Question

9) You invest $1,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 16% and a standard deviation of 20% and a Treasury bill with a rate of return of 6%. A portfolio that has an expected value in 1 year of $1,100 could be formed if you _________.

Multiple Choice

• place 40% of your money in the risky portfolio and the rest in the risk-free asset

• place 55% of your money in the risky portfolio and the rest in the risk-free asset

• place 60% of your money in the risky portfolio and the rest in the risk-free asset

• place 75% of your money in the risky portfolio and the rest in the risk-free asse

Answer 1

The expected return of the portfolio, E(R) = The expected value in one year/Current value - 1

E(R) = 1,100/1,000 - 1

E(R) = 1.1 - 1

E(R) = 0.1

E(R) = 10%

E(R) = Weight of risky asset * Expected return on the risky asset + Weight of Treasury bill * Expected return on the Treasury bill

Weight of risky asset + Weight of Treasury bill = 1

Weight of Treasury bill = 1 - Weight of risky asset

E(R) = Weight of risky asset * Expected return on the risky asset + ( 1 - Weight of risky asset) * Expected return on the Treasury bill

0.10 = Weight of risky asset * 0.16 + ( 1 - Weight of risky asset) * 0.06

0.10 = Weight of risky asset * 0.16 + 0.06 - 0.06 * Weight of risky asset

0.10 - 0.06 = Weight of risky asset * (0.16 - 0.06)

0.04 = Weight of risky asset * 0.10

Weight of risky asset = 0.04/0.10

Weight of risky asset = 0.4

Weight of risky asset = 40%

Option A is correct:

place 40% of your money in the risky portfolio and the rest in the risk-free asset