Efficient frontier

CFA Level I
#1

Got this question from the Wiley Qbank:

Which of the following statements is true?

a. An investment that is not on the efficient frontier is always high risk

b. An investment not on the efficient frontier always has the lowest returns

c. An investment that is not on the efficient frontier may create a portfolio that has a lower risk for the same return

The Qbank said the correct answer is C because: "The efficient frontier is the set of portfolios that gives investors the highest return for a given level of risk or the lowest risk for a given level of return. It thus follows that a portfolio that is not on the efficient frontier will have another portfolio with lower risk for the same return."

Can someone help me understand this? If the efficient portfolio is supposed to give the lowest risk for a given level of return, how the heck is there another portfolio with LESS risk for the SAME return?

#2

Hi,

The portfolio with less risk and the same return exists precisely because the initial investment is NOT on the efficient frontier, as stated in C. You can think of it in the mean-variance framework (graph with variance on the x-axis and return on the y-axis): from every portfolio below the efficient frontier (those above it are not attainable, by definition) you can extend a line upwards, keeping the variance constant, until you hit the frontier. That point will represent a portfolio with the same variance/risk (constant point on the x axis) and a higher return.

The same reasoning goes to get a portfolio with less risk for the same return, just extend the line to the left while keeping y (the variance) constant.

#3

This doesn’t make sense to me. Any point below the efficient frontier should give you a portfolio with less return for the same risk - not less risk for the same return. With the x-axis representing risk and the y-axis representing return, moving “below” the efficient frontier moves you down the y-axis (return) while maintaining the x-axis (risk).

EDIT: Never mind I get it it now. Choice C never said “below” the efficient frontier.