1. This exercise uses daily BMW returns in the bmwRet data set on the book’s website. For this exercise, assume that the returns are i.i.d., even though there may be some autocorrelation and volatility clustering is likely. Suppose a portfolio holds $1,000 in BMW stock (and nothing else).

(a) Compute nonparametric estimates of VaR(0.01, 24 h) and ES(0.01, 24 h).

(b) Compute parametric estimates of VaR(0.01, 24 h) and ES(0.01, 24 h)

assuming that the returns are normally distributed.

(c) Compute parametric estimates of VaR(0.01, 24 h) and ES(0.01, 24 h)

assuming that the returns are t-distributed.

(d) Compare the estimates in (a), (b), and (c). Which do you feel are most realistic?