4. (a) The following are monthly percentage price changes for two market indexes Month DJIA S&P 500 0.03 0.02 2 3 4 5 6 0.07 0.06 -0.02 -0.01 0.01 0.03 0.05 0.04 -0.06 -0.04 (i) Compute the monthly standard deviation for each index. (ii) Compute the covariance between the rates of return for the DJIA and the S&P 500. (iii) What is the correlation coefficient? What does it mean? (4+4+4=12 marks) (b) Consider the following data for two risk factors (1 and 2) and two securities (J and L): Ins=0.05, , =0.02, 1: =0.04, 6x=0.80, b)=1.40, 6-=1.60, 512 = 2.25 (i) Use APT to compute the expected returns for both securities. Fully show your working out. (ii) Suppose that Security J is currently priced at $22.50 while the price of Security L is $15.00. Further, it is expected both securities will pay a dividend of $0.75 during the coming year. What is the expected price of each security one year from now? (4+4=8 marks) (c) Fully showing your working out, derive the portfolio standard deviation for a two-security portfolio where one security is cash