Construct the efficient frontier

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Construct the efficient frontier

Optimal portfolios that comprise the efficient frontier tend to have a higher degree of diversification than the sub-optimal ones, which are typically less diversified.

The efficient frontier concept was introduced by Nobel Laureate Harry Markowitz in and is a cornerstone of modern portfolio theory. Optimal Portfolio One assumption in investing is that a higher degree of risk means a higher potential return.

Conversely, investors who take on a low degree of risk have a low potential return. According to Markowitz's theory, there is an optimal portfolio that could be designed with a perfect balance between risk and return. The optimal portfolio does not simply include securities with the highest potential returns or low-risk securities.

The optimal portfolio aims to balance securities with the greatest potential returns with an acceptable degree of risk or securities with the lowest degree of risk for a given level of potential return. The points on the plot of risk versus expected returns where optimal portfolios lie are known as the efficient frontier.

Selecting Investments Assume a risk-seeking investor uses the efficient frontier to select investments. The investor would select securities that lie on the right end of the efficient frontier.

Backtest Portfolio Asset Allocation

The right end of the efficient frontier includes securities that are expected to have a high degree of risk coupled with high potential returns, which is suitable for highly risk-tolerant investors.

Conversely, securities that lie on the left end of the efficient frontier would be suitable for risk-averse investors. Limitations The efficient frontier and modern portfolio theory have many assumptions that may not properly represent reality.

For example, one of the assumptions is that asset returns follow a normal distribution. Consequently, asset returns are said to follow a leptokurtic distribution or heavy-tailed distribution.

Additionally, Markowitz's posits several assumptions in his theory, such as investors are rational and avoid risk when possible; there are not enough investors to influence market prices; and investors have unlimited access to borrowing and lending money at the risk-free interest rate.

However, reality proves that the market includes irrational and risk-seeking investors, there are large market participants who could influence market prices, and there are investors who do not have unlimited access to borrowing and lending money.(Reference: The red dots form what is known as the Efficient Frontier.

Why is it called that? Because it’s the only place you should want to be. 🙂 Take the bright green dot, which could represent any non-red dot. This is the living breathing core of all rocket design. Delta Vee equals Vee Ee times Natural Log of Arr.

This is the secret that makes rocket design possible.

Construct the efficient frontier

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Types of indices.

Construct the efficient frontier

Stock market indices may be classified in many ways. A 'world' or 'global' stock market index — such as the MSCI World or the S&P Global — includes stocks from multiple regions.

Regions may be defined geographically (e.g., Europe, Asia) or by levels of industrialization or income (e.g., Developed Markets, Frontier Markets). A portfolio is efficient if there is no alternative with: Higher expected return with same level of risk; Same expected return with lower level of risk; Higher expected return for lower level of risk; Let’s take a portfolio of two assets and see how we can build the efficient frontier in excel.

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