The following table shows the betas and actual expected returns of 4 mutual funds in the market: ● Beta ● Actual expected Fund 1 0.5 Fund 2 0.8 Fund 3 1.4 Fund 4 1.9 The return rate of riskfree asset is rf = 5% and the market portfolio exists. You are given that Exactly two of the funds perform better than the market expectation (i.e. Actual expected return is strictly higher than market expected return) Exactly one of the funds performs worse than the market expectation. return 7.2% 10% 12% 16% (b) A fund manager launches a new fund (called Fund X) which 25% of the capital will be invested in Fund 1, 35% of the capital will be invested in Fund 3 and 40% of the capital will be invested in Fund 4. Compute the Jensen alpha and Treynor ratio of the Fund X.

Daniel Grady is the financial advisor for a number of professional athletes. An analysis of the long-term goals for many of these athletes has resulted in a recommendation to purchase stocks with some of their income that is set aside for investments. Five stocks have been identified as having very favorable expectations for future performance.  Although the expected return is important in these investments, the risk, as measured by the beta of the stock, is also important. (A high value of beta indicates that the stock has a relatively high risk.) The expected return and the betas for five stocks are as follows: Stock 1 2 3 4 5 Expected Return (%) 11.0 9.0 6.5 15.0 13.0 Beta 1.20 0.85 0.55 1.40 1.25   Daniel would like to minimize the beta of the stock portfolio (calculated using a weighted average of the amounts put into the different stocks) while maintaining an expected return of at least 11%. Since future conditions may change, Daniel…

Large-scale integrated (LSI) circuit chips are made in one department of an electronics firm. These chips are incorporated into analog devices that are then encased in epoxy. The yield is not particularly good for LSI manufacture, so the AQL specified by that department is 0.15 while the LTPD acceptable by the assembly department is 0.40. Assume the company is willing to accept a consumer's risk of 10 percent and a producer's risk of 5 percent. Find the sample size. Use Exhibit 10.16. Note: if the exact value of the computed LTPD ÷ AOQ ratio does not appear in Exhibit 10.16, use the next higher ratio. Note: Round up your answer to the next whole number.   How would you tell someone to do the test?

Consider the case where the left tail of the implied distribution is thinner than that of the log-normal distribution and the right tail of the implied distribution is fatter than that of the log-normal distribution with the same mean and standard deviation. Which of the following statements is correct?     A) The implied volatility of a deep out-of-the money put is greater than the one obtained from the Black-Scholes price.     B) The implied volatility decreases as the strike price increases.     C) The implied volatility of a deep out-of-the money call is smaller than the one obtained from the Black-Scholes price.     D) The implied volatility increases as the strike price increases. Please explain and justify your choice. In your answer, discuss the shape of the relation of implied volatility to the strike price and explain how this is obtained.