(Covariance with the market portfolio, finding beta) Assume that there are only three stocks in the market and that the optimal investment proportions in each stock A, B, and C is 1/3. Also assume that the variance of stock A is 0.1, the variance of stock B is 0.08, and the variance of stock C is 0.2. The covariance between stocks A and B is 0.08, the covariance between stocks B and C is –0.10, and the covariance between stocks A and C is 0.04.

a. Calculate the covariance between each stock and the market portfolio.

b. Calculate the systematic risk (beta) for each of the three stocks.