# performance of historical VaR parameters

An historical VaR measure is parameterized in terms of the confidence level and also number of periods. Specifically, the $\alpha$% T-period VaR is defined as the portfolio loss x in market value over time T that is not expected to be exceeded with probability (1 - $\alpha$).

I am looking for empirical backtesting research on the choice of T-period and $\alpha$% for producing stock portfolios. Usually this backtest research involves looking at the # of "exceptions" (violations of the predicted risk), convergence tests, the Kupiec, and Kupier test, or involves looking at the realized risk of a portfolio constructed to minimize the VaR measure.

An illustrative example of this research is here -- however, this study involves the Greek equity market and the sample consists of only 5 equities and my focus market is U.S. equity portfolios consisting of say 25+ securities for 3-month to 1-year holding periods. Another VaR study covering the Forex market is here.

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VaR is easily computed using R packages...you could probably cook up your own backtest in about 40 lines of code. –  Brian B Dec 8 '11 at 16:05
I have a broader experiment where I am looking for the most suitable general risk-measure for constructing optimal portfolios (risk-parity, Var@95, Var@99, CVAR, and 4 other measures). My optimization is non-convex (I'm including a non-linear transaction cost objective in my utility function) and over multiple periods so the the timing is computationally expensive. So I'd like to get one candidate for each class of risk measure based on some prior research rather than optimize over possible candidates which would take too much time and bias classes that had more members. –  Quant Guy Dec 8 '11 at 16:25
I'm not 100% sure but i think arma-garach is non-convex as well and arma-garach is used often because it preforms better in back testing –  pyCthon Jul 2 '12 at 2:28