Problem 3 (34 marks): As part of an investment team at a large Canadian investment company, you are analyzing the returns of two stocks: TD bank and Sobey. You consider five possible scenarios for the stocks' returns depending on how good the economy will be over the coming year. Assume TD bank has a 0.9 correlation with the market portfolio and Sobey has a -0.5 correlation with the market portfolio. The market portfolio has a standard deviation of 10%. The risk-free rate is equal to 4%. Economy scenario Probability Return on TD bank stock Return on Sobey stock Boom 30% 8% Above average 20% 8% Average 0.2 10% 10% Below average 0.2 0% 12% Recession -20% 15% a) Calculate the expected returns for each stock. (4 marks) b) Calculate the standard deviation for each stock. (8 marks) c) Calculate the correlation between the two stocks if the covariance of the returns = -35 (2 marks) d) Assume you have a portfolio with $5,000 invested in TD bank and $15,000 invested in Sobey. Calculate the expected return and standard deviation of returns for this portfolio. How well does diversification work in this case? Comment on why or why not diversification works. (10 marks) e) Calculate the beta of each stock? (4 marks) f) What is the beta of your portfolio in (d)? (2 marks) g) If the return on the market portfolio = 9%, is TD bank stock is correctly priced today? Show your work. (4 marks)