In this paper,we formulate pessimistic portfolio (Bassett et al.,2004) from Choquet utility maximization and coherent risk measure.It can be shown that the scheme is equivalent to optimization using conditional value-at-risk (Rockafellar and Uraysev,2000) both in continuous and discrete cases.By decomposing quantile loss function,a new parametric approach is proposed aiming at minimizing weighted downside risk exposure on a set of factors given fixed target return.We then conduct an empirical study on comparing portfolio efficiency among mean-variance,pessimistic portfolio and its parameterized version in global equity indices investment.Pessimistic portfolio offers the lowest return in frictionless environment,it also suffers from overconcentration and non-stationarity of tail risk.Deterioration of out-of-sample robustness can be possibly mitigated by stationary bootstrap method but averaged performance barely beats benchmark.Parametric pessimistic portfolio effectively reduces tail risk exposure and data-snooping bias in training samples and thus delivers a better risk-adjusted return.