Please explain question #12. attached document with the document is provided.

For problems 12-16, assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The T-bill rate is 7%.

12. Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund.

Chapter 5 For problems 12-16, assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The T-bill rate is 7%. 12. Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund. a. what is the expected return and standard deviation of your client's portfolio? Expected return: (0.30 x 7%) + (0.7 x 17%) = 14% per year Standard deviation: 0.70 x 27% = 18.9% per year b. Suppose your risky portfolio includes the following investments in the given proportions: Stock A 27% Stock B 33% Stock C 40% What are the investment proportions of your client's overall portfolio, including the position in T-bills? T-bills = 30% Stock A = .27 x .7 = .189 = 18.9% Stock B = .33 x .7 = .231= 23.1% Stock C = .4 x .7 = .28 = 28% c. What is the reward-to-volatility ratio (S) of your risky portfolio and your client's overall portfolio? Risky portfolio = (.17 - .07)/(.189) = .529 Overall portfolio = (.14-.07)/(.189) = .37 d. Draw the CAL of your portfolio on an expected return/ standard deviation diagram. What is the slope of the CAL? Show the position of your client on your fund's CAL. 13. Suppose the same client in the previous problem decides to invest in your risky portfolio a proportion (y) of his total investment budget so that his overall portfolio will have an expected rate of return of 15%. a. What is proportion y? Mean return on portfolio = Rf+ (Rp- Rf)y Y = (15% - 7%)/10% y = .8 b. What are your client's investment proportions in your three stocks and the T-bill fund? T-bills = 20% Stock A = .8 x .27 = .216 = 21.6% Stock B = .8 x .33 =.264 = 26.4% Stock C = .8 x .4 = .32 = 32% c. What is the standard deviation of the rate of return on your client's portfolio? .8 x .27 = .216 = 21.6% 14. Suppose the same client as in the previous problem prefers to invest in your portfolio a proportion (y) that maximizes the expected return on the overall portfolio subject to the constraint that the overall portfolio's standard deviation will not exceed 20%. a. What is the investment proportion, y? portfolio standard deviation = y x 27%. if client wants a standard deviation of 20% then y = (.20/.27) = .7407 b. What is the expected rate of return on the overall portfolio? .07 + (.17 - .07)y = .07 +.1 (.7407) = .1440 Chapter 6 2. When adding a risky asset to a portfolio of many risky assets, which property of the asset is more important, its standard deviation or its covariance with the other assets? Explain. The covariance can help measure the average tendency of the asset returns to vary in tandem. So covariance can help you identify the amount of diversification of your risky assets making them in a sense, less risky. Through diversification, some risks are being removed, such as industry risk. 5. The standard deviation of the market-index portfolio is 20%. Stock A has a beta of 1.5 and a residual standard deviation of 30%. a. What would make for a larger increase in the stock's variance: an increase of .15 in its beta or an increase of 3% (from 30% to 33%) in its residual standard deviation? Both increases are equally large, so neither increases are larger than the other. b. An investor who currently holds the market-index portfolio decides to reduce the portfolio allocation to the market index to 90% and to invest 10% in Stock A. Which of the changes in (a) will have a greater impact on the portfolio's standard deviation? The beta would have more effect because there is more allocation to the market index, which is greater affected by the beta than the residual standard. 16. Assume expected returns and standard deviations for all securities, as well as the risk-free rate for lending and borrowing, are known. Will investors arrive at the same optimal risky portfolio? Explain. Investors will not arrive at the same optimal risky portfolio. If investors have different borrowing and lending rate, then their indifference curves would be different. It also depends on their preference of risk taking. 20. Investors expect the market rate of return this year to be 10%. The expected rate of return on a stock with a beta of 1.2 is currently 12%. If the market return this year turns out to be 8%, how would you revise your expectation of the rate of return on the stock? Expected rate of return = risk free return + beta (market return - risk free return) revised : 0% + 1.2 (8 - 0) = 9.6% Chapter 7 9. What must be the beta of a portfolio with E(rp) = 20%, if rf = 5% and E(rm) = 15%? E(rp) = rf + B [E(rm) - rf] 20% = 5% + B (15% - 5%) B = 1.5 12. Consider the following table, which gives a security analyst's expected return on two stocks for two particular market returns: Market Return: 5%, 20 Aggressive Stock: 2%, 32 Defensive Stock: 3.5%, 14 a. What are the betas of the two stocks? Aggressive stock beta = (2 - 32)/(5 - 20) = 2.0 Defensive stock beta = (3.5 - 14)/(5 - 20 ) = 0.70 b. What is the expected rate of return on each stock if the market return is equally likely to be 5% or 20%? E[R] (aggressive stock) = .0.5 (2 + 35) = 17% E[R] (defensive stock) = 0.5 (3.5 + 14) = 8.75% c. If the T-bill rate is 8%, and the market return is equally likely to be 5% or 20%, draw the SML for this economy. d. Plot the two securities on the SML graph. What are the alphas of each? Alpha of aggressive stock is zero. Alpha of defensive stock is -2.4% e. What hurdle rate should be used by the management of the aggressive firm for a project with the risk characteristics of the defensive firm's stock? The hurdle rate is determined by the project beta, 0.70. The discount rate is 11.15%. If the Simple CAPM is valid, which of the situations in problems 13-19 below are possible? Explain. Consider each situation independently. 13. Portfolio A should have a higher expected return than Portfolio B, because it has a higher beta, which means it bears more risk. 14. Portfolio A should have a higher standard deviation than Portfolio B because higher volatility should mean higher expected returns. 15. It is possible for portfolio A to yield slightly lower return than market with a lot less deviation, or volatility. With the combine Risk-free rate in its portfolio, this is definitely possible. 16. Portfolio A in this scenario is also possible. The use of the risk-free rate could bring down a highly risky portfolio close to market expected returns and slightly lower volatility. 17. Portfolio A in this scenario is possible, but is a poorly chosen portfolio. The Beta for this portfolio should not be that much higher than market beta and yield a lower expected return. 18. This portfolio is highly viable and likely. The risk-free rate added to the portfolio can easily make this portfolio do-able. 19. This portfolio is also viable and likely for the same reasons as portfolio A in question 18. 21. A share of stock is now selling for $100. It will pay a dividend of $9 per share at the end of the year. Its beta is 1. What do investors expect the stock to sell for at the end of the year? Since Beta is equal to one, its expected rate of return should be equal to that of the market, 18% E(r) = (d + p1 - p0)/(p0) 0.18 = (9 + p1 - 100)/ (100) p1 = 109 25. Suppose the yield on short-term government securities (perceived to be risk-free) is about 4%. Suppose also that the expected return required by the market for a portfolio with a beta of 1 is 12%. According to the capital asset pricing model: a. What is the expected return on the market portfolio? E(r) = rf + b[Erm - rf] 18% = 5% + 1.6 [Erm - 5%] Erm = 13.12% b. What would be the expected return on a zero-beta stock? It is the same as the risk free return = 5%. c. Suppose you consider buying a share of stock at a price of $40. The stock is expected to pay a dividend of $3 next year and to sell it then for 41$. The stock risk has been evaluated at B = -0.5. Is the stock overpriced or underpriced? The stock is underpriced at 40$ a share. 32. Suppose two factors identified for the U.S. economy: the growth rate of industrial production, IP, and the inflation rate, IR. IP is expected to be 4% and IR 6%. A stock with a beta of 1 on IP and .4 on IR currently is expected to provide a rate of return of 14%. If industrial production actually grows by 5%, which the inflation rate turns out to be 7%, what is your best guess for the rate of return on the stock? The expected return on stock is 17.4% 35. Suppose the market can be described by the following three source s of systematic risk. Each factor in the following table has a mean value of zero (so factor values represent realized surprises relative to prior expectations), and the risk premiums associated with each source of systematic risk are given in the last column. Systematic Factor Risk Premium Industrial production, IP 6% Interest rates, INT 2 Credit Risk, CRED 4 The excess return, R, on a particular stock is described by the following equation that relates realized returns to surprises in the three systematic factors: R = 6% + 1.0 IP + .5 INT + .75 CRED + e Find the equilibrium expected excess return on this stock using the APT. Is the stock overpriced or underpriced? This stock is overpriced. Expected excess return = 16%