In modern portfolio theory, the efficient frontier (or portfolio frontier) is an investment portfolio which occupies the “efficient” parts of the risk–return spectrum. Formally, it is the set of portfolios which satisfy the condition that no other portfolio exists with a higher expected return but with the same standard deviation of return (i.e., the risk). The efficient frontier was first formulated by Harry Markowitz in 1952.
A combination of assets, i.e. a portfolio, is referred to as “efficient” if it has the best possible expected level of return for its level of risk (which is represented by the standard deviation of the portfolio’s return). Here, every possible combination of risky assets can be plotted in risk–expected return space, and the collection of all such possible portfolios defines a region in this space. In the absence of the opportunity to hold a risk-free asset, this region is the opportunity set (the feasible set). The positively sloped (upward-sloped) top boundary of this region is a portion of a hyperbola and is called the “efficient frontier”.
If a risk-free asset is also available, the opportunity set is larger, and its upper boundary, the efficient frontier, is a straight line segment emanating from the vertical axis at the value of the risk-free asset’s return and tangent to the risky-assets-only opportunity set. All portfolios between the risk-free asset and the tangency portfolio are portfolios composed of risk-free assets and the tangency portfolio, while all portfolios on the linear frontier above and to the right of the tangency portfolio are generated by borrowing at the risk-free rate and investing the proceeds into the tangency portfolio.
It is represented by plotting the expected returns of a portfolio and the standard deviation of returns. The y-axis is made up of the expected returns of the portfolio. The x-axis is labeled as the standard deviation of returns, which is a measure of risk.
A portfolio is then plotted onto the graph according to its expected returns and standard deviation of returns. The portfolio is compared to the efficient frontier. If a portfolio is plotted on the right side of the chart, it indicates that there is a higher level of risk for the given portfolio. If it is plotted low on the graph, the portfolio offers low returns.
Significance of an Efficient Frontier
The efficient frontier is the foundation for modern portfolio theory, which is the idea of how investors aim to create a portfolio that maximizes expected returns based on a specific level of risk. It helps investors understand the potential risks and returns in their portfolios and analyze how they compare to the optimal set of portfolios that are considered to be efficient. Doing so helps investors to accordingly change their investing strategies by understanding the level of risk that pertains to each portfolio.
It should be noted that there is no single efficient frontier for everyone. Each one is different for every investor because it depends on multiple factors – such as the number of assets in the portfolio, the industry of the assets, and the degree of the investor’s risk tolerance.
Limitations of an Efficient Frontier
The efficient frontier is built on assumptions that may not accurately portray realistic situations. For example, it assumes that all investors think rationally and avoid risks. It also assumes that fluctuations in market prices do not depend on the number of investors, and all investors enjoy equal access to borrowing money at a risk-free interest rate.
Such assumptions are not always true, as some investors may not make rational decisions, and some investors are high risk-takers. Not all investors obtain equal access to borrowing money as well.
Additionally, it assumes that asset returns result in a normal distribution. However, in reality, asset returns often do not follow a normal distribution, as it often varies three standard deviations away from the mean.
Expected Return = (Weight of A1 * Return of A1) + (Weight of A2 * Return of A2)
Portfolio Risk = √ [(Weight of A12 * Standard Deviation of A12) + (Weight of A22 * Standard Deviation of A22) + (2 X Correlation Coefficient * Standard Deviation of A1 * Standard Deviation of A2)]
Assumptions of the Efficient Frontier Model
- All investors have a common goal: avoid the risk because they are risk-averse and maximize the return as far as possible and practicable.
- Investors are rational and know all the facts about the markets. This assumption implies that all the investors are vigilant enough to understand the stock movements, predict returns, and invest accordingly. That also means that this model assumes all investors are on the same page regarding knowledge of the markets.
- There are not many investors who would affect the market price.
- Investors lend and borrow money at a risk-free interest rate.
- The markets are efficient.
- Investors have unlimited borrowing power.
- The assets follow a normal distribution.
- Markets absorb information quickly and accordingly base the actions.
- The investors’ decisions are always based on expected return and standard deviation as a measure of risk.
- This efficient frontier graph helps investors choose the portfolio combinations with the highest and least possible returns.
- This theory portrayed the importance of diversification.
- It represents all the dominant portfolios in the risk-return space.
- The theory can be applied, or the frontier can be constructed only when a concept of diversification is involved. If there is no diversification, the theory would certainly fail.
- The assumption that all investors are rational and make sound investment decisions may not always be true because not all investors would have enough knowledge about the markets.
- Also, the assumption that investors have unlimited borrowing and lending capacity is faulty.
- The real costs, like taxes, brokerage, fees, etc., are not considered while constructing the frontier.
- The assumption that the assets follow a normal distribution pattern might not always stand true. In reality, securities may have to experience returns far from the respective standard deviations, sometimes like three standard deviations away from the mean.
Efficient frontier and Investor Utility
The efficient frontier consists of the set of all efficient portfolios that yield the highest return for each level of risk. The efficient frontier can be combined with an investor’s utility function to find the investor’s optimal portfolio, the portfolio with the greatest return for the risk that the investor is willing to accept.