This is the first in a series of articles that will examine some of the most commonly used decision-making methods for the selection or rejection of individual projects throughout the project portfolio management process. These methods determine whether or not a given project (either proposed or in process) should be included in your next capital budget. After a brief discussion of the economic theories upon which these individual methods are based, I'll cite the rationales for (1) not relying on these theories alone and (2) using as well, and sometimes instead, practical rules of thumb in real-world decision making.

Although no specific background is assumed, a little prior knowledge of project management and corporate finance, including probability theory and statistics, will facilitate your reading of the articles. For those readers wanting or needing up-to-date tutorials on these subjects, the References provide pertinent information. In addition, the appendixes at the end of this article contain supplementary material for the reader interested in further insight into these topics. And, throughout this series, I'll illustrate how commercial, off-the-shelf (COTS) software tools can aid in the management of larger, more complex portfolios. In short, these articles will be about computer-assisted common sense.

### Overview

Projects—sometimes a mix of large-scale, mid-size, and small ones—are selected by senior management according to a variety of criteria, by a variety of techniques, and for a variety of reasons. Companies have begun to realize the value of using portfolio management principles and processes to select, prioritize, and manage both internal and external IT projects and the resources to execute those projects. Project portfolio management includes the processes to determine which projects should be started, stopped, or continued and to ensure that the projects selected and prioritized are in alignment with corporate objectives; and once selected, proper allocating resources among the projects within the portfolio to ensure maximum utilization of these resources. The primary objective of project portfolio management is to identify the proper mix of strategic and tactical projects that will enable an organization to meet or exceed the expectation of the organization's investment strategy.

Making investment decisions about proposed or in-process projects would not be a perilous matter if the future could be known with certainty; but, it cannot. In this connection, I'll discuss three separate types of project risk/uncertainty:

**Stand-alone risk**, which views the risk of a project in isolation, and hence without regard to portfolio effects.**Within-firm risk**, also called**corporate risk**, which views the risk of a project within the context of the firm's portfolio of projects.**Market risk**, which views a project's risk within the context of the firm's stockholders' diversification in the general stock market.

As you will see, a particular project might have highly uncertain returns, and hence have high stand-alone risk, yet taking it on might not have much effect on either the firm's corporate risk or that of its owners, once diversification is taken into account.

### Diversification (*Don't Put All Your Eggs in One Basket)*

Corporate diversification involves investing in projects whose returns are not highly correlated with the firm's other assets. With diversification, the poor performance of one project will sometimes be offset by the good outcome of another. The major stated objectives of corporate diversification are to stabilize earnings and reduce corporate risk. (Stockholder diversification occurs when stockholders hold a well-diversified portfolio of many dissimilar companies. There is some disagreement over the benefits of corporate diversification to reduce risk when investors can accomplish the same result more easily.)

The expected rate of return and the standard deviation (a measure of risk or uncertainty) provide information about the nature of the probability distribution associated with a single project or a portfolio of projects. However, these numbers say nothing about the way the returns on projects interrelate. A statistic that provides some information about this question is the correlation (ρ) between two projects, which varies in value between + 1 and - 1. When ρ = +1, the two projects (investments) are perfectly correlated and they rise or fall together; when ρ = 0, they're independent; and, when ρ = -1, the rise of one occurs with a decline of the same magnitude in the other.

Most projects are positively correlated with the firm's other projects, with the correlation being highest for projects in the firm's core business and less high (but still positive) for investments outside the core. However, the correlation is rarely +1.0. This being the case, some of the project's stand-alone risk can be diversified away to determine its within-firm risk.

Examples of IT projects not likely to be highly correlated with one another (and likely to have different risk-return distributions) are:

- Develop custom-made software internally
- Develop custom-made software by outsourcing
- Buy existing generic commercial software
- Create new Project Management Office
- Deploy new technology (for example, VoIP)
- Upgrade network and/or servers

One approach to determining which projects to invest in is to choose a desired level of expected return for your portfolio of projects and then pick those projects that minimize the risk (standard deviation or its square, the variance) of the return on the resulting portfolio. The discussion below will follow this path, which is described mathematically in Figure 1.

Fully understanding these equations is not a prerequisite to reading the rest of this article: Complicated as the equations shown at the top of Figure 1 may seem, they can be modeled fairly easily by using a spreadsheet such as Microsoft Excel. Then, using an optimization tool such as Palisade Evolver (an add-in for Microsoft Excel), you can minimize the portfolio's standard deviation (or its square, the variance) for different rates of return, subject to certain constraints.

The model as stated in Figure 1 is in its *bare-bones* form. However, you can extend it by adding any number of additional constraints: For example, you may want to add the constraint that your firm cannot spend more on any alternative portfolio than its expected budget. In general, firms will have a hard capital constraint that limits their ability to pursue additional projects that require additional capital. I'll have more to say on this last point—capital rationing—in a future article.

**Figure 1:** Modern project portfolio selection – Efficient Set Method

Note:I have equated risk with portfolio variance. Actually, the only part of the variance management (and stockholders) dislike isdownsidevariance. There are portfolio optimization models that minimize only the downside variance, but they're beyond the scope of this article. Such methods are, however, described in Chapter 10 of Reference 6.

Figure 2 shows the results of this modeling/optimization process: of the ten proposed projects (A, B, C, D, E, F, G, H, I, and J). Six projects (A, C, D, H, I, and J) have been selected automatically by Evolver because, of all possible portfolios having a mean return of 7.5, these six projects create a portfolio with the minimum variance (shown in cell D21). This optimization is achieved after Evolver repeatedly adjusts the proportion of your capital budget allocated to each project included in the portfolio of projects (as shown in cells G3:G12) until the optimum solution (minimum variance) is reached. These values correspond to w_{i} in Figure 1.

**Figure 2:** Computer determination of an efficient portfolio

Figure 3 shows the dialog box by which you "link" the Evolver optimizer to the Excel spreadsheet.

**Figure 3:** Specifying the *goals*, *variables*, and *limits* used by optimizer.

When the optimizer is run for different minimum expected returns (set in cell F17), the model gives you a family of minimum variance points that are located on the solid line (also known as the *efficient frontier*) drawn in Figure 4.

**Figure 4:** Graph of possible portfolios: *Efficient—blue; Inefficient—maroon*

The solid line in the graph shown in Figure 4 represents the *efficient frontier* or the *efficient set* and is the result of plotting the expected returns vs. standard deviation for different portfolio weights (w_{i}) found by the algorithm outlined in Figure 1. The dashed line is also derived from the same computation, but for any portfolios on this portion of the curve with a given standard deviation (risk) there is another portfolio on the solid portion of the curve above with a higher expected mean. Figure 4 shows that, as long as there is less than perfect correlation (as long as ρ<1) between pairs of projects, the diversification effect applies; that is, as seen in Figure 2, the standard deviation of a portfolio of many projects is less than the weighted average of the standard deviation of the individual projects. A detailed explanation of this result can be found in Chapter 7 of Reference 4.

There may be multiple portfolios that have the same standard deviation. Modern portfolio theory assumes that, for a specified standard deviation, a rational investor would choose the portfolio with greatest return. Similarly, there may be multiple portfolios that have the same return and modern portfolio theory assumes that, for a specific level of return, a rational investor would choose the portfolio having the lowest standard deviation. A portfolio is said to be *efficient* if there is no portfolio having the same standard deviation with a greater expected return and there is no portfolio having the same return with a lesser standard deviation. The *efficient frontier* is the collection of all efficient portfolios.

In general, the area on and to the right of the curve represents all the possible combinations of expected return and standard deviation for a portfolio of any size. For example, in a firm with 36 projects, one portfolio might be made up of, say, 25 projects. Another portfolio, of 18 projects. A third portfolio, a different set of 18 projects. Obviously, the combinations are virtually endless. But, those off the solid line are not optimum, as defined above.