Worked Example of Maximum Drawdown (Scenario With Clear Assumptions)

Direct answer

Maximum drawdown is the largest percentage decline from a prior peak to a later trough in an account’s equity (value) series. A worked example helps because you can compute it directly from assumed values, with every step and assumption stated.

Mechanism and definition

Assumptions for the example:

1. “Equity” means account value over time (after costs are already reflected in the values).
2. We use a simple discrete timeline with four recorded points.
3. Maximum drawdown is computed as the maximum of (Peak-to-trough drawdown), where drawdown at a point equals (Trough − Peak) ÷ Peak.
4. We express drawdown as a positive magnitude by taking the absolute value of the negative return.

Step-by-step mechanics:

• Step A: Identify each “peak” as the highest equity value seen so far up to each time point.
• Step B: For each time point, compute the percentage drawdown from the current peak to the current equity.
• Step C: The maximum drawdown is the worst (most negative) drawdown encountered across the whole series.

Evidence or worked example

Assumed equity series (no real-time data):

• Time 1: Equity = 10,000
• Time 2: Equity = 12,000
• Time 3: Equity = 9,000
• Time 4: Equity = 11,000

1. Time 1

• Peak so far = 10,000
• Drawdown = (10,000 − 10,000) ÷ 10,000 = 0% (magnitude 0%)

2. Time 2

• New peak = 12,000
• Drawdown = (12,000 − 12,000) ÷ 12,000 = 0% (magnitude 0%)

3. Time 3

• Peak so far = 12,000
• Trough at Time 3 = 9,000
• Drawdown = (9,000 − 12,000) ÷ 12,000 = −3,000 ÷ 12,000 = −25%
• Maximum drawdown magnitude so far = 25%

4. Time 4

• Peak so far remains 12,000 (because 11,000 is below 12,000)
• Drawdown = (11,000 − 12,000) ÷ 12,000 = −1,000 ÷ 12,000 ≈ −8.33%
• Worst drawdown remains −25% (magnitude 25%)

Result:

• Maximum drawdown for this assumed series = 25%.

How this “works” conceptually:

• The measure ignores how you got from 12,000 to 9,000 and focuses only on the largest peak-to-trough percentage fall within the provided sequence.

Limitations and risks

1. Sampling and timing limitations

• If equity values are recorded infrequently, the true trough between samples can be missed. That can understate maximum drawdown.

2. Peak definition depends on your chosen series

• Maximum drawdown depends on what “equity” series you use (e.g., different accounting for deposits/withdrawals or cost treatment). Different conventions can change the computed value.

3. It does not describe recovery shape

• Two accounts can share the same maximum drawdown magnitude but differ in duration, volatility during recovery, or how quickly the equity returns to the peak.

4. It does not guarantee future outcomes

• Historical or simulated drawdowns do not establish future performance. Market conditions and execution can change equity paths.

Verification or next question

You can independently verify the 25% result by recomputing each peak-to-trough drawdown from the same assumed equity points and confirming that the worst percentage decline occurs from the peak of 12,000 to the trough of 9,000.

A useful next question is: “How does the maximum drawdown change when the equity series is sampled more frequently (smaller time steps), or when deposits/withdrawals are treated differently?”