(a) Find the value at risk (VaR) for an investment of $100,000 at 2%. (That is, find out how low the value of this investment could be if we rule out the worst 2% of outcomes.) The investment is expected to grow during the year by 8% with SD 20%. Assume a normal model for the change in value.
(b) To reduce the VaR to $20,000, how much more expected growth would be necessary? Assume that the SD of the growth remains 20%.
(c) If the VaR of an investment is $20,000 for a one-year holding period, does that mean that the VaR for a two-year holding period is $40,000?