Drawdowns of a Sharpe-0.8 strategy

A strategy runs at 12% volatility with a Sharpe ratio of 0.8. (a) Compute the drift $m$ of log-wealth and the long-run probability of being more than 15% below the previous peak. (b) Evaluate the asymptotic expected maximum drawdown over 5 years from (3.21). Compute $m^2T/(2s^2)$ and say whether the asymptotic regime applies. (c) A Monte Carlo of 20,000 five-year paths gives a mean maximum log-drawdown of 0.202 and $P(\text{MDD} > 15\%) = 0.65$. Reconcile with (a) and (b).