3. Question 3 [50 marks] The table below reports the returns of assets A, B and C in four different states of the world, each equally likely. State of the world Return A Return B Return C Probability Boom 5% 0 5% 0.25 Growth 0 0 0 0.25 Downturn 0 5% 0 0.25 Recession 5% 5% 5% 0.25 a) Calculate the expected return and the variance for all assets and determine the expected return of any portfolio obtained by mixing any of the three assets. b) Calculate the covariance of assets A and B and the covariance of assets A and C. Within the set of portfolios composed of assets A and B only, determine the weights of the two assets for the minimum variance portfolio. c) Determine the variance of a portfolio assigning a weight of 50% to asset A and 50% to asset B. Compare this variance with that of a portfolio assigning 50% weight to asset A and 50% weight to asset C. Provide a short intuitive explanation for why diversification is helpful in one case but not in the other