In the middle of 2010, Charlotte Lynch had been working for a year as an analyst for an investment company that specialises in serving very wealthy clients. These clients often purchase shares in closely held investment funds with very limited numbers of shareholders. In late 2008, the market for certain types of securities based on real-estate loans simply collapsed as the sub-prime mortgage scandal unfolded. Charlottes firm, however, saw this market collapse as an opportunity to put together a fund that purchases some of these mortgage-backed securities that investors have shunned by acquiring them at bargain prices and holding them until the underlying mortgages are repaid or the market for these securities recovers. The investment company began putting together sales information concerning the possible performance of the new fund and made the following predictions regarding the possible performance of the new fund over the ensuing year as a function of the performance of the economy: State of the economy Probability Fund return Rapid expansion 10% 50% Modest growth 50% 35% No growth 35% 5% Recession 5% -100% Charlottes boss asked her to perform a preliminary analysis of the new funds performance potential for the coming year. Specifically, he asked that Charlotte address each of the following issues: Questions: (a) What are the expected rate of return and standard deviation? (6 marks) (b) What is the expected rate of return for the fund based on the Capital Asset Pricing Model? (3 marks) In addition to the information provided above, Charlotte observed that the risk-free rate of interest for the following year was 4.5%, the market risk premium was 5.5% and the beta for the new investment was 3.55. (c) Based on your analysis, do you think the proposed fund offered a fair return given its risk? Explain.