Optimal Investment Strategies for Controlling Drawdowns
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What they found
The authors solved the problem of an investor who wants to maximize long-run growth subject to never letting wealth fall more than a fixed percentage below its historical peak. The solution is a rule that scales exposure in proportion to the distance between current wealth and the drawdown floor: as a drawdown deepens, the position shrinks, and as wealth makes new highs, the position grows back. It is a rigorous version of the intuition that you should trade smaller when you are losing and larger when you are winning, and it shows what long-run growth costs when a maximum drawdown constraint is imposed.
See it drawn
Original diagrams for the ideas on this page. Illustrative, not real market data.
What you can use
- Position size should shrink as you approach your maximum acceptable drawdown and grow as you recover, in proportion to the cushion you have left.
- A hard drawdown limit is compatible with growth optimization, but it costs some long-run return; the paper quantifies the trade.
- The rule is the theoretical basis for the risk-budget scaling that prop firms and funds impose.
Caveats
Continuous-time model with a single risky asset and known parameters; real-world implementation requires discrete adjustments and parameter estimates. Mathematically demanding.
Tags: risk, drawdown, position-sizing, theory
Summaries are our own reading of the paper, not the authors' words. Educational only, not advice. Discuss it in Book Club.