Because of the outbreak of COVID-19, you expect that the likelihood of economic recession for 2021 would be as high as 60%. Based on this basic forecast, you further estimate the returns for three stocks when the economy state is either boom or recession. Your estimation is as follow:

Economic state Probability of State of Economy Returns if state occurs

Stock A Stock B Stock C

Boom 0.40 30% 20% 8%

Recession 0.60 -10% 0% 2%

The market risk premium is 4.5%, and the risk-free rate is 1.5%.

a. Which stock has the highest systematical risk, please show the calculation? (5 marks)

b. Which stock has the highest total risk, please show the calculation? (5 marks)

c. Based on your answers in (a) and (b), which stock do you think should have the highest expected return? Why? (2 marks)

d. If your portfolio is invested 30% in A, 30% in B, and 40% in C, what is the portfolio expected return? The standard deviation? (5 marks)

e. Given the portfolio information in (d), what is the portfolios market beta?