Question 3 (25 marks) Johnny has $400,000 to invest and is considering the merits of two stocks: HCBC & SBB. The two stocks have the following possible expected future returns: State of Affair Boom Normal Recession Probability 0.4 0.4 HCBC 40% 15% -10% SBB -15% 10% 25% 0.2 Johnny plans to invest 60% of his $400,000 in HCBC and the remainder in SBB. (a) Calculate the expected rate of return, variance and standard deviation of HCBC & SBB. (12 marks) (b) Assume that the covariance between HCBC and SBB is -0.012 (or - 120%). Calculate the expected rate of return, variance and standard deviation of Johnny's portfolio. (6 marks) (C) Suppose the risk-free rate is 6%, the market risk premium is 12%. Given the beta for HCBC is 1 and SBB is 0.5. Using the CAPM model, estimate the required rates of return of HCBC and SBB (2 marks) (d) Given the results above, determine whether HCBC and SBB are mis-priced (i.e., over, fairly or under-priced). Which stock should Johnny invest? Explain