July 2003FIN2101 BUSINESS FINANCE IIMODULE 2 CAPITAL ASSET PRICING MODEL (CAPM)QUESTION 1The best combination of expected value of return and standard deviation depends upon the investors utility function. Explain this statement.QUESTION 2Explain how the existence of a risk-free asset affects optimal portfolio selection.QUESTION 3Explain briefly just what the Capital Asset Pricing Model tells us.QUESTION 4Using the CAPM, estimate the appropriate required rate of return for the three shares listed below, given that the risk-free rate is 5% and the expected return on the market portfolio is 17%.ShareBeta A0.75 B0.90 C1.40QUESTION 5(a)Determine the expected return and beta for the following portfolio:SharePortfolio Weighting %BetaExpected Return % 1401.0012 2250.7511 3351.3015(b)Given the information above, draw the security market line and show where the securities fit on the graph. Assume that the risk-free rate is 8% and that the expected return on the market portfolio is 12%. How would you interpret these findings?July 2003QUESTION 6In five successive time periods, the market portfolio had a return of 10%, 12%, 6%, -4% and 1%. A given security had the following returns over the same five time periods: 15%, 13%, 4%, -12% and 2%.Calculate:(a)the standard deviation of returns;(b)the correlation of returns between the market portfolio and the security;(c)the systematic risk of the security.QUESTION 7Johnson Manufacturing Ltd is considering several investments. The rate on Treasury notes is currently 6.75% and the expected return for the market is 12%. What would be the required rates of return for each investment (using the CAPM)?SecurityBeta A1.50 B0.82 C0.60 D1.15QUESTION 8CSB Ltd has a beta of 0.765. If the expected market return is 11.5% and the risk-free rate is 7.5%, what is the appropriate required return of CSB (using the CAPM)?QUESTION 9The expected return for the general market is 12.8%, and the market risk premium is 4.3%. Tasaco, LBM and Exxos have betas of 0.864, 0.693 and 0.575 respectively. What are the corresponding required rates of return for the three securities?Questions 4, 5, 7, 8 and 9 taken from Petty et al, Financial Management, 2nd edn, Pearson Education, Sydney, 2000.July 2003FIN2101 BUSINESS FINANCE IISOLUTIONS TO TUTORIAL QUESTIONSMODULE 2 CAPITAL ASSET PRICING MODEL (CAPM)July 2003QUESTION 1The literature is a little deficient in clearly explaining the relevance of utility theory to portfolio selection and the notions of indifference curves and efficient frontiers. The students should understand not merely that a particular point on a diagram represents something but why it does and why an investor may choose to prefer that point as opposed to other possibilities.An individual investors choice between different portfolios will depend on personal preference (utility theory). The portfolio with the maximum utility is the one at the point of tangency of the opportunity set with the highest indifference curve. A risk averse investor will choose a portfolio which is at a point of tangency between his indifference curve and the efficient frontier.QUESTION 2When risk-free assets do not exist, the optimal portfolio selection will be found on the efficient frontier.With the introduction of a risk-free asset, we get a new efficient frontier which is drawn as the Capital Market Line (CML), with all points (except point M) on the “old” efficient frontier now dominated by points on the “new“ frontier.QUESTION 3CAPM attempts to provide a means of understanding the relationship between expected return and systematic or non-diversifiable or unavoidable risk and evaluation of securities in the following context. In market equilibrium, a security is expected to provide a return commensurate with its unavoidable risk. Put simply, the greater the unavoidable risk of a security, the greater the return that investors will expect from that security.QUESTION 421.8%or 0.218 0.05 - 0.17 1.40 0.05 k15.8%or 0.158 0.05 - 0.17 0.90 0.05 k14%or 0.14 0.05 - 0.17 0.75 0.05 kR - k b R kCBAFmjFjJuly 2003QUESTION 5(a) 12.8%or 0.128 0.0525 0.0275 0.048 0.15 0.35 0.11 0.25 0.12 0.40 k w kn1jjjp 1.0425 0.455 0.1875 0.40 1.30 0.35 0.75 0.25 1.00 0.40 b w bn1jjjp(b)Shares 1 and 2 seem to be right in line with the security market line, which suggests that they are earning a fair return, given their systematic risk. Share 3, on the other hand, is earning more than a fair return (above the security market line). We might be tempted to conclude that security 3 is undervalued.July 2003QUESTION 6Note that the question involves historical data and ex post analysis is therefore required.Step 1 Calculate the arithmetic mean returns for the security and the market portfolio0.05 50.01 0.04 - 0.06 0.12 0.10k0.036 50.02 - 0.12 - 0.04 0.13 0.15knkkmSn1ii