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Why do risk-averse investors choose Markowitz’s efficient frontier?
Since Harry Markowitz proposed the efficient frontier theory in 1952, this model has become an important part of the capital market. This theory helps investors build more efficient investment portfolios and minimize risks by analyzing various possible security combinations.
The fundamental purpose of the Markowitz model is to reduce the risk of the overall portfolio by selecting securities with different volatilities (risks), rather than just focusing on the expected returns of each security.
Risk-averse investors, as the name suggests, are more sensitive to the volatility of capital. They hope to reduce the risk of potential losses while obtaining reasonable returns. Markowitz theory provides a reasonable framework that allows risk-averse investors to choose the best investment portfolio between different risk levels.
Basic assumptions of the Markowitz model
When developing the Markowitz model, Markowitz made several basic assumptions:
- Investors are risk averse.
- The investor's utility function is convex downward, showing that as risk increases, investor satisfaction decreases.
- Investors base their decisions on a single-period model.
Determine an effective investment portfolio
The efficient portfolio in the Markowitz model is defined as the highest expected return that can be obtained at a certain level of risk. Investors consider the following when making decisions:
Under the same level of risk, investors will choose a portfolio with higher returns; and at the same level of returns, they will choose an investment portfolio with lower risk.
For example, at a specific risk level, there are multiple investment portfolios to choose from. The Markowitz model helps investors sort through these choices and pick the portfolio that best suits their own risk appetite.
Choose the best combination
In addition to determining an effective portfolio, risk-averse investors also need to consider their own risk preferences when choosing the best portfolio. For example, some investors have a weak tolerance for risk, which makes them more inclined to choose portfolios at the lower left of the efficient frontier, while less risk-averse investors may choose portfolios at the upper end of the efficient frontier.
According to Markowitz's theory, investors' optimal portfolio can be found at the tangent point of the efficient frontier and its utility curve, which marks the highest level of satisfaction they can obtain.
Introduction of Capital Market Line (CML)
With the introduction of risk-free assets, the Markowitz model can be further developed into the capital market line (CML), which reflects the trade-off between risky assets and risk-free assets. This development provides investors with more flexibility, allowing them to make more optimal choices at different risk levels.
The existence of the capital market line makes all portfolios of risky assets and risk-free assets more clearly divided, helping risk-averse investors better design their investment portfolios.
Defects of the Markowitz model
Although Markowitz's efficient frontier theory has certain theoretical foundation and practical application value, it also has some shortcomings. First, the model is relatively sensitive to input parameters, meaning that small changes can lead to significantly different portfolio allocations.
In addition, the model may suffer from instability when dealing with large portfolio sizes or high correlations between assets.
Because of the specific needs and market conditions of different investors, the applicability and effectiveness of the Markowitz model are often challenged.
Conclusion
In summary, Markowitz's efficient frontier provides a structured approach for risk-averse investors to find the best risk-return combination among diversified assets. Although it still has certain limitations, it is still an indispensable tool for investors who pursue balanced returns and control risks. In such a volatile market environment, investors need to think about: while pursuing returns, how to find the risk level that satisfies them most?
