You have an equally weighted portfolio of two assets with a total value of 100,000. You estimate the expected returns of the two assets as 0.1 and 0.12, respectively, and your latest estimate of the annual volatility was 0.2 and 0.3 with a correlation of 0.8. The latest daily return observations are -1.3% and 1.4%. You are using an exponentially weighted moving average model for the covariance matrix and have estimated a persistence of 0.6.

a. You want the 10-day 99% Value-at-Risk not to exceed 47,000. How would you change your portfolio to achieve this aim? Explain carefully the rationale for your result.

b. How would you approach the above problem if you had a portfolio of 3 or more assets and wanted to reduce the VaR by a given amount? Carefully discuss the approach you would be taking.