Let $4 million is invested in shares in ABC Ltd, which have an estimated return of zero and a standard deviation of 30 per cent per annum. Also assume that $7 million is invested in shares in XYZ Ltd, which have an estimated return of zero and a standard deviation of 20 per cent per annum. Returns of both shares follow a normal probability distribution and abnormally bad market conditions are expected 5 per cent of the time (assume that the correlation between the returns on the shares is 0.25)

(a)  Compute Value-at-risk (VaR) for ABC Ltd and XYZ Ltd individually.

(b)  Compute Value-at-risk (VaR) of a portfolio consisting of 60% investment in ABC Ltd and 40% investment in XYZ Ltd.

(c)  Explain the reason for the differences in results you find in (a) and (b) above.