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Department of Accounting and Finance
M.Sc. Finance
M.Sc. Investment and Finance
M.Sc. International Banking and Finance
And
M.Sc. International Accounting and Finance
40902: Finance II
Class Test
Tuesday 8th^ December 2009 10.30am – 11.30am (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. If more space is required the answer can be continued on the back of the page where the question appears (scrap pages for additional workings are attached to the back of the test). Please write clearly as illegible writing cannot be marked. Failure to follow these requirements will lead to a deduction of marks.
To Be Completed (please write clearly)
Registration Number 2009
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Course (please indicate by ticking appropriate box)
Finance Investment & Fin. Int. Banking & Fin
Int. Accounting & Fin
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TOTAL MARKS
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SOLUTIONS
Q1.
a) Determine the expected return and risk of a portfolio made up of 30 per cent of Y and 70 per cent of X, given the following information on these two securities and the correlation coefficient for the returns on the securities:
Security Expected Return Standard Deviation X 12 per cent 20 per cent Y 20 per cent 30 per cent
Correlation coefficient = +0. (6 marks) E(Rp) = wA E(RA ) + wB E(R (^) B) = 0.7 x 12 + 0.30 x 20 = 14.
VAR(R (^) p) = wA VAR(R (^) A) + wB VAR(R (^) B) + 2w (^) A w (^) B ρ (^) AB SD(R (^) A) SD(RA ) = 0.7 2 x 20 2 + 0.3 2 x 0.30 2 + 2 x 0.7 x 0.3 x 0.40 x 20 x 30 = 377. SD(R (^) p) = 19.
b) The portfolio formed above can be combined with another asset, Z, that offers a return of 24 per cent and a standard deviation of 36 per cent, to create a second portfolio. The returns on Z and the portfolio are independent. The composition of the second portfolio is 50 per cent for the first portfolio and 50 per cent for Z. Determine its expected return and risk. (4 marks) VAR(R) = wP^2 VAR(R (^) P ) + wZ VAR(R (^) Z) + 2w (^) P wZ ρPZ SD(RP ) SD(RZ ) = 0.50^2 x 19.44 2 + 0.50 2 x 0.36^2 + 0 (INDEPENDENT RETURNS COV(RP RZ )=0 ) = 418. SD(R) = 20.
Q2. a) If the correlation of X and Y is -1.0 instead of +0.4 determine the composition and expected return of the zero risk portfolio. (5 marks) w (^) X = SD(RY )/[SD(R (^) X) + SD(RY )] = 30/(20 + 30) = 0. w (^) Y = SD(RX )/[SD(RX ) + SD(RY )] = 20/(20 + 30) = 0.
E(RP ) = 0.60 X 12 + 0.40 X 20 = 15.
b) Determine the composition and expected return of an efficient portfolio offering a standard deviation of 12 per cent. (5 marks) See Attached Document
Q3. a) Given the following correlation matrix, and data on the standard deviations of securities, set out the corresponding variance-covariance matrix below (10 marks)
(5 marks)
e) An efficient portfolio with a beta of 0.50 has an expected return of 8 per cent with a standard deviation of 7.50 per cent. The shares on the ABC company also have a beta of 0.50 and an expected return of 8 per cent, with a standard deviation of 14 per cent. Can this be reconciled with the CAPM? (5 marks) According to the CAPM expected rates of return on assets depend on the risk free rate, the expected rate of return on the market portfolio and the asset betas. Differences in total risk do not directly influence expected rates of return. This implies that the same expected rates of return on the efficient portfolio and the shares of the ABC company are quite consistent with the CAPM despite the differences in the standard deviations of the returns on the two investments.
Not required for the answer. It can be noted that the same betas with different standard deviations implies that the correlation of returns with the market portfolio will differ. The co- efficient for an efficient portfolio is equal to one, while for ABC it must be less than one.
Q5. If the average variance of securities is 420 and the average covariance is 180, determine the standard deviations of equally weighted portfolios made up of 2, 5, 10 and 40 securities. Draw a diagram to illustrate the relationship between the standard deviation and the number of securities in the portfolio, and comment briefly on your results. (10 marks) No of Securities Adjusted Variance Term
Adjusted Covariance Term
Portfolio Variance
SD(R)
As the number of securities is increased the risk in the form of the standard deviation falls at a decreasing rate towards a limiting value given by the average co-variance. This reflects the proposition derived from portfolio theory that the risk of individual assets held in a portfolio is less important than the way in which their returns co-vary with the returns on other assets in the portfolio.
Q6. The beta of security A is 0.7 and its standard deviation is 20 per cent whereas the standard deviation of the return on the market portfolio is only 15 per cent. Determine the correlation of the returns on A and the market portfolio. (5 marks)
Q7. The expected return on the market is 15 per cent and the risk free rate is 6 per cent. Duo plc has two operating divisions. The first accounts for 70 per cent of the company’s assets leaving the second to account for the residual 30 per cent. Specialised (single division) companies operating in the same business as the first division, and financed entirely by equity, have a beta of 1.20. specialised
companies with comparable products to the second division and also financed entirely by equity have an average beta of 0.80. Duo plc is financed 60 per cent equity and 40 per cent debt.
a) Determine the cost of capital for each of Duo’s divisions. (5 marks) The cost of capital, in the sense of the required rate of return on investment, should reflect the beta risk of the asset in which the investment is to be made. As the two companies with similar businesses to the divisions of Duo do not employ any debt their equity betas reflect their asset risks. Therefore their betas should be employed without adjustment in determining the cost of capital for the two divisions.
b) Determine the required rate of return on Duo’s shares. (5 marks) The expected rate of return on the shares should reflect the average asset beta for the company adjusted for the gearing employed by the company.
Average asset beta = 0.7 x 1.20 + 0.3 x 0.80 = 1.
If the company can earn 16.80 on the first division’s assets and 13.20 on the assets of the second division it should, through the use of gearing, push up the expected return on equity to 22.20 per cent.
Q8. The return on the shares of Premonition plc last year was below the return that investors had anticipated at the beginning of the year. The rate of return on the market was also disappointing – producing a return of 6 per cent, well below the 15 per cent expected at the beginning of the year and only marginally above the risk free rate of 5 per cent. If Premonition’s beta is 1.20 evaluate the return recorded last year on the company’s shares of 8.40 per cent. (9 marks) E(R (^) PREB ) = R (^) F + β (^) PRE [E(Rm ) – R (^) F] = 5 + 1.20 [15 – 6] = 16.80 per cent
E(R (^) PRE|R (^) mt ) = R (^) F + β (^) PRE [R (^) mt – R (^) F] = 6 + 1.20 [6 – 5] = 7. AR (^) PRE,t = R (^) PRE,t – E(RAt|R (^) mt ) = 31 – 26 = 5% = 8.40 – 7. = 1.20 > 0
Q9. Draw two scatter diagrams and associated characteristic lines to show the key aspects of the relationship between market returns and the returns on
a) a security with a beta of 1.20 and a high level of diversifiable risk (4 marks) b) an efficient portfolio with a beta of 0.
