Portfolio Optimization with Drawdown Constraints

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# Portfolio Optimization with Drawdown Constraints - PowerPoint PPT Presentation

Portfolio Optimization with Drawdown Constraints. January 29, 2000. Alexei Chekhlov, TrendLogic Associates, Inc. Stanislav Uryasev &amp; Mikhail Zabarankin, University of Florida, ISE. Introduction. Losing client’s accounts is equivalent to death of business;

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### Portfolio Optimization with Drawdown Constraints

January 29, 2000

Alexei Chekhlov, TrendLogic Associates, Inc.

Stanislav Uryasev & Mikhail Zabarankin, University of Florida, ISE

Introduction
• Losing client’s accounts is equivalent to death of business;
• Highly unlikely to hold an account which was in a drawdown for 2 years;
• Highly unlikely to be permitted to have a 50% drawdown;
• Shutdown condition: 20% drawdown;
• Warning condition: 15% drawdown;
• Longest time to get out of a drawdown - 1 year.

- uncompounded portfolio value at time t;

- set of unknown weights;

- drawdown function.

• Three Measures of Risk:
• Maximum drawdown (MaxDD):
• Average drawdown (AvDD):
• Conditional drawdown-at-risk (CDaR):
Limiting the risk:
• MaxDD:
• AvDD:
• DVaR:
• Combination:
Continuous Optimization Problems:

MaxDD:

AvDD:

CDaR:

“technological” constraints:

Discrete Optimization Problems:

MaxDD:

AvDD:

CDaR:

, (g)+=max{0,g}.

Figure 1: MaxDD Efficient Frontier

Figure 2: AvDD Efficient Frontier

Figure 3: Efficient Frontier as a function of MaxDD

Figure 4: Efficient Frontier as a function of AvDD

Figure 5: MaxDDRatio as a function of MaxDD

Figure 6: AvDDRatio as a function of AvDD

Conclusions
• Introduced a one-parameter family of risk measures based on a notion of a drawdown (underwater) curve;
• Mapped Portfolio Allocation problem into linear programming problems to be solved using efficient computer solvers;
• Solved a particular real-life example on the basis of historical equity curves;
• CDaR-generated solutions are more stable for practical weights’ allocation.