Final answer:
The assumption that no rational investor wants a portfolio with an expected return below that of the minimum variance portfolio is false, as different investors have varying risk preferences. Investments with lower probabilities of loss can be considered safer, whereas those with high probabilities can be viewed as riskier but may also offer higher expected returns.
Step-by-step explanation:
The statement that no rational investor wants to hold a portfolio with an expected return below that of the minimum variance portfolio is false. A minimum variance portfolio is one that has the lowest level of volatility (or risk) for a given rate of return. However, investors have different risk tolerances and objectives. For instance, some may be willing to accept higher risk for a chance at a higher return, thereby favoring portfolios that may have a higher expected return but also higher variance compared to the minimum variance portfolio.
When assessing the safety of an investment, one must consider the probability of loss alongside the potential returns. An investment like the third investment, which has a lower probability of loss, could be considered the safest. Conversely, the first investment could be deemed the riskiest due to its highest probability of loss, while the second investment might be seen as the one with the highest expected return, given its balance of potential high profit and loss scenarios.
History has shown that high risk can be detrimental to an investment portfolio when the risks are not adequately managed. It is crucial to differentiate between high risk and high return. A high-risk investment can offer a high return, but it can also result in substantial losses, which can be harmful to an investor's portfolio.