N1569 Workshop 6
Use the Excel Workbook for Topic 6 to answer the following questions:
1. A portfolio contains cash positions of $1m, $2m, and $3m on three stocks named A, B, and C respectively. The stocks A, B, and C have market betas of 0.6, 1, and 1.2 respectively, with respect to an index whose excess returns are i.i.d. and normally distributed with an expectation of 2.5% and volatility of 35% per annum. Calculate the 10% 5-day Equity VaR of the portfolio.
2. A UK investor buys $1 million of UK stocks in a portfolio with beta 1.2 with respect to the UK market index, and $2 million of US stocks in a portfolio with beta 0.8 with respect to the US market index.
Suppose the FTSE 100, S&P 500, and £/$ volatilities are 15%, 10%, and 35% respectively, and their correlations are:
• ρUK, US = 0.7
• ρUK, £/$ = 0.4
• ρUS, £/$ = 0.5
Calculate the VaR due to each market risk factor and then aggregate this into:
(a) the equity VaR, and
(b) the total systematic VaR.
For each VaR figure, apply the normal linear model and use a 99% confidence level (i.e., α = 1%) and a risk horizon of h = 10 days. Express all your answers in $.