The Use of Modern Portfolio Theory in Contexts Lacking Revenue I. Public-Sector Inefficiency II. Modern Portfolio Theory and its Limitations III. Introducing the Market into the Realm of the Sub-Corporate IV. From Sub-Corporate Entities to the Public Sector In order to allocate resources effectively within an organization, one must know the respective strengths of that organization’s components in the context of the whole. Such a view explains the problems found in resource allocation in both the public and private sectors: the unambiguous market indicator of value, revenue, cannot at first blush be attributed to either the sub-corporate entities that comprise the business or to nonprofit agencies in their entirety. However, it is possible to determine optimal allocation of resources for the former by introducing the mechanisms of the market, in conjunction with the KVA methodology, and applying the findings of modern portfolio theory. The extension of this approach into the public sector becomes clear with the implementation of a market comparables approach. I. The Problem of Public-Sector Inefficiency While disagreements exist in the literature regarding the proper criteria for measuring public sector inefficiency, there’s consensus that there is great deal of room for improvement (Chao and Yu 2002). Recent studies drawing from stochastic frontier analysis and data envelopment analysis (see IFS 2003, Chapter 8) are particularly compelling, and doubts surrounding the methods for measuring efficiency do not interfere with a consistent flow of proposals for improvement (as reviewed by Tuckman 1985). According to Nissen and Barrett (2006), “Bureaucratic organizations are known well to excel in terms of efficiency when situated in stable, predictable environmental contexts, but this classic organizational structure is also known well to be exceptionally poor at anticipating and responding to change.” Many aspects of the public sector—including the United States Department of Defense—are characteristically steeped in bureaucracy and an environment of fast paced change, which puts them at risk of incurring greater inefficiencies and misuse of taxpayer dollars. Ultimately, efficiencies can be heightened while meeting the needs of the people through the introduction of market mechanisms which, “when 1 successful, breaks with some of the core institutions of hierarchical governance” (Christiansen 2002). Some basic differences between the public and private sectors are indicative of the disparity in efficiencies often attributed to them: Figure 1. Private and Public Sector Attributes (adapted from Sweeny, et. al.) Private Sector Public Sector Single Constituency: “Shareholders” Multiple Constituencies: “Stakeholders” Singular Focus: “Efficiency” Mixed Focus: “Efficiency” and “Equity” Clear Measure of Success: “Bottom Line” No Clear Measure of Success The reputed inefficiencies of the public sector relative to the private are natural byproducts of these differences: under the private-sector scheme, the focus is clear, the basis for performance measurement self-evident, and the body on whose behalf accountability is upheld is easily identifiable. In general, these are not features of the public sector, and therefore the prospect of achieving an efficient public sector is contingent upon change at a fundamental level. In the past, there have been scattered instances of such change on a micro level: market-like conditions have been introduced with success into very specific arms of the public sector, including education (e.g., Zuckerman and de Kadt 1997; Peterson 2007), electricity (e.g., Fabrizio 2007) and health care (e.g., Klein 2006). In addition, isolated commercial practices have been imported into the operations of various government entities (e.g., in Defense Acquisitions: Sweeny, et. al. 1989; Cox, et. al 2001). However, these efforts that attempt to regulate when and where market forces are used and corner them into particular facets of the public sector, in reality tend to drive inefficient bureaucracy down more deeply into the system. Furthermore, these changes on the surface do not alter the underlying motivations for a 2 workforce and therefore cannot align them optimally, as occurs in the ideal market system. This re-imagining of the public sector is centered around human tendencies as built into market mechanisms; and central to its realization is the radical visualization of public assets as ultimately an investment made by taxpaying citizens. If the public sector is to be responsive to the needs of the taxpayers, then “the objective…is to give more citizens a stake in reform” (Graham 1996). Further, recasting citizens as investors introduces market forces that blur the lines between the private and public sectors; a market-oriented public-sector and the efficiencies resulting from it can only arise given “citizens who know that they have a stake in a better outcome and hold officials accountable for achieving it” (Dohrmann 2004). However, the obstacle to full realization of this framework is the practical concern of how public entities can be treated and tracked as corporation-like entities without the benefit of revenue streams; the resolution of which is addressed in a later portion of this paper.1 In visualizing the public sector in terms of the marketplace, we strive to break away from the cost-based budgeting approaches associated with government agencies attempting to simply break even, instead aiming for a model in which decision-makers seek to accrue to themselves the highest possible revenue at feasible costs. Here, revenue is the truest indicator of value and is measured in common units of money. By opening up these operations to the influences of the market and establishing unambiguous estimates for the value of non-profit services and products, leadership can effectively gauge the impact of their investment decisions. Furthermore by treating the various capabilities and processes as if they were independent entities within a market, we can apply the tools of portfolio theory to better inform these leaders of the optimal investment choices available to them. Effectively, the body of taxpayers asserts its investment priorities. It then becomes the responsibility of public-sector leaders at the enterprise level—with the aid of modern portfolio theory—to allocate the tax “investments” effectively. 1 Some public sector activities, programs, institutions may not be amenable to a market forces based approach due to their inherently unique purposes. We do not mean to imply that all public sector activites, programs and institutions would benefit from our approach. However, there are a large number that have common processes such as accounting. In these cases, it may be more prudent to conduct our analysis at the process or function level rather than the whole entity level. 3 II. Modern Portfolio Theory Modern Portfolio Theory, as initiated by Markowitz (1952), considers a method of resource allocation for the investor in the for-profit sector, assuming that he/she desires to maximize expected return over all feasible portfolios while keeping the risk/variance constrained Starting here, Markowitz proceeds to formalize the intuition behind investment diversification. To apply MPT, one needs to be able to compute mean values of the return for every stock in a portfolio as well as the correlation between the returns within a portfolio. These values are estimated based on historical data. The capability provided by MPT can be used to accommodate an investor’s preference in the tradeoff between return and risk associated with every portfolio under consideration. Thus, portfolio theory suggests a way of optimally allocating capital for the investor in the private sector. However, we also believe it to be of utility as an optimization tool for the allocation of resources within a firm among its constituent parts, and ultimately as a method for resource allocation among the “portfolios” of capabilities and process found in the public sector. Detractors have perceived a number of flaws in MPT. These include: 1) MPT assumes that risk is synonymous with volatility. In fact, a number of early empirical studies (e.g., Haugen and Heins, 1975) demonstrate little correlation between risk (when defined as volatility) and returns. Murphy (1977) concludes that “Efficiency is not an accurate description of the capital markets and may not even be a very good description; there are serious problems with the risk/reward relationship.” Fama and French (1992) find that “the relation between β and average return for 1941-1990 is weak, perhaps nonexistent, even when β is the only explanatory variable.” Logically the strict correspondence between risk and volatility seems suspect: volatility, 4 in treating all motion indiscriminately, punishes upward trends just as much as the downward ones investors wish to avoid. An adequate solution may be simply to use “downside risk.” As Harlow (1991) explains, “Downside-risk measures are attractive not only because they are consistent with investors' perception of risk, but also because the theoretical assumptions required to justify their use are very simple…a number of well known risk measures, including the traditional variance (standard deviation) measure, are special cases of the downside-risk approach.” 2) MPT assumes that portfolio returns can, in general, be adequately represented by the normal distribution (reference [1]). 3) MPT assumes away all transaction costs and taxes. The last point is certainly unrealistic in the private sector, but (presumably) in the application to the public sector where the investor is represented by the leadership of an agency and the “companies” in which investments are made, are controlled, this assumption can be made. The downside-risk solution to the first problem and the incorporation of the possibility of “skewness” (problem 2) are features of the so-called Post-Modern Portfolio Theory, developments which are traced by Libby and Fishburn (1977) and Rom and Ferguson (1993). In addition to these noted drawbacks to MPT, there exists a central limitation, as Markowitz himself acknowledges: it only purports to address the second half of the resource allocation process. As mentioned above, MPT provides the investor with efficient portfolios after he has chosen the investments to be considered. In DoD IT, for instance, this would correspond to the allocation of resources throughout a given, existing IT infrastructure. A reasonably worthwhile allocation of resources using MPT presupposes a reasonably efficient investment structure. This limitation may be resolvable using the attractors search algorithm (ASA). An attractor is a set of n equities (n-attractor) such that the corresponding optimal portfolio cannot be improved by replacing one of the n equities by any other equity outside the n equities. For example, using MPT we allocate resources among 5 equities (i.e., 1,2,3,4,5). If one of the five equities, e.g., 2, in this portfolio can be replaced by another equity, e.g. 7, such that the performance of the corresponding optimal portfolio: 5 1,7,3,4,5 is better than the original portfolio, then the original portfolio is not an nattractor. The properties of an n-attractor are: 1. Optimal portfolio of n stocks is an n-attractor 2. There may be more than one n-attractor given the same risk-reward parameters. (biology references) 3. Given an efficient search algorithm, e.g. ASA, it may be possible to select the best performing attractors from the set of n-attractors having common risk-reward parameters Kanevsky’s ASA [patent by VK] allows for an effective search through all equity subsets of a given cardinality n. Since the computational complexity of the ASA is feasible, an investor can extend the search to ever higher cardinalities until his risk-reward expectations are met. III. The Method in the Sub-Corporate Case The firm faces the same fundamental problems in allocating resources to its components as agencies do in the public sector. Just as non-profits have no revenue streams, so do sub-corporate entities in the private sector lack information regarding their true value. Opening up the internals of a firm to the voice of the market—acknowledging that the boundary around the company is a permeable one—by inviting investment in individual components of the firm structure can be for certain companies a way of achieving the transparency needed to be able to allocate overall company resources effectively. Some companies are in fact already doing this in essence through “tracking stocks” (e.g., Disney). This system would benefit both sides of investment: increased transparency will enable corporate leadership to identify inefficiencies and know where investors are willing to place their capital, while investors will benefit by the additional control over their investment. Despite the potential advantages, selling stock in individual company components does not exist under present equity market conditions. However, via the KVA methodology, sub-corporate entities can at least be treated as members of a free market 6 with their own revenue streams. KVA is basically a method for describing all outputs in common units which can then be priced at a given historical point in time based on revenue generated at that same point in time. Assuming a direct relationship between knowledge and the value stemming from it, knowledge value added delivers a capability for allocating revenue to subcorporate-level entities by describing all process outputs in common units. Value can be described as the knowledge needed to produce the common units of output, a notion which can be operationalized in numerous ways (Housel and Bell 2001), and has already been implemented in numerous for-profit (e.g., AT&T; Housel et al. 2005) and non-profit organizations (e.g., to examine the return on investment of intelligence information systems in the Department of Defense; Rios and Housel 2005). As demonstrated in Figure 2, applying KVA at the sub-corporate level transforms the problem at hand into the same one that appertains to the corporate level. Given a history of resource allocation, sub-organizations can be seen as members of a market for such entities. Given a desired set of risk and reward characteristics, a portfolio of suitable “equities” can be extracted from this market (a process represented here by the “Kanevsky Attractor Prediction Algorithm”) and subjected to the tools of modern portfolio theory just as is currently routine for the equities market on the company level. This is done given the inputs of expected ROI, volatility in the history of the ROI, and the correlations between the ROI histories of the different assets chosen. In this way, optimization of even a portfolio of sub-corporate entities is possible. Figure 2. The correspondence between the problems of corporate-level investment optimization (currently practiced) and sub-corporate level optimization (enabled through KVA). 7 Sub-Corporate Level Corporate Level KVA ROI Over Time Revenue Allocation Equities Market ? Theoretical Sub-Corporate Equities Market Kanevsky Attractor Prediction Algorithm ? Kanevsky Attractor Prediction Algorithm Selected Equities Portfolio of Selected Equities Equities Earning Variables: Expected earnings (mean), earnings volatility (standard deviation), equity diversification (correlation) Expected Earnings Variables: Expected ROI (mean), ROI volatility (standard deviation), equity diversification (correlations). MPT Optimal Portfolio: Allocation of capital that provides the highest expected returns for a given level of risk 8 Example for the Sub-Corporate Case: ABC Radiology, Inc To illustrate the method, we have generated historical data for the fictitious ABC Radiology, Inc. This company provides services for a wide variety of health professionals, including the operation and maintenance of X-ray, CAT scan, and MRI technologies as well as the interpretation of the results from such devices. In addition, they manufacture such mechanisms at a high-quality level for sale in many areas of the health care industry. The company operates under three major segments: testing services (including the operation of radiological equipment and interpretation of results), technical services (specialized repairs the company is contracted to undertake), and production and sales (the manufacture of such instrumentation is but a small component of the company’s aggregated operations since it is so specialized). In addition, there are accounting and human resources departments. Table 1 shows the results of a typical KVA analysis conducted for ABC Radiology, Inc. This analysis makes possible the allocation of REVENUE based on the amount of knowledge embedded within each segment’s core processes. Given a periodic application of the KVA methodology, the company can Table 1. KVA Analysis for ABC Radiology, Inc. Learning Department Executions Time Total Knowledge Expenses Revenues ROK ROI STD DEV % of Rev. Accounting 15 800,000 12,000,000 $1,100,000 $1,200,000 109.09% 9.09% 4.0% 12.00% Human Resources 10 1,000,000 10,000,000 $900,000 $1,000,000 111.11% 11.11% 3.2% 10.00% Testing Services 0.5 110,000,000 55,000,000 $5,000,000 $5,500,000 110.00% 10.00% 3.0% 55.00% Technical Services 30 500,000 15,000,000 $1,200,000 $1,500,000 125.00% 25.00% 8.5% 15.00% Production and Sales 5 1,600,000 8,000,000 $650,000 $800,000 123.08% 23.08% 7.0% 8.00% 100,000,000 $8,850,000 $10,000,000 112.99% 12.99% 9.83% 100.00% Totals Revenue per Knowledge Unit: $0.10 9 build a historical record of sub-corporate revenues and arrive at a variance (shown as standard deviation) and correlations between the earnings of the various segments. In effect, we have all the information needed to extend the notion of portfolio theory as applied to investments in companies down into a sub-corporate market. Since here we are dealing with all the components in a given company, and not the optimal combination of sub-corporate entities across companies, there is no need for the Kanevsky Attractor Prediction Algorithm. We can now optimize this portfolio of five investments according to the tenets of Markowitz’ portfolio theory (here we use the dynamic chart available at http://www.spreadsheetmodeling.com/Portfolio%20Optimization%20%20Dynamic%20Chart.htm). Figure 3 below shows the allocation distribution for an optimized portfolio given KVA data taken weekly over a period of fifteen weeks. Portfolio Weights Portfolio Weights in an Optimal Portfolio 60% 50% 40% 30% 20% 10% 0% 1 2 3 4 5 Asset Figure 3. Weights for ABC Radiology’s portfolio assets (1=accounting; 2=human resources; 3=testing; 4=technical; 5=production and sales). Armed with isolated KVA analyses, a company’s leadership can determine which parts of the company are adding value and which need improvement, as well as map out the direction for such improvement. However, the success of a given company’s components relies not only on these improvements from within, but also on external market factors 10 (e.g., demand). Hence, we believe that the full potential of the KVA methodology on the aggregate level can be achieved only with its coupling to the techniques of portfolio theory, which takes into account—via historical volatility—the influences of the overall market on each entity within the company. Figure 4 shows the plot of the ROI figures over time for the five company segments, as well as for the company when allocating based on the percentage of overall revenue represented by the respective segments in the first KVA analysis (“company”). The ROI figures based on the optimized portfolio are also shown. The results indicate the importance of applying MPT as the natural completion of a KVA approach: as expected from the theory, the optimized portfolio routinely outperforms the overall company portfolio based on the single KVA analysis, which cannot take into account the dynamics that can drive optimum growth. KVA in and of itself can reveal the inner workings of a company at a given moment in time, but it is portfolio theory that keeps an eye on change and future earnings to guide investment, with the help of inputs available through KVA. ROI Data, with Overall Comapny and Optimal Portfolio 60.00% 50.00% 40.00% Accounting HR 30.00% Testing Technical Production 20.00% Company Optimal 10.00% 0.00% Week Week Week Week Week Week Week Week Week Week Week Week Week Week Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 -10.00% Figure 4. ROI Data. 11 IV. Extending to the Public Sector According to the Department of Defense Guide for Managing Information Technology as an Investment and Measuring Performance (1997), “Congress has determined that waste and inefficiency in Federal Information Technology (IT) programs undermine the confidence of the American people and reduces the Federal Government’s ability to adequately address vital public needs” (1-1). The Guide aims to outline the “performance and results-based management” (1-2) required by federal legislation for IT operations. However, it neglects to do so in the context of the “invisible hand” of the market, which supports a results-based approach even on the lowest level of operation in the for-profit sector. Instead, it offers intricate guidelines for organizing speculation and prolific methods for measuring performance in hindsight—in other words, further bureaucracy. The central problem is the attitude that “effectiveness” and “efficiency” need to be balanced at every level of operation, which is typical of a “rule-intensive organization” (Nissen and Barrett 2006) such as DoD. The authors of the Guide regard “effectiveness” as the degree of success in which a government entity meets its predetermined goals and mission, and “efficiency” is the degree to which the resources that work toward these goals are allocated well. Effectiveness is a passive measure seen relative to static standards imposed by upper-level management, while efficiency is intrinsic to the entity, apt for performance measures, and hence able to be optimized. The model for DoD governance set forth in the Guide, and dominant currently in the department, stresses the need to attach measures of both effectiveness and efficiency to every level of organization, as illustrated in Figure 5. 12 Figure 5. A standard model for DoD governance. Adapted from Department of Defense, 1997. r Accountability ENTERPRISE Executive Information Mission Results Integration & Planning Resource Allocation FUNCTIONAL Management Information Unit Results PROGRAM/PROJECT Activity/Task Information Workplace Results This top-down structure is based around the premise that missions must be defined at every level of DoD operations, a practice which stifles creative solutions to larger problems that can only be achieved through collaboration between entities, and which is prone to mass inefficiencies caused by the constant shifting of priorities within government affairs. Introducing market forces into DoD would undermine this current notion of “effectiveness”: supply and demand would come to define mission and goals at lower levels, and they in turn would become more fluid. However, where conventional notions of effectiveness change, efficiencies will abound once “output-based” and 13 “outcome-based” goals are realigned so as to allow for the natural market forces to work. These projected efficiencies are apparent in the observation that the roles of accountability and integration delegated in the above diagram are in fact end products of the capitalistic market system in the for-profit sector (Davis 2007), and given the methodology outlined above, more effective resource allocation is possible as well. Introducing efficiencies into the public sector is a matter of pushing “outcome-based” goals as far up the hierarchy as possible, to the level of the investor, embodied here in the general body of taxpaying citizens. Hence, while the public defines the desired outcomes expected of local and federal government agencies (e.g., emergency safety services), the government agencies themselves focus on output, or producing the best possible products or services under efficient use of the taxpayer resources. Leadership at all levels of the government not only will be able to find creative solutions to overarching problems by joining up with other public- or private-sector organizations where their previous commitment to a specific “mission” could have precluded them from doing do, but they must. Given the pressure of being responsible for profits, lower-level management will have it in their best interests to integrate or realign with others where they believe efficiency will result. Information at lower levels in the organization is more readily available to lower-level management, and in deemphasizing specific missions at these levels, we can allow this management to act on it. An organization with such characteristics is modeled in Figure 6, to be held in contrast with Figure 5. 14 Figure 6. A less standard model for governance, is when the effective democratic consensus is upheld by budgeting decisions made at the enterprise level, which is defined as investments in members of relevant markets. ENTERPRISE: Maintains taxpayer “missions” through appropriate funding. FUNCTIONAL FUNCTIONAL PROGRAM/PROJECT FUNCTIONAL PROGRAM/PROJECT PROGRAM/PROJECT Public/Private Divide Introducing the market into the public sector can be accomplished in a manner akin to the methodology previously discussed. The additional problem in dealing with the non-profit sector is that there exists no measure of revenue when taking the agency or organization in the aggregate. The KVA analysis would provide common units, but there would still be no manner of formulating a return on investment. The method we propose of estimating non-profit sector revenue streams is a Market Comparables approach, which assumes that “though the macro functions performed by governments are monopolistic and centralized, many of the processes to accomplish those functions are comparable to those in the private sector” (Cook and Housel 2005). Hence, subcorporate entities can provide revenues, with proper scaling, for similar segments in the public sector, which in turn allows for a revenue breakdown for that segment’s core processes, by which investments can be made. The method is further demonstrated in Housel, et. al. (2007) and Joyce and Roosma (1991). 15 Corporate Level Sub-Corporate Level Public Sector Revenue Streams on Process Level KVA KVA ROI Over Time ROI Over Time Market Comparables Equities Market ? Kanevsky Attractor Prediction Algorithm Revenue Allocation Revenue Allocation on the Sub-Process Level Theoretical Sub-Corporate Equities Market Theoretical Sub-Process Equities Market ? ? Kanevsky Attractor Prediction Algorithm Kanevsky Attractor Prediction Algorithm Selected Equities Portfolio of Selected Equities Portfolio of Selected Equities Equities Earning Variables: Expected earnings (mean), earnings volatility (standard deviation), equity diversification (correlations) Expected Earnings Variables: Expected ROI (mean), ROI volatility (standard deviation), equity diversification (correlations). Expected Earnings Variables: Expected ROI (mean), ROI volatility (standard deviation), equity diversification (correlations). MPT Optimal Portfolio: Allocation of capital that provides the highest expected returns for a given level of risk 16 Example for the Public Sector Case: The XYZ County Healthcare System The XYZ County Healthcare System is a fictional public network of healthcare programs, facilities, and services. The core component of the system is the XYZ County Hospital, with other services offered through its cancer clinic and heart center. However, all of these outlets rely on the system’s radiology division. Since the XYZ County Healthcare System is a public-sector organization, it has no revenue streams to track and there is often difficulty allocating resources to its components, like the radiology division, on a true value basis. The radiology division consists of three segments: testing services (using X-ray, CAT scan, and MRI tools in support of operations across the system), analytical services (professional interpretation of results from the use of such technologies) and technical services (including the maintenance and upgrading of radiological technologies throughout the system). Table 2. Initial KVA Analysis for XYZ County Healthcare System—Radiology Division Learning Total Department Executions Expenses Time Knowledge Testing Services 0.5 5,000,000 2,500,000 $5,000,000 ? ? ? % of Rev. ? Technical Services 20 75,000 1,500,000 $1,200,000 ? ? ? ? Analytical Services 4 5,000,000 20,000,000 $650,000 ? ? ? ? 24.5 10,075,000 24,000,000 $6,850,000 ? ? ? ? Totals Revenue per Knowledge Unit: Revenues ROK ROI STD DEV ? Table 2 shows a preliminary KVA analysis for the radiology division, and indicates that no new information is found, since the (public) healthcare system has no overall revenues. At this point, a market comparables approach is pursued, between the division of radiology in this public-sector organization and the for-profit ABC Radiology, Inc. (discussed above). 17 It should be noted, at this point the method diverges depending on the scope of the problem being tackled. One possibility afforded by portfolio theory is a comparison between the core processes of the for-profit radiology company’s core processes and those of the public radiology division, with the aim of determining the best allocation of resources among the components within the division. On the other hand, looking at radiology as a component of the healthcare system as a whole, our task can be the proper allocation between the various divisions and capabilities. In other words, KVA is flexible in that it can be implemented on a variety of levels for the company or organization under study. In addition, the latter task of valuing the radiology division in the context of the whole is particularly prone to ambiguities without this methodology, since the output of the division (i.e., radiological analysis) is used as the input in virtually all other divisions.2 In comparing ABC Radiology, Inc. and the XYZ Radiology Division, we note that their core processes are identical, only organized in different ways (“testing services” for ABC corresponds to the combination of “testing services” and “analytical services” in XYZ). The main difference lies in volume: ABC performs the same services as the XYZ division, but on a larger scale. Thus, we will take the revenue figures from the appropriate segments of ABC and, after adjusting for the disparity in volume, apply them to XYZ. Revenues are assigned to XYZ segments after being scaled down based on a ratio of executions. However, the KVA revenues given to each segment depend on the amount of knowledge embedded in each segment, not in the volume of executions. Therefore, the original revenues are summed to form an aggregate for XYZ, and then are redistributed based on knowledge. Tables 3 and 4 present the results. Table 3. Market Comparables Data Volume Ratio (XYZ/ABC) Testing and analysis 0.091 Technical 0.15 Revenues from Comparable $500,000 $225,000 2 Conventional methodologies tend to see such operations as essential and thereby overvalue them, irregardless of actual performance. In this way, our radiology division is comparable to IT systems in the DoD, whose output is simply supportive input for other aspects of the organization. 18 Table 4. KVA Analysis for XYZ Radiology Division Learning Department Executions Time Total Knowledge Expenses Revenues ROK ROI STD DEV % of Rev. Testing Services 0.5 5,000,000 2,500,000 $70,000.00 $75,520.83 107.89% 7.89% 3.00% 10.42% Technical Services 20 75,000 1,500,000 $40,000.00 $45,312.50 113.28% 13.28% 8.50% 6.25% Analytical Services 4 5,000,000 20,000,000 $550,000.00 $604,166.67 109.85% 9.85% 7.00% 83.33% 24,000,000 $660,000.00 $725,000.00 109.85% 9.85% 6.68% 100.00% Totals Revenue per Knowledge Unit: $0.03 With a KVA history, the portfolio can be optimized as in the sub-corporate case. The resulting weights provide an optimized ROI (Figure 8) that is consistent with the theory by overperforming on average, although this case differs slightly from the allocation scheme derived from the first analysis’ revenue breakdown. 19 ROI Data, with Overall Company and Optimal Portfolio 35.00% 30.00% 25.00% 20.00% Testing 15.00% Technical Analytical 10.00% Company Optimal 5.00% 0.00% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 -5.00% -10.00% Figure 8. ROI Data 20 V. Marginal Revenue The relationship between marginal revenue and marginal cost is not helpful in the present analysis, because equivalence of the two is only achieved under the condition of maximized profit. In the case of non-profit organizations we are missing profits as well as revenues, rendering the relationship pointless. 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