Finance II Test Solutions for M.Sc. Finance and International Accounting students, Study Guides, Projects, Research of Finance

Download Finance II Test Solutions for M.Sc. Finance and International Accounting students and more Study Guides, Projects, Research Finance in PDF only on Docsity! Department of Accounting and Finance M.Sc. Finance And M.Sc. International Accounting and Financial Studies Finance II Class Test A and B SOLUTIONS Tuesday 6th December 2005 11.00am – 12.00pm (1 hour) Instructions for Candidates Answer ALL Questions (in the spaces provided) [Failure to comply will result in papers not being marked] Calculators must not be used to store text and/or formulae nor be capable of communication. Invigilators may require calculators to be reset. All answers are to be written in the spaces provided in ink. Please write clearly as illegible writing cannot be marked. If more space is required the answer can be continued on the back of the page where the question appears. Failure to follow these requirements will lead to a deduction of marks. To Be Completed (please write clearly) Family Name: Other Name: Course (please indicate by ticking appropriate box) M.Sc. Finance M.Sc. IAFS For Examiners Use Only Comments TOTAL MARKS AWARDED To identify the efficient portfolio recognise that a risk of 12 per cent lies halfway between portfolio P (the zero risk portfolio) and Y. Therefore the portfolio will be made up of 50 per cent of P and 50 per cent of Y, but P is made up of 60 per cent of X and 40 per cent of Y. This implies that the efficient portfolio will be structured as follows: = 50 [0.60 X + 0.40 Y] + 0.50 Y = 0.30 X + 0.20 Y + 0.50 Y = 0.30 X and 0.70 Y Q2. The average variance of shares is 900. a) Determine the standard deviation of an equally weighted portfolio of 90 securities if the returns across securities are independent. VAR(Rp) = 1/90 x 900 = 10 SD(Rp) = √10 = 3.162 (8 marks) b) Determine the standard deviation of a portfolio of 100 securities if the average variance is 900 and the average covariance is 360. VAR(Rp) = 1/N AV.VAR + (1 – 1/N) AV.COV = 1/100 900 + (1 – 1/100) 360 = 9 + 356.4 = 365.4 SD(Rp) = √365.4 = 19.115 (8 marks) Q3. Given the following variance-covariance matrix calculate the risk of an equally weighted portfolio arks) Q4. a) Determine the risk and return on an efficient portfolio made of 40 per cent of the risk free rate and 60 per cent of the market portfolio if the risk free return is 6 per cent and the market portfolio offers an expected return of 15 per cent with a standard deviation of 20 per cent. E(Rp) = (1 – w) RF + w E(Rm) = 0.40 x 6% + 0.60 x 15% = 11.4% E(Rp) = 6% + (15% - 6%) 0.6 = 6% + 5.4 =11.4% per cent with a standard deviation of 16 per cent. The standard deviations of the return on A and B are 20 and 24 per cent respectively. If the correlation of the returns on A with market portfolio is 0.5 what is the correlation of the returns of B with the market portfolio? (6 marks) As E(RA) = E(RB) and returns are consistent with the CAPM this implies βA = βB βA = РAm SD(RA)/SD(Rm) = (0.5 x 20)/16 = 10/16 = 0.625 βB = 0.625 = РBm SD(RB)/SD(Rm) = (РBm 24)/16 РBm = (0.625 x 16)/24 = 0.4167 Q6. Assuming returns can be explained by the CAPM draw two diagrams a) The first to illustrate a characteristic line for a security with a beta of more than one and a relatively high expose to non-systematic risk. (7 marks) Dispersion of observations around the characteristic line indicates the non- systematic risk exposure. Rjt Rjt = RF (1 – βj) + βjRmt + ejt X X βj >1.0 X X X X X X X X X Rmt RF(1 – βj) X b) The second to illustrate a portfolio made up of 20 per cent of the risk free asset and 80 per cent of the market portfolio. (7 marks) An efficient portfolio implies all observations fall on the characteristic line (zero non-systematic risk). CHARACTERISTIC LINE RPt X X RF(1 – βj) X RF x 0.2 X X Βp = 0.8 Rmt