The file d-hwp3dx8099.txt contains dates and the daily simple returns of Hewlett-Packard, the CRSP value-weighted index, equalweighted index, and the S&P 500 index from 1980 to 1999. The returns include dividend distributions. Transform the simple returns to log returns. Assume that the tail probability of interest is 0.01.

Calculate value at risk for the following financial positions for the first trading day of year 2000.

(a) Long on Hewlett-Packard stock of $1 million dollars and the S&P 500 index of $1 million using RiskMetrics. The α coefficient of the IGARCH(1,1) model for each series should be estimated.

(b) The same position as part (a), but using a univariate ARMA–
GARCH model for each return series.

(c) A long position on Hewlett-Packard stock of $1 million using a two-dimensional nonhomogeneous Poisson model with the following explanatory variables: (1) an annual time trend, (2) a fitted volatility based on a Gaussian GARCH model for Hewlett-Packard stock, (3)
a fitted volatility based on a Gaussian GARCH model for the S&P 500 index returns, and (4) a fitted volatility based on a Gaussian GARCH model for the value-weighted index return. Perform a diagnostic check for the fitted models. Are the market volatility as measured by the S&P 500 index and value-weighted index returns helpful in determining the tail behavior of stock returns of HewlettPackard? You may choose several thresholds.