Question 1 :

Suppose that there are 2 stocks and 5 states of the world. Each state can occur with equal probability. Given the returns in the table below :

	State1	State 2	State 3	State 4	State 5
Stock A	5	7	1	8	3
Stock B	9	6	5	4	8

a) Calculate the expected return and variance of each stock and the covariance between the returns.

b) Find the expected return and variance of a portfolio with equal proportions of both stocks. Explain the contrast between the variance of each stock and the portfolio variance

Question 2 :

a) Write two mathematical definitions of Value-at-risk and explain each of them verbally. When are these two definitions equivalent to each other?

b) When losses are normally distributed with mean and standard deviation , derive the formula of Value-at-risk which is aR() = + using the appropriate definition of Value-at-risk ( is the confidence level). (Hint: One of the definitions at section a.)

c) Prove that the Value at Risk aR() = (^2) ()^2 where () is the expected value of . (Hint: () = )