Calculating Your Worst Expected Streak

Knowing the theoretical probability of a 10-loss streak is useful, but traders need a concrete, actionable calculation: "Given my win rate, payoff ratio, and trading horizon, what is the maximum drawdown I should expect?" This article provides the methods, formulas, and spreadsheet implementations to answer this question precisely.

The calculation integrates three pieces: the longest expected losing streak length, the typical loss size during that streak, and the time window over which to expect it. Together, these give a maximum expected drawdown—the benchmark against which traders should size positions and allocate risk.

Key takeaways

• Expected longest streak depends on win rate and number of trades: Use log(N) / log(1/(1-p)) to compute it.
• Streak size must be converted to dollar drawdown using average loss: If average loss is $1,200 and longest expected streak is 8, drawdown is $9,600.
• Payoff ratios and unequal loss sizes complicate the calculation: A 60% win rate with 1:1.5 payoff means average loss differs from average win; the full formula accounts for this.
• Drawdown severity has two components: loss frequency (probability of long streaks) and loss magnitude (size of each loss).
• Professional traders target maximum expected drawdown of 10–15% of bankroll: Higher acceptance is possible but requires larger bankrolls or smaller position sizes.

Step 1: Calculate the Expected Longest Losing Streak

The basic formula (from the previous article) is:

E[Longest losing streak] ≈ log(N) / log(1 / (1 - p))

Where:

• N = total number of trades over your horizon
• p = win probability
• (1 - p) = loss probability

Example 1: A Day Trader

• Win rate: p = 0.55
• Trading horizon: 4 years = 1,000 trading days per year × 4 = 4,000 trades
• Loss probability: 1 - p = 0.45

E[Longest streak] = log(4,000) / log(1 / 0.45)
                  = log(4,000) / log(2.222)
                  = 8.29 / 0.8047
                  = 10.3 trades

Over a 4-year career, expect a longest losing streak of approximately 10 consecutive losses.

Example 2: A Position Trader

• Win rate: p = 0.60
• Trading horizon: 2 years = 50 trades per year × 2 = 100 trades
• Loss probability: 1 - p = 0.40

E[Longest streak] = log(100) / log(1 / 0.40)
                  = log(100) / log(2.5)
                  = 4.605 / 0.916
                  = 5.0 trades

Over a 2-year period with 100 trades, expect a longest losing streak of approximately 5 losses. This is much shorter than the day trader's because the total number of trades is smaller, providing fewer opportunities for long streaks to form.

Step 2: Estimate the Average Loss Per Trade

The magnitude of each loss depends on position sizing and the payoff ratio. There are two approaches:

Approach A: Fixed Dollar Risk Per Trade

If the trader always risks a fixed dollar amount (e.g., $1,000), then:

Average loss per trade = Risk amount
                       (For this approach, it is simply the amount risked)

This is straightforward but only applies to traders with fixed-dollar position sizing.

Approach B: Percentage-of-Bankroll Risk (Proportional Sizing)

If the trader risks a constant percentage f of bankroll per trade, then:

Average loss per trade = f × Current bankroll
                       (This changes as bankroll grows or shrinks)

For the initial calculation, use the starting bankroll:

Average loss per trade = f × Starting bankroll

Example: A trader starts with a $50,000 account and risks 2% per trade. Average loss is 0.02 × $50,000 = $1,000.

Approach C: Accounting for Payoff Ratios

If the trader's historical trades show a win average of W and a loss average of L, then:

Payoff ratio r = W / L
Average win = Expected win size
Average loss = W / r

This requires historical trade data. For a 60% win-rate trader with trades averaging +$1,500 on wins and -$1,000 on losses:

Payoff ratio r = 1,500 / 1,000 = 1.5
Average win = $1,500
Average loss = $1,000

During a losing streak, each trade is a loss (size $1,000). A 10-loss streak is $10,000 in losses. But in the surrounding sequences, 60% of trades are wins ($1,500 each). The net effect on bankroll is not just the loss magnitude but the loss magnitude minus the compounded wins that would have occurred without the streak.

For a refined calculation, use the ratio of losses to wins:

Effective average loss per trade (accounting for win ratio)
  = Average loss × (1 - p) + Average win × p
  = 1,000 × 0.4 + 1,500 × 0.6
  = 400 + 900
  = $500 expected value per trade

But during a LOSING STREAK, each trade is a loss:
Average loss per trade during streak = $1,000

The losing streak is worse than the average because it replaces expected wins with actual losses.

Step 3: Calculate Maximum Expected Drawdown

The maximum expected drawdown is the loss amount during the longest streak:

Max expected drawdown ($) = E[Longest streak] × Average loss per trade

Max expected drawdown (%) = Max drawdown ($) / Starting bankroll

Example 1: Day Trader Recap

• Expected longest streak: 10 losses
• Average loss per trade: $1,200 (fixed 2% of $60,000 bankroll)
• Maximum expected drawdown: 10 × $1,200 = $12,000
• As percentage: $12,000 / $60,000 = 20%

Example 2: Position Trader Recap

• Expected longest streak: 5 losses
• Average loss per trade: $800 (2% of $40,000 bankroll)
• Maximum expected drawdown: 5 × $800 = $4,000
• As percentage: $4,000 / $40,000 = 10%

Step 4: Evaluate Against Risk Tolerance

Compare the calculated maximum expected drawdown against a predetermined risk target. Professional traders typically follow these guidelines:

• Conservative (fund managers, large accounts): Maximum drawdown target = 5–10% of bankroll
• Moderate (professional traders): Maximum drawdown target = 10–15% of bankroll
• Aggressive (early-stage or high-edge traders): Maximum drawdown target = 15–25% of bankroll

If the calculated maximum exceeds the target, adjust by:

1. Reducing position size: Halve risk per trade, which halves the maximum drawdown.
2. Increasing bankroll: Double the starting capital, which effectively halves the maximum drawdown as a percentage.
3. Improving the edge: Increase the win rate or payoff ratio to reduce the expected streak length.

Practical Spreadsheet Calculation

Most traders implement this in a spreadsheet. Here is a template:

Input cells:
  A1: Win probability (p) = 0.55
  A2: Loss probability (1-p) = 0.45
  A3: Number of trades (N) = 2000
  A4: Risk per trade ($) = 1000
  A5: Starting bankroll ($) = 50000

Calculations:
  B1: = LN(A3) / LN(1 / A2)  [Expected longest streak]
  B2: = B1 * A4              [Max drawdown in dollars]
  B3: = B2 / A5              [Max drawdown as percentage]

Output:
  Expected longest streak: (B1)
  Maximum drawdown ($): (B2)
  Maximum drawdown (%): (B3)

Refinement: Accounting for Partial Streak Recovery

In the simplified calculation above, the worst drawdown occurs at the end of the longest losing streak. In reality, traders may recover partially between losses (e.g., if some trades are partial losses or reduced size during drawdown).

For a more sophisticated model, define:

Streak drawdown = sum of losses during the streak
Interim recovery = expected wins that occur during and after the streak
Net maximum drawdown = Streak drawdown - Interim recovery

This is complex to compute analytically, so many traders use simulation instead.

However, for a conservative estimate (which is safer), assume zero interim recovery—that is, treat the longest streak as a continuous sequence of total losses with no wins in between. This gives an upper bound on expected drawdown.

Worst-Case Streak Calculation Workflow

Real-World Scenario: The Undercapitalized Swing Trader

A swing trader has documented a 56% win rate over 250 trades. The trader plans to trade full-time and needs to make $3,000 per month. The trader's backtest shows:

• Average win: $800
• Average loss: $750
• Payoff ratio: 1.07

The trader has $25,000 in trading capital and sizes positions to make $250 per win ($800 - $750 = $50 expected value per trade, targeting 5 wins per day × 20 days = $250 per day gross).

Let's calculate the maximum expected drawdown:

Expected number of trades in 1 year = 250 trading days × 2 trades per day = 500
E[Longest streak] = log(500) / log(1 / 0.44)
                  = 6.215 / log(2.27)
                  = 6.215 / 0.821
                  = 7.6 losses

During a 7-loss streak:

Losses = 7 × $750 = $5,250
Max drawdown as % = $5,250 / $25,000 = 21%

The trader should expect a 21% drawdown before the end of the first year. With $25,000 capital, this means a drop to $19,750.

Given the trader's income needs ($3,000/month = $36,000/year), the trader is undercapitalized. The trader needs both to:

1. Increase bankroll to at least $35,000–$40,000 to tolerate the drawdown.
2. Reduce daily profit target, accepting $150/day instead of $250/day, which halves position size and halves maximum drawdown to ~10%.

Without addressing both issues, the trader faces a sequence like: 5 winning trades ($4,000 profit), then a 7-loss streak ($5,250 loss), bringing the account from $25,000 to $23,750. The trader is underwater before month 2.

Connecting to Ruin Probability

The maximum expected drawdown calculation complements the ruin probability formula. Ruin probability answers: "How likely is it that I hit zero?" Maximum expected drawdown answers: "How far down will I go before I recover?"

Both are necessary for risk management:

• High ruin probability + moderate max drawdown: The edge is weak, and the bankroll is insufficient. The trader will likely go broke.
• Low ruin probability + high max drawdown: The edge is strong, and temporary drawdowns are expected and survivable. The trader can persist through bad periods.
• Low ruin probability + low max drawdown: The edge is strong, and position sizing is conservative. This is the ideal state but often means lower profits.

A trader with a 54% win rate, targeting a 50% bankroll gain, and a 20% maximum expected drawdown faces roughly a 5% ruin probability and will experience a $20,000 drop (on a $100,000 account) at some point. Both numbers should be acceptable to the trader before executing the strategy.

Limitations and When to Use Simulation

The closed-form formulas above assume:

1. Independent trades: Outcomes are not correlated (true for some strategies, false for others).
2. Constant win probability: The p value does not change over time (risky assumption; edge often degrades).
3. Constant position size: Risk per trade does not vary (false for dynamic sizing).
4. No slippage or commissions: Losses are as backtested (overly optimistic).

If these assumptions are violated significantly, use Monte Carlo simulation instead. Run 10,000 simulated sequences of trades with the observed win rate and payoff distribution, and measure the maximum drawdown across all simulations. The 95th percentile of drawdowns gives a more realistic worst-case estimate.

Many trading platforms (TradeStation, NinjaTrader, MetaTrader with add-ons) include built-in simulators. For custom work, Python libraries like NumPy and SciPy make simulation straightforward.

Summary

Calculating maximum expected drawdown requires three steps: estimate the expected longest losing streak using E[streak] = log(N) / log(1/(1-p)); determine average loss per trade from position size or historical data; and multiply to get dollar and percentage drawdowns. Compare the result to a risk target (typically 10–15% for professional traders). If drawdown exceeds the target, reduce position size, increase bankroll, or improve the trading edge. This calculation, combined with ruin probability, provides a complete picture of bankroll risk.

Next

→ Monte Carlo Simulations for Ruin Risk