Efficient Frontier Definition and Tutorial for Investment Modeling

Investment risk planning with the Efficient Frontier

Intermediate

Efficient Frontier is a term used in portfolio theory to describe the combinations of portfolios that offer the highest return at any given level of risk. It is often depicted on a risk-return plot with risk on the x-axis and return on the y-axis. It is the top half of the hyperbola starting at the Minimum Variance Portfolio. The hyperbola, called the Opportunity Set, is the collection of all portfolio combinations of all risky assets.

Synonym: portfolio frontier, efficient portfolio

For context, the ideal portfolio is one that maximizes return while minimizing risk. In practice this requires an estimation of both return and risk which is difficult to accomplish. The Theory also states that all investors view the world using mean-variance optimal portfolios, which we know couldn't be farther from the truth. The estimation of risk requires many calculations that only professional investors are capable and interested in performing consistenly over time. Therefore, while investing on Efficient Frontier is a nice goal and something every investor should strive for, here is where practicality differs from from theory by a wide margin.

In a Sentence

Joy: In practice, what percentage of investors actually calculate the Efficient Frontier?
Doc: Well, probably close to zero. Remember it's a theory.

Video

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Efficient Frontier definition for investment modeling (4:17)

Video Script

The script includes two sections where we visualize and demonstrate the creation of an efficient frontier.

Visualize

We're sitting in Excel and this is a snippet from our boot camp course.

We cover all of the curves, lines and dots here in one 40-minute video there, but because most people can't sit still for that long, we have eleven separate 4-5 minute videos like this one. I'll provide a link to the boot camp video if you prefer one video. (See the tutorial Ace Your Portfolio Theory Exam).

Ok, let's keep it simple and focus on the Efficient Frontier, which is part of Modern Portfolio Theory, developed by Harry Markowitz in the 1950s.

First of all, we have a chart, with expected return on the y-axis and expected risk on the x-axis. Here we are using the expected timeframe, which uses past observations as input, then after making adjustments, you have what is baked-in to market expectations. Of course there is a lot to setting expectations, and that is a focus of the boot camp.

Now, the Efficient Frontier is the green circle that extends from the tip, or the Minimum Variance Portfolio, all the way up. So at every level of risk, sits a portfolio with the highest level of return, and that's the one the investor would prefer over all others below that level of return.

And this parabola contains all portfolios invested in all risky assets around the world, plus all of the combinations of weights to all assets. So this is a big and theoretical concept.

For academic theories to work, scholars include a list of assumptions, meaning holding other variables constant. And here is a list of assumptions for MPT to review later.

Demonstrate

Let's now demonstrate what's going on here and make it more practical. Imagine simplifying this by narrowing our focus to just four large US stocks, Microsoft, eBay, Abbott Labs and Merck.

Let's say this dot corresponds with a portfolio constructed with 100% in eBay, and 0% in the other three stocks. Next, this dot could be 50% eBay and 50% Microsoft. And maybe a portfolio that sits here could be a combination of 25% in all four stocks. We walk through the math elsewhere, but the takeaway should be that through diversification, a portfolio of non-correlated assets has lower risk than the sum of the component stocks. And here, the Efficient Frontier shows the portfolios with the highest expected return at each level of expected variance.

Quiz

Click box for answer.

In practice, the Efficient Frontier is often measured using historical timeframes. | True or False?

True

Portfolios on the Efficient Frontier represent the highest expected return at every level of expected risk. | True or False?

True

Questions or Comments?

Still unclear on the efficient frontier? Leave a question in the comments section on YouTube or check out the Quant 101 Series and and specifically the tutorial Ace Your Portfolio Theory Exam.

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Efficient Frontier Definition and Tutorial