Question

Assume you are considering a portfolio containing Asset 1 and Asset 2. Asset 1 will represent 63% of the dollar value of the portfolio, and Asset 2 will account for the other 37%. The projected returns over t6 years, 2021-2026, for each of these assets are summarized in the following table: a. Calculate the projected portfolio retur, fp, for each of the 6 years. Data Table - X b. Calculate the average expected portfolio return, fp, over the 6-year period. c. Calculate the standard deviation of expected portfolio returns, Sp, over the 6-year period. d. How would you characterize the correlation of returns of the assets 1 and 2? e. Discuss any benefits of diversification achieved through creation of the portfolio. (Click on the icon here in order to copy its contents of the data table below into a spreadsheet.) a. The projected portfolio return, lo, for 2021 is %. (Round to two decimal places.) Projected Return Year Asset 1 Asset 2 The projected portfolio return. p. for 2022 is %. (Round to two decimal places.) 2021 -8% 31% 2022 15% 6% The projected portfolio return, lp, for 2023 is %. (Round to two decimal places.) 2023 26% -8% 2024 3% 19% The projected portfolio return, fp, for 2024 is %. (Round to two decimal places.) 2025 - 10% 34% 2026 33% -16% The projected portfolio return, lp, for 2025 is % (Round to two decimal places.) Print Done The projected portfolio return, fp, for 2026 is %. (Round to two decimal places.) b. The average expected portfolio return, 1, over the 6-year period is %. (Round to two decimal places.) c. The standard deviation of expected portfolio returns, Sp, over the 6-year period is %. (Round to three decimal places.) d. How would you characterize the correlation of retums of the assets 1 and 2? The assets are correlated. (Select from the drop-down menu.) e. Discuss any benefits of diversification achieved through creation of the portfolio. (Select the best choice below.)

Answer 1

a]

Expected return of two-asset portfolio R_p = w₁R₁ + w₂R_2,

where R_p = expected return

w₁ = weight of Asset 1

R₁ = expected return of Asset 1

w₂ = weight of Asset 2

R₂ = expected return of Asset 2

A B C 1 Year Asset 1 2021 -8.00% 2022 15.00% 2023 26.00% 2024 3.00% 2025 -10.00% 2026 33.00% Asset 2 31.00% 6.00% -8.00% 19.00% 34.00% -16.00% D Portfolio Return 6.43% 11.67% 13.42% 8.92% 6.28% 14.87%

A B 1 Year 2 2021 3 2022 4 2023 2024 6 2025 7 2026 Asset 1 -0.08 0.15 0.26 0.03 Asset 2 0.31 0.06 -0.08 0.19 0.34 -0.16 Portfolio - Return = (0.63*B2)+(0.37*C2) =(0.63*B3)+(0.37*C3) =(0.63*B4)+(0.37*C4) =(0.63*B5)+(0.37*C5) =(0.63*B6)+(0.37*C6) =(0.63*B7)+(0.37*07) -0.1 0.33

b]

Average portfolio return over 6 year period is calculated using AVERAGE function in Excel

Average portfolio return over 6 year period is 10.27%

I AB 3 1 Year Asset1 2 2021 -8.00% 2022 15.00% 4 2023 26.00% 5 2024 3.00% 6 2025 - 10.00% 7 2026 33.00% Asset 2 31.00% 6.00% -8.00% 19.00% 34.00% -16.00% Average 1 Portfolio - Return 6.43% 11.67% 13.42% 8.92% 6.28% 14.87% 10.27%! 8

c]

Standard deviation of portfolio returns is calculated using STDEV.S function in Excel

Standard deviation of portfolio returns is 3.620%

D9 X fax =STDEV.S(D2:07) | A B C 1 Year Asset 1 2 2021 -8.00% 3 2022 15.00% 4 2023 26.00% 2024 3.00% 2025 -10.00% 2026 33.00% Asset 2 31.00% 6.00% -8.00% 19.00% 34.00% - 16.00% Average Std. Dev. Portfolio - Return 6.43% 11.67% 13.42% 8.92% 6.28% 14.87% 10.27% 3.620%

d]

The correlation between Asset 1 and Asset 2 is calculated using CORREL function in Excel

The correlation between Asset 1 and Asset 2 is -1.00

010 - x fc =CORREL(B2:37,02:07) A A B C 1 Year Asset 1 2021 2022 15.00% 2023 26.00% 2024 3.00% 2025 -10.00% 2026 33.00% Asset 2 31.00% 6.00% -8.00% 19.00% 34.00% -16.00% Average Std. Dev. Correlation Portfolio - Return 6.43% 11.67% 13.42% 8.92% 6.28% 14.87% 10.27% 3.620% (1.00)!

The assets are negatively correlated

e]

Negative correlation between assets in a portfolio reduces the overall risk of the portfolio, as the factors affecting the returns of one asset do not affect the other asset. Hence, the returns of the assets do not move together.

The answer is (A) - by combining negatively correlated assets, the overall portfolio risk is reduced.