The Maths Every Day Trader Should Know
How can a profitable approach lose so much money?
Explore how position sizing and compounding turn a trade distribution into an account path, including drawdowns that a positive average can hide.
By ContextChart Research · 5 min
Published
Same outcomes. A different experience.
Try it yourself
Ending balance from the same 100
$115
Maximum drawdown: 2.0% with separated losses; 9.6% with clustered losses.
Losses separated · +1.2R win / −1R loss
Losses together · +1.2R win / −1R loss
- Losses separated
- Losses together
- Losses separated: largest decline and recovery
- Losses together: largest decline and recovery
Read the plotted values
| Trade | Losses separated | Losses together |
|---|---|---|
| 0 | 100 | 100 |
| 1 | 102.4 | 98 |
| 2 | 100.35 | 96.04 |
| 3 | 102.76 | 94.12 |
| 4 | 105.23 | 92.24 |
| 5 | 103.12 | 90.39 |
| 6 | 105.6 | 92.56 |
| 7 | 108.13 | 94.78 |
| 8 | 105.97 | 97.06 |
| 9 | 108.51 | 99.39 |
| 10 | 111.12 | 101.77 |
| 11 | 108.89 | 104.21 |
| 12 | 111.51 | 106.72 |
| 13 | 114.18 | 109.28 |
| 14 | 111.9 | 111.9 |
| 15 | 114.59 | 114.59 |
P marks the preceding peak; T marks the trough. Shading spans the decline and recovery.
1. Losses separated: largest decline 2.0%, from trade 1 to 2. Previous peak recovered at trade 3, 2 trades after the peak and 1 after the trough.
2. Losses together: largest decline 9.6%, from trade 0 to 5. Previous peak recovered at trade 10, 10 trades after the peak and 5 after the trough.
The same ten +1.2R wins and five −1R losses, with fixed fractional sizing, no cash flows, and no extra costs or constraints. The numbers are teaching assumptions, not a sizing recommendation.
The idea
A trading record can have a positive average result while its account experiences a difficult or destructive path. Position size connects those two facts.
When you risk a fixed fraction of current equity, each result acts on the money left after the previous trade. Returns multiply. They do not simply add.
For an illustrative two-period example, gaining 20% and then losing 20% leaves 96% of the starting account. The percentage gain and loss cancel arithmetically, but the account has fallen 4%. The loss acted on a different base.
Larger exposure increases the effect of both favourable and unfavourable trades. It can also reduce compounded growth even when average trade expectancy remains positive. The path's volatility matters because losses shrink the capital available for subsequent gains.
Drawdown measures the fall from a previous equity peak. Time underwater measures how long the account remains below that peak. Neither can be reconstructed from win rate alone.
The amount risked turns trade outcomes into account growth and drawdown, so positive average R does not describe the whole money result.
How this experiment works
Keep the illustrative trade outcomes fixed and change the fraction of current equity risked. Compare the resulting account paths, including the worst decline from a peak.
Then rearrange the same outcomes. With fixed fractional sizing, fixed payouts, no cash flows, and no other trading constraints, the final product is unchanged. The drawdown and the experience of getting there can change substantially.
The career explorer adds another ingredient: money moving into or out of the account. Once withdrawals, contributions, or changing risk policies enter, sequence can affect the ending balance too.
How we use this
Our career-scenario work separates trade performance from the policy that translates it into cash. It asks how the same sequence behaves under different sizing assumptions and whether the account survives the demands placed on it.
Those scenarios are teaching models, not a validated distribution of future ContextChart profits. Their value is making assumptions and failure paths visible before interpreting a large ending balance.
Show the maths
With equity W, a fraction f risked per trade, and net trade outcome r in R:
Next equity = W × (1 + f × r)
Final equity = starting equity × product of all trade growth factors
Expected arithmetic return and expected log growth answer different questions. The latter tracks the average logarithm of the growth factors, when those factors are positive. A possible complete loss requires separate treatment; its logarithm is not finite.
What this does not establish
The illustration omits broker liquidation, minimum position sizes, changing execution, and losses beyond the assumed outcomes. A smooth simulated result is only as credible as its assumptions. Explore recovery and shared exposure before treating the average as a plan.