Calculating the portfolio standard deviation

Question

Problem 1. The shares of the following three companies have been included in the portfolio:

	Required Return in Accordance with Systematic Risk	Standard Deviation of Returns	Beta
Bank Ltd.	?	20	1.2
Trade Ltd.	?	30	0.8
ALD Ltd.	?	25	?
Market Portfolio	12	16	?
Risk free	5	0	-

a) Calculate the Required Return of the Bank Ltd. and Trade Ltd. Are they adequately priced with respect to the forecasted return? If the forecasted return for Bank Ltd. is 15 % and for Trade Ltd. 9% what would be the best optimal decision of the portfolio manager, i.e. for which shares it would be appropriate to increase, reduce or retain the same weights in a portfolio?
                                   
b) ALD Ltd has jus paid out the $2.00 dividend that is expected to grow at 5 percent forever. The share price is $20.00. Calculate the beta for this company. What is required return?
                                   
c) You have decided to form a portfolio with the following weights: 50 percent Bank Ltd (B), 23 percent Trade Ltd. (T) and 27 percent ALD Ltd. (ALD). Also, Cov(R_E,R_t) = -0.03, ρ_ALD,B = -0.5 and ρ_T,ALD = 0.5 . Calculate the portfolio’s standard deviation?
                                   
d) How can you obtain 17 percent portfolio return by investing exclusively in Trade Ltd? Show calculation.
                                     
e) What is the beta for this new portfolio comprising just one share?
                                   
Problem 2. You are holding a stock that has a beta of 1.8 and is currently in equilibrium.  The required return on the stock is 15 percent, and the return on an average stock is 10 percent.  What would be the percentage change in the return on the stock, if the return on an average stock increased by 40 percent while the risk-free rate remained unchanged?

Problem 3. Discuss the recent trend of a decline in the number of companies that pay out dividends. What are the return components for a potential investor and how does this change affect return components?
                                   
Problem 4. What are the main assumptions about the prevailing investor risk perception in finance? It this pattern easily confirmed in the market? What are the reasons for this deviation (if any)?
                                   
Problem 5. Comment whether you agree with the following statement: ”Going public establishes a true market value for the firm and ensures that a liquid market will always exist for the firm’s shares.”