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The third statement is false. The parametric approach typically assumes asset returns are normally or lognormally distributed with time-varying volatility. The RiskMetrics^TM approach is actually a special case of the GARCH model. Both the exponential and historical standard deviation approaches create a variance-covariance matrix that is estimated under the assumption that all asset returns are normally distributed. Exponential smoothing methods and the historical standard deviation methods both apply a set of weights to recent past squared returns. The difference is that in the historical standard deviation method all weights are equal whereas more recent returns are weighted more heavily in exponential methods.