Reference no: EM133075969

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: 

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: ??(??) = ??)