A US investor holds a portfolio with $10m invested in iShares Gold Trust (IAU), which is traded on the New York Stock Exchange, and $30m invested in the iShares Gilt Trak Index Fund (IE), which is traded on the London Stock Exchange. The returns on IAU have a volatility of 40%, the IE index returns have a volatility of 15% and the two returns have a correlation of 0.6. The GDP/USD exchange rate has a volatility of 10% and a correlation of -0.3 with IAU and a correlation of 0.2 with IE. Assume that the discounted expected return on every risk factor is zero.

(a) Calculate the 1% 10-day normal linear total Value-at-Risk (VaR) of the portfolio, in $.

(b) Decompose this total 1% 10 day normal linear VaR into VaR due to (i) uncertainty in the EFT returns, and (ii) the VaR due to uncertainty in the exchange rate returns.

(c) In what circumstances, would you expect the total VaR to be greater than, equal to, or less than the sum of the two risk factor VaRs? What is the case in this numerical example? Give reasons.