Equity Curve Simulator: Compare Risk, Returns and Drawdown

An equity curve simulator creates hypothetical account paths from a set of assumptions. Here, you choose a starting balance, an assumed win probability, a net payoff, a loss fraction and a number of trades. The simulator generates 1,000 sequences and applies the same outcomes to two risk settings. The useful result is a range of possible model outcomes, not one persuasive-looking line.

A live account history records what happened. A backtest applies trading rules to historical data. This simulation does neither: it uses independent two-outcome draws, with no prices, entry signals or broker connection. The binomial model described by NIST provides the count-of-wins framework; the balance and sizing rules are stated below.

Each point represents the balance after a completed model trade, with no other open positions. Balance and equity coincide at those points in this simplified account. A real equity curve can also include unrealized profit and loss while positions are open. This tool therefore cannot reveal the deepest intratrade fall that a live account might experience.

Start with the default 100-trade horizon, then change one assumption at a time. Both settings begin with $1,000, an assumed 50% win probability and a net payoff of 1. Setting A loses 1% of its current balance on a losing trade; B loses 2%. These percentages are comparison inputs, not recommended risk levels.

Both the winning payoff and the losing amount are net assumptions: they already include whatever trading costs you intend to represent. There is no extra commission deduction. A gross reward/risk estimate cannot simply be entered as a net payoff without accounting for costs. The risk/reward calculator addresses a different task: planning the price levels and conditional outcomes of one trade.

Run the calculation after editing the inputs. Compare the results table first, then inspect a selected path. Changing the seed creates another sample from the same assumptions; it does not discover a new market condition. A zero loss fraction is a useful mathematical control: that setting's balance stays unchanged.

Use two wins followed by two losses, written WWLL, to see the calculation without a large sample. This is a deliberately selected teaching sequence, separate from the simulator's seeded sample. With net payoff 1, each win adds the current risk amount and each loss subtracts it. For current balance B, a win gives B_next = B × (1 + f × b), while a loss gives B_next = B × (1 − f). Here f is written as a fraction: 1% means 0.01.

A's first risk amount is $10. After its first win, the next amount is 1% of $1,010, or $10.10. Before the first loss it is $10.201. The model retains these fractions through the calculation and rounds only the display; rounding every trade to cents would define a different model.

The final balances are approximately $999.80 and $999.20, corresponding to returns of about −0.02% and −0.08%. Two equal-percentage gains and two losses do not cancel because each percentage is applied to a changing base. The example explains compounding; it does not rank a risk setting as suitable for a real account.

The simulator summarizes 1,000 ending balances with the 10th, 50th and 90th percentiles, labelled P10, P50 and P90. P50 is the median. P10 describes the lower part of this simulated sample; P90 describes its upper part. They are positions within the generated results, not probabilities that your future account will reach particular amounts.

A pointwise median curve can switch which paths contribute at different steps. It need not be one complete sequence that the model actually generated. Likewise, the P10–P90 band does not mean that 80% of whole paths remain inside it from beginning to end. Use the selected-path view when you want a single, internally consistent journey.

Percentiles use the Type 7 linear-interpolation convention documented in R's quantile reference. Between two ranked observations, the reported cut point can lie between their values. For the illustrative sorted sample 100, 200, 400, 800, this rule gives P10 = 130, P50 = 300 and P90 = 680. Ties and interpolation are reasons not to interpret every percentile as an exact count of paths strictly below it.

The mean ending balance is the sum of all ending balances divided by the number of paths. The median is the middle of their sorted distribution. One selected path is a single outcome. A few large ending balances can pull the mean above the median, so these summaries answer different questions.

Return to the four-trade example with p = 50% and b = 1. There are 16 equally probable win/loss sequences. Across that complete set, the exact mean ending balance is $1,000 for both risk settings. The medians are $999.80001 at 1% and $999.20016 at 2%. The arithmetic mean can preserve the starting amount while the middle result is lower.

For this model, the theoretical mean is E[B_N] = B0 × [1 + f × (p × b − (1 − p))]^N, with p and f written as fractions. It follows from the expected multiplier per independent trade. That formula is not the median, a most-likely path or a forecast of trading performance.

A sample of 1,000 random paths need not contain every four-trade sequence equally often. Its displayed mean therefore need not equal the exact $1,000 expectation. Changing the seed changes this sampling variation; changing an assumption changes the distribution being sampled.

For each path, keep a running high that includes the starting balance. At a later point, drawdown = (running high − current balance) ÷ running high × 100%. Maximum drawdown is the largest such percentage in that path. A loss at the start counts even if the balance has never risen above its initial value.

In WWLL, A reaches $1,020.10 and then ends at $999.80001. Its maximum drawdown is 1.99%. B reaches $1,040.40 and ends at $999.20016, giving 3.96%. These are falls from the preceding peaks. They differ from the approximately −0.02% and −0.08% returns measured from the original $1,000.

The results table first calculates maximum drawdown for each complete path, then summarizes those 1,000 values. Measuring drawdown only from the median balance curve would answer a different question and could conceal the falls individual paths experienced.

Here the observations occur after trades close. MetaTrader 5 distinguishes balance and equity drawdowns; open-position losses may create deeper equity lows between these observations. A firm's trailing-drawdown rule also has its own reference, timing and breach conditions. This statistical chart does not reproduce that contractual limit.

Switch among the six ways to arrange two wins and two losses in the four-trade explorer. The steps and drawdowns change, while the ending balance stays fixed for each risk setting. This holds because f and b stay constant and there are no deposits, withdrawals or early stopping rules.

For W wins and L losses, the ending balance is B0 × (1 + f × b)^W × (1 − f)^L. Multiplication gives the same result regardless of the order of those factors. With 1% risk and payoff 1, WWLL has a maximum drawdown of 1.99%, while WLWL has approximately 1.01%; both end at $999.80001.

Across the simulator's random paths, the number of wins can also differ. Those paths can therefore finish at different amounts even when every input is identical. It would be misleading to explain all variation in terminal results as an effect of trade order.

Profit Factor summarizes the money earned on winning trades relative to money lost on losing trades. It does not preserve the full sequence. Under fractional sizing, rearranging wins and losses can also change those individual money amounts, even though the final product above stays the same. Keep the model and the metric's input data distinct.

A fair comparison holds the win/loss outcomes constant while changing the risk fraction. Otherwise, one setting may look better simply because it received a more favourable random sample. Here A and B use the same outcome at every corresponding path and trade; only the amount applied to each balance differs.

• Keep the seed, win probability, payoff and horizon fixed when comparing the two risk fractions.
• Change one assumption, run again and compare the same summary measures rather than choosing the most attractive curve.
• Inspect a selected path alongside the percentile table to connect the distribution with a complete sequence.

Both curves use the same balance scale and the horizontal axis counts completed trades. A steeper line does not tell you how much time elapsed. More model trades do not automatically represent a longer calendar period if real trading frequency varies.

The entered fraction also does not calculate a tradable lot size. Contract specifications, stop distance and executable quantities belong to position sizing. This model assumes that its fractional monetary amounts can be applied exactly, including amounts smaller than a real instrument permits.

Every loss is exactly −1 model R and every win is +b model R. The win probability, payoff and risk fraction remain fixed; outcomes are independent. A real strategy may have break-even trades, changing winners and losers, clustered losses or changing market conditions. These behaviours are not added merely by running more sequences.

Costs belong in the net assumptions, but that convention does not simulate individual fills. A gap can create a loss larger than the planned amount. Slippage, liquidity, currency conversion, margin requirements and overlapping positions can alter an actual account path. TradingView's strategy-testing documentation also treats costs and execution assumptions explicitly; this simpler simulator is not a historical execution backtest.

With a loss fraction below 100%, each finite model loss multiplies a positive balance by a positive number. The calculation therefore does not reach exact zero in finitely many trades. That mathematical property says nothing about avoiding real account depletion, minimum trade sizes or forced liquidation. No ruin threshold or real-world probability of bankruptcy is calculated here.

Use the tool to understand sensitivity: what changes when one assumption changes, which measures move together, and what a single curve leaves out. A more stable simulation estimate still describes the chosen model. The credibility of the assumptions must come from separate evidence and a clearly defined trading process.

Does a 50% win probability guarantee half the trades will win?

No. It assigns the same 50% chance to each independent draw. A finite path can contain more or fewer wins. The fixed WWLL example deliberately contains two of each; the random simulator does not impose that count.

Why does the same seed give the same result?

The seed initializes a deterministic sequence of pseudorandom draws. The same seed, parameters and model version reproduce the sample. Reproducibility makes comparisons checkable; it does not make the generated outcomes predictive.

Why can a 50% win rate and payoff of 1 end below the starting balance?

Percentage gains and losses apply to changing balances. One +1% step followed by −1% multiplies the balance by 1.01 × 0.99 = 0.9999. The theoretical mean across all possible independent paths and one particular ending balance are different quantities.

Is P10 a worst-case result?

No. Lower results can occur within the sample, and the model can omit important real-world outcomes. P10 is a sample percentile under the entered assumptions, not a loss limit or a guarantee about the future.

Can I use the simulator to choose a safe risk percentage?

It compares consequences within a simplified model; it cannot establish a universally safe percentage. Account rules, execution, financial circumstances and the reliability of the assumptions are outside this calculation. The example inputs are not recommendations.

How is this different from Profit Factor?

Profit Factor describes the relationship between aggregate profits and losses in a completed sample. This simulator generates hypothetical sequences from probability, payoff and sizing assumptions. Neither summary substitutes for the missing price path, account rules or evidence about future results.