Maximum drawdown and risk tolerances

Due to the numerous studies of asymmetric portfolio returns, asymmetric risk measures have widely been used in risk management with extensive uses on the methodology of n-degree lower partial moment (LPM). Unlike the initial studies, we use the risk measure of n-degree maximum drawdown, which is a special case of n-degree LPM, to investigate the reduction impacts of n-degree maximum drawdown risk on risk tolerances generated by management styles from US equity-based mutual funds. We found that skewness does not impose any significant problems on the model of n-degree maximum drawdown. Thus, the tolerance effect of maximum drawdown risk in the n-degree M-DRM models is a decrease in fund returns. The n-degree CM-DRM optimization model decreased investors' risk more than two conventional models. Thus, the M-DRM can be accommodated with risk-averse investors' approach. The efficient set of mean-variance choices from the investment opportunity set, as described by Markowitz, shows that the n-degree CM-DRM algorithms create this set with lower risk than other algorithms. It implies that the mean-variance opportunity set generated by the n-degree CM-DRM creates lower risk for a given return than covariance and CLPM.