Consider a portfolio equally invested in two assets: APPLE and MICROSOFT. Portfolio market value is 100 million. The daily volatility for APPLE stock returns is 0.04, and the daily volatility for MICROSOFT stock returns is 0.05. The correlation between APPLE and MICROSOFT stock returns is 0.7.
1. Compute VaR(1-day, 95%) of the portfolio by computing individual VaR on each asset, and then sum up the individual VaRs.
2. Compute VaR(1-day, 95%) of the portfolio based on the full covariance approach.
3. Compute VaR(1-day, 95%) of the portfolio based on the one factor model approach. The only factor affecting stock returns is the market, and the daily volatility of the market (?m) is 0.03. The market exposure (?) for APPLE is 0.5, and for MICROSOFT is 0.2.
4. VaR on a portfolio can be measured by three approaches: (1) VaR (one factor), measured by the one factor model; (2) VaR (full covariance), measured by the full covariance model; (3) VaR (summation of individual VaRs), measured by adding up all individual VaRs. Discuss theoretically the order of the three VaRs.