  We consider the portfolio choice problem for a long-run investor in a general
continuous semimartingale model. We suggest to use path-wise growth optimality
as the decision criterion and encode preferences through restrictions on the
class of admissible wealth processes. Specifically, the investor is only
interested in strategies which satisfy a given linear drawdown constraint. The
paper introduces the numeraire property through the notion of expected relative
return and shows that drawdown-constrained strategies with the numeraire
property exist and are unique, but may depend on the financial planning
horizon. However, when sampled at the times of its maximum and asymptotically
as the time-horizon becomes distant, the drawdown-constrained numeraire
portfolio is given explicitly through a model-independent transformation of the
unconstrained numeraire portfolio. Further, it is established that the
asymptotically growth-optimal strategy is obtained as limit of numeraire
strategies on finite horizons.
