Use excel in all of the problems. 6) An investor holds a portfolio of stocks and

Question

Use excel in all of the problems. 6) An investor holds a portfolio of stocks and is considering investing in the DBB Company. The firm's prospects look neutral and you estimate the following probability distribution of possible returns: Conditions Returns on DBB Recession Below Average Average Above Average Boom -30% -15% 15% 28% 40% 0.10 0.20 0.40 0.20 0.10 Returns on DVi -15% 4% 8% 20% 2290 a)How much is the expected return for DBB? b)How much is the coefficient of variation for DBB? c) 99.73% of the time in what range (what specific values) would you expect the returns for DBB? Use the Empirical Rule Now let's say you want to add another asset, DVI, to your portfolio. You sell 30% of DBB to purchase DVI. How much is your expected return for this portfolio? e) How much is the coefficient of variation for the new portfolio? f)Do you consider this portfolio more or less risky than the individual stocks? Explain

Explanation / Answer

A B C=A*B D E*A*D Condition Probability Return on DBB(percent) Expected Return on DBB(percent) Return on DV1(percent) Expected Return on DV1(percent) Recession 0.1 -30 -3 -15 -1.5 Below average 0.2 -15 -3 4 0.8 Average 0.4 15 6 8 3.2 Above average 0.2 28 5.6 20 4 Boom 0.1 40 4 22 2.2 TOTAL 9.6 8.7 a) Expected Return of DBB 9.60% Expected Return of DV1 8.70% b) CALCULATION OF COEFFICIENT OF VARIATION Coefficient of variation=(Standard Deviation of return)/(Expected Return) Standard deviation of return=Square Root (Variance of Return) A B c=B-9.6 D=(C^2) E=D*A Condition Probability Return on DBB(percent) Deviation of return from expected return Deviation squared (Deviation squared)*(Probability) Recession 0.1 -30 -39.6 1568.16 156.816 Below average 0.2 -15 -24.6 605.16 121.032 Average 0.4 15 5.4 29.16 11.664 Above average 0.2 28 18.4 338.56 67.712 Boom 0.1 40 30.4 924.16 92.416 TOTAL 449.64 VARIANCE OF RETURN OF DBB 449.64 Standard Deviation of DBB 21.20472 (449.64^0.5) Coefficient of variation for DBB 2.208825 (21.20472/9.6) c) 99.7 Rule states that 99.73% of the time value of time the value of a variable will be within + or - 3 times standard deviation around the expected or mean value Standard deviation=21.20472 Upper limit=9.6+3*21.20472 73.21415 Lower Limit=9.6-3*21.20472 -54.0141 Range for 99.73% of time -54.04% To 73.21% d) Sell 30% of DBB and add 30%of DV1 Expected return of DBB= 9.60% Expected return of DV1= 8.70% Weight of DBB in portfolio           0.70 Weight of DV1 in portfolio 0.3 Expected Return of portfolio           9.33 (0.7*9.6+0.3*8.7) Expected Return of portfolio 9.33%

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