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Portfolio Optimization with Drawdown Constraints

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;

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Portfolio Optimization with Drawdown Constraints

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  1. Portfolio Optimization with Drawdown Constraints January 29, 2000 Alexei Chekhlov, TrendLogic Associates, Inc. Stanislav Uryasev & Mikhail Zabarankin, University of Florida, ISE

  2. 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.

  3. - 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):

  4. Limiting the risk: • MaxDD: • AvDD: • DVaR: • Combination:

  5. Continuous Optimization Problems: MaxDD: AvDD: CDaR: “technological” constraints:

  6. Discrete Optimization Problems: MaxDD: AvDD: CDaR: , (g)+=max{0,g}.

  7. Reward/Risk Ratios: MaxDD

  8. Reward/Risk Ratios: AvDD

  9. Table 1: MaxDD Solution

  10. Table 2: AvDD Solution

  11. Figure 1: MaxDD Efficient Frontier Figure 2: AvDD Efficient Frontier

  12. Figure 3: Efficient Frontier as a function of MaxDD Figure 4: Efficient Frontier as a function of AvDD

  13. Figure 5: MaxDDRatio as a function of MaxDD Figure 6: AvDDRatio as a function of AvDD

  14. Underwater Curves: MaxDD and AvDD:

  15. 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.

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