Question 2: Applications (60 points) Suppose that you have just started your first job as a junior investment analyst at a hedge fund. You have the data on average annual returns (that is, yield) and risk levels for the following five securities that your fund is holding (e.g. corporate bonds): Security # Return (in %) Risk 2.5753 4.3934 14.2423 43 10.2303 3.3583 Table 1: Risk-return characteristics of five portfolio securities. The risk index is a number between 0 and 100 that is increasing with security's market risk (e.g. risk index of 0 represents a risk-free security such as a government bond). Suppose that you wish to use these data to estimate the following regression model: Y; = B1 + B2X 2 + Ui, (1) for i = 1, ...,5, where Y is return (in percent and X/2 is the risk index for security i. (g) (7 points) You're considering purchasing a bond that has a yield of 12%. No risk index is available for this bond. Based on your estimates, what risk index can you expect to be associated with such bond? (h) (6 points) Suppose that you're considering adding a new bond to your portfolio. This bond has a return of 8% and has a risk index of 8. On the basis of this return and risk index only, it this a good investment proposition? (i) (7 points) Suppose that you wish to test a hypothesis that risk has no effect on security's return against an alternative that it has a positive effect. Formulate the appropriate hypothesis and using your estimates test it at 5% level of significance. Show all steps, and clearly indicate your final decision whether to reject this Ho