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# Portfolio Possibilities Curve Definition and Tutorial

A term likely to show up on a test, but has limited practical value because portfolio managers focus on the top half, the Efficient Frontier.
1. Define - Define the Portfolio Possibilities Curve.
2. Context - Use Portfolio Possibilities Curve in a sentence.
3. Video - See the video for the graphical depiction.
4. Script - Follow along with the transcript below.
5. Quiz - Test yourself.
Updated: February 18, 2021
Measuring all possible portfolios on two planes is difficult to imagine, but is an important component of Modern Portfolio Theory.

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## Understanding the Portfolio Possibilities Curve

Intermediate

Portfolio Possibilities Curve is a term from portfolio theory referring to all of the lowest-risk portfolios from the Opportunity Set. At each level of return, this curve includes the one portfolio with the lowest risk. This represents the edge, or border, of the parabola containing all combinations of portfolios drawn from every risky asset. Graphically, it is depicted on a risk-return plot with risk on the x-axis and return on the y-axis.

Synonyms: Portfolio Curve, Portfolio Possibility Curve

For context, imagine being in the 1960s, and you're developing the first workable scientific and academic solution to quantify investment risk. To explain these concepts scholars named each line and curve and the term describing the outer line of the parabola as the portfolio possibilities curve stuck.

The XY scatterplot quantitatively demonstrates a trade-off of return versus risk and the benefit of diversification. The portfolio possibilities curve represents the whole curve where the efficient frontier is only the top half. The efficient frontier is more well known because it is the only solution a theoretical investor would choose because it shows the highest returning portfolio at every level of risk.

### In a Sentence

Doc:  Why would investors avoid the lower half of the Portfolio Possibilities Curve?
Joe:  Wouldn't it be like driving through a dangerous neighborhood when the freeway is just as fast?

### Video

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

Portfolio Possibilities Curve definition for investment modeling (4:37)

### Video Script

The script includes two sections where we visualize and demonstrate the concept of the Optimal Portfolio.

#### 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 in this chart in eleven separate 4-minute videos, and video 22 (see Quant 101 instead) from the boot camp covers all of it, but you'd have to be willing to still for 40 minutes. I'll provide a link at the end.

Ok, let's keep it simple and focus on the Portfolio Possibilities Curve. This is all part of Modern Portfolio Theory, or MPT, developed by Harry Markowitz in the 1950s.

The Portfolio Possibilities Curve is the dark green curve at the edge of this parabola, and it extends down here as a mirror of the top. It is actually made up of portfolios with the lowest risk at each level of return.

Recall each dot here is a unique portfolio made up of holdings of stocks, bonds, real estate, stamps, and really any variable asset in the world. This is theory, and for any academic theory 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 practical, imagine 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. I used liquid assets like stocks because they're priced daily, making it easier to calculate return and risk.

On the chart, expected return is on the y-axis and expected risk is on the x-axis. And how does the expected timeframe differ from the historical timeframe? There's a lot to it, but basically, modelers make adjustments to past observations to set expectations, which is a 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. For that same level of return, wouldn't you rather invest all the way over here, where the risk is much lower? This might be a spot with 25% invested in all four stocks. We walk through the math elsewhere, but the takeaway should be that a rational investor would invest only in portfolios that lie on the Portfolio Possibilities Curve, and really only those on the top half of the parabola because they offer the lowest risk at every level of return.

### Quiz

The Portfolio Possibilities Curve is a subset of the Efficient Frontier. | True or False?

False. The other way around.

The Portfolio Possibilities Curve shows the one point with highest level of return at each level of risk. | True or False?

False. It shows two points at each level of risk. Except for at the tip of the parabola which is called the Minimum Variance Portfolio.

Still unclear on the Portfolio Possibilities Curve? Leave a question in the comments section on YouTube. Also, see a tutorial page and video called Ace Your Portfolio Theory Exam from the Quant 101 Course.

### Related Terms

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

## What's Next?

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