Final answer:
The introduction of a risk-free rate to efficient portfolios extends investment possibilities, creates a straight line efficient frontier called the Capital Market Line, and provides a higher expected return for any given risk level except for the tangential portfolio and the risk-free asset. The correct answer is option c.
Step-by-step explanation:
The question at hand pertains to the efficient portfolios and the impact of introducing a risk-free security on investment possibilities. When lenders and borrowers are given a risk-free rate to work with, they can indeed extend the range of investment possibilities. Moreover, through the combination with efficient portfolios, the presence of a risk-free asset changes the nature of the efficient frontier. Instead of being a curvilinear set, it becomes a straight line, which represents all possible combinations of the risk-free asset and the market portfolio, known as the Capital Market Line (CML). Finally, for any given level of risk, the introduction of a risk-free asset offers an opportunity to obtain a higher expected return — except in the case where the investor is already holding the tangential portfolio (the market portfolio) or is invested entirely in the risk-free asset.
Therefore, the answer to the student's question is that by combining lending and borrowing at the risk-free rate with the efficient portfolios, we can (I) extend the range of investment possibilities; (II) change the set of efficient portfolios from a curvilinear to a straight line; and (III) provide a higher expected return for any level of risk, except for the tangential portfolio and the risk-free asset. The correct choice from the given options would be (c) I, II, and III.