Sally Rogers has decided to invest her wealth equally across the following three assets. 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.

States

Probability

Asset M Return

Asset N Return

Asset O Return

Boom

33%

13%

24%

5%

Normal

51%

11%

15%

11%

Recession

16%

5%

4%

13%

a. 1- What is the expected return of investing equally in all three assets M, N, and O?

% (Round to two decimal places.)

2-What is the expected return of investing in asset M alone?

% (Round to two decimal places.)

3-What is the standard deviation of the portfolio that invests equally in all three assets M, N, and O?

% (Round to two decimal places.)

4-What is the standard deviation of asset M?

% (Round to two decimal places.)

5- By investing in the portfolio that invests equally in all three assets M, N, and O rather than asset M alone, Sally can benefit by increasing her return by (........ %) and decrease her risk by( (....... %). (Round to two decimal places.)

b. 1- What is the expected return of a portfolio of 50% asset M and 50% asset N?

% (Round to two decimal places.)

2- What is the expected return of a portfolio of 50% asset M and 50% asset O?

% (Round to two decimal places.)

3- What is the expected return of a portfolio of 50% asset N and 50% asset O?

% (Round to two decimal places.)

4- What is the standard deviation of a portfolio of 50% asset M and 50% asset N?

% (Round to two decimal places.)

5- What is the standard deviation of a portfolio of 50% asset M and 50% asset O?

% (Round to two decimal places.)

6- What is the standard deviation of a portfolio of 50% asset N and 50% asset O?

% (Round to two decimal places.)

7- 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? (Select the best response.)

A. No, none of the portfolios using a 50-50 split reduce risk.

B. Yes, a portfolio of 50% of asset M and 50% of asset N could reduce the risk to 1.49%.

C. There is not enough information to answer this question.

D. Yes, a portfolio of 50% of asset M and 50% of asset O could reduce the risk to 1.49%.