Here at Folio, efficient frontiers are our daily bread: we talk about them in our marketing materials, we graph them, test them, tweak them, and we love showing our clients where their hand-crafted portfolio choices stand against the efficient frontier.

However, newcomers to portfolio optimization sometimes misunderstand what we mean by “efficient frontier.” We do not blame them: the expression is used in different ways in different disciplines. In this article, we contrast efficient frontiers in finance theory and in project portfolio management.

Efficient Frontiers in Finance

In Markowitz’s modern portfolio theory, the efficient frontier is obtained by plotting, for each feasible portfolio of financial instruments, its expected return (i.e., its probability-weighted average return over all risk scenarios) against its risk exposure (i.e., the standard deviation or variance of this return).

It is beyond the scope of this short post to explain the underlying math. We will simply point out that it is the existence of correlation between individual financial assets (e.g., stocks) that allows us to combine them into portfolios yielding a higher return for the same amount of risk.

Ultimately, the math acrobatics are meant to address this question: how can I allocate 100% of my capital amongst various financial instruments so as to achieve the highest possible return for a given risk level I am willing to accept?

Any such allocation is deemed to be an efficient portfolio, in the sense that it is impossible to achieve a greater return without taking on more risk. The collection of all these efficient portfolios then constitute the efficient frontier (the upper part of the blue curve below).

Return vs. risk: the efficient frontier as defined in finance theory. Source: Bob Taylor.

A number of results, most notably Sharpe and Lintner’s Capital Asset Pricing Model (CAPM), further build upon this concept by making equilibrium assumptions about the market players.

For those wishing to drill deeper, here is a very concise technical introduction to modern portfolio theory.

Efficient Frontiers in Project Portfolio Management (PPM)

PPM also makes heavy use of the concept of efficient frontier, but it has a different meaning than in finance theory.

First of all, it addresses a different question, namely: to what extent does a higher investment level enable me to create more value by funding more (or different) projects?

By plotting the value created by a portfolio against the investment necessary to fund it, or, as it is often summarized, its total benefit against its total cost, we answer a question similar to, albeit different from, the one posed in finance. For a given cost level what is the maximum total value I can create by picking the right combination of projects?

Portfolio benefit vs. cost: the efficient frontier as defined in PPM. Generated by Folio Priority System.

From here, cost benefit analysis tells us how we can generate (an approximation of) the efficient frontier by ranking candidate projects by decreasing benefit-to-cost ratio — a method we can intuitively link to the decreasing slope of the red curve.

For a more rigorous treatment, we know that ranking alone is insufficient in the presence of complicating issues such as multiple funding levels, disparate project sizes, or project interdependencies, many of which occur in real-life applications.

Does This Mean PPM Ignores Risk?

No, it certainly doesn’t.

Managing portfolio risk is a critical component of success for organizations seeking to implement portfolio optimization. It raises a number of questions: What is the nature of the portfolio risks? Can they be diversified away? How do systemic risks affect the risk of the portfolio? How much risk can my organization tolerate?

One way to address at least project-specific risk is to penalize risky projects by considering their risk-adjusted benefit rather than their expected benefit when creating the efficient frontier.

Portfolio-level risks such as energy or commodity prices present another level of complexity which must be addressed separately from individual project adjustments.

In this post, we just wanted to lay out the possibly-confusing dual terminology. We will address risk more extensively in a future post.