Benefits of diversification . Sally Rogers has decided to invest her wealth equa

Question

Benefits of

diversification.

Sally Rogers has decided to invest her wealth equally across the following three assets.??a.??What are her expected returns and the risk from her investment in the three? assets? How do they compare with investing in asset M? alone???

Hint?:

Find the standard deviations of asset M and of the portfolio equally invested in assets? M, N, and O.

b.??Could Sally reduce her total risk even more by using assets M and N? only, assets M and O? only, or assets N and O? only? Use a? 50/50 split between the asset? pairs, and find the standard deviation of each asset pair.

??States

Probability

Asset M Return

Asset N Return

Asset O Return

??Boom

3535?%

1212?%

2121?%

44?%

??Normal

5555?%

1010?%

1414?%

1010?%

??Recession

1010?%

44?%

11?%

1212?%

a.??What is the expected return of investing equally in all three assets? M, N, and? O?

nothing?%

?(Round to two decimal? places.)

??States

Probability

Asset M Return

Asset N Return

Asset O Return

??Boom

3535?%

1212?%

2121?%

44?%

??Normal

5555?%

1010?%

1414?%

1010?%

??Recession

1010?%

44?%

11?%

1212?%

Explanation / Answer

Assset M:

Expected return = 10.10%

standard dev = 2.23%

investment in M, N and O

Average = 11.45%

standard dev = 0.94%

p(x) return p*x p*(x - mean)^2 0.35 12.0% 0.042 0.0001264 0.55 10.0% 0.055 0.0000006 0.1 4.0% 0.004 0.0003721

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