14. 15. Security A has a standard deviation of .64% and Security B has a standar

Question

14.

15. Security A has a standard deviation of .64% and Security B has a standard deviation of 1.39%. If the correlation coefficient between the returns of the two securities is 0.86, what is the standard deviation of a portfolio that is invested 40% in A and 60% in B.

17. Suppose that we have identified two important systematic risk factors: the growth rate of gross domestic product, labeled GDP, and the 30-year bond interest rate, labeled BR. Whole Hog Farms, Inc. has a beta 1.1 on GDP and 0.9 on BR. Whole Hog has an expected stock return of 12%. GDP is expected to be 5.5% and BR 6%. If gross domestic product grows by 3% and the 30-year bond rate turns out to be 9%, and no unexpected news specifically concerning Whole Hog occurs, within the Arbitrage Pricing Theory framework, what is your best guess for the realized rate of return on Whole Hog stock?

18. Assume two factors have been identified as the important sources of systematic risk: the growth rate in industrial production, IP, and the rate of change in the price of West Texas crude oil, OIL. Suppose also that the expected return on a well-diversified IP factor portfolio, E(rIP) is 8% and E(rOIL) is 12%. Now consider the Low Ride Automobile Co. with ?IP = 1.3 and ?OIL = -0.2. Assume rf = 6%. Within an Arbitrage Pricing Theory framework, what is the fair rate of return on Low Ride?

19. The offering price of the Titanic Fund is $18.65 per share and the fund is sold with a front-end load of 5%, what is the net asset value of this open-end fund?

Explanation / Answer

15. Security A has a standard deviation of .64% and Security B has a standard deviation of 1.39%. If the correlation coefficient between the returns of the two securities is 0.86, what is the standard deviation of a portfolio that is invested 40% in A and 60% in B.

Variance of a portfolio = Weight of Stock A^2 * SD of Stock A^2 + Weight of Stock B^2 * SD of Stock B^2 + 2*Weight of Stock A* Weight of Stock B*SD of Stock A*SD of Stock B*Correlation

Variance of a portfolio = 40%^2*0.64%^2 + 60%^2*1.39%^2 + 2*40%*60%*0.64%*1.39%*0.86

Variance of a portfolio = 0.000112832

Standard deviation of a portfolio = Variance of a portfolio^(1/2)

Standard deviation of a portfolio = 0.000112832^(1/2)

Standard deviation of a portfolio = 1.06%

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