1. Values for the NASDAQ composite index during the 1500 days preceding March 10, 2006 and December 15, 2008 have been provided to you (Sheet 1). Calculate the 1-day 99% VaR on March 10, 2006 and December 15, 2008, for a $10 million portfolio invested in the NASDAQ composite index using the methods indicated below.
a) (10) The basic historical simulation approach,
b) (10) The exponential weighting scheme with λ = 0.94,
c) (10) Extreme value theory with u = 0.03,
2. Using the data describing a universe of risky assets (found in the attached spreadsheet - Sheet 2), and where there is a risk-free rate of 4.5%, find the optimal (tangent) PF of risky assets in three cases. Assume the variance of the market portfolio is 10.
a) (10) Where no short sales are allowed.
b) (10) Where short sales in the sense of Lintner are allowed.
c) (5) For the PF in a), where the investor wishes only 80% of the systematic risk of the optimal, risky PF, how much of the investors capital should be invested in the risk-free rate?