3. CAPM You have been provided the following data on the securities of three firms, the market portfolio, and the risk-free asset: Security Expected Return Standard Deviation Correlation* Beta Firm A 0.13 0.12 (i) 0.9 Firm B 0.16 (ii) 0.4 1.1 Firm C 0.25 0.24 0.75 (iii) The market portfolio 0.15 0.1 (iv) (v) The risk-free asset 0.05 (vi) (vii) (viii) *With the market portfolio. a) Fill in the missing values in the table. b) Is the stock of Firm A correctly priced according to the capital-asset-pricing model (CAPM)? What about the stock of Firm B? Firm C? If these securities are not correctly priced, what is your investment recommendation for someone with a well-diversified portfolio?
Corporate Financial Management Problem Set 6 Autumn Term 2016 2 4. CAPM The expected rate of return on an index fund that closely tracks the S&P’s 500 index (market portfolio) is 14 %, and its standard deviation is 16 %. The Treasury Bill rate (risk free rate) is 6 %. Please explain your answers and show all necessary calculations. Using the capital asset pricing model: a) If an investment with a beta 0.8 offers an expected rate of return of 9.8 %, does it have a positive NPV? b) If the market expects a rate of return of 11.2 % from stock X, what is its beta? In addition to the information given above assume: John (an investor) has $ 10 million invested in long- term corporate bonds. This bond portfolio’s expected annual rate of return is 9 %, and the annual standard deviation is 10 %. c) Instead of investing everything in long-term corporate bonds, John is considering putting all the money in a combination of the S&P 500 tracking index (described above) and Treasury Bills. Can this strategy improve John’s expected rate of return without changing the risk of the portfolio?