Drawdown Analysis and Management

Drawdown Analysis and Management

Max drawdown, recovery analysis, conditional drawdown at risk, stop-loss design, de-leveraging rules, and drawdown-based position sizing.

When to Activate

• User analyzing drawdown characteristics of a strategy or portfolio
• Designing stop-loss or de-leveraging rules
• Evaluating whether a drawdown is within expected bounds or signals strategy failure
• Position sizing based on maximum acceptable drawdown
• Comparing strategies using drawdown-adjusted performance metrics
• Setting risk limits expressed as drawdown thresholds

Core Concepts

Drawdown Definitions

Drawdown at time t

• DD(t) = (Peak(t) - Value(t)) / Peak(t)
• Peak(t) = max(Value(s) for s <= t) — running high-water mark
• Always non-negative; zero when portfolio is at a new high

Maximum Drawdown (MDD)

• MDD = max(DD(t)) over the observation period
• The single worst peak-to-trough decline
• Most commonly cited drawdown statistic
• Depends heavily on observation period length — longer periods yield larger MDD

Drawdown Duration

• Time from peak to trough (decline phase)
• Time from trough to recovery of previous peak (recovery phase)
• Total underwater period = decline + recovery
• Some drawdowns never fully recover within the observation window

Average Drawdown

• Mean of all drawdown episodes exceeding a threshold
• More stable than MDD as a risk measure
• Conditional Drawdown at Risk (CDaR): expected drawdown conditional on exceeding a quantile — analogous to ES for drawdowns

Distribution of Maximum Drawdown

For a random walk with drift mu and volatility sigma:

• Expected MDD scales with sqrt(T) and sigma
• For a GBM process, approximate: E[MDD] proportional to sigma * sqrt(T) for long periods
• Even strategies with positive expected return will experience significant drawdowns
• MDD is a single extreme statistic — high variance across realizations
• A strategy with 10% annual return and 15% vol has approximately 50% probability of a >20% drawdown over 10 years

Drawdown-Adjusted Performance Metrics

Calmar Ratio: Annual return / Max drawdown — higher is better, but MDD is a single point Sterling Ratio: Annual return / (Average of N largest drawdowns + 10%) — more robust than Calmar Burke Ratio: Annual return / sqrt(sum of squared drawdowns) — penalizes multiple deep drawdowns Ulcer Index: sqrt(mean of squared drawdowns) — continuous measure of drawdown pain Pain Index: mean of all drawdowns — captures both depth and duration of underwater periods

Methodology

Stop-Loss Design

Fixed Percentage Stop-Loss

• Exit when position declines X% from entry (e.g., 2% per trade, 10% portfolio level)
• Simple and transparent
• Risk: whipsaw — stopped out just before recovery
• Size the stop relative to the strategy's expected volatility and holding period

Trailing Stop-Loss

• Stop moves up with price but never down
• Trail by fixed percentage (e.g., 10% from peak) or ATR multiple (e.g., 3x ATR)
• Lets winners run while limiting drawdown
• ATR-based stops adapt to current volatility regime

Volatility-Adjusted Stop

• Stop distance = k * current_volatility (e.g., k * 20-day realized vol)
• Wider stops in high-vol environments, tighter in low-vol
• Reduces whipsaw in volatile markets while maintaining discipline in calm markets

Time-Based Stop

• Exit if position has not reached profit target within N days
• Addresses opportunity cost of capital in stagnant positions
• Combine with price-based stop for multi-dimensional exit logic

De-Leveraging Rules

Systematic rules for reducing exposure during drawdowns:

Linear De-Leveraging

• Reduce exposure proportionally to drawdown depth
• Target leverage = base_leverage * (1 - DD / max_allowed_DD)
• At max allowed drawdown, leverage = 0 (fully de-risked)
• Example: base leverage 1.5x, max DD 20% — at 10% DD, leverage = 1.5 * (1 - 0.5) = 0.75x

Stepped De-Leveraging

• Define discrete threshold levels:
  • DD < 5%: maintain full exposure
  • 5% < DD < 10%: reduce to 75% exposure
  • 10% < DD < 15%: reduce to 50% exposure
  • DD > 15%: reduce to 25% or exit entirely
• Less sensitive to noise than continuous de-leveraging
• Clear and easy to implement and communicate

Volatility-Conditional De-Leveraging

• Target constant volatility: leverage = target_vol / current_vol
• When realized vol spikes (usually correlated with drawdowns), leverage automatically decreases
• Vol targeting naturally reduces exposure in crisis and increases in calm
• Documented improvement: vol-managed portfolios have lower MDD and higher Sharpe

Drawdown-Based Position Sizing

Sizing from Maximum Acceptable Drawdown

• Given max acceptable DD, strategy vol, and leverage:
• Position size = max_DD / (expected_MDD_per_unit_vol * strategy_vol)
• Example: max acceptable DD = 15%, strategy vol = 20%, expected MDD ratio = 2.5
  • Position size = 15% / (2.5 * 20%) = 30% of capital

Kelly-Drawdown Tradeoff

• Full Kelly criterion maximizes growth but has severe drawdowns (expected MDD approximately 50-60%)
• Fractional Kelly (typically 0.25-0.5 of full Kelly) dramatically reduces expected MDD
• f = 0.5 Kelly approximately halves expected MDD while reducing growth rate by only 25%
• Optimal fraction depends on the investor's drawdown tolerance

Recovery Analysis

• Recovery time = f(drawdown depth, return rate, volatility)
• For a strategy with annual return r and drawdown D: approximate recovery time = -ln(1-D) / r
• A 50% drawdown requires 100% gain to recover — arithmetic of losses is brutal
• With 10% annual return, recovery from 30% DD takes approximately 3.6 years; from 50% DD, approximately 7 years
• Compounding during recovery helps but does not eliminate the asymmetry

Examples

Maximum Drawdown Analysis

Strategy equity curve peak: $1,000,000 (March 2020)
Strategy equity curve trough: $720,000 (March 23, 2020)
Recovery to new peak: $1,050,000 (August 2020)

Maximum drawdown: (1,000,000 - 720,000) / 1,000,000 = 28%
Decline duration: 15 trading days
Recovery duration: 105 trading days
Total underwater period: 120 trading days

Calmar ratio (annualized return 15%): 15% / 28% = 0.54

Vol-Targeting De-Leverage

Strategy target vol: 10% annualized
Current realized vol (20-day): 25% annualized (crisis)

Leverage adjustment: 10% / 25% = 0.40
Original allocation: $5M -> Reduced to: $5M * 0.40 = $2M

When vol normalizes to 12%:
Leverage adjustment: 10% / 12% = 0.83
Allocation: $5M * 0.83 = $4.15M (gradually re-risking)

Result: portfolio volatility stays approximately constant at 10% target.
Historical backtest shows MDD reduced from 35% to 18% with vol targeting.

Conditional Drawdown at Risk

Drawdown distribution from 10,000 Monte Carlo paths (252-day horizon):
  Median MDD: 8.5%
  75th percentile MDD: 12.3%
  95th percentile MDD: 19.8%
  99th percentile MDD: 27.1%
  CDaR(95%): average of worst 5% of MDD outcomes = 23.4%

Use CDaR(95%) = 23.4% as the risk budget.
If maximum acceptable loss is $2M on a $10M portfolio (20%):
  Position is slightly oversized — reduce to $10M * (20/23.4) = $8.55M.

Stepped De-Leveraging in Practice

Portfolio: $50M, base leverage 2x, gross exposure $100M.

Drawdown trajectory and responses:
  Day 1-20:  DD = 3%    -> Full exposure ($100M gross)
  Day 21:    DD = 6%    -> Reduce to 75% ($75M gross), sell $25M
  Day 35:    DD = 11%   -> Reduce to 50% ($50M gross), sell $25M
  Day 42:    DD = 8%    -> Hold at 50% (do not re-lever until new high or DD < 5%)
  Day 60:    DD = 2%    -> Restore to 75% ($75M gross)
  Day 80:    DD = 0%    -> Restore to 100% ($100M gross)

Rules: only re-lever when drawdown decreases below the previous threshold.
Prevents whipsaw from rapid threshold crossing.

Quality Gate

• Maximum drawdown must be computed on daily (not monthly) frequency to capture intra-month extremes
• Drawdown analysis must cover at least 3 full market cycles or 10+ years of data
• Stop-loss levels must be backtested for whipsaw frequency and net impact on returns
• De-leveraging rules must include re-leveraging logic to avoid permanent risk reduction
• Vol-targeting must use appropriate volatility estimator (realized vol, EWMA, or GARCH) — not just sample vol
• Drawdown metrics must be reported alongside return metrics in all strategy evaluations
• Monte Carlo simulation of drawdown distribution should complement historical analysis
• Recovery time analysis must accompany any drawdown report
• Position sizing must be consistent with stated maximum drawdown tolerance
• Drawdown triggers must be clearly documented and communicated to all stakeholders before they occur