Financial Risk Management

a) Using R, download data for the S&P 500, IBM and Microsoft from January 1, 2000 to January 1, 2010.

b) Compute all summary statistics for the returns to the S&P 500, IBM and Microsoft:

mean return
variance
standard deviation
skewness
kurtosis

c) Generate a covariance matrix and a correlation matrix for these assets.

d) Use the Jarque-Bera test to determine if the returns to these assets are normally distributed.

e) Generate a QQ-plot for each asset.

f) Compute the volatility of the S&P 500, IBM and Microsoft using: simple moving averages with a 30-day window historical simulation with a 100-day window exponentially-weighted moving averages using lambda = 0.94 GARCH(1,1)

g) Compute VaR at the 95% level of confidence for a $1,000,000 portfolio consisting of 30% S&P 500, 50% IBM and 20% Microsoft using each of the four volatility models.