First Officer · Strategy Testing and Uncertainty · About 30–40 minutes
Safety rule: A simulated worst case is not the worst loss that can happen in real markets.
Your mission today
By the end you can explain a simple outcome shuffle, calculate drawdown and state what Monte Carlo cannot prove.
Before you start
Complete C07.1 and C07.2. Bring a coin, six paper cards and a calculator. All outcomes below are invented classroom figures.
1. Same wins and losses, different order
Imagine six cards placed on a table. Three show +1R and three show −1R. An R-multiple describes a trade result relative to its initial planned cash risk. If that risk is $10, a −1R result means −$10 under the model. Shuffle the cards. The total across six cards is always zero R, but the path may feel very different. Alternating win and loss cards never creates a long losing streak. Placing all three loss cards together can create a three-trade decline. Monte Carlo simulation repeats random draws or reorders under stated assumptions to show a range of possible outcomes. It does not know tomorrow's market. A simple coin-flip demonstration makes the uncertainty easier to see. The coin has a specified model probability; a trading strategy does not magically inherit that probability just because you can shuffle its past results.
2. Count the cash loss before the optimistic path
Use the invented sequence −1R, −1R, −1R, +1R, +1R, +1R. Starting at zero R, the running totals are −1, −2, −3, −2, −1 and 0R. The largest decline from the starting peak is 3R. At $10 initial planned risk per trade, that equals −$30 in this simplified fixed-size model before any additional fees. If the three wins came first, the running totals would be +1, +2, +3, +2, +1, 0R. The largest peak-to-trough decline would still be 3R, even though the worst absolute equity level differs. A different order, such as win-loss-win-loss-win-loss, produces a smaller observed peak-to-trough fall. All paths end at zero. This is why a final balance alone cannot explain the discomfort or capital requirements created by a sequence.
3. What the word drawdown actually measures
Drawdown means the drop from a previously reached equity peak to a later low. The peak can be the account's starting balance. Suppose hypothetical equity moves from $1,000 to $1,020, then $990. The drawdown from that $1,020 peak is $30, not merely the $10 difference from the starting balance. As a percentage of the peak, it is $30 / $1,020 × 100, or approximately 2.94%. A later recovery changes the current drawdown but not the maximum drawdown already experienced. Report drawdowns in cash, percent and R when their denominators are defined. If the risk amount varies from trade to trade, a simplified fixed-$10 model will no longer reproduce the real cash path. Never mix those measurements without explaining the assumptions.
4. Shuffling and random sampling answer different questions
A shuffle without replacement takes the same observed trade results and changes only their order. It preserves the total return and count of wins and losses by construction. A resampling with replacement may choose a past result more than once and omit another, producing different totals. Both are demonstrations under historical sample assumptions. Neither captures a market shock absent from the sample. Imagine a backtest containing only small normal-market losses. Shuffling those losses cannot magically create a large unobserved gap. Real costs, order failures and correlated positions can create losses outside the model. The simulation can help a student ask 'Could I tolerate several losses together?' It cannot answer 'What is the guaranteed worst outcome?' Avoid claiming a statistically precise safety boundary from a tiny classroom sample.
5. A coin-flip model is only a model
Suppose a fair coin represents a win or loss, each with a 50% model probability. The chance of three specified consecutive losses under independent tosses is 0.5 × 0.5 × 0.5 = 0.125, or 12.5%. That is the probability of the three particular tosses all being losses. It is not the probability of at least one three-loss run anywhere in a long trading sequence. It also does not describe a real strategy unless its outcomes genuinely follow those assumptions. Financial markets can change regime, produce clustered losses and incur costs. Independence means one outcome does not change the probability of another under the model. Market outcomes may violate that assumption. Use the coin to learn the calculation, then state why applying it to trading requires evidence.
6. Use the result to improve planning, not marketing
Prepare three handwritten paths using your six outcome cards. For each, record the running R total, highest running balance and deepest fall from that peak. At the end, explain whether the total outcome changed and whether the risk experience changed. Try a second exercise where a stopped trade loses −1.5R because of an invented adverse fill. The previous six-card model no longer describes all outcomes, so report the new assumption clearly. Ask how much cash reserve and emotional tolerance a risk charter needs, but do not derive a live position size solely from this toy example. A prudent conclusion is that losing streaks can be worse than an average trade suggests, and that simulations are sensitive to the data and rules supplied. The next stage will ask you to defend those assumptions as a researcher.
Common mistake
A learner shuffles a few winning trades and announces a guaranteed maximum drawdown. The shuffle cannot include shocks missing from the input outcomes. Fix the claim by labelling the model, assumptions and missing risks.
Plain-English glossary
- Monte Carlo: repeated random sampling or rearrangement under stated rules.
- R-multiple: realised result divided by initial planned risk.
- Drawdown: fall from a prior equity peak.
- Independence: one event does not change another event's model probability.
- Resampling: choosing observations again to form new simulated sequences.
Try it yourself
Use three +1R and three −1R cards to make four different sequences. Calculate running balance and maximum drawdown for each. Then compute the probability of three specified consecutive losses from a fair coin, and state two reasons a real strategy may differ.
What you can now do
- Explain the experiment and its key limitations.
- Recalculate loss or drawdown with the correct unit.
- Preserve a complete, dated and independently reviewable record.
Next lesson
CP01.1 · One Market. One Strategy. One Operating Plan. Continue into Captain research and operations, including the CP07 extension.
