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In this talk I will show that parameterized continuous-time Markowitzs mean--variance efficient strategies could reach any given target with arbitrarily high probabilities.This result indicates that the very popular risk measure VaR (Value at Risk) may not be a proper measure in guiding investment practice.This,in turn,motivates the introduction of certain stopped strategies where stock holdings are liquidated whenever the parameterized Markowitz strategies reach the present value of the mean target.The risk aspect of the revised Markowitz strategies are examined via expected discounted loss from the initial budget.