A Note on Optimal Estimation From a Risk-Management Perspective Under Possibly Misspecified Tail Behavior
研究在资产收益率真实分布尾部厚度与管理者所用分布不一致时，如何选择估计方法以最小化VaR的估计偏差，发现高斯最大拟似然估计（最小二乘型）优于最大似然估计和稳健估计。
Many financial time series show leptokurtic behavior—that is, fat tails. Such tail behavior is important for risk management. In this article I focus on the calculation of Value-at-Risk (VaR) as a downside-risk measure for optimal asset portfolios. Using a framework centered on the Student-t distribution, I explicitly allow for a discrepancy between the fat-tailedness of the true distribution of asset returns and that of the distribution used by the investment manager. As a result, numbers for the overestimation or underestimation of the true VaR of a given portfolio can be computed. These numbers are used to rank several well-known estimation methods for determining the unknown parameters of the distribution of asset returns. Minimizing the absolute (percentage) mismatch between the nominal and actual or true VaR leads to the choice of a Gaussian maximum quasilikelihood estimator—that is, a least squares type of estimator. The maximum likelihood estimator has less satisfactory behavior. Outlier-robust estimators perform even worse if the required confidence level for the VaR is high. An explanation for these results is provided.