efficient frontier

Efficient frontier – What is it?

The efficient frontier is the collection of all efficient portfolios in a market. But, what does that actually mean? How can investors distinguish between efficient portfolios and inefficient ones?

Learning objectives

  • Understand the concept of an efficient portfolio.
  • Identify the main features of the efficient frontier.

The mean-variance framework

Not all portfolios of assets are equally good. Some are better than others. Therefore, it is important for investors to place their funds in the best portfolios that can be constructed in a market. They should avoid investing in suboptimal portfolios. But, how can they tell apart good portfolios from the bad ones? To answer that question, we need a method to compare portfolios. The method we will use compares portfolios in terms of their return and risk. In modern portfolio theory, this is known as the mean-variance framework. That is, the “mean” captures return and the “variance” captures risk. Furthermore, we will rely on two reasonable assumptions:

  1. Investors prefer more return to less return.
  2. Investors prefer less risk to more risk.

The first assumption is based on investors’ insatiable appetite for higher returns. If portfolios A and B have the same level of risk, and if B offers a higher return than A, all investors would prefer B to A. The second assumption is related to investors’ aversion toward risk. That is, if portfolios A and C have the same level of return, but C is less risky than A, investors would choose C over A.

Choosing among portfolios

We illustrate these choices in Figure 1. Investors prefer B over A because of an insatiable appetite for higher returns. Moreover, they prefer C over A because of their general dislike for risk. Therefore, portfolio A is inefficient compared to portfolios B and C. As a result, rational investors should avoid investing in portfolio A. It is dominated by portfolios B and C.

efficient vs inefficient portfolios
Figure 1: Efficient portfolios vs inefficient portfolios

Tracing the efficient frontier

In general, investors should seek the portfolio with the highest return among portfolios that have the same level of risk. And, they should search for the portfolio that bears the least risk among portfolios that offer the same return. We examine this strategy in Figure 2.

Portfolios A, B, and D have the same level of risk. Among these portfolios, investors would choose D as it has the highest return. If there are no other portfolios that offer a higher return than D for the same level of risk, then D is an efficient portfolio.

Furthermore, portfolios A, C, and E offer the same level of return. Among them, portfolio E carries the least amount of risk. So, investors would prefer E over A and C. We consider E an efficient portfolio if there is no other portfolio that has less risk for the same amount of return.

efficient frontier
Figure 2: Efficient frontier

In summary, both D and E are efficient portfolios. If we connect all efficient portfolios (D, E, and others), we end up with the efficient frontier. Therefore, the efficient frontier is the collection of all efficient portfolios within a market. It includes the portfolios that have the best risk-return profile in that market. Portfolios that are not part of the efficient frontier are inefficient. Investors should avoid them as for any inefficient portfolio (say A), they can find an efficient portfolio that offers either more return (D) or less risk (E).

Comparing portfolios that lie on the efficient frontier

Stock markets in countries such as the US and UK contain thousands of stocks. On top of that, there are bond markets, derivatives market, alternative investments, and so on. This multitude of securities offers investors endless possibilities in terms of constructing portfolios. We have so far argued that investors should invest in efficient portfolios and avoid inefficient ones. While this is helpful in terms of limiting choices, there are still many efficient portfolios to choose from! So, how should investors decide? The answer is “it depends.” More specifically, it depends on whether or not there is a risk-free asset available in the market.

If there is, then there is a single optimal risky portfolio. This makes investors’ life much easier as all they need to do is to decide how to split their funds between the optimal risky portfolio and the risk-free asset. We defer further discussion of this to our next post, which is dedicated to the optimal risky portfolio.

If there is no risk-free asset in the economy, then investors’ choice of an efficient portfolio is determined by their degree of risk aversion. For example, looking back at Figure 2 again, an investor who is uncomfortable with a high degree of risk could prefer E over D. Both portfolios are efficient, so they are both good investments, but E carries much less risk than D. On the other hand, another investor who is happy to bear a high level of risk in order to pursue high returns would choose to invest in D instead of E.

In summary, in the absence of a risk-free asset, all portfolios that lie on the efficient frontier are good investment opportunities. Investors, then, should select an efficient portfolio based on the amount of risk they are comfortable bearing.

Minimum variance portfolio and maximum return portfolio

As a final note, let’s discuss the two endpoints of the efficient frontier. This is shown in Figure 3.

The leftmost portfolio is the minimum variance portfolio (MVP). As the name suggests, this is the efficient portfolio that has the lowest level of risk. An investor who is highly risk-averse could invest their funds in the MVP.

At the other extreme, we have the maximum return portfolio (MRP). Among all efficient portfolios, MRP offers the highest level of return. So, if an investor has a low degree of risk aversion and wishes to pursue the highest return available in the market, she can invest in the MRP.

minimum variance portfolio and maximum return portfolio
Figure 3: Minimum variance and maximum return
What is next?

This post is part of our free course on investments. In the previous post, we showed you how to quantify the risk of a portfolio using variances and covariances. Our next post discusses how to locate the optimal risky portfolio when there is a risk-free asset available in the market.

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