wrote above, but in the shorter notation. Now note that p(i) = y(i) * s(i) and substitute this in the formulas. This entails

P/L per unit (1) = SUM {y(i) * s(i)} / SUM {s(i)}

P/L per unit(2) = SUM {y(i)} / N.

The second formula is simply the average of the y(i), i.e. of the tradewise profits per unit. That is, the profit per unit is first computed for each trade separately, and then averaged across trades. The first formula, on the other hand, can be recognized as a weighted average of the y(i), where each trade i is weighted by its number of contracts s(i).

Some people seem to deny that there is a difference, but I think that it is quite obvious from the formulas that these two will generally not produce the same result. Mathematically the two outcomes will be necessarily equal if the covariance between y(i) and s(i) is exactly equal to 0 (that is, if the correlation between y(i) and s(i) is 0, or the variance of y(i) is 0, or the variance of s(i) is 0).

Now the clue is that you probably used the first formula, whereas C2 probably uses the second formula. I’m not sure of the latter, because Matthew never confirmed this. But you can recalculate this to check whether this explanation holds for your system.

A further difference, pointed out earlier by Sam Cook, can be caused by the difference between open and closed trades. I believe that what C2 writes behind Cumu \$ includes the open trades, whereas what C2 writes behind P/L per unit is based on closed trades only. So if you used the Cumu \$ of C2 in your computation of the first formula then this will of course not agree with the second formula if you have open trades.

Both formulas have some merits. The first formula has the advantage that it takes the relative trade sizes s(i) / SUM {s(i)} into account, thus providing a measure that is close to the system as the vendor intended it to be. Smaller trades will have less influence on the outcome. Note that the absolute trade sizes s(i) do not matter in that multiplying each s(i) by 100 will still produce the same outcome.

The second formula has the advantage that it describes what will happen if a subscribes makes all the trades with 1 contract, ignoring the size recommendations of the system. This is perhaps not what the vendor intended, but some subscibers do this, e.g. because they do not have enough capital. Then the second formula is important, because it sometimes happens that P/L per unit (1) is positive while P/L per unit (2) is negative. This implies that if a subscriber trades with 1 contract per trade, he would get a net loss instead of profit.

Jules