The capital allocation line (CAL) represents all combinations of a risky asset and a risk-free asset. The slope of the CAL reflects the trade-off between risk and return. The efficient frontier includes only risky portfolios, and the security market line (SML) shows expected return as a function of beta under the CAPM.

The flatter the investor’s indifference curve, the less risk averse they are. Dana Wu’s leveraged investment in the market portfolio implies lower risk aversion than Andrew Lopez, who prefers a more conservative allocation with a higher proportion in risk-free assets.

The efficient frontier represents portfolios that offer the highest expected return for a given level of risk. However, investors with different risk tolerances will choose different optimal portfolios along the frontier based on their individual indifference curves. It is incorrect to say that all investors will choose the same portfolio on the efficient frontier.

Each investor has a unique risk–return trade-off, represented by their indifference curves. The portfolio that is tangent to the highest attainable indifference curve on the efficient frontier is the optimal portfolio for that investor, as it provides the maximum utility given their level of risk aversion.

A risk-averse investor will not choose a portfolio if another offers higher return with the same or lower risk. Portfolio Alpha is dominated by Beta—Beta has lower risk and only slightly lower return, making Alpha unattractive. Beta and Gamma could both be rational choices depending on the investor’s tolerance for risk, but Alpha would be eliminated.

In the Markowitz framework, the optimal portfolio is found where the investor's highest attainable indifference curve is tangent to the efficient frontier. This point reflects the best combination of risk and return based on the investor’s utility function (risk preference). It is not necessarily the lowest risk or highest return portfolio.

Flatter indifference curves reflect lower risk aversion, meaning the investor is more willing to accept additional risk for smaller increases in expected return. Therefore, Lee, being less risk averse, will choose a portfolio with higher risk and higher expected return than Chen, who will prefer a more conservative allocation.

According to Markowitz portfolio theory, the optimal portfolio for a given investor lies where their highest attainable indifference curve is tangent to the efficient frontier. This point represents the portfolio that maximizes the investor's expected utility, balancing risk and return according to their unique preferences.

Risk-averse investors require higher expected returns to compensate for taking on higher levels of non-diversifiable (systematic) risk. This fundamental relationship is captured by models like the Capital Market Line (CML) and Security Market Line (SML), which both demonstrate a positive slope between risk and expected return.

The optimal portfolio is not necessarily the one with the lowest risk, but rather the one that provides the highest utility for the investor, given their unique risk-return preferences. Some investors may prefer higher-risk portfolios if they also offer higher expected returns that match their utility preferences.