An investor holds a portfolio of stocks and is considering investing in the DBB

Question

An investor holds a portfolio of stocks and is considering investing in the DBB Company. The firm's prospects look neutral and you a) How much is the cxpcctcd 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. d) 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? 0 Do you consider this portfolio more or less risky than the individual stocks? Explain.

Explanation / Answer

a) Expected return of DBB = 9.6% b) Standard deviation = 449.64 = 21.20 % Coeffecient of variation = 21.2/9.6 = 2.21 Workings are given below: DBB conditions return-r p r*p d=r-E® d^2 d^2*p std dev recession -30 0.1 -3 -39.6 1568.16 156.816 below average -15 0.2 -3 -24.6 605.16 121.032 average 15 0.4 6 5.4 29.16 11.664 above average 28 0.2 5.6 18.4 338.56 67.712 boom 40 0.1 4 30.4 924.16 92.416 9.6 449.64 21.20 DVI conditions return-r p r*p d=r-E® d^2 d^2*p recession -15 0.1 -1.5 -24.6 605.16 60.516 below average 4 0.2 0.8 -5.6 31.36 6.272 average 8 0.4 3.2 -1.6 2.56 1.024 above average 20 0.2 4 10.4 108.16 21.632 boom 22 0.1 2.2 12.4 153.76 15.376 8.7 104.82 10.24 c) 99.73% of the times the value of the returns would lie between      -3*21.2 and 3-21.2; ie between -63.6% and +63.6% d) Expected return of the new portfolio{      = Return of DBB*0.7 + Return of DVE*0.3 = 9.6*0.7+8.7*0.3 = 9.33% e) Standard deviation of the portfolio = [ (wgt1 ^2 * s1 ^2) + (wgt2 ^2 * s2 ^ 2) + (2 * w1 * w2 * cov12) ] ^ .5 where wgt1 is the weight of asset 1 wgt2 is the weight of asset 2 s1 is the standard deviation of asset 1 s2 is the standard deviation of asset 2 cov12 is the covariant of assets 1 and 2 (0.7^2*21.2^2 + 0.3^2*10.24^2+2*0.7*0.3*197.48)^0.5 17.68 Coefficient of variation of the new portfolio = portfolio expected returns/standard deviation of the portfolio 17.68/9.33 1.89 Calculation of covariance of DBB and DIV: deviations from mean DBB DIV dbb*div p dbb*div*p -39.6 -24.6 974.16 0.1 97.416 -24.6 -5.6 137.76 0.2 27.552 5.4 -1.6 -8.64 0.4 -3.456 18.4 10.4 191.36 0.2 38.272 30.4 12.4 376.96 0.1 37.696 197.48 f) Tabulations: expected std coefficient return deviation of Variation DBB 9.6 21.2 2.21 DIV 8.7 10.24 1.18 Pertfolio 9.33 17.68 1.89 AS the CV of the portfolio is greater than that of DIV and lesset than that of DBB, it is more risky than DIV and less risky thanDBB.

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