As described in Berkowitz and O’Brien (2002) and Berkowitz and O’Brien (2006), trading portfolios at large financial institutions exhibit two key characteristics: they are driven by a large number of financial variables, such as stock returns, credit spreads, or yield curves, and these variable have time-varying volatilities and correlations. To accurately capture risks in such portfolios, it is important for risk managers to select Value-at-Risk (VaR) methodologies that adequately handle these two characteristics. This paper presents one such VaR methodology that is based on Dynamic Factor Models (DFM, see for instance Stock and Watson (2002)).
When a trading portfolio is driven by a large number of financial variables, Historical Simulation (HS-VaR) is the standard industry practice for computing VaR measures (see, among others, Perignon and Smith (2010) and Berkowitz, Christoffersen, and Pelletier (2009)). HS-VaR treats past realizations of the financial variables as scenarios for future realizations. Although the HS-VaR is easy to compute, it is not well-suited to capture the time-varying volatilities in financial variables (Pritsker (2006)). Barone-Adesi, Giannopoulos, and Vosper (1999) and Hull and White (1998) introduced Filtered Historical Simulation (FHS-VaR) as a way of handling time varying volatility in VaR estimation.
In cases where the VaR depends on multiple financial variables, Barone-Adesi, Giannopoulos, and Vosper (1999) and Pritsker (2006) suggest filtering each variable independently. Univariate filtering imposes a high computational burden, because filtering must be done one variable at a time. In addition, FHS-VaR does not explicitly capture time-varying correlations among the financial variables, which may be important particularly during times of financial stress.
We introduce DFM-VaR as a means of capturing the time-varying volatilities and correlations of a large number of financial variables in a VaR estimation. Our main assumption is that the large panel of variables are driven by a smaller set of latent factors. By modeling financial variables through a DFM with time-varying volatilities and correlations among the latent factors, the number of volatilities and correlations to be estimated is greatly reduced, resulting in computational efficiency.
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Dynamic Factor Value-at-Risk for Large, Heteroskedastic Portfolios
