Question

In: Finance

Assume you are considering a portfolio containing two​ assets, L and M. Asset L will represent...

Assume you are considering a portfolio containing two​ assets, L and M. Asset L will represent 44 % of the dollar value of the​ portfolio, and asset M will account for the other 56 %. The projected returns over the next 6​ years, 2018-2023​, for each of these assets are summarized in the following​ table: a. Calculate the projected portfolio​ return, r p​, for each of the 6 years. b. Calculate the average expected portfolio​ return, r overbar Subscript p​, over the​ 6-year period. c. Calculate the standard deviation of expected portfolio​ returns, s Subscript p​, over the​ 6-year period. d. How would you characterize the correlation of returns of the two assets L and​ M? e. Discuss any benefits of diversification achieved through creation of the portfolio.

Projected Return
Year Asset L Asset M
2018 13% 21%
2019 15% 17%
2020 16% 16%
2021 18% 14%
2022 17% 13%
2023 19% 11%

Solutions

Expert Solution

1. Return for each year : weight of asset L* return of asset L + weight of asset M* return of asset M

Year Asset L Asset M
2018

13

21 0.44*13+0.56*21 = 17.48
2019 15 17 0.44*15+0.56*17 = 16.12
2020

16

16 0.44*16+0.56*16 = 16
2021 18 14 0.44*18+0.56*14 = 15.76
2022 17 13 0.44*17+0.56*13 = 14.76
2023 19 11 0.44*19+0.56*11 = 14.52

2. Average Return over 6 years = (17.48 + 16.12+ 16 + 15.76 + 14.76 + 14.52)/6

= 94.64/6 = 15.77

3. Standard Deviation over 6 years:

Year

Expected Return D =Expected Return - Average Return D^2
2018 17.48 =17.48-15.77 = 1.71 2.9127
2019 16.12 =16.12-15.77 = 0.35 0.1202
2020 16 =16-15.77 = 0.23 0.0514
2021 15.76 =15.76-15.77 = -0.01 0.0002
2022 14.76 14.76-15.77 = -1.01 1.0268
2023 14.52 14.52-15.77 = -1.25 1.5708
Total 5.6821

Standard Deviation = square root of((sum of D^2)/number of observations)

= square root of (5.6821/6)

= square root of(0.9470) = 0.9732

d. If you observe the returns you will notice that when the return of L increases , the return of M falls. This means that the returns are moving in opposite direction, hence they are negatively correlated.

e. The advantage of dividing your investment over a more than one asset (namely diversification) is that it enables to lower the overall risk of the investment. That is, if the returns of one asset fall, it is not necessary that returns of the second asset will follow the same pattern. In such a case, the negative impact of one asset is subset to an extent by the impact produced by the second asset.


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