QUESTION 3 (25 marks)

(a) An investor is considering to invest in asset and , Asset return is 5%, where is a Binomial random variable with parameters = 5 and = 0.6. Asset return is 3%, where is a Poisson random variable with parameter = 3. Calculate the following:

(i) Mean. (4 marks)

(ii) Variance. (4 marks)

(iii) Semi-variance. (4 marks)

(iv) Probability of shortfall with a level of 7%. (4 marks)

(b) An investor with payoff of has the following probability density function, (): () = { 0 < 0.5 3 0.5 Where = 0.5 and the amounts are in units of $ thousands.

(i) Calculate the semi-variance of the return. (4 marks)

(ii) Given the initial investment is 0.8, calculate the () at 10% level. (5 marks)