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We consider the portfolio choice problem for a long-run investor in a generalcontinuous semimartingale model. We suggest to use path-wise growth optimalityas the decision criterion and encode preferences through restrictions on theclass of admissible wealth processes. Specifically, the investor is onlyinterested in strategies which satisfy a given linear drawdown constraint. Thepaper introduces the numeraire property through the notion of expected relativereturn and shows that drawdown-constrained strategies with the numeraireproperty exist and are unique, but may depend on the financial planninghorizon. However, when sampled at the times of its maximum and asymptoticallyas the time-horizon becomes distant, the drawdown-constrained numeraireportfolio is given explicitly through a model-independent transformation of theunconstrained numeraire portfolio. Further, it is established that theasymptotically growth-optimal strategy is obtained as limit of numerairestrategies on finite horizons.

The numeraire property and long-term growth optimality for drawdown-constrained investments