How is maximum drawdown incorporated as a portfolio constraint?

Question

AcadiFi · Accepted Answer

Maximum drawdown (MaxDD) is path-dependent—it depends on the entire return sequence, not just terminal values or moments. This makes direct incorporation in single-period mean-variance impossible. Practical approaches:

1. CDaR (Conditional Drawdown at Risk): Chekhlov-Uryasev-Zabarankin formulation using historical scenario paths. Minimize average drawdown in the worst β% of scenarios subject to return target. Linear programming solvable with scenario-based simulation.

2. Drawdown-Constrained Kelly: reduce position sizes below optimal Kelly fraction to stay within drawdown tolerance. Approximate: if Kelly suggests 25% allocation but max tolerable drawdown is 15%, fraction Kelly (half-Kelly) reduces expected drawdown by roughly 50%.

3. Volatility Scaling: target constant volatility by dynamically adjusting exposure inversely to realized volatility. Reduces clustering of losses during high-vol regimes when drawdowns typically deepen.

4. Options Overlay: buy OTM puts or put spreads sized to cap drawdown at chosen level. Adds cost but provides contractual guarantee versus empirical estimates.

5. Risk Parity with Drawdown Cap: dynamic rebalancing that reduces exposure when drawdown approaches threshold. Similar to constant proportion portfolio insurance (CPPI).

6. Stochastic Optimization: multi-period formulation using scenario trees with drawdown penalty. Computationally intensive but optimal.

```mermaid
flowchart TB
  A[Return Paths] --> B[Compute Drawdowns]
  B --> C[CDaR Objective]
  C --> D[Scenario LP]
  D --> E[Optimal Weights]
```

Empirical observation: maximum drawdown correlates with volatility and tail risk but depends heavily on autocorrelation and regime shifts. Trend-following strategies have smoother equity curves than mean-reverting despite similar volatilities. Institutional mandates increasingly specify max drawdown limits (e.g., 20% for pension funds), pushing risk budgeting toward path-dependent metrics rather than pure volatility.

How is maximum drawdown incorporated as a portfolio constraint?

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