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Consider a portfolio equally invested in two assets: TESCO and MORRISON. Portfolio market value is 100 million. The annualized volatility for TESCO stock returns is 40%, and the annualized volatility for MORRISON stock returns is 30%. The correlation between TESCO and MORRISON stock returns is 0.8. Use this information to answer question (1.1) and question (1.2).
1.1) Calculate the VaR on each asset and the VaR on the portfolio based on the full covariance approach assuming normally distributed returns with a 95% confidence level for a 10-day holding period and 250 business days in a year.
1.2) Compute VaR of the portfolio based on the beta model with one common factor assuming normally distributed returns with a 95% confidence level for a 10-day holding period and 250 business days in a year. The only factor affecting stock returns is the market, and the daily volatility of the market (σm) is 0.03. The market exposure (β) for TESCO is 0.5, and for MORRISON is 0.2.
1.3) VaR on a portfolio can be measured by four approaches: (1) VaR (full covariance), measured by the full covariance model; VaR (Diagonal model with one common factor) (3) VaR (beta model with one common factor); (4) VaR (undiversified measured by adding up all individual VaRs. You are required to rank the VaRs computed based these four approaches and provide a theoretical discussion on the rank you provide.
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