2. An insurance company is backtesting its VaR methodology using data from March 6, 2017 to March 31, 2017 (i.e., a total of 20 daily observations). Table 1 shows the daily equity returns of the insurance company and the estimated daily 5% VaRs over this period. (a) What is the hit sequence for this 20 observations? () (b) Calculate the likelihood ratio statistic for the unconditional coverage test. Would you reject the null hypothesis with 95% confidence? (Hint: The 95% quantile of ^2 1 is 3.84) () (c) Calculate the likelihood ratio statistic for the independence test. Would you reject the null hypothesis with 95% confidence? (Hint: The 95% quantile of ^2 1 is 3.84) ()

Date March 6 March 7 March 8 March 9 March 10 March 13 March 14 March 15 March 16 March 17 Table 1 : Daily Returns and Vars Return VaR Date Return VaR 0.00076 0.014 March 20 0.00709 0.020 0.01110 0.013 March 21 -0.02291 0.020 0.00084 0.016 March 22 -0.02365 0.019 -0.01626 0.015 March 23 0.00662 0.029 0.00453 0.022 March 24 0.01294 0.028 0.00804 0.022 March 27 -0.01678 0.029 -0.00101 0.022 March 28 0.01304 0.032 0.00231 0.021 March 29 -0.02412 0.032 0.01035 0.031 March 30 -0.03408 0.030 -0.02001 0.014 March 31 0.0008 0.042 Date March 6 March 7 March 8 March 9 March 10 March 13 March 14 March 15 March 16 March 17 Table 1 : Daily Returns and Vars Return VaR Date Return VaR 0.00076 0.014 March 20 0.00709 0.020 0.01110 0.013 March 21 -0.02291 0.020 0.00084 0.016 March 22 -0.02365 0.019 -0.01626 0.015 March 23 0.00662 0.029 0.00453 0.022 March 24 0.01294 0.028 0.00804 0.022 March 27 -0.01678 0.029 -0.00101 0.022 March 28 0.01304 0.032 0.00231 0.021 March 29 -0.02412 0.032 0.01035 0.031 March 30 -0.03408 0.030 -0.02001 0.014 March 31 0.0008 0.042