# Understanding the Efficient Frontier: Maximize Returns, Minimize Risk

![Efficient Frontier](https://www.investopedia.com/thmb/lJr40mGLmFweO8jg-S-mTpwZkbU=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/efficientfrontier_final-a7219a2140a446ab814daf2c8279d429.jpg)

*— Investopedia / Katie Kerpel*

> **Definition**
>
> The efficient frontier is a set of portfolios that offer the greatest anticipated return for their level of risk or the least risk for an expected return.

## What Is the Efficient Frontier?

The efficient frontier is a concept that is integral to modern portfolio theory, as developed by American economist Harry Markowitz. This frontier is the group of optimally-diversified portfolios that maximizes [expected return](https://www.investopedia.com/terms/e/expectedreturn.asp) for a given level of risk, or presents the lowest risk for a given level of [expected return](https://www.investopedia.com/terms/e/expectedreturn.asp). The efficient frontier is graphically represented as a curved line with risk on the x-axis and expected return on the y-axis. Whether or not a portfolio is optimal or sub-optimal depends on where it appears in relation to the line.

### Key Takeaways

*   The efficient frontier is a graph that helps investors understand risk versus return, plotting portfolios with the highest expected return for a given level of risk.
*   Developed by Harry Markowitz in 1952, the efficient frontier is central to modern portfolio theory and emphasizes diversification to optimize returns while minimizing risk.
*   The efficient frontier highlights the trade-off between risk and reward, with portfolios on the curve demonstrating optimal returns for their risk levels through diversified assets.
*   Criticisms of the efficient frontier include its reliance on assumptions which may not reflect real-world conditions, like normally distributed returns and rational investor behavior.
*   Investors can use the efficient frontier to select investments based on their risk tolerance: risk-averse investors gravitate towards the left side, while risk-tolerant investors look to the right side of the curve.

## Explaining Efficient Frontier in Modern Portfolio Theory

The efficient frontier theory was introduced by Nobel Laureate [Harry Markowitz](https://www.investopedia.com/terms/h/harrymarkowitz.asp) in 1952 and is a cornerstone of [modern portfolio theory (MPT)](https://www.investopedia.com/terms/m/modernportfoliotheory.asp). The efficient frontier rates portfolios (investments) on a scale of return (y-axis) versus risk (x-axis). The [compound annual growth rate (CAGR)](https://www.investopedia.com/terms/c/cagr.asp) of an investment is commonly used as the return component while standard deviation (annualized) depicts the risk metric.

The efficient frontier graphically represents portfolios that maximize returns for the risk assumed. Returns are dependent on the investment combinations that make up the portfolio. A security's standard deviation is synonymous with risk. Ideally, an investor seeks to fill a portfolio with securities offering exceptional returns but with a combined standard deviation that is lower than the standard deviations of the individual securities.

The less synchronized the securities (lower [covariance](https://www.investopedia.com/terms/c/covariance.asp)), the lower the standard deviation. If this mix of optimizing the return versus risk paradigm is successful, then that portfolio should line up along the efficient frontier line.

A key finding of the concept was the benefit of diversification resulting from the curvature of the efficient frontier. The curvature is integral in revealing how diversification improves the portfolio's risk/reward profile. It also reveals that there is a diminishing marginal return to risk.  

![Most investment choices involve a tradeoff between risk and reward.](https://www.investopedia.com/thmb/3bsz7F-eb8xFGYyCA1p3MmAmk1M=/420x0/filters:no_upscale():max_bytes(150000):strip_icc()/efficient_frontier-5bfc379b46e0fb00265f15ab.jpg)

**

> **Important**
>
> Adding more risk to a portfolio does not gain an equal amount of return—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.

## Limitations and Critiques of Efficient Frontier Theory

The efficient frontier and modern portfolio theory involve assumptions that might not reflect reality. For instance, they assume asset returns follow a normal distribution.

In reality, securities can have returns, or [tail risk](https://www.investopedia.com/terms/t/tailrisk.asp), that are over three [standard deviations](https://www.investopedia.com/terms/s/standarddeviation.asp) away from the mean. Consequently, asset returns are said to follow a [leptokurtic](https://www.investopedia.com/terms/l/leptokurtic.asp) distribution or heavy-tailed distribution.

Also, Markowitz assumes that investors are rational, can't affect market prices, and have access to unlimited borrowing and lending at a risk-free rate of return.

But in reality, markets have irrational, risk-seeking investors, big players who might affect prices, and investors without unlimited borrowing and lending access.

## Important Factors When Using the Efficient Frontier

In investing, higher risk is assumed to bring higher returns. Conversely, lower risk means lower returns. 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. Optimal portfolios form the efficient frontier on a plot of points of [risk versus expected returns](https://www.investopedia.com/terms/m/markov-analysis.asp).

A risk-seeking investor would choose securities on the right end of the efficient frontier. The right end 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](https://www.investopedia.com/terms/r/riskaverse.asp) investors.

## Why Is the Efficient Frontier Important?

The curvature of the efficient frontier graphically shows the benefit of diversification and how this can improve a portfolio's risk versus reward profile.

## What Is the Optimal Portfolio?

An optimal portfolio is one designed with a perfect balance of risk and return. The optimal portfolio looks to balance securities that offer the greatest possible returns with acceptable risk or the securities with the lowest risk given a certain return.

## How Is the Efficient Frontier Constructed?

The efficient frontier rates portfolios on a  coordinate plane. Plotted on the x-axis is the risk, while return is plotted on the y-axis—annualized standard deviation is typically used to measure risk, while compound annual growth rate (CAGR) is used for return.

## The Bottom Line

The efficient frontier, a concept developed by economist Harry Markowitz, demonstrates the importance of appropriate portfolio diversification with its graphic representation of balanced risk and return in investment portfolios. That is, portfolios on the efficient frontier provide optimal returns for specific risk levels. Risk-seeking investors might target portfolios on the right side of the frontier for higher potential returns, while risk-averse investors might focus on the left side for lower risk. The efficient frontier isn't without critics, so it's important to understand its assumptions and limitations, including its potential for deviation from real market conditions.  

> **Article Sources**
>
> 1.  The Nobel Prize. "[This Year's Laureates Are Pioneers in the Theory of Financial Economics and Corporate Finance](https://www.nobelprize.org/prizes/economic-sciences/1990/press-release/)."
>     
> 2.   Investment Management Consultants Association. "[The Efficient Frontier in Modern Portfolio Theory: Weaknesses and How to Overcome Them](https://investmentsandwealth.org/getattachment/8ac04ae1-e30d-4c52-9015-c58b105e652c/IWM13JulAug-EfficientFrontierMPT.pdf)," Page 1.
>     
> 3.  Investment Management Consultants Association. "[The Efficient Frontier in Modern Portfolio Theory: Weaknesses and How to Overcome Them](https://investmentsandwealth.org/getattachment/8ac04ae1-e30d-4c52-9015-c58b105e652c/IWM13JulAug-EfficientFrontierMPT.pdf)," Pages 1-2.
>     
> 4.  Investment Management Consultants Association. "[The Efficient Frontier in Modern Portfolio Theory: Weaknesses and How to Overcome Them](https://investmentsandwealth.org/getattachment/8ac04ae1-e30d-4c52-9015-c58b105e652c/IWM13JulAug-EfficientFrontierMPT.pdf)," Page 3.