b. A mean-variance investor has utility function , where is portfolio expected return, is portfolio standard deviation, and is the investors risk-aversion coefficient. If the risk-free rate of return is 2%, the average return on the market index is 8%, and the standard deviation of the market index is 30%, what risk-aversion coefficient would justify investing 100% in the market index? (9 marks)

c. Suppose the value of a portfolio over a 30-day period is log-normally distributed so that the 30-day log-return has mean 1.274% and standard deviation 8.601%.

For a standard normal random variable with zero mean and unit variance, the probability that z is less than or equal to -1.645 is approximately 5%. What is the 30-day 5% VaR of the portfolio, expressed as log-returns?

What is the 60-day 5% VaR?