In: Finance
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% |
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.