In R, compute the VaR and Expected-Shortfall (ES) for (a). the normal distribution with

mean = 0 and standard deviation = 0.3 10000/

250 and (b) the t4 distribution with the same

values of and . (Note that if we assume that the horizon is t = 1 day, then a value of = 0.3/

250

corresponds to an annual volatility of approx 30%. The value of 250 corresponds to the fact that there

are approx. 250 trading days in a calendar year. The multiplier of 10000 is there simply to make the

numbers more readable.) You should compute the VaR and ES for the following values of :

0.90, 0.95, 0.975, 0.99, 0.995, 0.999, 0.9999, 0.99999, 0.999999

What do you notice? Now compute the ES to VaR ratio for each value of - what do these ratios

imply?