value at risk probability density function

For the normal method, the first quartile is 1, meaning that 25% of the failures occur on consecutive days. This result suggests that half of the time, two consecutive failures occur within 5 to 7 days, much more frequently than the 20 expected days. However, the median of the time between failures for the year 2002 ranges between 5 and 7.5 for the three methods. PortfolioID VaRID VaRLevel TBFI LRatioTBFI PValueTBFI Observations Failures TBFMin TBFQ1 TBFQ2 TBFQ3 TBFMax TestLevel To better understand how these results change given market conditions, look at the years 20 for the 95% VaR confidence level. This result suggests that all methods have issues with the independence assumption. Notice that all tests fail the time between failures independence test ( tbfi), which takes into account the times between all failures. Real vaued probability distributions must have monotonically non-decreasing cumulative. Regarding independence, most tests pass the conditional coverage independence test ( cci), which tests for independence on consecutive days. Not all choices of correspond to a valid probability distribution. However, the frequency results at the 99% level are generally rejections. The results are similar to the previous results, and at the 95% level, the frequency results are generally acceptable. 'S&P' 'EWMA99' 0.99 red reject reject accept reject accept reject reject 'S&P' 'Historical99' 0.99 yellow reject reject accept reject accept reject reject 'S&P' 'EWMA95' 0.95 green accept accept accept accept accept reject reject 'S&P' 'Historical95' 0.95 yellow accept accept accept accept accept reject reject Using a varbacktest object, run the same tests on the portfolio for the three approaches at both VaR confidence levels. For more information on the tests methodologies and the interpretation of results, see varbacktest and the individual tests. Also, one failure may make it more likely that other failures will follow in subsequent days. This result suggests that the VaR violations are not independent, and there are probably periods with multiple failures in a short span. Both confidence levels got rejected in the conditional coverage independence, and time between failures independence ( cci and tbfi columns). The 99% VaR does not pass these same tests, as indicated by the yellow and reject results. The 95% VaR passes the frequency tests, such as traffic light, binomial and proportion of failures tests ( tl, bin, and pof columns). 'S&P' 'Normal99' 0.99 yellow reject reject accept reject accept reject reject In the parametric method, the asset returns are assumed to follow a known probability distribution whilst the Monte Carlo method assumes that asset returns are. 'S&P' 'Normal95' 0.95 green accept accept accept accept reject reject reject PortfolioID VaRID VaRLevel TL Bin POF TUFF CC CCI TBF TBFI

Value at risk probability density function