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Backtesting portfolio value‐at‐risk with estimated portfolio weights
Author(s) -
Du Zaichao,
Pei Pei
Publication year - 2020
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12524
Subject(s) - value at risk , portfolio , heteroscedasticity , econometrics , expected shortfall , univariate , portfolio optimization , autoregressive conditional heteroskedasticity , skewness , autoregressive model , modern portfolio theory , computer science , mathematics , statistics , economics , risk management , multivariate statistics , volatility (finance) , management , financial economics
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.