Final answer:
The option that cannot lie on the efficient frontier is 'd. A portfolio with the lowest possible return and the highest possible risk,' as efficient portfolios are characterized by the best possible return for a given risk level, not the combination of highest risk and lowest returns.
Step-by-step explanation:
The question is related to the efficient frontier concept introduced by Harry Markowitz in Modern Portfolio Theory. According to the theory, portfolios that lie on the efficient frontier offer the best possible expected return for a given level of risk. The efficient frontier itself is a graphical representation of optimal portfolios that offer the maximum expected return for a given level of risk or the minimum risk for a given level of return.
Among the options given:
The correct option that cannot lie on the efficient frontier is d. A portfolio with the lowest possible return and the highest possible risk. This is because the efficient frontier consists of portfolios that are optimized for the highest return at every level of risk. Therefore, a portfolio that offers both the lowest return and highest risk would not be considered efficient and would not appear on the efficient frontier.
Historically, a high risk level has often proven to be detrimental to an investment portfolio when the associated higher returns do not materialize, leading to significant losses for investors.