Backtesting portfolio value‐at‐risk with estimated portfolio weights
研究了在估计投资组合权重和多元动态模型时，如何对投资组合风险价值进行有效的回溯测试，提出了量化估计风险的理论和实用方法，并通过模拟和实证验证了其有效性。
This article theoretically and empirically analyzes backtesting portfolio value‐at‐risk (VaR) with estimation risk in an intrinsically multi‐variate framework. It particularly takes into account the estimation of portfolio weights in forecasting portfolio VaR and its impact on backtesting. It shows that the estimation risk from estimating portfolio weights and that from estimating the multi‐variate dynamic model make the existing methods in a univariate framework inapplicable. It proposes a general theory to quantify estimation risk applicable to the present problem and suggests practitioners a simple but effective way to implement valid inference to overcome the effect of estimation risk in backtesting portfolio VaR. In particular, we apply our theory to the efficient mean‐variance‐skewness portfolio for a multi‐variate generalized autoregressive conditional heteroscedasticity model with multi‐variate general hyperbolic distributed innovations. Some Monte Carlo simulations and an empirical application demonstrate the merits of our method.