Problem Set 7 ECN 134 Financial Economics Mojaver CAPM Prof Farshid 1 Two investment advisers are comparing performance One averaged a 19 rate of return and the other 16 However the beta of the first investor was 1 5 whereas that of the second was 1 a Can you tell which investor was a better selector of individual stocks aside from the issue of general movements in the market b If the T bill rate were 6 and the market return during the period were 14 which investor would be the superior stock selector c What if the T bill rate were 3 and the market return were 15 yau 2 a A mutual fund with beta of 0 8 has an expected rate of return of 14 If r f 5 and you expect the return on the market portfolio to be 15 should you invest in this fund What is the fund s alpha b What passive portfolio comprised of a market index portfolio and a money market account would have the same beta as the fund Show that the difference between the expected rate of return on this passive portfolio and that of the fund equals the alpha from part a Answer a E rP rf b P E rM rf 5 0 8 15 5 13 a 14 13 1 You should invest in this fund because alpha is positive b The passive portfolio with the same beta as the fund should be invested 80 in the market index portfolio and 20 in the money market account For this portfolio E rP 0 8 15 0 2 5 13 14 13 1 a 3 Karen Kay a portfolio manager at Collins Asset Management is using the capital asst pricing model for making recommendations to her clients Her research department has developed the information shown in the following exhibit Forecast Returns Standard Deviations and Betas Forecast return Standard Deviation Beta Stock X 14 0 36 0 8 Stock Y 17 0 25 1 5 Market Index 14 0 15 1 0 Risk free rate 5 0 a Calculate expected return and alpha for each stock b Identify and justify which stock would be more appropriate for an investor who wants to i add this stock to a well diversified equity portfolio ii hold this stock as a single stock portfolio 4 Assuming the CAPM or one factor model holds what is the cost of equity for a firm if the firm s equity has a beta of 1 2 the risk free rate of return is 2 the expected return on the market is 9 and the return to the company s debt is 7 RE 2 1 2 9 2 10 4 5 On line Text Co has four new text publishing products that it must decide on publishing to expand its services The projects are of equal risk s of 1 6 The risk free rate is 7 and the market rate is expected to be 12 The projects are expected to earn as follows What projects should be selected and why Empirical Tests of the CAPM 1 Describe some of the ways the CAPM is applied in practice The four items mentioned at the beginning of the chapter are Professional portfolio managers use the CAPM to determine appropriate security returns These managers also have their performances evaluated based on the reward to variability ratios of their portfolios relative to the CML or SML Regulatory commissions use the CAPM to help determine the appropriate cost of capital for regulated firms Courts use the CAPM to determine the discount rate to use in calculating the present value of lost future income Firms use the SML to find a benchmark hurdle rate to use in discounting cash flows for capital budgeting projects Feedback This confirms that the student understands that there are real world applications to the theoretical CAPM model 2 When portfolio performance is measured what type of benchmark may be used The benchmark portfolio should be broadly based since it is a proxy for the unobservable market portfolio Examples include but are not limited to the S P500 Index the NYSE Composite Index and the Wilshire 5000 Index Benchmark error refers to the fact that the proxy for the market portfolio may not be mean variance efficient when the true market portfolio is not efficient The proxy index may also be inefficient Also different proxies may lead to substantially different conclusions even though they tend to be highly correlated with each other Feedback This question tests whether the student understands some of the difficulties that are encountered when trying to apply the CAPM especially the ideas of expected returns versus actual returns and finding a proxy for the unobservable market portfolio Efficiency Market Hypothesis 1 Explain the three forms of efficient market hypothesis Include in your discussion the information sets involved in each form and the relationships across information sets and across forms of market efficiency Also discuss the implications for the various forms of market efficiency for the various types of securities analysts The weak form of the efficient markets hypothesis EMH states that stock prices immediately reflect market data Market data refers to stock prices and trading volume Technicians attempt to predict future stock prices based on historic stock price movements Thus if the weak form of the EMH holds the work of the technician is of no value The semistrong form of the EMH states that stock prices include all public information This public information includes market data and all other publicly available information such as financial statements and all information reported in the press relevant to the firm Thus market information is a subset of all public information As a result if the semistrong form of the EMH holds the weak form must hold also If the semistrong form holds then the fundamentalist who attempts to identify undervalued securities by analyzing public information is unlikely to do so consistently over time In fact the work of the fundamentalist may make the markets even more efficient The strong form of the EMH states that all information public and private is immediately reflected in stock prices Public information is a subset of all information thus if the strong form of the EMH holds the semistrong form must hold also The strong form of EMH states that even with inside legal or illegal information one cannot expect to outperform the market consistently over time 2 What is an event study It is a test of what form of market efficiency Discuss the process of conducting an event study including the best variable s to observe as tests of market efficiency Difficulty Difficult Answer A event study is an empirical test which allows the researcher to assess the impact of a particular event on a firm s stock price To do so one often uses the index model and estimates et the residual term which measures the firm specific component of the stock s return This