How to compare trading costs honestly

What a headline figure actually is 

An advertised cost figure is a summary statistic. Behind it sits a population of quotes: every price shown on that instrument, in every hour, across whatever window whoever compiled it chose. The single number that reaches the page is one summary of that population, produced by one method, and the method is almost never printed beside it. Two things follow. The number is true, in the sense that whoever compiled it can reproduce it from the data. And it is not comparable, in the sense that a differently compiled number describing a different population is a different measurement wearing the same label.

A distribution of quotes does not go on a banner, so something has to stand in for it, and every candidate summary discards most of what the population contains. The useful question is therefore never whether a headline figure is honest. It is which summary it is, computed over what, and what it threw away to become a single number.

Typical and minimum are different statistics 

Two summaries dominate published cost figures, and they answer different questions. A minimum, usually printed with the word from in front of it, is the narrowest reading in the sample. It describes the most favourable moment in the window, and by construction a single observation is enough to produce it. A typical or average figure describes the middle of the sample: either the arithmetic mean of every reading, or the median that half the readings sit below. It describes the sample as a whole, and no individual quote is obliged to match it.

Both can be published truthfully from the same sample, and the distance between them measures how skewed the distribution is rather than anyone's candour. Spread distributions are skewed by their nature: the narrow readings cluster tightly because there is a floor beneath them, while the wide readings run a long way out, since nothing bounds how far a quote can widen when participation thins.

The two headlines in that block differ by a multiple and neither is wrong. They answer different questions. A comparison that sets one firm's minimum against another firm's average has not compared two firms. It has compared two statistics, and it would produce the same gap if both figures had come from the same firm.

What a headline leaves out 

Even a correctly matched pair of summaries describes one component, of one side, of one trade. Everything in the round turn assembled earlier in this module that a headline spread figure omits is listed below, and the list is why a comparison of headlines is not a comparison of costs.

• The commission, where one is charged. A spread figure and a commission figure describe two halves of one arrangement, so a spread read without the fee beside it describes half of it.
• The far side of the trade. A round turn crosses the spread once and meets a per side commission twice, so a figure quoted per side is half of what a completed trade pays.
• Financing. A position held past the daily cut off carries an adjustment for every night it stays open, and that adjustment appears in no spread or commission figure.
• Conversion. Where an instrument settles in a currency other than the account's, every component is converted at a rate that carries its own markup.
• The distance between the price requested and the price filled. It is quoted nowhere in advance and charged as nothing, and it is a real cost of the same trade.
• The instrument. A figure compiled on the most heavily traded pair a firm quotes says nothing about the cost of a thin one at the same firm.
• The size. An arrangement that applies a minimum charge per dealing costs proportionally more at small sizes than a figure stated per lot suggests.
• The arrangement. A firm operating several pricing models publishes a different figure for each of them, and a headline is conventionally drawn from the narrowest.
• The window. A figure compiled over one month and a figure compiled over a year are different measurements, and most pages carrying either one do not date it.

A cost is not a number until it is pinned to a trade 

A cost figure becomes a comparable quantity at the moment it is attached to a specific trade. Three coordinates are needed, and a fourth whenever the account settles in something other than the instrument's own currency. The instrument comes first, because the unit a spread is quoted in is worth a different amount in every market, and because an arrangement that quotes tightly on one instrument is under no obligation to do so on another.

Size comes second, and it does more work than it appears to. A spread cost and a commission stated per lot both scale exactly with size, so where an arrangement charges strictly pro rata the ranking established at one size holds at every other. Where a minimum charge per dealing applies instead, it does not, and the arrangement quietly becomes a different arrangement below the size at which the minimum bites.

In money the arrangement behaves as expected and the smaller trade costs less. Expressed as a cost per unit dealt, which is what a comparison actually needs, the same arrangement is several times more expensive at the smaller size. Nothing about the terms changed between the two halves of that block. Only the size did.

The ranking can turn on the holding period 

The third coordinate is how long the position stays open. It is the one most often left out of a comparison, because spread and commission are settled at the moment of dealing while financing accrues afterwards. An arrangement is a set of terms rather than a single number, and a firm that quotes tightly is under no obligation to apply a modest markup to the reference rate its financing is calculated from.

The ranking reverses between the same day case and the fifth night on nothing but a difference in financing rates. The two arrangements are level at exactly one night, which is the point at which the advantage in dealing cost is consumed by the difference in the overnight charge. A comparison that stopped at the round turn would have produced a stable answer, and the wrong one for every position held longer than a day.

A method that produces a comparable number 

What survives all of that is a procedure rather than a number. The steps below produce one figure per arrangement that can honestly be set beside another. It is deliberately laborious, and the labour is precisely what the headline was standing in for.

1. One instrument, named, and the same instrument on both sides of the comparison.
2. One size, stated in the units the instrument is dealt in, and resembling the size actually dealt rather than the size that makes the arithmetic tidy.
3. One holding period, stated as a number of nights, including the case of no nights at all where a position is opened and closed the same day.
4. One account currency, since every component has to arrive in the same currency before any of it can be added together.
5. Every component listed, including the ones that are nil under a given arrangement. A nil entry is information. An absent entry is an omission that reads like a nil.
6. Both sides of the round turn, since a figure quoted per side is half of a completed trade.
7. The same summary statistic on both sides of the comparison. A minimum set against an average measures the difference between two methods.
8. Each figure traced to a document rather than to a page of marketing: the contract specification for the instrument, and the published terms for the charge.
9. The whole calculation repeated at a second size and a second holding period. A ranking that survives all three cases is a property of the arrangements. A ranking that flips is a property of the case.

Where a figure can be checked 

Every input that method needs comes from one of two documents, and the two are the same at every firm. A contract specification states the instrument's contract size, the unit it is quoted in, its smallest increment, its trading hours and the basis on which its financing is calculated. The published terms of an arrangement state what is charged, on what basis, per side or per round turn, and whether a minimum applies. A headline is a summary of what those documents contain, and never the other way round.

A published figure that traces back to neither document is a marketing claim rather than a term. That is a category, not an accusation, and it does not make the figure false. It means nobody outside the firm that printed it can reproduce it, and a quantity nobody can reproduce cannot carry a comparison. The questions below are the ones a figure either answers or does not.

• Which instrument, and on which pricing arrangement.
• Which statistic: the narrowest reading, the mean, or the median.
• Over what window, ending on what date.
• At what size, and whether a minimum charge applies below it.
• Measured on orders filled or on quotes displayed, which are two different populations and not interchangeable.
• Whether the figure is a term the firm is bound to, or a description of past behaviour it is not bound to repeat.

Where practitioners disagree 

The largest disagreement is whether the distance between the price requested and the price filled belongs in a cost comparison at all. One tradition excludes it: it is not quoted, not charged and not disclosed in advance, so a quantity nobody can compile beforehand cannot enter a comparison made beforehand. Another insists on it, since for anything dealt in size or dealt around a release it can exceed the spread and the commission together, and a comparison that omits the largest component has measured the small ones precisely. The practical compromise, comparing quoted costs in advance and measuring realised costs afterwards from statements, satisfies neither position fully.

A second disagreement concerns financing. Because the calculation rests on reference rates no firm sets, one view treats it as a market cost rather than a firm's charge and leaves it out of a comparison between firms. The counter is that the markup applied over the reference rate belongs entirely to the firm, and that excluding financing makes every arrangement look alike on the exact dimension where they diverge most for a position held for weeks.

A third concerns the unit. Cost in money is what a statement shows. Cost expressed back in the instrument's own increment, as the size block above did, travels between sizes and instruments but conceals how much money is at stake. Cost expressed against a measure of the instrument's usual daily range travels between instruments of different volatilities and is the least standardised of the three, since no two compilers define the range the same way. Nothing settles the choice, and the common error is not picking the wrong unit. It is changing unit halfway through a comparison without saying so.

The same test, applied to the figures on this site 

The figures published here are subject to the test above, and they are written to be read through it. The typical EUR/USD spread on the arrangement that separates the two components is 0.1 pips, published with its commission of $3.50 per lot, per side beside it, because either half on its own describes half an arrangement. Both are typical figures rather than minimums, both describe one instrument on one pricing arrangement, and neither is a floor or a commitment about any individual quote. The terms of every arrangement sit on the pricing and execution pages, and the contract specification of each instrument states the conventions the arithmetic above depends on.

No claim is made in this lesson about which firm the method favours, and that includes this one. The method is the deliverable. What it produces depends on the instrument, the size and the holding period put into it, and the answer belongs to whoever does the arithmetic rather than to whoever publishes the headline.