Efficient Frontier

What is the Efficient Frontier?

The efficient frontier represents portfolios offering the highest expected return for a given risk, or the lowest risk for a given return. It is a curved line on a risk and return chart, where the x-axis is represents the level of risk (as measured by the standard deviation of asset returns) and the y-axis is the expected return. To be considered as efficient, a portfolio must lie on the frontier, where those portfolios positioned below the curve are perceived as suboptimal due to offering lower returns for the same risk level. The efficient frontier is part of the asset allocation process and is widely used by investors to construct diversified portfolios that aim to maximize return potential while managing risk.

How Does an Efficient Frontier Work?

To understand the efficient frontier , we need to plot all the portfolios that we want to explore on a risk-return graph. Below is an example, in which each point represents a different mix of assets. As we can see, portfolios A and B are offer better returns than portfolios C and D respectively, because offer more attractive expected return for the same level of risk, or lower risk for the same expected return. The efficient frontier contains of all portfolios of risky assets that a risk-averse investor will choose, depending on their investment objective and risk tolerance profile. Rational investors will not choose any portfolio that is positioned below the curve (in this case, these are portfolios C and D).

Practical Example

In this example we have an exercise that requires us to create an efficient frontier chart assuming a two-asset portfolio. Provided is monthly price data for the two assets – an equity and a bond index fund.

Download the full solution from the free downloads section.

What are the Efficient Frontier’s Assumptions?

The efficient frontier relies on several key assumptions from Modern Portfolio Theory (MPT), which are listed below.

• First, it assumes that all investors are rational and risk-averse, which suggests preference for higher returns for a given level of risk, or lower risk for a given level of return respectively
• Risk is defined as the volatility of returns and is quantified by the standard deviation of the portfolio’s returns
• Asset returns are assumed to follow a normal distribution, which would allow risk and return to be fully captured by the mean and standard deviation
• It assumes that markets are efficient and no investor has informational advantage over another since all information is already priced in
• Transaction costs are not taken into account, which allows for unlimited portfolio rebalancing (i.e. buying and selling assets does not incur fees or taxes)
• Investors have unlimited access to borrowing or lending money at a constant risk-free interest rate
• The model assumes a single period investment horizon, meaning that all investors are assumed to have the same time horizon when making investment decisions

What is the Efficient Frontier in CAPM?

The efficient frontier in the Capital Asset Pricing Model (CAPM) is extended and simplified by the introduction of a risk-free asset, which fundamentally changes the shape of the frontier. In its original form, developed by Harry Markowitz in the 1950s, the Modern Portfolio Theory does not include a risk-free asset and focuses only on risky assets such as bonds, equities, etc. This results is a curved efficient frontier showing the optimal risk-return portfolio combinations.

The Capital Allocation Line (CAL) represents the risk and return trade-off for a portfolio that combines the risk-free asset and risky assets. It is shown as a line chart where one axis measures risk and the other expected returns and its slope allows investors to pick different points depending on their risk tolerance level.

As shown on the chart below, every point on the CML represents a combination of the market portfolio and the risk-free asset.

Limitations of an Efficient Frontier

Despite that it is a powerful tool in portfolio theory, there are several criticisms of the efficient frontier which highlights some of its limitations. Most of them are fundamental and are linked to the assumptions made in the MPT. Below we outline the most important ones.

• The concept assumes that all investors are rational and risk-averse, which isn’t always the case.
• It is built using historical data and estimates could be unstable as small changes can significantly alter the optimal portfolio (also referred as sensitivity issues). Therefore, critics argue that using past data to predict future performance is unreliable, especially in volatile markets.
• Markets are assumed to be efficient with all information already reflected in asset prices, which may not be the case in less efficient areas of the market such as stocks with small market capitalisation.
• It uses the normal distribution, meaning that returns follow a bell-shaped curve, where most returns cluster around the average (mean), and extreme returns (very high or very low) are rare. There is no consideration of skewness (asymmetry) or fat tails (extreme outcomes such as the 2008 global financial crisis) in the return distribution.
• No taxes, transaction costs, or liquidity issues are factored in. Critics of the efficient frontier often argue that these assumptions oversimplify reality, which results in models that break down during highly volatile and unpredictable market conditions.
• Static portfolio allocation – being based on a single-period model with a fixed asset mix, it doesn’t consider the possibility of economic or investor lifecycle changes, tactical allocation or regular portfolio rebalancing.

Conclusion

The significance of the efficient frontier  is that by illustrating the risk and return trade-off, it helps investors identify the most effective asset combinations to maximize returns for a given level of risk.

It uses mean-variance optimization, where each portfolio’s expected return is calculated as the weighted average of asset returns, and risk is measured by the portfolio’s standard deviation, factoring in correlations between assets. Portfolios on the frontier are efficient, while those below it are suboptimal. However, there are also critics highlighting the limitations of the efficient frontier such as overreliance on historical data and high input sensitivity along with the assumption for normal distribution of returns and efficient markets.

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