Tim has $10,000 and is considering investing in two stocks - HACC and Vincent. The followings are the returns of these stocks under different states of the affair:

State of Affair	Probability	HACC	Vincent
Pandemic	0.2	2%	16%
No Pandemic (Normal)	0.3	3%	10%
No Pandemic (Boom)	0.5	14%	5%

a) Calculate the expected rate of return, variance and standard deviation of HACC & Vincent. (5marks)

b) Suppose Sam forms a portfolio with the stocks of HACC and Vincent. If he wants the portfolio to have 8.6% expected return, how much should he invest in HACC? Calculate the variance and standard deviation of this portfolio given the covariance between HACC and Vincent is -0.0022 (or -0.22%). (6 marks)

c) Explain why the risk of Sams portfolio is lower than the weighted average risk of HACC and Vincent. (5 marks)

d) Suppose the risk-free rate is 3%, the market risk premium is 6% and the betas for HACC and Vincent are 0.7 and 1.3 respectively. Using the CAPM model, estimate the required rates of return of HACC & Vincent. (8 marks)

e) Should Sam buy HACC or Vincent? Justify your answer by checking whether the two stocks are overpriced or underpriced. (4 marks)

f) Vincent is having higher beta while HACC is having a larger standard deviation. Explain why the results of beta and standard deviation can be different even though both of them are measuring risk. (4 marks)