The following table shows the investments of SP Ltd, which are classified into three sub-categories.

Assumptions:

(a) Returns are independently and normally distributed.

(b) Each category is treated as a two-asset portfolio.

(c) Time horizon is as follows: Long-term investment: one-year Short-term investment: one-month Managed funds: six months 

Required:

1. Calculate the VaR for each category at 95% and 99% confidence levels assuming that the covariance of the returns is zero.
2. Ignore (1). The covariance of the portfolios are as follows: Short-term investments: 0.01 Long-term investments: 0.02 Managed funds: 0.03 Calculate the VaR for each category at 95% and 99% confidence levels. Compare your answers with those in (1). What conclusion can you draw? (Adjust annual returns proportionately for time horizons of less than a year, e.g., monthly return is assumed to be 1/12 of annual return.)

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Long-term investment: Quoted bonds. Quoted equities. Short-term investment: Quoted bonds.. Quoted equities.. Funds under external management: Quoted bonds.. Quoted equities. value $ 51,552 337,514 225,637 70,033 242,766 117,210 return (%) 5.5% 13.8% 2.4% 12% 4.8% 15.2% expected return 0.02 0.05 0.005 0.025 0.03 0.04