A US investor has $50m in a diversified portfolio of 300 US stocks with a portfolio beta, βUS =1.2. The current USD-GBP spot exchange rate is S = 2 $

per £. The US investor also holds £40m in 35 UK stocks with a portfolio beta of βUK =1.5 . The volatility of the UK all-share index is σUK =25% p.a. while for the

USall-shareindex σUS = 30% p.a., and for the USD-Sterling exchange rate σS =40% p.a. The correlations between these returns are ρUK ,S = 0.2, ρUS ,S = 0.3and ρUS,UK=0.7.

 

(a) Show how in practice, the variance-covariance method can be used to estimate the 10-day VaR (5th percentile) for this portfolio. State any assumptions required. 

(b)  You have a portfolio of 20 written (European) calls written on stock-A, and you also hold 50 calls on stock-B. Assume all the calls have a strike price K = 100, maturity of 1-year and C0 = 5, while the initial stock prices are SA = SB = 100. Assume the mean daily return on each stock is 0% and the annual standard deviation is 20% pa for stock-A and 25% for stock-B and the correlation between the stock returns is ρ = 0.75. The risk-free rate is 5%pa.

 

(i) Carefully outline the steps you would take to calculate the 5-day VaR (at the 1st percentile) of this portfolio using Monte-Carlo Simulation.

(ii) Why might you get different VaR forecasts from MCS and historical simulation?

Answer rating: 100% (QA)

To estimate the 10day VaR for the portfolio we can use the variancecovariance method which assumes that the distribution of portfolio returns is approximately normal The formula for the 10day VaR is V... View the full answer