The Maths Every Day Trader Should Know
What does this trade really cost?
See spread, commission, slippage, and financing in relation to the money at risk and the movement a trade is trying to capture.
By ContextChart Research · 4 min
Published
Make the cost visible
Try it yourself
Cost of each trade
0.05R
$5 ÷ $100 planned price risk.
Break-even win probability in this binary model
47.7%
Wins pay +1.20R, losses −1R, then every trade pays 0.05R.
A cheaper-looking cost ratio alone does not establish a better trade. Changing the stop or size also changes the rest of the trade.
A constructed example. Change the inputs to explore the relationship; these are not suggested trade settings.
The idea
The same transaction cost can be a small inconvenience on one trade and most of the opportunity on another.
Suppose an illustrative trade pays $4 in total execution costs. Against $100 of planned price risk, that cost is 0.04R. Against $20 of planned price risk, it is 0.20R. The broker charged the same money. The second trade has a larger hurdle relative to its scale.
Spread is one part of that hurdle: the difference between the prices at which you can buy and sell. Commission, slippage, and financing can add to it. Depending on the data and accounting method, some costs may already be reflected in recorded execution prices.
Comparisons become clearer when every item uses the same units. A spread in broker points must be converted into price distance or cash before comparing it with a stop. A charge in dollars must be converted to the account currency where necessary.
This helps explain why a busy chart can still offer expensive trades. The relevant question is how much achievable movement remains after the cost, over the time you intend to hold.
A cost becomes meaningful when you compare it with the risk and opportunity it consumes.
Three meanings of break-even
Returning to the entry price, covering all trading costs and funding a regular withdrawal are different requirements. An exit at entry can still lose money after costs. An after-cost trading profit can still be insufficient for an income goal. State which requirement the number is answering.
How this experiment works
Hold the illustrative cash cost constant and change the planned price risk. Then change the cost while keeping the risk fixed.
Watch the cost in R and the break-even requirement move together. This is an accounting relationship. It does not show that widening a real stop improves the strategy: doing so also changes size, trade outcomes, and holding time.
How we use this
Our intraday research compares instruments using spread relative to their trade geometry. In the samples tested, spread explained much of the difference in after-cost outcomes between otherwise similar brackets.
The noise study also showed why descriptions such as “clean” and “choppy” need a separate cost calculation. A visual impression can contain useful information, but it cannot tell us what execution will consume.
The historical experiments charged their stated spread convention. They did not establish a complete live cost model including every commission, financing charge, or execution delay.
Show the maths
Using a stated initial planned-risk denominator:
Cost in R = total cash cost ÷ initial planned cash risk
Net outcome = gross outcome − costs not already included
For a simple bracket with fixed loss of 1R, gross winning payout b R, and additive cost c R, the break-even win probability is (1 + c) ÷ (1 + b).
What this does not establish
A typical spread is not the cost of every future fill. Costs can change around releases, rollover, gaps, and thin markets. Measure the conditions your trades actually meet, and keep the cost convention visible when comparing records. The clock also affects whether the same distance means the same thing all day.