Question 2 (a) Assume that the economy can be in three possible states (S) next year: boom, normal, or slow economic growth. An expert source has calculated the probability of each state as follows: P(boom)=0.3, P(normal)=0.5, and P(slow)=0.2. The returns for Stock A, RA, and Stock B, RB, under each of the economic states are provided in the probability model below. REQUIRED: i. ii. State Boom Probability (S) RA RB 0.3 0.20 0.30 Normal 0.5 0.12 0.10 Slow 0.2 0.05 0.00 What is the correlation between the returns of Stock A and Stock B? (10 marks) You want to create a portfolio consisting of equal weights in the shares of Stock A and shares in Stock B. What is the volatility of your portfolio? (4 marks) iii. Assume that the beta of Stock A is 0.8 and that the standard deviation of the market return is 5%. Calculate the proportion of systematic risk in the total risk (measured as the standard deviation) of Stock A. (8 marks) (b) Suppose the risk-free interest rate is 4% and the market portfolio has an expected return of 10% and a volatility of 16%. Star plc stock has a 30% volatility and a correlation with the market of 0.6. You want to create a portfolio consisting of shares in Star plc plus a risk-free asset. You would like this portfolio to have the same beta as the market. What proportion of your money should you invest in each asset? (4 marks) (c) Lancaster Foods plc has just paid a dividend of 10 per share in 2014. An analyst has estimated that the theoretical (target) price of the stock is 122.34 per share based on a forecast that the company's dividends will increase by 20% in 2015, 18% in 2016, 5% in 2017 and at an undisclosed constant rate thereafter. The analyst report does not disclose the equity discount rate used to compute the value of the stock, but this report does reveal that it is based on the CAPM using a beta of 1.8, an expected return on the market of 10% and a risk-free rate of 5%. Estimate the dividend growth rate used by the analyst for the years from 2018 onwards to obtain the theoretical (target) price of 122.34. (12 marks) (d) What are the three theoretical arguments behind the efficient markets hypothesis? Discuss the behavioural challenges to each of these arguments. (12 marks)