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# Opportunity Set Definition and Tutorial

A scholarly term that is difficult to imagine.
1. Define - Define the Opportunity Set of investments.
2. Context - Use Opportunity Set in a sentence.
3. Video - See the video for the concepts.
4. Script - Follow along with the transcript below.
5. Quiz - Test yourself.
Updated: February 17, 2021
The investment opportunity set is a theoretical term with great importance. See why below.

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## The Investment Opportunity Set from Portfolio Theory

Intermediate

Opportunity Set is a term used in portfolio theory referring to all possible combinations of portfolios drawn from every risky asset. Graphically it is depicted on a risk-and-return plot with risk on the x-axis and return on the y-axis. It takes the shape of a parabola.

Synonym: Feasible Set

For context, try to count the number of risky investments out there. A list would include real estate investment trusts, real property, gold, stocks, bonds, notes, government agencies, collectibles, art, currencies and even private small businesses.

Now imagine being able to evaluate the return of all of those investments on a monthly basis for a long study period of say 60 months. From there you could calculate the co-movements of each investment against all other investments. Using the resulting covariance measures a covariance matrix is required to calculate portfolio variance. With this and forecasts for the return of each investment a loop can be written to create all portfolio plots on the risk-and-return scatterplot. The resulting parabola is the investment opportunity set.

With the millions of investments available you can see how the simplified concept of an investment opportunity set in theory becomes difficult to imagine, and impossible to implement in practice.

### In a Sentence

Doc:  The Opportunity Set includes all portfolio combinations of all variable assets.
Mia:  So it's like counting stars. It only works in theory. Right?

### Video

This video can be accessed in a new window/App , at the YouTube Channel or from below.

Opportunity Set definition for investment modeling (5:04)

### Video Script

The script includes two sections where we visualize and demonstrate the concept of the Opportunity Set.

#### 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 on this chart in eleven separate 4-minute videos, and Portfolio Theory (opens in a new window) from Quant 101 covers all of it, but you'd have to be willing to sit still for 28 minutes. I'll provide a link at the end.

Ok, let's keep it simple and focus on the Opportunity Set, which is also referred to as the Feasible Set. This is all part of Modern Portfolio Theory, or MPT, developed by Harry Markowitz in the 1950s.

The Opportunity Set is the set of green dots within this parabola, and the number of dots approaches infinity, because portfolio combinations approach infinity. I drew 10 portfolios. Also, imagine the bottom half of the parabola extending underneath as a mirror of the top side.

Think of each dot as a unique portfolio made up of holdings of stocks, bonds, real estate, coins, stamps, and really any variable asset in the world. This is theory and for academic theories to work, it is common for scholars to include a list of assumptions, meaning holding other variables constant. And here is a list of assumptions for MPT to review later.

To make this more practical, imagine simplifying this by narrowing all of the world's assets to just four large US stocks, Microsoft, eBay, Abbott Labs and Merck, as we did in the boot camp. Using liquid assets like stocks helps because they're priced daily, which makes calculating return and risk easier. Unlike stocks, a stamp collection isn't priced every day, so is difficult to calculate expected return and risk like in this example.

Speaking of that, on the chart, expected return is on the y-axis and expected risk is on the x-axis. How does the expected timeframe differ from historical timeframe? Well there's a lot to it, but basically it is common to use past observations and make adjustments to arrive at an expected timeframe, which is the focus of the boot camp.

#### Demonstrate

Let's now demonstrate what's going on here. 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. This one could be 33% in each of eBay, Microsoft and Abbott Labs. And finally, this could be 25% in all four stocks.

We walk through the math elsewhere, but the takeaway should be that through diversificaiton, a portfolio of non-correlated assets has lower risk than the sum of the component stocks. It is called the Opportunity Set because that parabola represents all of the possible combinations of portfolios available, and you'd always prefer to be up and to the left, with higher return and lower risk.

### Quiz

The portfolios with the highest return at any level of risk sit on the top edge of the Opportunity Set. | True or False

True. This is also known as the efficient frontier.

The Opportunity Set includes only the portfolios around the edge of the parabola. | True or False

False. The portfolios around the edge are form what is known as the portfolio possibilities curve.

Still unclear on the Opportunity Set? Leave a question in the comments section on YouTube or check out the Quant 101 Series.

### Related Terms

Our trained humans found other terms in the category Modern Portfolio Theory you may find helpful.

## What's Next?

• To see all terms in the Glossary, click Outline.
• To learn about the Normal Distribution in Excel, click Back.
• Save Internet bandwidth and the electricity serving annoying ads. Click Tip.
• For another term about portfolio theory, Optimal Portfolio, click Next.

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