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Optimal Portfolio Definition and Tutorial

Practitioners know the optimal portfolio is no magic bullet. It isn't a destination. It's a starting point.
  1. Define - Define the optimal portfolio of investments.
  2. Context - Use optimal portfolio in a sentence.
  3. Video - Learn the concepts with video.
  4. Script - Follow along with the transcript below.
  5. Quiz - Test yourself.
face pic by Paul Alan Davis, CFA
Updated: February 18, 2021
To balance theory with practice is a differentiator for aspiring portfolio managers. Keep reading to learn more.

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Understanding the Optimal Portfolio Theory of Investments


Optimal portfolio is a term used in portfolio theory to refer to the one portfolio on the Efficient Frontier with the highest return-to-risk combination given the specific investor's tolerance for risk. It's the point where the Efficient Frontier (supply) and the Indifference Curve (demand) meet.

Synonym: Optimal Set

For context, it is important to remember that 'optimal' refers to the one best solution based on numerous estimates derived from the past. First, risk is estimated using backward looking data. Second, covariances, or co-movements of investments typically use backward-looking data as a starting point. Third, estimates for future returns, which represent the numerator in the portfolio optimization function have a great deal of uncertainty.

Many beginners trade on the first 'optimal' portfolio selected, without realizing it is just one solution of many nearby solutions that offer the portfolio manager a better risk and return trade-off. This is especially true when including portfolio turnover, risk factor exposures, industry group weights and unrealistic expectations for risk from the risk model and return from the alpha model.

So, in practice, typically the portfolio manager will adjust parameters in the portfolio optimization program to find a better 'optimal' solution before submitting a list of securities to trade.

In a Sentence

Doc:  The theoretically optimal portfolio is often based on estimates using data from historical periods.
Lia:  Why is it called 'Optimal' if we know the future will never be like the past?


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

Optimal Portfolio definition for investment modeling (4:45)

Video Script

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


We're sitting in Excel and this is a snippet from our boot camp course (Quant 101).

There we cover all of the curves, lines and dots shown here in one 40-minute video, but because most people don't have that much time, we have eleven separate 4-5 minute videos just like this one. I'll provide a link to the boot camp video Portfolio Theory (opens in a new window) at the end if you'd like the whole story.

Ok, let's keep it simple and focus on the Optimal Portfolio, 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 the focus of the boot camp.

Now, the Optimal Portfolio, marked OP here, is where one investor's Indifference Curve, in light green meets the top of the Efficient Frontier.

The Efficient Frontier is the dark green line that represents the highest level of return at each level of risk from all of the millions of portfolios invested in all risky assets around the world.

So this is a very theoretical concept and only institutional investors with their portfolio optimization programs go through this, and even then quantifying risk tolerance is difficult, if not impossible. Also, for academic theories to work, scholars include a list of assumptions, meaning holding other variables constant. And here is a list of assumptions to review later.


Let's demonstrate this by talking about two points on the Indifference Curve and thinking about the word indifference. Here the client would require a higher rate of return to accept this higher level of risk. Because these curves don't cross there is no match between supply and demand.

And as we slide up the curve, to another spot where the investor would be indifferent, and be willing to accept higher risk for higher return. Right there, at the OP, the market supply, or portfolios offered by the market here match what the investor is willing to accept, so there is a match between supply and demand. This is the point called the Optimal Portfolio.

Keep in mind that a risk-averse investor, like a retiree, may have a curve way above this one, and they'd be less willing to accept market risk.


Click box for answer.

The Optimal Portfolio should be considered a preliminary portfolio because it is based on estimates. | True or False?


The numerator in the function that derives the optimal portfolio weights to securities is portfolio variance. | True or False?

False. It is the array of expected returns.

Questions or Comments?

Still unclear on the Optimal Portfolio? Check out the web page and video Ace Your Portfolio Theory Exam.

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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