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Folio Technologies partner Lee Merkhofer will be giving a 2-day training workshop through EUCI on project portfolio management in the utilities industry on March 23-24, 2010, in Toronto, Ontario. Details and registration available here.

In this insightful video commentary, Charles Alsdorf, of Deloitte Financial Advisory Services and with whom Folio often collaborates, outlines the importance of capital budgeting and capital efficiency in the midst of (or coming out of) the recession. Among Charles’s points, the following trends and recommendations (all addressed in Folio Priority System) are worth noting:

• an increased scrutiny on spending, hence the need for an audit trail,
• the need for a thorough and quantified treatment of risk in the prioritization process,
• the importance of a tool that levels the play field and allows the comparison of “apples and oranges” across business units,
• the value of thinking about capital budgeting as more than just go/no-go decisions.

Project interdependencies pose a particular challenge in portfolio optimization. Such dependencies fall into two broad categories:

• Hard dependencies: project A is required for project B to be funded. This is typically the case of infrastructure projects. For example, project A might represent an investment in a new data center (IT), the acquisition of a protein crystallography capability to improve drug discovery (biotech), or the implementation of a pilot smart meter project with a view to a broader smart grid implementation later (utilities). In all of these cases, project A by itself is likely to have a very poor benefit-to-cost ratio. Its sole raison d’etre is to enable other projects — the prizes on which we truly have our eyes.
• Soft dependencies: project A affects the value of project B. This dependency can be positive or negative, and occur on the benefit side or the cost side. For example, there has been much talk recently about whether Apple’s new iPhone 3GS cannibalizes the market share of the iPod Touch (an unfavorable benefit dependency). Conversely, the launch of a new line of product leveraging some of the supply chain elements of an existing offering should create cost-of-goods-sold benefits (a favorable cost dependency).

In this post, we only concern ourselves with hard dependencies. The wrench that foundation projects throw into a portfolio optimization effort is this: how do we prioritize projects that seem to provide little intrinsic benefit, yet are indispensable for “juicier” projects to be available? A simple examination of their benefit-to-cost ratio is clearly inadequate if by benefit we only mean their intrinsic benefit. But is there a possibility of simply redefining what benefit means for such foundation projects? Is it possible to somehow augment the benefit of these foundation projects with the benefit of the projects they enable? Unfortunately, the answer is no: things get more complicated in the presence of multiple dependencies. The following example gives us a window into why.

Illustrative Example

Consider the following mock portfolio. We simplify the presentation by reducing each project to two numbers: its benefit and its cost (we won’t go into the details of how we boiled down the benefit to a single value, here). An arrow represents a requirement: the project at the origin of the arrow is required for the project at the end of the arrow to be available.

The following table tells the story of what the optimal portfolio looks like for an increasingly higher budget. (The reader could easily verify this by hand.)

This table showcases some of the subtleties associated with the valuation of a foundation project. If somebody were to ask, what is the “full benefit” of project #2 (not just its intrinsic benefit), the answer would be very different (if at all defensible) depending on the line we examine in this table.

At the heart of this difficulty lies the following fact: in the presence of dependencies no easy ranking method allows one to decide how or when to fund certain foundation projects. Instead, a full-blown optimization is required, taking into account the entire universe of projects. We have already discussed this topic in this previous post.

Folio Priority System automatically handles such complex dependencies in a seamless and user-friendly way.

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.

At its most basic level, prioritizing projects is often accomplished by ranking them by decreasing benefit-to-cost (B/C) ratio. The projects featuring the biggest “bang for the buck” are then at the top of the list, and all that is left to do is determine how many top projects can be funded given the available budget.

The following table illustrates where to draw the funding line, assuming a $10 million budget.

Notice in passing that we would not want to go below a B/C ratio of 1, since funding such a project would yield less benefit than it would cost.

What are the problems with ranking?

Ranking furnishes a fine first cut at an optimal portfolio, but fails to fully address the following situations — all encountered by our clients.

• Ranking cannot handle interdependencies. If project X is required before project Y can truly yield benefits, or even be undertaken at all, clearly looking at the B/C ratio of X alone is inadequate. A mesh of interdependencies is common with complex infrastructure or IT projects, for examples. In that case, a comprehensive optimization of this network of projects is indispensable.
• More commonly, ranking fails to consider alternative funding levels. Imagine that each of the projects on the list, instead of an all-or-nothing choice, could be funded in various cheaper alternatives than the all-out version, featuring a spectrum of lower costs and lower benefits. Conventional ranking would simply pick, for each project, the one alternative with the highest B/C ratio. However, it can sometimes be optimal to try to cut costs on one project to enable another project to be funded in a more expensive alternative.
• Finally, ranking ignores fine-tuning, i.e., the so-called knapsack problem. The knapsack problem is often perceived to be an academic and unnecessary complication for real-life portfolio optimization. In the remainder of this article, we go through a real-life case study to evaluate the validity of this perception.

What is the knapsack problem?

Bear with us as we indulge in one short theoretical paragraph. The knapsack problem goes as follows: imagine you have a bunch of objects of various values and weights, from which you have to select any number to fit into a knapsack. Your goal is to create the most valuable knapsack possible, without of course exceeding the allowable weight capacity.

Source: Dake under Creative CommonsAttribution-Share Alike 2.5 Generic license.

The parallel with portfolio optimization is obvious: value is the benefit, weight is the cost, and the weight capacity of the knapsack is your budget constraint.

A ranking approach to this problem, therefore, would order the objects by decreasing density: the yellow object right underneath the pack has the highest “value density” — i.e., B/C ratio — (2.5$/kg) and will go in first: it adds a lot of value relative to a small weight consumed. The green box at the top left will go last, if at all: its value density is the lowest (.33$/kg).

Now imagine we start fitting these objects into the knapsack by picking the highest-density objects first, very much like we ranked projects by B/C ratio in the table above and started funding them, until we hit our limit.

As many of us know from experience, we might then decide to make some changes “on the margin”: even though object 26 was the last one to go in, it leaves a lot of unused room in the knapsack. It turns out if I removed object 23 and placed object 27 instead, I would fill the entire sack, even though I have sacrificed a higher B/C object for a lower one. The degree of “shuffling on the margin” is difficult to build a good intuition for. Many practitioners dismiss this phenomenon as, precisely, marginal.

We wanted to put this question to the test: is ranking really insufficient? Do we really need to optimize and deal with the nagging knapsack problem, or can we be content with the simpler ranking method?

Does optimization really matter in real life?

Optimization really does better than ranking in “real life.” The following example is taken from a portfolio of 901 real client projects (the data has been disguised by linear rescaling, but the shape of the curves and the conclusions are strictly identical).

The red curve represents the efficient frontier of the simple ranking method. The blue curve represents the efficient frontier of a full-blown optimization.

Notice how an optimization is able to extract more value for certain budget levels than a straightforward ranking. Why is that? There are two main reasons why optimization fares better:

• Optimization switches alternative funding levels in and out as appropriate. Even though a given project may have one clear winner funding level, featuring a higher B/C ratio than other funding level alternatives for this project, it is sometimes appropriate to be less “greedy” and fund a less costly version so as to enable another high-yielding project to be funded. This is the dominant effect in area C of the curve, where optimization systematically beats ranking by about $8 million.There are actually very few projects featuring multiple, alternative funding levels in this database.
• Optimization can handle big discrepancies in project spending. Of course, the most dramatic benefit of optimization over ranking can be seen at A. A single, very expensive project “holds up” other projects from being funded in the ranking method because the expensive project still comes first due to its high B/C ratio. In the optimization solution, rather than holding up the budget gap, other, lower B/C ratios are “filled into the knapsack” until such time as the big project can be funded. At that point, the red curve abruptly catches up with the blue one. The same phenomenon happens at B with another project, and, to a smaller extent, in other places along the curve where kinks are visible. The more heterogeneous the project sizes, the more value a straight ranking method is likely to leave on the table. At its worst discrepancy ca. a $46 million budget, 19% of the value is missed by the ranking method.

This case study should not be interpreted as an indictment of B/C-ranking. But it clearly illustrates one of the advantages of optimization in the presence of multiple funding levels and heterogeneously sized projects.

Folio Technologies partner Lee Merkhofer will be giving a 2-day training workshop through EUCI on project portfolio management in the utilities industry on May 19-20, 2009, in San Francisco. Details and registration available here.