(a) Explain the meaning of a model and describe the basic features of a financial model. [4 marks]
(b) Outline the basic assumptions that underlie Markowitz portfolio theory. [5 marks]
(c) The variance of a portfolio containing 2 securities ‘A’ and ‘B’ is given by
s_p^2=W_A^2 s_A^2+W_(B )^2 s_B^2 +2W_A W_B ?_((A,B) ) s_A s_B
Where W_A= Proportion of security A in the portfolio
W_B = Proportion of security B in the portfolio.
Show that when (ds^2 p)/(dW_A )=0 , W_A= (s_B^2-?_((A,B) ) s_A s_B)/(s_A^2+s_B^2-?2??_(A,B) s_A s_B ) [6 marks]
(c) You are evaluating an investment in two companies whose past ten years of returns are shown below:
Company Percent return during the year
1 2 3 4 5 6 7 8 9 10
ABC 37 24 -7 6 18 32 -5 21 18 6
XYZ 32 29 -12 1 15 30 0 18 27 10
(i) Calculate the standard deviation of each company’s returns. [6 marks]
(ii) If you placed 50% of your investment in each, what would be the standard deviation of your portfolio? [3 marks]
(iii) Calculate the correlation coefficient of the companies returns. [4 marks]
(iv) What percentage investment in each would result in the lowest risk? [2 marks]
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