Before revision:  We explicitly characterize the growth-optimal strategy and show that it enjoys the numeraire property within the class of investments satisfying the drawdown constraint , when sampled at the times of its maximum and asymptotically as the time-horizon becomes distant . Finally , it is established that the asymptotically growth-optimal strategy is obtained as limit of numeraire strategies on finite horizons.
After revision:  We explicitly characterize the growth-optimal strategy and show that it enjoys the numeraire property within the class of investments satisfying the drawdown constraint , 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.