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		29 %		14 %		25 %		2 %
Normal		47 %		11 %		16 %		11 %
Recession		24 %		2 %		5 %		14 %

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

________

(Round to two decimal places.)

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

________

(Round to two decimal places.)

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

__________

(Round to two decimal places.)

What is the standard deviation of asset M?

_________

(Round to two decimal places.)

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

___________ %

(Round to two decimal places.)

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

______ %

(Round to two decimal places.)

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

______ %

(Round to two decimal places.)

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

_______ %

(Round to two decimal places.)

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

___________ %

(Round to two decimal places.)

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

_____%

(Round to two decimal places.)

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 O could reduce

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

D. Yes, a portfolio of 50% of asset M and 50% of asset N could reduce the risk to 0.990.99 %.

Answer 1

Solution (a)

1: What is the expected return of investing equally in all three assets M, N, and O

Return of Portfolio in Boom = 1/3 (14%) + 1/3 (25%) + 1/3 (2%) = 13.67%

Return of Portfolio in Normal = 1/3 (11%) + 1/3 (16%) + 1/3 (11%) = 12.67%

Return of Portfolio in Recession = 1/3 (2%) + 1/3 (5%) + 1/3 (14%) = 7.00%

Expected Return Portfolio = 0.29 × (13.67%) + 0.47 × (12.67%) + 0.24 (7%)

= 11.59%

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

Expected Return Asset M = 0.29 × (14%) + 0.47 × (11%) + 0.24 (2%)

= 9.71%

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

Standard Deviation of Portfolio = [0.29 × (0.1367 – 0.1159)² + 0.47 × (0.1267 – 0.1159)² +0.24 × (0.07 – 0.1159)² ] ^1/2

= [0.29 x 0.0004 + 0.47 x 0.0001 + 0.24 x 0.0021] ^1/2

= 2.45%

4. What is the standard deviation of asset M

Standard Deviation of M = [0.29 × (0.14 – 0.0971)² + 0.47 × (0.11 – 0.0971)² +0.24 × (0.02 – 0.0971)² ] ^1/2

= [ 0.29 x 0.0018 + 0.47 x 0.0002 + 0.24 x 0.0059] ^1/2

= 4.36%