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 estimate the following probability distribution of possible returns: 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. 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? f) Do you consider this portfolio more or less risky than the individual stocks? Explain.

Explanation / Answer

6.

a.

Expected return for DBB = R1*P1 + R2*P2 + R3*P3 +R4*P4 + R5*P5

Expected return for DBB = (-30%)*.1 + (-15%)*.2 + 15%*.4 + 28%*.2 + 40%*.1

Expected return for DBB (x)= 9.6%

b.

Coefficient of variation = Standard Deviation (SD)/ Mean

Standard Deviation (SD) = (P1*(x – R1)^2 + P2*(x – R2)^2 + P3*(x – R3)^2 + P4*(x – R4)^2 + P5*(x – R5)^2 )^.5

SD =(.1*(.096 - (-.3))^2 + .2*(.096 - (-.15))^2 + .4*(.096 - .15)^2 + .2*(.096- .28)^2 + .1*(.096- .40)^2 )^.5

SD = 21.20%

Thus,

Coefficient of variation = 21.20/9.6 = 2.20

C.

At 99.73%

Lower range = mean – 3*SD = 9.6% - 3*21.20%= -54%

Higher Range = mean + 3*SD = 9.6% + 3*21.20% = 72.2%

d.

Expected return of DVI = R1*P1 + R2*P2 + R3*P3 +R4*P4 + R5*P5

Expected return of DVI = (-15%)*.1 + (4%)*.2 + 8%*.4 + 20%*.2 + 22%*.1

Expected return of DVI = 8.7%

Now after shifting 30% of asset to DVI

Portfolio Return = 70% *( return on DBB) + 30% *(Return on DVI)

Portfolio Return = .7*9.6% + .3*8.7%

Portfolio Return = 9.33%

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