Question

Assume you are considering a portfolio containing two assets, Land M. Asset L will represent 59 % of the dollar value of the portfolio, and asset M will account for the other 41 %. Assume that the portfolio is rebalanced at the end of each year. The expected returns over the next 6 years, 2018dash2023, for each of these assets are summarized in the following table: Year 2018 2019 2020 2021 2022 2023 Projected Return Asset L Asset M 13% 20% 14% 19% 17% 15% 16% 13% 17% 11% 20% 11% a. The expected portfolio return, rp, for 2018 is %. (Round to two decimal places.) The expected portfolio return, rp, for 2019 is The expected portfolio return, rp, for 2020 is The expected portfolio return, re, for 2021 is % (Round to two decimal places.) %. (Round to two decimal places.) % (Round to two decimal places.) The expected portfolio return, fp, for 2022 is %. (Round to two decimal places.) The expected portfolio return, rp, for 2023 is %. (Round to two decimal places.) b. The average expected portfolio return, ip, 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. If asset L represents 41% of the portfolio and asset M 59%, the average expected portfolio return, , over the 6-year period is %. (Round to two decimal places.) If asset L represents 41% of the portfolio and asset M 59%, the standard deviation of expected portfolio returns, Sp, over the 6-year period is %. (Round to three decimal places.) e. Compare your answers to the answers from parts b and c. Which of the following statements is correct? (Select the best choice below.) A. Changing the weights of the two assets will increase the standard deviation of the portfolio if less weight is put on the more variable asset and will increase the expected return of the portfolio if more weight is put on the asset with the higher expected return. B.Changing the weights of the two assets will lower the standard deviation of the portfolio if less weight is put on the more variable asset and will lower the expected return of the portfolio if less weight is put on the asset with the higher expected return. C.Changing the weights of the two assets will lower the standard deviation of the portfolio ifless weight is put on the less variable asset and will lower the expected return of the portfolio if less weight is put on the asset with the lower expected return. D. Changing the weights of the two assets will lower the standard deviation of the portfolio if more weight is put on the more variable asset and will increase the expected return of the portfolio if more weight is put on the asset with the higher expected return.

Answer 1

Since the assets weights are rebalanced each year, the weight remain same Expected return = 0.59* Return from asset L+0.41 * return from asset M Asset L(%) Asset M (%) 20 Year 2018 2019 2020 2021 2022 2023 Return from portfolio (%) 15.87 16.05 16.18 14.77 14.54 16.31 b) The average retrun for the 6 years from the portfolio is (15.87 +16.05 +16.18 +14.77 + 14.54 +16.31)/6 15.62 To calculate the standard deviation use the excel formula Standard deviation = 0.765

if the asset L consist of 41% and asset M consist of 59%, then average return would be Asset L (%) Asset M (%) Year 2018 2019 2020 2021 2022 2023 Return from portfolio (%) 17.13 16.95 15.82 14.23 13.46 14.69 average 15.38 Standard deviation 1.50 B is correct Changing the asset of the two assets will lower the standard deviation of the portfolio if less weight is put on more variable asset and will lower the expected return if less weight is put on the asset with the higher expected return A is not correct because less weight on more variable asset will reduce the standard deviation C is not correct because if less weight is put on more variable asset then standard deviation would be less and with less weight on lower return asset,the total return should increase D is not correct because putting more weight on variable asset should increase the standard deviation.