Lee Merkhofer Consulting Priority Systems

Technical Terms Used in Project Portfolio Management (Continued)





























random variable

a variable whose value is unknown an subject to variations due to chance. Random variables can be discrete, which means they can only take on a finite number of possible values, or continuous, which are variables that can have any values within a continuous range.

Random variables are typically denoted by a capital letter (e.g., X). If a probability distribution can be associated with a random variable, the distribution tells what the possible values of X are and the probabilities assigned to each.

range sensitivity index (RSI)

An index defined to measure the degree to which subjects, when assigning weights, properly account for the ranges specified for their assessment. Experiments show that for most subjects and most weight assessment methods, there is insufficient adjustment based on range. The RSI is equal to 1.0 when the weights are adjusted fully based on range and equal to 0 when no weight adjustment is made. The farther the RSI is from 1.0, the less sufiient the adjustment.

range sensitivity principle

A mathematical result demonstrating that the weights assessed for an additive value function must be sensitive to the ranges used for their assessment. The normalized form of the additive value function:

V(x1,x2...xN) = w1V1(x1) + w2V2(x2) ... + wNVN(xN)

will be such that each single-attribute value function, Vi(xi), will equal zero or one when its performance measure xi is at its worst or best performance level, respectively. Each wi weight will equal the value assigned by the decision maker to swinging the xi performance measure from its worst to its best level.

Suppose that the range encompassing the worst and best levels of performance for the i'th performance measure is changed from R to R'. If the change in range produces new worst and/or best levels of performance, a correction factor will need to be applied to the previously assessed wi weight. If the value function is linear, for example, the correction is simpy the ratio R'/R. Doubling the range will, in the linear case, cause the weight to double. The range sensitivity principle merely states that weights are sensitive to the ranges used for their assessment. This fact can be used to strategically set ranges to produce weights consistent with importance weights so as to minimize the impact of importance weight bias.

ranking curve

A graph derived from a ranked list of projects, where the ranking is based on the ratio of some measure of project benefit to project cost. Specifically, the curve is a plot of cumulative cost (as projects are added to the project portfolio in rank order) vs. cumulative benefit (obtained by cumulating the benefit measure). Most project portfolio management tools provide a ranking curves as outputs. As explained in the paper on efficient frontiers vs. ranking curves, ranking curves appear similar to, but are different than, the efficient frontier of project portfolios.

Ranking curve

Ranking curve

ranking theorem

A result of the principle of economic efficiency. Suppose there are multiple, independent projects that compete for funding from a fixed budget. It those projects are ranked based on the ratio of project value to project cost and then selected from the top down until the budget is exhausted, then the value of the resulting project portfolio will either equal or come very close to that of the value maximizing portfolio. The first project on this list yields the biggest bang-for-the-buck and should be funded fi rst, followed by the second on the list, etc., up to the point when the budget has been exhausted (or the benefit-to-cost ratio drops below 1, whichever comes first).

Project costs and benefits are the incremental costs and benefits that result from the decision to conduct the project compared to what would occur if the project is not conducted. Project costs must include all costs required to secure the project benefits. In comparing the various projects, those projects with the highest B/C ratio would be ranked as the most efficient

The only potential for error (assuming the above assumptions includng that projects are independent and that the capital budget is the active constraint for selecting projects) occurs if the portfolio identified through ranking fails to consume the entire budget. In that case, it is possible that there is another portfolio that spends more of the available budget that would produce a higher total value. In practice, especially if the budget is large enough to fund many projects, the difference in the value obtained from strict ranking and that of a truly optimal portfolio is typically small.

There are several real-world complications for applying the ranking theorem. For one, project costs and benefits often occur over time. To account for timing, discounted, present-value equivalents are typically used to express project values and project costs. Another complication is projects conducted over multiple budget periods (e.g., multi-year projects), Such projects often require funding not just from the current budget period, but from one or more future budgetting periods as well. In this case, multi-year projects are typically priotized along with other projects in each budget period based on the ratio of total discounted project value to total discounted remaining costs. Risk is another complication. To account for risk, project value is expressed as a risk adjusted value. Benefi t-to-cost ranking demands that there be only one dimension to cost. It is unable to accommodate multiple constraints.

The ranking theorem is useful because it provides an simple and intuitive way to prioritize projects and identify high-value project portolios without the need to use portfolio optimization tools designed to solve the knapsack problem. The ranking theorem is often the basis for the project prioritization capabilities provided by project portfolio management tools, though a few include portfolio optimization capability. Full-blown optimization, unlike simple ranking, recommends portfolios that yield the biggest bang-not just "for the buck" (i.e., along a single cost dimension, but-for the multiple resource constraints faced by an organization. MCDM often includes sophisticated optimization methods for choosing the values of decision variables. Optimization methods, such as linear programming, integer programming, and dynamic programming, provide project prioritization consistent with benefit cost and incremental benefit cost analyses, also taking account of the impact of budget constraints in creating an optimized project set.

rank reversal

Arises when adding or deleting an alternative (e.g., a candidate project) to the list of options under consideration causes the ranking of other (independent) alternatives to reverse.

Rank reversal

Rank reversal example

This result occurs with some multi-criteria analysis scoring models, most notably for the analytic hierarchy process (AHP), where the inclusion or exclusion of even a poorly ranked project (an irrelevant alternative) can cause project scores (which are derived from pairwise comparisons across all alternatives) to change in such a way that project rankings change. Although there is debate over the matter, rank reversals based on irrelevant alternatives are generally regarded to be inconsistent with rational decision making. (Why should my preference for one option over another change if an option I don't want is removed from consideration?). Project portfolio management tools based on AHP may include a mode of operation that prevents rank reversals from occurring, however this "fix" does not address the fundamental logical questions involved.

real options analysis

A method for valuing projects, assets, and businesses using concepts originally developed to value financial options. Real options analysis is most useful for large capital budget decisions in situations involving significant uncertainties (especially market uncertainties) and where management has flexibility to adapt decisions to unexpected developments. For example, real options analysis is often used for mergers and acquisitions, facility expansion decisions, oil exploration, contract valuation, and prioritizing R&D projects.

Real options analysis is based on the recognition that there is an important similarity between financial investments and business projects. In finance, a stock option (specifically, a "call-option contract") allows (but does not force) the owner to buy a fixed number of shares of the stock at a specified date for a specified price. The owner will want to exercise the option and buy the stock if its price goes up, but not if the stock price goes down. Similarly, projects involve options. For example, a project to construct a new factory provides options to postpone construction if the economy slows. Building a new factory also includes options to temporarily shut down or abandon the plant to cut losses, as well as to expand its size to meet an unexpected demand for more production. The options inherent in physical assets are termed "real" to distinguish them from classic financial options.

In the 1997, Robert Merton, Myron Scholes, and Fischer Black won a Nobel price for deriving a model for computing the price of call- and other types of options. This work provided the foundation for developing an analogous method for valuing the options (flexibility) inherent in projects. As with financial options, the value of the options implicit in a project increases the value of that project. For example, a factory with operating options is more valuable than an identical factory that does not include options, and the extra value is the value of the options that are available.

Traditional financial valuation methods, including net present value (NPV), typically under-value projects because they fail to adequately account for the value of management flexibility to exercise the project's inherent options. Expected net present value (ENPV) can include the value of flexibility (if "downstream decisions" are represented in the decision tree), and most authors include ENPV as subset of the methods available for real options analysis. Similarly, multi-attribute utility analysis (MUA) can account for the value of management flexibility by including project evaluation criteria related to the option value of the project. However, real options analysis also includes solution methods that derive option values from the market prices of underlying assets. Thus, for example, a real options analysis of an oil drilling project could derive the project's value in part based on market prices for barrels of oil, similar to the way the value of a call option on a stock can be derived from the behavior of the market price of that stock.

A major benefit of real options analysis is the insights that it provides for managing projects so as to leverage flexibility and limit downside risks. Although in most cases it may not be practical or even possible to apply the most sophisticated real option solution techniques to value many projects, real options theory has shown how simpler methods, including ENPV and MUA can be used to more accurately account for option value by recognizing multiple decision pathways and better accounting for the cost of risk.

regression analysis

A statistical technique applied to data to determine the degree of correlation among one or more variables; that is, to quantify the extent to which the variables tend to move together. Typically, regression analysis seeks an equation, called a regression equation or regression function, that relates a dependent variable to one or more independent variables. In this way, regression analysis may be used to suggest potential cause-effect relationships, although it cannot by itself be used to prove such relationships.

relational database

A collection of data elements organized into separate tables (sometimes referred to as "relations") of predefined categories in a way that makes it easier to access and combine data elements. The structure allows data from different tables to be accessed and reassembled in different ways without having to reorganize the tables.

The concept of a relational database was developed in 1970 by Edgar Codd, of IBM, whose objective was to accommodate in an efficient way a user's ad hoc request for selected data. The standard application program used to interface to a relational database is the structured query language (SQL). Most business database management systems use relational databases and project portfolio management tools are often advertised as storing data in a relational database.

release management

The coordination and bundling of projects and project tasks for the purpose of optimally synchronizing the release of new products and services. Release management can be important when business value depends on interdependent projects, or when launch date serves as a rally point for the completion of the projects. The term originated in the field of software engineering, where it involves managing the IT project lifecycle, including development, testing, deployment and support of software releases.

For projects focused on new products, release management and project portfolio management are closely related, since shifting projects dates for the purpose of resource balancing can have a significant impact on the value of the portfolio.

residual risks

The risks that remain after management has taken action to mitigate the risks identified during project planning. Residual risks are those that must be considered when deciding whether to conduct the project.


One of the basic and essential means available to an organization for conducting projects and other operations, such as money, plant, labor, assets, and raw materials.

resource balancing

A component of resource management focused on balancing the supply and demand for the resources needed for conducting projects. Key inputs for efficient resource balancing are forecasts of the demands for various resources and the supply of those resources. The general goal is to achieve near 100% resource utilization without over-allocating resources across projects. Also, called resource leveling, the process mainly involves leveling or smoothing the demand for resources by adjusting the start and end dates for projects or the tasks that make up those projects so as to reduce peaks and valleys in resource demand.

Various software tools are available to support resource balancing. However, as explained in the section of the paper on tools for resource balancing, such tools rarely if ever attempt to optimize the selection of projects based on the people and other resources that are available. Instead, the typical approach is to select projects subject only to a constraint on total project costs (including labor costs), and then to phase the selected projects by shifting start and end dates for tasks. Since it is typically undesirable to delay project completion dates, resource balancing mainly looks for ways to shift work that is not on the critical path, and network analysis techniques, including PERT charts, are often used to aid the process.

resource management

The field concerned with effectively managing an organization's resources, including people, money, materials, equipment, and services. A key focus is resource allocation, the efficient deployment and use of the organization's resources. Human resource management refers to the special case of managing people resources, and the topic is typically defined to include the management of payroll and benefits, education and professional development, and other human resource functions. Resource balancing is a key technique used for resource management.

return on investment (ROI)

The ratio of project income to project cost. Typically, project income is specified as the average annual net income from a project, and project cost is the total invested capital:

ROI is annual net income divided by project cost

For example, a project that costs $100,000 and is expected to return $20,000 annually would have an ROI of 20%.

As indicated by its definition, ROI is a measure of the financial benefits obtained from a project over a specified time period in return for the required investment, with the result expressed as a percentage. ROI is widely used (especially in the private sector) both to justify a proposed project and to evaluate, after the completion of the project, the extent to which the desired return was achieved.

ROI is similar to internal rate of return (IRR) in that it provides a measure of "bang-for-the-buck." However, it is even simpler in that in that it does not distinguish, nor is it sensitive to, the time at which project cash flows occur.

Like IRR, ROI is most often used as a go/no-go screen for selecting projects. A minimum required ROI is specified, referred to as the hurdle rate. The hurdle rate is often based on the company's weighted average cost of capital (WACC), the average return on a portfolio of all the firm's securities (equity and debt). Alternatively, the hurdle rate may be set higher or lower depending on the company's appetite for risk and shareholders' expectations for company performance. Projects with ROI's less than the hurdle rate are rejected.

When used to rank projects, ROI has significant limitations. If project income varies from year to year, ROI will depend significantly on the period chosen for computing average income. ROI also has most of the limitations of IRR. It ignores non-financial project benefits, can't properly account for project risks and interdependencies, and does not provide a basis for quantifying the value of alternative project portfolios. Since future cash flows are not discounted, ROI ignores the preference that should be given to projects whose cash inflows occur sooner in time. Thus, ROI is particularly unsuitable for ranking projects that produce incremental revenues or cost savings that persist over multiple years.

return on net assets (RONA)

A measure of the financial performance for a company:

RONA is net income divided by net assets

Net income is after tax profit and working capital is current assets minus current liabilities. Asset intensive businesses often use RONA to indicate how effectively the firm's asset base is being used to create profit.


A characteristic of a situation or action wherein a number of outcomes are possible, the particular one that will occur is uncertain, and at least one of the possibilities is undesirable.

risk adjusted discount rate

A discount rate intended for application to a risky (uncertain) future cash flow. A risk adjusted discount rate is higher than a risk free discount rate. If an investment involves risk, then it will have to provide a higher rate of return to compensate for that risk.

The risk-free discount rate is often selected to be the return available from market investments that involve little or no risks, such as the rate of return available from short term US treasury securities. The risk adjusted discount rate can be regarded as the risk-free rate plus a risk premium appropriate given the level of risk.

Risk adjusted discount rates represent one of two popular methods for accounting for risk when valuing projects that produce uncertain future returns. With risk-adjusted discount rates, the expected value generated by the project is estimated in each future time period. The time stream of expected values is then discounted at the risk adjusted rate to obtain the project net present value (NPV). A competing approach is to compute the certain equivalent of each uncertain value, and then to discount the certain equivalents at the risk free discount rate. Both approaches involve questionable assumptions related to the way they attempt to disentangle risk and time preference. However, estimating a risk adjusted discount rate is particularly problematic in that, for example, it can be shown that it is not appropriate to use the same rate for cash flows that occur in different time periods.

risk adjusted value

A measure of value that accounts for risk or uncertainty. Due to risk aversion, people and organizations typically assign a lower value to assets or investment opportunities that have more risk than to otherwise similar investments that are less risky. The most common way of adjusting for risk is to compute a reduced value for the investment that is said to be "risk adjusted." Various methods are available for computing a risk adjusted value, including real options analysis, certain equivalents, using risk-adjusted discount rates, or applying subjective "haircuts" to forecasted returns.

risk assessment

A systematic process of evaluating the likelihood and magnitude of the risks involved in a projected activity or undertaking.

risk aversion

The preference that humans commonly have that causes them to prefer certain or sure consequences over comparable uncertain ones. A decision maker is said to display risk aversion if, when faced with the choice between the expected value of the uncertain consequences to a risky project and the uncertain consequences themselves, he or she would choose the expected, certain value. The degree of risk aversion can be quantified by measuring decision maker risk tolerance.

risk free rate

The rate of return available from riskless investments, usually taken to be short-term US government securities.

risk management

Risk management refers to the practice of identifying risks in advance of commitment, analyzing them and taking precautionary steps to reduce/curb the risks.

risk matrix

A graphic display for visualizing and comparing risks. Initially adopted by the US military, the tool is currently used by many organizations as a simple means for analyzing risks. The idea behind the risk matrix is to distinguish various levels for the two main dimensions of risk, (1) likelihood of occurrence and (2) magnitude of impact. For example:

Basic Risk Matrix

A basic risk matrix

Each cell in the risk matrix represents a possible combination of likelihood and impact. Since the seriousness of a risk is roughly related to the product of likelihood and impact, colors (e.g., green, yellow, and red) are often used to emphasize this result. The number of rows and columns and the particular way in which they are defined (e.g., quantitatively or qualitatively) can be varied depending on the application.

To use the risk matrix, a list of relevant risks is generated. For example, if a company is considering introducing a new consumer product, a possible risk might be that a customer could be injured by that product. For each identified risk, the likelihood of the risk event (e.g., not very likely versus very likely) and the seriousness of the consequences (e.g., minor cut versus serious permanent disability) are estimated. The results are then used to place each risk within the appropriate cell of the risk matrix. Risks can then be prioritized from top-right down to bottom left.

The main benefit of the risk matrix is that it provides a visual display that differentiates high-probability/low-impact and high-impact/low-probability risks. Because multiple risks can be displayed simultaneously, the approach benefits from the comparative ease that people have in making pairwise comparisons as opposed to the greater difficulty associated with drawing absolute judgments. Within a risk management process, the matrix provides documentation demonstrating that risks have been identified and deliberately evaluated. Also, the matrix can be used to show how the likelihood and impact of risks change and therefore move within the matrix, for example, over time at different stages in a project's investment life cycle or as a result of candidate risk mitigation strategies.

Another attractive characteristic is that the matrix works well in a group decision-making environment. For example, the risk matrix can be drawn on a white board or pages taped together from a flip chart. Post-It Notes can then be used to place risks within the matrix. The exercise promotes brainstorming and a team approach helps avoid the extremes of too pessimistic or too optimistic views that might be expressed by individuals.

The main limitations of the risk matrix relate to the simplistic, subjective way by which risk is measured. Poor resolution often results because rows and columns are often defined qualitatively, so that the same cells can be assigned to risks of very different magnitude. Also, due to errors in either the assessment of risks or the cells in which they are placed, the risk matrix can mistakenly assign higher qualitative ratings to quantitatively smaller risks. The risk ratings assigned to cells are typically just a function of the product of likelihood and impact, so the approach ignores the fact that very high consequence/low probability risks are generally of greater concern to organizations than the product would suggest, and the error is greater for organizations with lower risk tolerance. Effective allocation of resources to risk-reducing countermeasures cannot be based solely on the category ratings assigned by risk matrices—the effectiveness of the risk-reducing measures must be considered as well. These and other limitations imply that risk matrices should be used with caution, and only with careful explanations of underlying judgments.

risk mitigation

Actions taken to reduce risks based on lowering the probability and/or impact of a risk to below some acceptable level or threshold. In the context of project management, risk mitigation typically involves revising the project's scope, budget, schedule or objectives.

risk premium

When used in the context of decision analysis, the difference between the expected value of a lottery and its certain equivalent. The risk premium associated with a gamble can be interpretted as the amount of expected value the decision maker is willing to give up in order to avoid the risk of the gamble. The more risk averse the decision maker, the larger the risk premium will be.

When used in the context of investing, the risk premium has an analogous definition, It is the incremental return that compensates an investor for accepting an investment considered to be risky. The risk premium is the difference between the expected return from the risky investment and the return available from a risk free investment.

risk register

Also called a risk log. a table or spreadsheet created by ah organization's risk managers that summarizes identified risks, provides an assessment of their severity and indicates the action or steps to be taken to manage those risks. Its key function is to provide management and key stakeholders wit information on the main risks faced by the organization and what is being done about them.

risk tolerance

A measure of an individual's or organization's willingness to accept risk when making choices. Risk tolerance may be assessed and quantified as a parameter in a utility function. See the section of the paper on risk for how this may be accomplished.

root cause analysis

A method of problem solving focused on identifying the root causes of problems, including problems for the successful completion of projects. A factor is considered a root cause if its removal from the event sequence doesn't merely make the undesired problem consequence less likely, it prevents it from occurring in the first place. The root causes of problems may be physical, human error, or organizational. Root cause analysis is based on the philosophy that effective management requires more than merely "putting out fires," but finding a way to prevent them.

Root cause analysis can be conducted in two ways: you can: (1) look for things that can go wrong and then identify the potential impacts on the project of each such event or 2) identify all the essential functions that the project must perform or goals that it must reach to be considered successful and then identify all the possible modes by which these functions might not be achieved