The uncomfortable case looks like this. Equity is up over the quarter, the chart on the performance tab slopes the right way, and when you pull the list of closed trades every single one of them lost money. Nothing is broken and nobody is lying. The gain came from revaluation on positions still open, and the trading process, which is the only part of the operation you actually control, has been losing money the whole time behind a rising line.
This is the single most important decomposition on a mixed book, and it is invisible on any screen that shows one equity series. A rising line answers the question did the account grow. It does not answer whether the growth came from decisions, from the market, or from money walking in the door.
Four terms behind one equity line
Change in equity over any period resolves into four components that need to be reported separately because they have different owners and different persistence.
Booked results from closed positions. This is the output of the trading process, it is final, and it is the only term where the counterfactual is clean: those decisions are complete and their outcome is known. It is also the term with the smallest number of observations, which is why it is noisy and why a single quarter of it means less than people assume.
Revaluation on open positions. The mark moved and you did nothing. It is real in the sense that the equity is genuinely different, and provisional in the sense that it can reverse before it is ever booked. Attributing it to skill requires an argument about why those positions are open, and that argument is usually weaker than the number implies.
Financing and frictions. Fees, funding on perpetual positions, borrow cost, and the spread paid on entry and exit. Small per event and cumulatively decisive on any book that turns over. This term is almost always negative and almost never presented on its own.
External flows. Deposits and withdrawals. A book that received a subscription has more equity and has not made a penny, and any performance figure that fails to neutralise flows will read as a return that nobody earned.
Two figures on one page, both defensible
Anyone who works with a performance screen for long enough finds two numbers that appear to describe the same thing and do not match. A return quoted at the top of a page against one derived from the chart, or a risk adjusted ratio in one panel that differs from the same ratio elsewhere. The instinct is to assume one is wrong. That instinct is usually mistaken, and acting on it publicly is expensive.
The reasons two such figures legitimately differ are well understood and there are only a handful of them.
- Measurement window. A statistic over 1M and the same statistic over 1Y are different statistics. The period controls on this page run from 1D to 1Y, and a ratio computed over ten sessions and one computed over two hundred are not comparable, whatever the label above them says.
- Annualisation. Whether a figure has been scaled to an annual equivalent, and what periodicity it was scaled from, changes it by a large multiple. Two correct calculations on the same data, one annualised and one not, look like a contradiction.
- Which return series. Returns on equity including flows, returns on equity with flows neutralised, returns on invested capital, or returns computed on trade level results are four different series over the same book. Each is legitimate and each answers a different question.
- Sample composition. The view selector determines which accounts are in the sample. ALL ACCOUNTS (REAL) and BLOCKCIRCLE ONLY are different populations, PAPER is a different population again, and a figure that includes a simulated account is not describing the same book as one that excludes it.
- Sample length and observation frequency. A ratio built from daily observations and one built from a smaller number of trade level observations will differ even over an identical window, because the denominator is estimated from different data.
None of that means a product is miscalculating anything, and asserting that it is, without having done the work, is a claim you will have to withdraw. The correct move is to identify which question each figure answers and then use the one that matches yours.
Isolating a series by changing one control at a time
The procedure for working out what a figure describes is the same procedure you would use on any instrument you did not build. Hold everything fixed except one control and observe what moves.
- Fix the account view and step the period through 1D, 7D, 14D, 1M, 3M and 1Y, recording the figure at each step. If it changes at every step, it is window dependent, which tells you it is a period statistic rather than an inception to date one. If it barely moves between 3M and 1Y, you are probably looking at a figure with a fixed start date.
- Fix the period and step the view through the selector. Note the figure for the cumulative all accounts row and for each individual account, including the ones listed with counts beside them such as Alpaca and Secondary. If the cumulative figure is not a value weighted combination of the individual ones, the aggregation is doing something you need to understand before quoting it.
- Establish what the count next to each account name enumerates by comparing it against your own record of positions and closed trades for that account. Two accounts showing 16 and 11 tell you the sample sizes behind their respective statistics, and a ratio computed on 11 observations deserves a wide error band regardless of what it prints.
- Reproduce one figure by hand for a single account over a short window from your own transaction record. Agreement to a reasonable tolerance tells you which series it is. Disagreement tells you which term is being included or excluded, and that is usually flows or financing.
Three passes of that and you know exactly what each number on the page is conditioned on. Write it down once, in the same document as your reporting policy, and the question never has to be re-litigated in a meeting.
What the decomposition changes in a review
The reason to do any of this is that the four terms carry different information about what happens next. Booked results tell you whether the process works. Revaluation tells you what the market has done to positions you have chosen not to close. Financing tells you what the operation costs to run. Flows tell you nothing about skill at all.
A quarter where booked results are negative and revaluation is strongly positive is a specific situation with a specific diagnosis. Either the exit discipline is cutting winners and holding losers, which shows up as small booked losses against large open gains in the same names, or the book has drifted from a trading strategy into a passive long position that happens to be working. Both are worth knowing and neither is visible in the equity line.
The inverse case matters too. Booked results positive, revaluation negative, equity flat. That is a process that is working while the open book bleeds, and the honest reading is that position sizing on the open positions is undoing the trading. In both cases, the conversation with an allocator is far easier when you brought the decomposition yourself rather than having it extracted from you.
Report the four terms every period, with the same definitions, and let the equity line be the sum of things you have already explained rather than the headline that has to be explained afterwards.