This contains setup information needed for #16 - #20.

Generic numerical entry instructions: Enter only your final numerical answer, rounded and expressed as requested and the only non-number you should enter (if appropriate) is a period as 12.34 or a minus sign immediately in front of an answer to denote a negative number. The system will insert a comma for you for large numbers. Do not include an equals sign, dollar sign, percent sign, quotes, a space, any text, or punctuation (except the period or minus sign if appropriate). For example, if asked to round to the nearest 2 decimal places, -$1,234.567 should be entered as -1234.57, not as -$1,234.57 with the dollar sign, not as (1234.57) with parentheses, and not as -1234.56 which is rounded incorrectly. If asked for the nearest integer, enter 1234 and nothing else. The negative sign (if needed) should be to the left of the + sign on your keyboard. A rate of return of 12.36% rounded to the nearest 3 decimal places should be entered as 0.124, not as 12.4%, not as 0.123, not as 0.1236, etc., but only as 0.124). Please read again how your answer is to be expressed before entering it.

ABC is a risky debt fund with an expected return of 5% and a standard deviation of 9%, and XYZ is a risky equity fund with an expected return of 16% and a standard deviation of 20%. These two funds have a correlation coefficient of 0.51. The risk-free rate is 2%.

Write down the above information on your answer sheet for #16.

A pension fund manager decides to invest 45% of the pension fund in ABC, 45% in XYZ, and the remaining funds in the risk-free asset. What is the expected return of the pension fund's assets (considering that the funds will be invested in a portfolio of ABC, XYZ, and the risk-free asset).? Express your answer in decimal format, rounded accurately to 4 decimal places (e.g., 1.23456% should be entered as 0.1235 and nothing else).

This continues from #17.

Generic numerical entry instructions: Enter only your final numerical answer, rounded and expressed as requested and the only non-number you should enter (if appropriate) is a period as 12.34 or a minus sign immediately in front of an answer to denote a negative number. The system will insert a comma for you for large numbers. Do not include an equals sign, dollar sign, percent sign, quotes, a space, any text, or punctuation (except the period or minus sign if appropriate). For example, if asked to round to the nearest 2 decimal places, -$1,234.567 should be entered as -1234.57, not as -$1,234.57 with the dollar sign, not as (1234.57) with parentheses, and not as -1234.56 which is rounded incorrectly. If asked for the nearest integer, enter 1234 and nothing else. The negative sign (if needed) should be to the left of the + sign on your keyboard. A rate of return of 12.36% rounded to the nearest 3 decimal places should be entered as 0.124, not as 12.4%, not as 0.123, not as 0.1236, etc., but only as 0.124). Please read again how your answer is to be expressed before entering it.

What will be the standard deviation of the pension funds assets (a single number, considering that the pension fund will be invested in portfolio of all 3 assets)? Enter your answer in decimal format, accurate and rounded to 4 decimal places (e.g., 12.345% should be entered as 0.1235 and nothing else).

(Note: In working this part, it may be helpful to proceed in two steps by first considering a hypothetical risky-fund only portfolio that consists only of ABC and XYZ, and then after that to consider a portfolio of hypothetical risk-fund portfolio and the risk-free asset this approach avoids the need to use a formula for the variance of a 3-asset portfolio).

Question 18

This uses setup information from #16

Generic numerical entry instructions: Enter only your final numerical answer, rounded and expressed as requested and the only non-number you should enter (if appropriate) is a period as 12.34 or a minus sign immediately in front of an answer to denote a negative number. The system will insert a comma for you for large numbers. Do not include an equals sign, dollar sign, percent sign, quotes, a space, any text, or punctuation (except the period or minus sign if appropriate). For example, if asked to round to the nearest 2 decimal places, -$1,234.567 should be entered as -1234.57, not as -$1,234.57 with the dollar sign, not as (1234.57) with parentheses, and not as -1234.56 which is rounded incorrectly. If asked for the nearest integer, enter 1234 and nothing else. The negative sign (if needed) should be to the left of the + sign on your keyboard. A rate of return of 12.36% rounded to the nearest 3 decimal places should be entered as 0.124, not as 12.4%, not as 0.123, not as 0.1236, etc., but only as 0.124). Please read again how your answer is to be expressed before entering it.

This uses the setup information from #16 but introduces a new investor (not the pension fund manger) who is the basis of questions #18-#20.

A new investor (not the pension fund manager) has invested 60% in ABC fund and 40% in the risk-free asset (see #16 setup for information on ABC and the risk-free). What is this new investor's expected return? Enter your answer in decimal form, rounded and accurate to the nearest 4 decimal places (e.g., 1.2345% should be entered as 0.1235 and nothing else).

Question 19

This continues from #18 (which uses setup information from #16)

Generic numerical entry instructions: Enter only your final numerical answer, rounded and expressed as requested and the only non-number you should enter (if appropriate) is a period as 12.34 or a minus sign immediately in front of an answer to denote a negative number. The system will insert a comma for you for large numbers. Do not include an equals sign, dollar sign, percent sign, quotes, a space, any text, or punctuation (except the period or minus sign if appropriate). For example, if asked to round to the nearest 2 decimal places, -$1,234.567 should be entered as -1234.57, not as -$1,234.57 with the dollar sign, not as (1234.57) with parentheses, and not as -1234.56 which is rounded incorrectly. If asked for the nearest integer, enter 1234 and nothing else. The negative sign (if needed) should be to the left of the + sign on your keyboard. A rate of return of 12.36% rounded to the nearest 3 decimal places should be entered as 0.124, not as 12.4%, not as 0.123, not as 0.1236, etc., but only as 0.124). Please read again how your answer is to be expressed before entering it.

This continues from #18.

Consider the new investor from #18, who has invested 60% in ABC fund and 40% in the risk-free asset (the same ABC and risk-free as in the setup information in #16). What is the standard deviation of this new investor's portfolio? Enter your answer in decimal form, rounded and accurate to the nearest 4 decimal places (e.g., 1.2345% should be entered as 0.1235 and nothing else).

Question 20

This continues from #18-19 (which uses setup information from #16)

Generic numerical entry instructions: Enter only your final numerical answer, rounded and expressed as requested and the only non-number you should enter (if appropriate) is a period as 12.34 or a minus sign immediately in front of an answer to denote a negative number. The system will insert a comma for you for large numbers. Do not include an equals sign, dollar sign, percent sign, quotes, a space, any text, or punctuation (except the period or minus sign if appropriate). For example, if asked to round to the nearest 2 decimal places, -$1,234.567 should be entered as -1234.57, not as -$1,234.57 with the dollar sign, not as (1234.57) with parentheses, and not as -1234.56 which is rounded incorrectly. If asked for the nearest integer, enter 1234 and nothing else. The negative sign (if needed) should be to the left of the + sign on your keyboard. A rate of return of 12.36% rounded to the nearest 3 decimal places should be entered as 0.124, not as 12.4%, not as 0.123, not as 0.1236, etc., but only as 0.124). Please read again how your answer is to be expressed before entering it.

This continues from #18-19.

Consider the new investor from #18, who has invested 60% in ABC fund and 40% in the risk-free asset. This investor is considering switching funds (selling ABC, and using XYZ instead--see the setup information from #16 for information on XYZ). The weights in XYZ and the risk-free asset will be different than the weights on ABC and the risk-free (i.e.g, they will no longer be 60% and 40%). If the investor chooses the weights in XYZ and the risk-free asset to achieve the same overall expected return as before (your answer from #18), what is the standard deviation the investor will face? Enter your answer in decimal form, rounded and accurate to the nearest 4 decimal places (e.g., 1.2345% should be entered as 0.1235 and nothing else).