GB2398899A - Method of risk analysis of a business - Google Patents

Abstract

There is disclosed a Risk Balance sheet method which presents rationalised statistical information on predicted future performance of business activities, or predicted decision outcomes. The Risk Balance sheet method of this invention process identifies potential outcomes of business activities or decisions. In the method, a risk model is applied, to quantify the likelihood and value of the possible outcomes. The model accounts for possible combinations of key business conditions, represented as probability distributions. The Risk Balance sheet method produces risk and return data that can be graphically represented as a Risk Profile. Alternatively, the data can be summarised textually as a Risk Balance sheet method in a format that is similar to a traditional accounting balance sheet. The Risk Balance sheet method enables prospective returns to be assessed in relation to the risks that must be incurred to seek them. The Risk Balance sheet method summarises risk and return data as key Metrics, which are discrete quantitative measures that can be compared with criteria that define risk tolerability.

Description

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METHOD OF RISK ANALYSIS

Background

A traditional accounting balance sheet shows how the assets owned by a business are financed from its liabilities. In accountancy practice, the traditional balance sheet is supplemented by a Profit and Loss (P&L) account. The P&L account shows activities such as sales, costs, profits or loss during the financial year up to the date of the balance sheet. Therefore, the P&L account indicates recent profitability of the business. However, neither the balance sheet nor the P&L account gives any indication of future performance. Nor do they indicate the risk exposure of invested capital. Risk exists whenever capital is invested under conditions of uncertainty.

Corporate governance has become an important issue in recent years. Pressure is increasing on companies to provide information about the risks to which they expose investors. There is a need, therefore, for an effective and simple- to- understand method of evaluating and communicating the risks to which an organization and its stakeholders are exposed.

In practice, business performance cannot be predicted with certainty, because conditions that affect the performance outcome cannot themselves be predicted.

Therefore, a decision outcome cannot be predicted with certainty, because conditions that affect the decision outcome cannot themselves be predicted. In each case, there is actually a spectrum of possible outcomes. Some outcomes may be acceptable, but others may be unacceptable. The possibility of unacceptable outcomes that involve loss of capital represents the risk. The objective of the risk balance sheet is to present information that enables prospective returns for a business activity or decision to be assessed in relation l À a to the risks that must be incurred in order to seek those returns.

There is a need, also, for an effective and simple-to-understand method for demonstrating that risks have been responsibly considered during decision- making processes.

Methods exist for establishing what is known as the Net Present Value (NPV) of a project which is currently being undertaken, or which a company is deciding whether to pursue. This NPV is calculated by estimating income and expenditure related to the project, together with the time (relative to the time of NPV calculation) at which the income will be realised and the time at which the expenditure will be made. Typically, time intervals (quarterly or annually) are used. Assuming that annual time intervals are used, for each year counting from the start of the project, a net figure Scan be calculated by subtracting expenditure from income for each year. The net present value is calculated by discounting each Cjvalue to account for interest between the current time and the time at which the income is realised. NPV can be calculated using equation (1) N r NPV= ' . =O(l+r)' (1) where: Cj is the net income estimated for year; N is the number of years over which the value of the project is being calculated; and r is the assumed annual interest rate.

Some techniques are deterministic and based upon fixed point analysis and thus do not take into account uncertainties which are inevitably involved in the l Ace: ::' c:e es. :e calculation of NPV values. For example, it is very difficult to estimate the likely income which a project will realise, and indeed, although e.g. construction costs associated with many projects often occur early in a project's life cycle, they too are very difficult to estimate accurately.

Probabilistic methods for assessing project risk have been proposed, and more specifically, methods for calculating NPV values using probabilistic methods.

However, there is no satisfactory way of generating and presenting data indicative of risks to which a company is exposed.

It is a feature of the present invention to obviate or mitigate at least one of the disadvantages set out above.

Summary of the Invention

The present invention thus relates to a risk balance sheet (sometimes hereinafter referred to as a "RiBsheet "), and overcomes limitations of traditional accounting practices (as represented by the balance sheet and P&L account). A risk balance sheet does this by predicting and presenting statistical information on future business performance, in a textual format that is analogous to that of a traditional balance sheet. The risk balance sheet process also provides a simple-to-understand method for demonstrating that risks have been responsibly considered during decisionmaking processes.

According to the present invention, and in one embodiment thereof, there is provided a statistical method for assessing the risk and returns for a business activity or decision, the method comprising: (a) identifying primary conditions which determine a return generated À À . . À ::. Àe c:e::: ce. ..

by the business activities or decisions; (b) estimating both a range of values for the identified conditions and probabilities that the conditions will assume for each value within the said range; (c) estimating risks and returns for said business activities or decisions for possible combinations of the conditions identified; (d) estimating the likelihood of each possible combination of conditions; (e) graphically representing the likelihood of the risks and returns as risk profile data in which the risk profile data provides a representation of a likelihood distribution characterizing both favourable outcomes and risks, forming non-favourable outcomes; (f) summarising said risk profile data as a numerical value of discrete quantitative measures representing financial or non-financial measurements capable of comparison with criteria which distinguish whether said risk is acceptable; and (g) presenting the discrete quantitative measures textually as a risk balance sheet, in a format which parallels a typical company accounting balance sheet.

A preferred feature of the above embodiment is where the method is carried out as a sequence of steps for assessing the risk and returns for a portfolio of business activities or decisions. Another preferred embodiment of the above method includes the further steps of: À ::e e:.À: ::.e À r (g) providing justification for the subjective judgement used in the assessment method; (h) providing justification for the risk models and calculations used in the method; and (i) recording the origin and derivation of the data used in the assessment method.

Yet another preferred feature of the above method is where each of steps (a) through (g) are individually recorded as part of the method. A still further preferred feature of the above method is where each of steps (h) through (j) are individually recorded as part of the method. In carrying out the method of the present invention, the method may be computerimplemented.

In another aspect of the present invention, there is also provided a computer- implemented method for assessing and for recording the verification of the assessment of the statistical risk and returns for a business activity or decision, said method comprising the steps of: (a) identifying and recording primary conditions which determine a return generated by the business activities or decisions; (b) estimating and recording both a range of values for the identified conditions and probabilities that the conditions will assume for each value within the said range; (c) estimating and recording risks and returns for said business activities or decisions for possible combinations of the conditions identified; I.: ce. te. t'cest (d) estimating and recording the likelihood of each possible combination of conditions; (e) graphically representing and recording the likelihood of the risks and returns as risk profile data in which the risk profile data provides a representation of a likelihood distribution characterizing both favourable outcomes and risks, forming non-favourable outcomes; (f) summarising and recording said risk profile data as a numerical value of discrete quantitative measures representing financial or non-financial measurements capable of comparison with criteria which distinguish whether said risk is acceptable; and (g) presenting and recording the discrete quantitative measures textually as a risk balance sheet, in a format which parallels a typical company accounting balance sheet.

A further preferred embodiment of the present invention is where the method comprises the step of summarizing principle statistical risk and return data as discrete quantitative values on a risk balance sheet form containing a plurality of primary parameters, said primary parameters constituting a summary form of references of a hierarchy of additional forms which provide additional discrete quantitative values and parameters and detail the derivation of the discrete quantitative values and parameters, including graphical risk profiles from which the risk balance sheet is derived.

In the preceding method, desirably the method is one which effects and records as well as presents the assessment and the statistical risk and return data, said data being summarised as the mean value of positive returns in a risk profile À :: e. .e ': #' Àe:. c: Àe multiplied by the probability of a positive return. Desirably, the method of effecting recording and presenting the assessment and the statistical risk and return data, is where the data is summarised as the mean negative value of negative returns in a risk profile multiplied by the probability of a negative return.

Still further, in another embodiment, the method of effecting recording and presenting the assessment and the statistical risk and return data, is where the data is summarised as the mean negative value of negative returns in a risk profile allowing for risk aversion, multiplied by the probability of a negative return.

Again, as a preferred embodiment, according to the present invention, the method of effecting recording and presenting the assessment and the statistical risk and return data, is where the data is summarised as return discrete quantitative values together with the discrete quantitative risk values.

In yet another embodiment, desirably the method of effecting recording and presenting the assessment and the statistical risk and return data, is where the data is summarised as return discrete quantitative values together with adjusted risk discrete quantitative values.

In another aspect of the present invention, the above described method may be carried out where the method of effecting recording and presenting the assessment and the statistical risk and return data, is where the data is summarised as the ratio of discrete quantitative values of the return divided by the risk discrete quantitative values.

In yet another embodiment of the present invention, the method may be carried out where the steps of effecting recording and presenting the assessment and the statistical risk and return data, is performed where the data is summarised as a return value calculated as the ratio of the return discrete quantitative value À 1 :: e:e I::: cee. :. At: ce' divided by the adjusted risk discrete quantitative value.

A preferred embodiment of the present invention is also where the method of effecting recording and presenting the assessment and the statistical risk and return data, is carried out where the data is summarised as a certainty equivalent factor calculated as the mean negative value of negative returns in a risk profile allowing for risk aversion.

Yet another embodiment of the present invention is where the method of effecting recording and presenting the assessment and the statistical risk and return data, is performed where the data is summarised as a maximum credible loss factor which is the modulus of the greatest negative return in a risk profile.

The invention also includes an embodiment where the above-described method is carried out where the steps of effecting recording and presenting the assessment and the statistical risk and return data, is performed so that the data is summarised as a return on capital employed factor calculated as the ratio of the return factor divided by a maximum credible loss factor.

In general, the method of the present invention can be is applied to assessing the risk and returns for a portfolio of business activities or decisions. Also, the present invention applies to a method as outlined above for calculating and presenting financial returns for said business or said decision.

In yet another aspect of the present invention, there is also provided an improvement in a method for predicting future performance of at least one activity of a business enterprise, in which the improvement includes the steps comprising: generating a probability distribution representing future performance of the # 1 e # : : : # at least one activity; computing a mean value of the said probability distribution above a predetermined threshold; computing a probability of the future performance being above said predetermined threshold from the said probability distribution; and multiplying the said mean value by the said probability to obtain a value indicative of future performance.

In the above improvement, most desirably there is included the further steps of computing a mean value of the said probability distribution below the predetermined threshold; computing a probability of the future performance being below said predetermined threshold from the said probability distribution; and multiplying the same mean value of the said probability distribution below the predetermined threshold by the said probability of future performance being below said predetermined threshold to obtain a further value indicative of future performance.

The above improvement may also be carried out where the metric (value) and the further metric are combined to create a combined value indicative of predicted future performance.

Another improvement of the present invention relates to a method for assessing l :: A:: ::e ÀÀ: .. :: aes the risk and returns of a business activity or decision presented as a risk balance sheet, the method steps characterized by: (a) identifying and recording primary conditions which determine a return generated by the business activities or decisions; (b) estimating and recording both a range of values for the identified conditions and probabilities that the conditions will assume for each value within the said range; (c) estimating and recording risks and returns for said business activities or decisions for possible combinations of the conditions identified; (d) estimating and recording the likelihood of each possible combination of conditions to thereby provide graphic representation and recording of the likelihood of the risks and returns as risk profile data in which the risk profile data provides a representation of a likelihood distribution characterizing both favourable outcomes and risks, forming non- favourable outcomes to obtain data representing the likelihood of risk.

Because the risk balance sheet method of this invention is a predictive process, it is based on a rationalized analysis and prediction of future business performance. The risk balance sheet records and justifies any subjectively derived elements of the prediction. It also includes facilities for tracking and auditing the derivation of any data used.

The method of this invention thus provides a risk balance sheet which provides a means to demonstrate good corporate governance, since the risk balance sheet provides a method to demonstrate that an organization is being managed responsibly with due consideration of rationalized, audited predictions of risks :e:e: : : c:: and returns. The risk balance sheet also has a more general application, because it provides a basis for riskbased decision making. A risk-based decision is one that considers the balance between the risks and returns of a decision, to assess the merits of making the decision.

The present invention therefore provides a convenient and easy to understand method of presenting data relating to predicted future performance of at least one activity of a business enterprise. The data may be presented in a form analogous to a traditional balance sheet, thereby making the data readily understand to individuals who utilize such balance sheets, e.g. accountants, decision makers, etc. A preferred feature of the risk balance sheet of the method of the present invention is that it presents statistical risk and return data for a business activity or decision or for a portfolio of activities or decisions. The risk and return data presented on a risk balance sheet may be financial data or non-financial data.

Also, another preferred feature of the risk balance sheet is that it records and presents the basis and rationalization of the statistical risk and return data that it employs.

To facilitate interpretation of the risk and return data, a particularly preferred feature of the risk balance sheet is that it presents the risk and return data summarized as discrete quantitative values or factors (sometimes referred to as "Metrics" which are numerical measures that aid interpretation of the Risk Profile data) that can be compared with assessment or decision criteria.

To facilitate interpretation of the risk and return data by management and stakeholders, a further preferred feature of the present invention is that it presents some of the key Metrics in a format analogous to a traditional company balance sheet.

À 68 a :e #:e: :: : : : Another preferred feature of the risk balance sheet of the method of the present invention is that it presents risk and return data for business activities or decisions assessed individually. A further preferred feature of the present invention is that it presents risk and return data for portfolios of business activities or decisions assessed in combination. Yet another preferred feature of the present invention is that risk and return data for portfolios of business activities or decisions, assessed in combination, accounting for correlation between the activities or decisions.

A further particularly preferred feature of the present invention is that it also presents risk and return data in a graphical format, termed a 'Risk Profile', and presents a range of additional statistical parameters and ratios in addition to those that appear on the main risk balance sheet.

Another advantage of the risk balance sheet generated by the method of the present invention, particularly using computer generated methods, is that it is capable of providing methods which provide, amongst other features, assessment of business activities and decisions, production and storage of statistical risk and return data, recording the basis, origin and auditability of the risk and return data and its rationalization, and analysis and presentation of the statistical risk and return data, both graphically as a Risk Profile and in textual format on a risk balance sheet.

Description of Drawings

Having thus generally described the invention, reference will now be made to the accompanying drawings, illustrating preferred embodiments of the invention, and in which À 1 8 1, e Figure 1 is a schematic illustration showing how a Risk Model is used to generate risk and return data from the probability distribution of key conditions, and also shows how the data can be displayed graphically in the form of a Risk Profile and be summarized in textual format on a risk balance sheet; Figure 2 is a schematic illustration of a probability tree which may be used in the method illustrated in Figure 1; Figure 3 is a schematic illustration of a Monte Carlo Simulation process which may be used in the method illustrated in Figure 1; Figured is a graph illustrating net present value distributions for use in the method of Figure 1 created using the probability tree of Figure 2 and the Monte Carlo Simulation process of Figure 3 and a Taylor Series approximation; Figure 5 is a schematic illustration showing adaptation of the Monte Carlo Simulation process of Figure 3 as adapted to handle different activities with common uncertain variables; Figure 6 is a discrete NPV distribution for use in the method of Figure 1; Figure7 is an illustration similar to that of Figure 6, in which two NPV are shown; Figure 8 is a continuous NPV distribution showing certainty equivalents; Figure 9 is a graphical representation which illustrates a Risk Profile with low risk; ::, c: I:. e: :' :. :: se.

Figure 10 is a graphical representation which illustrates a Risk Profile with high risk; Figure 11 illustrates a schematic outline of a risk balance sheet for a business organization, represented as several business activities; Figure 12 illustrates a schematic outline of a risk balance sheet when used for decision-making; Figure 13 is a schematic illustration outlining further details of the method of Figure 1; and Figure 14 is a tree diagram of typical example to which the method of Figure 10 can be applied.

Detailed Description and Examples

In the following description and with reference to the accompanying drawings, reference will be made to certain known metrics. Prior to describing the Figures in detail, it will be useful to refer to the meaning of certain metric terms. Typical of the metric terms/references used in this application appear, for example, in the principle Risk Balance Sheet shown in Figure 11 as well as in other drawings.

Some of the principle key risk balance sheet metrics can be summarized as follows: Return: Mean value of positive returns in a Risk Profile, multiplied by the probability of a positive return.

Risk: Mean (negative) value of negative returns in a Risk Profile, multiplied by the probability of a negative return.

cq.; t#e;e t' I. i.e Adjusted Risk: Mean (negative) value of negative returns in a Risk Profile allowing for risk aversion, multiplied by the probability of a negative return.

Risk Balance: Return plus Risk.

Adjusted Risk Balance: Return plus Adjusted Risk.

Return on Risk: The ratio Return/it k Return on Adjusted Risk: The ratio RetUrn/Adusted Risk Certainty Equivalent: Mean value of negative returns in a Risk Profile, allowing for risk aversion.

Maximum Credible Loss: Modulus of greatest negative return in a Risk Profile.

Return on Capital Employed: The ratio RetUrn/Maximum Credible Loss The risk balance sheet summary form (described hereinafter) also references additional forms that present the graphical Risk Profiles and distribution parameters associated with those Risk Profiles. Some of these distribution parameters are: P.: Probability of an outcome with a negative value.

P+: Probability of an outcome with a positive value.

Px: Probability of an outcome with a value exceeding value x.

I i i 8 1, 8# e r8 8. 8e Ill 8 e e8 e 8 Value: Mean value of all outcomes with a negative value.

Value+: Mean value of all outcomes with a positive value.

S2: Variance of the values of all outcomes about the mean value of all outcomes S. 2: Variance of the values of outcomes with a negative value about the mean value of outcomes with a negative value.

S+2: Variance of the values of outcomes with a positive value about the mean value of outcomes with a positive value.

Other references to metric terms will be made in the detailed description.

A Risk Profile represents risk data graphically and a risk balance sheet is a textual, non-graphical representation of the risk data. Through statistical processing of the Risk Profile data, the risk balance sheet summarizes the data in terms of a relatively small number of key quantitative risk balance sheet Metrics. As defined hereinabove, a risk balance sheet Metric is a numerical measure that aids interpretation of the Risk Profile data.

Turning now to the Figures, by way of background, and by way of simple example, a business that manufactures and sells a product would normally consider certain key conditions in a model which would be simulated relative to the activity or decisions for such a business, based on an estimation from the value of the identified key conditions. Typical parameters or factors could be income parameters, namely production capacity, sales demand, product sales price; other parameters would involve cost parameters such as labour, raw material and overhead. As is understood by those skilled in the art, such key Àee. e e e À Àe ÀÀ À e ee À À eec e À e ace À e À e À e ce. e eve e e conditions or parameters cannot be precisely predicted.

One approach to overcoming this uncertainty would be to predict mostlikely values of the conditions and, by applying the risk model of this invention, predict a most-likely value of the return. However, this approach ignores the uncertainty in the prediction. Although the most likely return may be acceptable, there may be other returns which are less likely but which are unacceptable. This approach, therefore, ignores the risks.

Referring to Figure 1, the risk model 1 is used to carry out the method of the present invention by providing for a statistical method for assessing the risk and returns for a business activity or decision, which can be implemented by providing values of the key conditions 2 which are predicted as probability distributions 3. This enables the assessment process to account for both the favourable and unfavourable conditions, and their relative likelihood. In addition there may be key conditions that represent discrete events that could occur and, if they did occur, would significantly impact the return generated. The probability of these events is also predicted. Such a risk model may be applied many times to predict the return for many possible combinations of conditions and events identified. The probability of each combination is also estimated.

This risk balance sheet assessment method of the present invention thus produces risk and return data 4 that describes a spectrum of possible outcomes, each with a probability and a value. This data constitutes the Drisk data[3 for the business activity or decision because it includes data on any unacceptable outcomes that involve loss of capital, i.e. the risks.

The risk and return data is amenable to direct graphical representation in the form of a Risk Profile 5. Alternatively, it can be summarised in textual format, as a risk balance sheet 6. A Risk Profile (see Figure 9 as described hereinafter) is a À c c c c probability distribution of the returns (from the possible outcomes) of the business activity. The 'spread' 7 of the probability distribution is indicative of the uncertainty in the prediction, brought about by the fact that the conditions that affect business performance or decision outcomes cannot be predicted with certainty.

As a specific example, for illustration purposes only, the following provides a non- limiting example of the method of the present invention based on an NPV probability distribution calculation for obtaining risk data 4. Thus, the risk model 1 may include, e.g. a discounted cash flow model modelling suitable incomes and expenditures over time for the business activity under consideration.

Thus, if y is defined as the NPV for the activity or project under consideration, and x, is the Ah input parameter to the risk model (i.e. one of the factors of figure 1) then: = f(x) (2) In the above equation, x can be x' to xn.

Given that the distribution of each x; is known, the objective is to propagate these distributions through the risk model represented by y=f(x) to generate the correct probability distribution p(y) for the activity's NPV.

There are several methods which can be used to calculate p(y). Three methods are described below, with reference to an example based upon a decision relating to an oilfield development project with three uncertainties: uncertainty in recoverable oil reserves, uncertainty in (average) oil price over the life of the project, and uncertainty in (average) cost of capital over the life of the project.

One method of the present invention can be based a probability tree, whichis e.88 8 e e8 8 8 e 8 8 e e c 8 8 e 8 ee 8 8 e 8 6 8 Be À ee 8 8 8 8 see 8 8. e one of several techniques known to those skilled in this art and is representative of one system for use in the present invention. Probability trees represent discretised probability distributions of input variables. They are analysed in the same way as known event trees. Consequences are assigned to end points, and are calculated using the combination of variable values represented by the series of branches leading to that end point. Figure 2 shows an example of a simplified probability tree for use in the method of the present invention.

Referring to Figure 2, and by way of example, it can be seen that uncertainty in oil reserves can be represented by three possible values (Low, Medium, High), uncertainty in oil price is represented by two possible values (Low, High) and uncertainty in cost of capital can be represented by two possible values (Low, High). Given the small number of values being used for each uncertainty, a significant degree of grouping can take place with respect to possible values for the variables. This can lead to inaccuracies in an NPV distribution produced, particularly at the tails of the distribution. In many implementations, a greater number of values can be modeled for each uncertainty to provide a more accurate NPV distribution.

It can be seen from Figure 2 that the uncertainties associated with each of the three variables result in twelve different NPV values NPV' to NPV'2, which are dependent on each of the three variables. Each of these NPV values can be computed using the values of each variable which lead to that NPV. Each NPV value will have an associated probability value calculated using the probabilities associated with each of the values of three variables. That is, assuming that the three variables are independent, if there is a probability of 0.5 of medium oil reserves, a probability of 0.4 of high oil price and a probability of 0.6 of high cost of capital, then NPV8 has a probability of: 0.5 x 0.4 x 0.6 = 0.12 À À À À a * À. À . . À. . . . À À 1 À Thus, each of values NPV'to NPV,2 has a probability, and these probability values can be plotted against the respective NPV to create a discrete probability distribution for NPV.

An alternative method of implementing the risk model 2 of Figure 1 which can be used is the known Monte Carlo Simulation (MCS), which is schematically illustrated in Figure 3. Unlike probability tree implementations (described with reference to Figure 2), in which input uncertainties are grouped together into two or three outcomes at each node, MCS allows the full range of the distribution of each input uncertainty to be used. For each loop of the simulation the uncertain input variables (in this case Reserves, Oil Price and Cost of Capital) are sampled from their individual distributions, a sample NPVis calculated using a predefined discounted cash flow model, and then calculated values are stored.

The process described above will generate a single NPV value on the basis of random selections for each variable, the selections being biased by the probabilities associated with different values of the variable. This process is repeated, typically a few thousand times, to generate a range of NPV values which can be used to create a discrete NPV distribution. It will thus be appreciated that a MCS approach allows a full range of NPV values to be considered, not only those at the end of branches, as in the method illustrated in Figure 2.

A third method (using techniques generally known as and referred to as the Taylor series approach) can be used in some cases, and allows the mean and standard deviation of the output NPV distribution to be calculated on the basis of the mean and standard deviation of the inputs to the risk model.

The calculations for the mean and standard deviations are well known in the art. e eve

eÀ À À À À À À e À e e ee e ece À e e ece e ee. e e Such calculations can be efficiently made, as compared with the probability tree or MCS approaches. However, the approach is biased on the assumption that all distributions are Normal and the NOV calculation is linear. This is not always the case.

Figure 4 shows NPV distributions produced using each of the three methods described above. However, the probability tree used to generate the relevant part of the graph of Figure 4 was more detailed than that shown in Figure 2, although it still only considered the same three uncertainties. The probability tree used to generate the values of Figure 4 modeled uncertainty about oil reserves using five branches at the first node, uncertainty about oil price using five branches at the second node, and uncertainty about cost of capital using three branches at the third node.

As set out above, the probability tree approach may only provide a limited number of NPV results. There are seventy-five distinct outcomes in the tree used, and some of those may result in groups of common categories when the distribution is generated.

The MCS method, when used, allows all possible NPVs to be generated and provides better distribution results (see Figure 4).

Other known more elaborate probability trees, with more input uncertainties and more branches per node, would help avoid 'coarseness' in the NPV distribution created using the probability tree approach and can be used if desired.

In some applications, it is desirable to model a number of business activities together, and to model the correlating effects between activities. One approach which allows correlation to be modeled is to use a very large combined probability tree representing all combinations of uncertainties across all À decisions. This is undesirable because of the size of the probability tree that is required.

Another possible approach involves using each individual probability tree to compute conditional distributions with respect to a common input. This is very complex to implement in practice as there are many possible combinations of decisions to consider and the inputs that cause correlation are not always continuous variables. Discrete events such as political risk or resource limitations are very non-linear in the way in which they influence the individual NPV distributions and the total NPV distribution. Such complications make the modeling of correlation using probability trees very difficult to perform and automate.

Embodiments of the present invention can use the Monte Carlo Simulation to conveniently model common factors between business activities. All activities are modeled at the same time, and input variables which are common to several activities (e.g. oil price) are passed to the NPV calculation for each activity in the same MCS loop. These variables have the same values across the various activities in each loop. Correlating effects are thereby modeled implicitly. This is schematically illustrated in Figure 5, where it can be seen that activities B and C both share inputs X3 and X5.

The Taylor Series approach described briefly above offers a simple way of modeling correlations between decisions but only if all NPV models are linear and all inputs Normal (such as oil price uncertainty). Uncertainties that are not in the form of linear Normal variables, such as low probability/high consequence risks (e.g. accident risks or political risk), invalidate the Taylor Series methodology, potentially causing significant errors. Provided these (non-linear) correlating influences are not the dominant correlating influences, then the Taylor Series approach is suitable.

À * À Other more complex forms of correlation between variables can exist, and these can also be modeled in embodiments of the invention. For example, inputs to the same or different activities may in some way be correlated with another input. For example, if two variables are associated in such a way that as one increases the other increases or decreases, if the other variable increases, the variables are positively correlated, while if the other variable decreases, the variables are negatively correlated.

Direct modelling dependencies as described above are very easy to implement and the conditional probabilities needed should, in most cases, be easy to estimate from historical data, or subjective judgement. However, the method becomes complex and difficult to implement in cases of more than two variables.

In such cases there are potentially many more conditional probabilities, both to estimate from data and to model. Thus, alternative methods may be more appropriate.

One such alternative method involves using a cross correlation matrix R. to represent the correlations between variables. Each element of the cross correlation matrix is a Pearson correlation co-efficient of the type described above.

A cross correlation matrix for three variables a, b, c may be of the form: a b c a 1 0.8 -0.2 b 0.8 1 0.5 c -0.2 0.5 1 It can be seen from the example cross correlation matrix, that all variables are À À À * À . eÀ À À c À ee À perfectly correlated with themselves, a and b showing strong positive correlation, a and c show weak correlation, while b and c showing a positive correlation.

Simulation of n variables showing correlation according to a correlation matrix R is now described. Firstly, an n x n matrix L is created containing the Eigenvectors of R. and an n x n diagonal matrix is created containing the Eigenvalues of R. A matrix M is then created according to the following equation: M= a22 Independent random variables, ye, Y2, ... An. are simulated with zero mean and standard deviation. This can be expressed in the following equation: YeO,( where: 'lidenotes a joint Normal probability distribution. O represents a zero column vector indicating that the mean of all elements of Y is zero, and I is a diagonal unit matrix indicating that the elements of Y have unit standard deviation, and that cross-correlations between different elements of Y are zero; and Y is the column vector Yn Having generated Y as described, a further matrix X is created: À . À À C À 1 e À À X = MY The elements of X are a linear combination of the components of Y. Thus, the elements of X are correlated in some way. Having created the matrix X it is a straightforward matter to re-scale X to give each element its correct mean and standard deviation, in accordance with known properties of its distribution. This allows the matrix X' be created: X'=SX B where: S is a diagonal matrix containing the desired standard deviations; B is a column vector of the desired mean values; X' contains the desired, correlated values for each of the n variables.

Creating X using the above equation produces values which are in accordance with the cross-correlation matrix R. The cross-correlation of X is given by E[XXT].

E[XXT] = E[MWTMT] = M E[YYT] MT since M is constant. But:

E[YYT] =; since the elements of Y are independent with unit standard deviations.

Therefore: E[XXT] = M; MT = M MT = LW,/2W,/2LT = LWLT However, a property of Eigenvalues and Eigenvectors is that LWLT is equal to the original matrix R from which the Eigenvalues and Eigenvectors were derived * 8 À * * * À ÀÀ À * 8 e, * 8 * À À * 8 8 * 8 À * À Thus: E[XXT] = LWLT = R The foregoing description uses a cross-correlation matrix containing Pearson coefficients.

In Figure 1, the creation of a suitable risk model 1 has been detailed, showing specifically that given input variables having defined probability distributions, e.g. a suitable discounted cash flow model, and information as to the relationships (if any) between variables, an NPV distribution for both individual activities, and combinations of activities can be created using Monte Carlo Simulation. If the relationships are such that a single variable is input to more than one activity, MCS provides a way of modelling this implicitly, otherwise the modelling techniques described above are used to correctly input variables into the model, on the basis of the known relationships.

Referring now to Figure 6, there is illustrated a frequency distribution for a particular activity or combination of activities. This distribution can be analysed in a number of different ways to create various metrics. These metrics are as follows: Mean or expected value of all outcomes, NPV, is the arithmetic mean of the distribution, which is the sum of each value in the distribution, weighted by its frequency, fj ( This metric definition can be applied in a case where Monte Carlo Simulation was used, and outcomes were valued as NPV as with other metric factors).

A further metric is the probability, P. of a negative NPV value (i.e. the probability that the activity will result in a loss). This is the number of outcomes for which the À À À À À À . À À À À À À À . À À À NPV was less than zero, divided by the number of outcomes N. Further metrics include the mean of all negative NPV values, NPV. Such metric calculations are well known.

These are two metrics which usefully summarise a distribution. The first is Risk, which is defined as follows: Risk=|P À NP: That is, Risk is defined to be the probability of a negative value, multiplied by the mean of the negative values.

A similar metric, Return, can be defined as follows: Returr=|P+ À NP\| It can be seen from the two preceding equations that: Return - Risk = NP) The present invention may use two single metrics which valuably capture properties of the NPV distribution. These metrics can form the basis for decisions relating to which projects to pursue, and a project is considered to be viable only if it satisfies the inequality: Risk < Return When different projects or combinations of projects are considered, the # À 1 combination which offers the best Risk Balance is that which is deemed most desirable, where Risk Balance is defined by: Risk Balance = Return Risk From the two preceding equations, it can be seen that: Risk Balance =

NPS

The foregoing description of metrics and their use in determining project viability does not take into account a decision maker's risk aversion characteristics. This can be disadvantageous if the extremes of the distribution of Figure 6 are such that the maximum loss is so undesirable, that a decision maker would avoid this possibility, even given knowledge of its very low probability. Figure 7 shows an example of such a circumstance where the probability of a loss is relatively low, and the probability of a gain is relatively high. Figures 6 and 7 could, in theory, have the same Risk and Return values. However, they clearly present a decision maker with a wholly different scenario.

Two approaches can be used to capture this difference. A first approach involves calculating the variance of negative outcomes about the mean of negative outcomes using known equations, while a second approach involves calculating certainty equivalents, again with known equations. In general terms, risk aversion need only be considered for negative, not positive outcomes.

An alternative approach to using variances uses utility theory. Here, the aim to is maximise the expected utility of the NPV, not maximise its average as in the case of a risk balance calculation.

Expected utility of all outcomes is defined by the following known equation; À c.

À À 1 8 8 , 8 À À À ee. À a a's À . À . À Àe a 8 U(NPVi N.U,.f, where U. is the utility of the Ah component of the distribution, and is determined using an appropriate utility curve, mapping each NPV value or range of values to an appropriate utility value.

It should be noted that the units of expected utility are generally arbitrary and convey little meaning to the decision-maker. A more useful measure is obtained by taking each expected utility value and converting it back into NPV units using the inverse of the utility curve mentioned above. The resulting value is known as the certainty equivalent. The certainty equivalent is so called because it represents that value to which the decision maker should be indifferent when offered that value as compared to having to face the uncertainty of the original distribution.

The following additional metrics can therefore be defined: Certainty Equivalent of the Expected Utility of negative outcomes = CE = U1(EU) where U-' is the inverse of the function defining the utility curve.

Certainty Equivalent of the Expected Utility of positive outcomes = CE+ = U-1{EU+} These certainty equivalents, CE and CE+, are analogous to the '' r À I v e À À À . 8

V

8 1 8 NPV and the NPy values defined previously respectively. For a risk neutral decision maker the following can apply: CE =

NPV

and CE+ = NPy However, for a risk averse decision maker CE would be greater (more negative) than NPV and CE+ would less than NPy. This is shown in the distribution plotted in Figure 8, where it can be seen that the values marked are as indicated.

Adjusted' versions of various equations such as the risk equation and the return-risk equation are also known in the art.

Given the inherent problems of accurately creating utility curves, in some embodiments of the present invention, three predefined curves representing low, medium and high risk aversion may be used. A user can select the curve which best represents his or her risk aversion behaviour, and it is this curve that it is used to compute utility value and the corresponding certainty equivalents. This approximation is considered worthwhile given that considerable complexity is involved in accurately constructing utility curves for specific application, and given also that such curves can not be guaranteed to provide good levels of accuracy.

C À 1 C C6 1 e 1 c c e 8 C Eric I.'l C À C . e I c I A number of metrics have been described for a discrete probability distribution such as that illustrated in Figure 6. However, in some cases, the probability distribution will instead be defined by a continuous probability density function, P(NPV), and in such cases, it may be desirable to compute the metrics by directly manipulating this function.

It will be appreciated that Risk, Return and their utility adjusted equivalents can be computed using known continuous metrics of equations.

Figure 9 shows a Risk Profile with greater uncertainty than that in Figure 10. The greater uncertainty is indicative of greater risk. The risk 8 for the Risk Profile in Figure 9 indicates a higher probability of a more significant unacceptable outcome than the risk 8 in Figure 10, even though the most likely and statistical average returns are similarfor the Risk Profiles in Figures 9 and 10.

Using the metrics described above, the present invention provides a convenient way for presenting data indicative of the form of the NPV distribution. This is the Risk Balance sheet, an example of which is shown in Figure 11. This Figure thus illustrates one example of a risk balance sheet, modelled as a 'portfolio' of business activities, each of which is represented on the risk balance sheet. The part of the risk balance sheet headed 'Returns' 10 shows a Metric for the outcomes that are predicted to result in a positive return. The Metric is the Return' 11, a statistical measure of the positive returns. This is presented separately for each 'activity' in the portfolio of business activities, identified in Figure 11 as Activities X, Y and Z(18).

The part of the risk balance sheet headed 'Risks' 12 shows a Metric for the outcomes that are predicted to result is a negative return. The Metric is the 'Risk' 13, a statistical measure of the negative returns. Risk is, therefore, a negative ÀÀ À À À À e À À C À À À À C À À À À value. This is also presented separately for each Activity X, Y. Z (19).

The part of the risk balance sheet headed 'Returns' also shows the 'Total Return' 14, which is the overall return for the outcomes (from the combined Risk Profile) that are predicted to result in a positive return.

The part of the risk balance sheet headed 'Risks' shows the 'Total Risk' 15, which is similarly the overall risk from the outcomes (from the combined Risk Profile) that are predicted to result in a negative return.

In general, the Total Return 14 presented on a risk balance sheet is not simply the arithmetic sum of the return presented individually 11 for each Activity 18.

Similarly, the Total Risk 15 is not simply the arithmetic sum of the risk presented individually 13 for each Activity 19.

This is because, when combining the risk data for activities that have been assessed individually, consideration has to be given to correlation effects.

Correlation results from the fact that a degree of inter-dependency generally exists between risk models and Risk Profiles that are independently produced for each activity in the portfolio of the business activities that represent an organization. This correlation is reflected in the overall Risk Profile for the organization, but not in the Risk Profiles independently produced for individual activities.

Therefore, under both 'Returns' 10 and 'Risks' 12 on the risk balance sheet, provision is made for displaying the 'Correlation Effects' 16 not accounted for in the results for the individual Activities.

Another factor presented on the part of the risk balance sheet headed 'Risks' 12 is primarily concerned with enumerating and accounting for the uncertainty in the À c predicted risk-return relationships (as represented by the 'spread' 7 of a Risk Profile, see Figure 9).

Specifically, this factor is required in order to be able to take account of 'risk aversion'. Risk Aversion is aversion to outcomes that produce greater negative returns even though their likelihood is predicted to be proportionately less. Such aversion results from the fact that the consequential impact of a large negative return can exceed its actual, directly quantified loss, in monetary terms. For example, the loss incurred could have an impact that ultimately threatens the existence of the business organization.

Risk aversion is accounted for in the risk balance sheet by artificially increasing the statistical value of any outcomes (in the overall Risk Profile) that result in a negative value that exceeds a threshold value. Under 'Risks' 12 on the risk balance sheet therefore, provision is made for displaying the effects 17 of any risk aversion applied to the Risk Profile data.

The risk balance sheet of Figure 11 is analogous to a traditional accounting balance sheet. However, in place of assets and liabilities which are represented by such a traditional balance sheet, the risk balance sheet shows returns (analogous to assets), and risks (analogous to liabilities).

Any risk balance sheet contains metrics relating to one or more activities or combinations of activities at a given point in time. In this case, the risk balance sheet is shown to be created in April 2003, using NPV calculations extending to March 2004. In a similar way to a traditional balance sheet, the risk balance sheet is organised into columns and rows. Descriptive information is provided in a first column 6, discrete amounts are provided in a second column 7, and totals of the discrete amounts of column 7 are shown in a third column 8.

À a À e À e e e À

C

ces e ee e Returns are shown in a section 9 of the balance sheet. Returns for three activities X, Y and Z which are currently being undertaken by the company are shown individually. It will be appreciated that the Return metric for each activity will be calculated using an NPV distribution for that activity which was described above. The total 10 of these individual return values is displayed within the risk balance sheet. In this case this total is ú8.25 Million.

It has been noted above that it is desirable to take into account correlating effects between different activities. As described previously, this can be done by generating a NPV distribution for the combination of activities, using a model which takes correlating factors into account. The Return metric 11 of such a combined NPV distribution for activities X, Y and Z is shown in the risk balance sheet and marked 'Total Return'. It will be appreciated that the Correlating Effects 12 can be calculated by subtracting the Return of the combined NPV distribution from the return computed by simple addition of the Return metrics for the individual activities. Thus, although the risk balance sheet shows that correlating effects 12 are an amount to be subtracted from the straightforward addition of Return metrics for activities X, Y and Z. in practice the two totals are computed and subtracted to provide the value for correlation effects.

Risks are shown in an area 13 of the risk balance sheet. A separate Risk value is again shown for each of activities X, Y. and Z. with a combination 14 of these risk values using a straightforward summation also being shown. Correlation effects are again computed by subtracting the Risk value of the combined NPV distribution from the total risk computed by summation. In the case of Risk, aversion effects are also taken into account, although in the case of the risk balance sheet of Figure 13, they do not affect the risk value. In general terms, the total risk 15 is computed using an appropriate equation, thus taking into account aversion effects modelled by a suitable utility curve. Subtracting the Risk of the combined NPV distribution for activities X, Y. and Z then provides the *e e * À d* e À À a * À * * 8 * ** À aversion effects 16, and subtracting each of the individual risks from the Risk computed using the combined NPV distribution provides the correlation effects 17.

A Risk balance 18 can be computed and included in the risk balance sheet. An area 19 of the risk balance sheet provides a summary of the information contained therein.

The risk balance sheet of Figure 11 provides information relating to activities currently being undertaken by a company. In many cases it will be desired to use the modelling methodology described above to take decisions as to which, if any, future projects should be pursued. The present invention provides a tool for aiding such decision-making in the form of a decision risk balance sheet, an example of which is shown in Figure 12.

Referring to Figure 12, it can be seen that the decision risk balance sheet is structured in a similar way to that of Figure 11. That is an upper area provides Return data, a lower area provides Risk data, and the constituent data within these areas is similar to that shown in Figure 11. The Total Return from Figure 11 is combined as a "Base Case" 20 in Figure 12. Similarly, the Total Return from Figure 11 is combined as a "Base Case" 21 in Figure 12.

Referring to the Returns section, individual return metrics for six decisions A to F are shown. These individual values are added to provide the value 22. A Total return value 23, and a correlation effects value 24 can be computed as described above.

The Risks section again contains individual Risk metrics for each of the six decisions, together with a total of these values 25 obtained by straightforward addition. A total Risk value 26, a correlation effects value 27 and an aversion effects value 28 are also included and can be computed as described with À reference to Figure 13. A risk balance 29 is also included as described above.

The total Return value 23 represents the total return of all decisions A to F. that is, it models the position if each of decisions A to F are pursued. It will usually be desirable for a decision maker to model the position as if all the different combinations of the decisions A to F are pursued, and to compare the Risk Balances in each case. In this way, a number of different risk balance sheets for different combinations of decisions are created, and these allow the decision maker to determine the combination of decisions which provides the highest Risk Balance. When carrying out such a process, it will be appreciated that the default position of deciding to follow none of decisions A to F should also beconsidered and compared with other risk balance values.

The method of computing risk balances, and associated metrics for activities and decisions which has been described above, can conveniently be implemented using a suitable computer program. An implementation of such a computer program is now described. In a preferred embodiment of the present invention, the implementation is carried out using conventional programming using standard operating systems. Such an implementation provides a graphical user with an interface (GUI) to aid user interaction.

Figure 13 illustrates how a complete system, operating as a computer program, for creating risk profiles and risk balance sheets as described above can operate.

The system comprises three modules, an identification module 30, a quantification model 31 and a presentation module 32. The schematic illustration of Figure 13 shows how the system can operate to model activities A, B. C and Z. It will be appreciated that any suitable number of activities can be modelled in a similar manner. The present invention as described above is concerned primarily with the Presentation module 32 of the system, however the identification module 30, and the quantification module 31 will be described À À À À À À À À À ÀÀ . . À . . . . À À À . À À À À À À À briefly for completeness.

The identification module 30 is concerned with identifying the risks which affect each project to be modelled. Correlating factors between these risks are also identified, comprising correlating factors within a single activity, and correlating factors between activities. The identification module 30 provides a suitable interface to allow these factors to be input to the system.

The quantification module 31 takes as inputs the risks and correlating factors which are identified by the identification module 30, and removes any factors considered to have an insignificant effect on the activities being modelled. When this has been done probability distributions for each risk can be created using historical data relating to that risk. Similarly, the correlating factors which have been identified by the identification module 30 are quantified. The quantified risks and correlation factors are output by the quantification module 31 to the presentation module 32.

The presentation module 32 includes within it an analysis engine 33. The purpose of the analysis engine 33 is to take the data which is output from the quantification module 31 and apply it to suitable business models 34 to create NPV distributions. The form of the business models within the analysis engine can be predefined for particular projects. For example, preferred embodiments of the invention provide a plurality of different business models for use with different projects, such as a first business model which is suitable for an oil field development project, and an alternative business model which is suitable for a pharmaceutical development project. These business models will take the form of discounted cash flow models which have been described above. NPV distributions for each individual activity can be created using Monte Carlo Simulation in the manner described above. It will be recalled that the data is applied to each business model a number of times so as to create a number of . À . À . . À . . . . . À À À À NPV values which are combined to form NPV distributions 35 for each individual activity. The process of Monte Carlo Simulation is denoted by step 36 in Figure 15.

In addition to carrying out Monte Carlo Simulation to create an NPV distribution for each individual activity, this embodiment also carries out a Monte Carlo Simulation 37 to create an NPV distribution 38 which represents the NPV of each of the model activities taken in combination. The Monte Carlo Simulation 38 will model correlating influences between activities as has been described above.

Having created the NPV distributions 35, 38 metrics 39, 40 can be computed from the NPV distributions using equations known in the art. These metrics can then be displayed in a risk balance sheet 41 the form of which has been described above. This risk balance sheet can be displayed to a user either by means of a display screen or output to a conventional printer. Additionally, the implementation provides a graphical user interface to allow a user to perform various analyses of the risk balance sheet and its associated NPV distributions.

Two windows from a known graphical user interface 42, 43 are shown for the purposes of example in Figure 13.

In order to explain the operation of the graphical user interface, an example will now be presented of how the process described above can be used to assist a company in a series of decisions which need to be taken in connection with a pharmaceutical development project. Figures 14 show amounts in dollars and it will be appreciated that the denominations used will usually be consistent.

À Figure 14 is a tree diagram showing five decisions which need to be taken during the life cycle of a project. A first decision is taken in July 1988, a second decision is taken in April 1991, a third decision is taken in May 1995, a fourth decision is August 1996 and a fifth decision is taken in December 2001. In the following À # À À À À À À a À À À . . À À À example, the risk balance sheet which would be presented to decision makers at the time of each of these decisions is described.

In Figure 14 the first part of the project life cycle is modelled using the following criteria, which result in the Risk Balances described above.

There is a 1/3 chance of Product A being very successful There is a 1/3 chance of Product A being moderately successful There is a 1/3 chance of Product A being unsuccessful There is a 1/3 chance of Product B being very successful There is a 1/3 chance of Product B being moderately successful There is a 1/3 chance of Product B being unsuccessful If Product A is very successful it will have a risk balance from future costs/revenues of $137M If Product A is moderately successful it will have a risk balance from future costs/revenues of $35M If Product A is unsuccessful it will have a risk balance from future costs/revenues of - $15M If Product B is very successful it will have a risk balance from future costs/revenues of $11 OM If Product B is moderately successful it will have a risk balance from future costs/revenues of $27M If Product B is unsuccessful it will have a risk balance from future costs/revenues of ($32M) Research costs $10M, whichever product is researched (therefore $20M if both are researched). .

The various NPV values are propagated backwards to the previous step so as to be available for display in the risk balance sheet. Typically the most lucrative value at each point is chosen. For example, it can be seen that research Product A has a risk balance of $47Million, researching Product B has a risk balance of $35Million, while researching both Product A and B has a risk balance of $60Million. Thus it is decided to research both of Products A and B as described above. It should be noted that the NPV values outlined in this paragraph relate only to product development. It will be appreciated that similar values have been used to create the Risk Balances for the other decisions shown in Figure 14, however these are not discussed in further detail here. Derivation of these values can be carried out using a suitable risk model and the process of Monte Carlo Simulation described above.

For the reasons set out above, the company decides to research both Products A and B in July 1988. The next decision point is 3 April 1991 (Figure 14), when a decision is to be taken as to which of the products A and B which have been researched is to be developed. It is assumed that the Products are mutually exclusive, and therefore developing both products further is not an option.

Each key risk balance sheet parameter that appears on the principal risk balance sheet summary form (Figure 4) references a hierarchy of additional forms.

These forms provide additional Metrics and parameters, and detail the derivation of the key Metrics and parameters, including the graphical Risk Spectra from which the risk balance sheet is derived. The risk balance sheet uses an inductive reasoning model to justify and rationalize the adoption of the subjectively derived elements of the risk models and their input data. The predictive element of the risk balance sheet process most desirably uses the combined application of historical data and informed subjective judgement.

À d e a À À À À * In carrying out the computerized method of the present invention, appropriate computer hardware well known to those skilled in the art can be employed.

Suitable algorithms can be developed by persons skilled in that art having regard to the art knowledge, and given the information relating to the present invention.

Thus, algorithms using conventional techniques can be provided for facilitating the creation of risk models, repetitive calculation using application-specific risk models, storing and manipulating the risk data, presentation of risk data as Risk Profiles, presentation of the risk data as a risk balance sheet, recording the basis, origin and auditability of the risk data and its rationalization, reviewing the data in a risk balance sheet, and reviewing the basis, auditability and rationalization of the data in a risk balance sheet. The computer executable software desirable includes means for recording the justification of the subjective judgement. The computer executable software also desirably includes means for tracking and auditing the data used and its derivation. Desirably, in the computer executable software, the additional risk balance sheet forms open up in a hierarchy of separate windows, to enable users to easily reference the basis of the information presented.

The metrics used in the method of the present invention will be seen to be more effective than the raw Risk Profile data in communicating and assessing the risk- return relationship of a business activity or decision. This is due to the fact that they are relatively few in number, and further, since they are discrete quantitative values that can be compared with criteria defined to represent the expectations and risk aversion of the stakeholders in a business activity or decision process.

As will be evident from this specification, the risk balance sheet format is closely analogous to the traditional accounting balance sheet since it shows potential returns from a business activity or decision. However, in contrast to a traditional balance sheet where the assets are equal to the liabilities, the risk balance sheet generated by the method of the present invention differs by virtue of the fact that a total return does not need to balance with the total risk. The Risk Balance is À: :: À À: ::e À À. À À À ce À . . À Àe essentially a balancing figure, because it is the return plus the risk. Therefore, the Risk Balance always balances with the Total Return plus the Total Risk (Total Risk being a negative value).

It will be evident from the above description that, by way of example, a business organization may consist of many units that operate with a degree of autonomy, or which are simply recognized as distinct profit centres. In reality therefore, the risk model 1 in Figure 1, described above, may actually represent a collection of inter-dependent risk models. Each model can be used to produce a set of risk and return data and a Risk Profile for a specific business unit. Therefore, a business is modeled as a 'portfolio' of business activities, and the overall Risk Profile for the organization is obtained by producing a combined Risk Profile for its portfolio of activities. It will also be noted that the method of this invention provides a risk balance sheet which has a general application since it can be used for any type of risk-based decision making. c . c

Claims (24)

À C 4 C C C C l, C CLAIMS

1. A statistical method for assessing the risk and returns for a business activity or decision, the method comprising: (h) identifying primary conditions which determine a return generated by the business activities or decisions; (i) estimating both a range of values for the identified conditions and probabilities that the conditions will assume for each value within the said range; 0) estimating risks and returns for said business activities or decisions for possible combinations of the conditions identified; (k) estimating the likelihood of each possible combination of conditions; (1) graphically representing the likelihood of the risks and returns as risk profile data in which the risk profile data provides a representation of a likelihood distribution characterizing both favourable outcomes and risks, forming non-favourable outcomes; (m) summarising said risk profile data as a numerical value of discrete quantitative measures representing financial or non-financial measurements capable of comparison with criteria which distinguish whether À À À c À . . À . k' À À À À À À said risk is acceptable; and (n)presenting the discrete quantitative measures textually as a risk balance sheet, in a format which parallels a typical company accounting balance sheet.

2. A method as defined in claim 1, said method being carried out as a sequence of steps for assessing the risk and returns for a portfolio of business activities or decisions.

3. A method as defined in claim 1 or 2, including the further steps of: (g) providing justification for the subjective judgement used in the assessment method; (h) providing justification for the risk models and calculations used in the method; and (i) recording the origin and derivation of the data used in the assessment method.

4. A method as defined in any one of claims 1 to 3, wherein each of steps (a) through (g) are individually recorded as part of the method.

5. A method as defined in claim 2, wherein each of steps (h) through (j) are individually recorded as part of the method. À c

# b À À À b

6. A method as defined in any one of claims 1 to 4, wherein said method is computer-implemented.

7. A computer-implemented method for assessing and for recording the verification of the assessment of the statistical risk and returns for a business activity or decision, said method comprising the steps of: (a) identifying and recording primary conditions which determine a return generated by the business activities or decisions; (b) estimating and recording both a range of values for the identified conditions and probabilities that the conditions will assume for each value within the said range; (c) estimating and recording risks and returns for said business activities or decisions for possible combinations of the conditions identified; (d) estimating and recording the likelihood of each possible combination of conditions; (e) graphically representing and recording the likelihood of the risks and returns as risk profile data in which the risk profile data provides a representation of a likelihood distribution characterizing both favourable outcomes and risks, forming non-favourable outcomes; _ b b b # # $ #$ 8 C # r 8 $ À # # (f) summarising and recording said risk profile data as a numerical value of discrete quantitative measures representing financial or non-financial measurements capable of comparison with criteria which distinguish whether said risk is acceptable; and (g) presenting and recording the discrete quantitative measures textually as a risk balance sheet, in a format which parallels a typical company accounting balance sheet.

8. A method as claimed in any one of claims 1 to 7, comprising the step of summarizing principal statistical risk and return data as discrete quantitative values on a risk balance sheet form containing a plurality of primary parameters, said

primary parameters constituting a summary form of

references of a hierarchy of additional forms which provide additional discrete quantitative values and parameters and detail the derivation of the discrete quantitative values and parameters, including graphical risk profiles from which the risk balance sheet is derived.

9. A method as defined in any one of claims 1 to 8, said method effecting recording and presenting the assessment and the statistical risk and return data, said data being summarised as the mean value of positive returns in a risk profile multiplied by the probability of a positive return.

10. A method as defined in any one of claims 1 to 9, said method effecting recording and presenting the assessment e feeÀ e e e e e c e e e e e e À À Je. e ale À e and the statistical risk and return data, said data being summarised as the mean negative value of negative returns in a risk profile multiplied by the probability of a negative return.

11. A method as defined in any one of claims 1 to 10, said method effecting recording and presenting the assessment and the statistical risk and return data, said data being summarised as the mean negative value of negative returns in a risk profile allowing for risk aversion, multiplied by the probability of a negative return.

12. A method as defined in any one of claims 1 to 11, said method effecting recording and presenting the assessment and the statistical risk and return data, said data being summarised as return discrete quantitative values together with the discrete quantitative risk values.

13. A method as defined in any one of claims 1 to 12, said method effecting recording and presenting the assessment and the statistical risk and return data, said data being summarised as return discrete quantitative values together with adjusted risk discrete quantitative values.

14. A method as defined in any one of claims 1 to 13, said method effecting recording and presenting the assessment and the statistical risk and return data, said data being summarised as the ratio of discrete quantitative values of the return divided by the risk discrete quantitative values.

::: e. ate c:e À. cee.

15. A method as defined in any one of claims 1 to 14, said method effecting recording and presenting the assessment and the statistical risk and return data, said data being summarised as a return value calculated as the ratio of the return discrete quantitative value divided by the adjusted risk discrete quantitative value.

16. A method as defined in any one of claims 1 to 15, said method effecting recording and presenting the assessment and the statistical risk and return data, said data being summarised as a certainty equivalent factor calculated as the mean negative value of negative returns in a risk profile allowing for risk aversion.

17. A method as defined in any one of claims 1 to 16, said method effecting recording and presenting the assessment and the statistical risk and return data, said data being summarised as a maximum credible loss factor which is the modulus of the greatest negative return in a risk profile.

18. A method as defined in any one of claims 1 to 17, said method effecting recording and presenting the assessment and the statistical risk and return data, said data being summarised as a return on capital employed factor calculated as the ratio of the return factor divided by a maximum credible loss factor.

19. A method as defined in any one of claims 1 to 18, wherein said method is applied to assessing the risk and returns for a portfolio of business activities or decisions. e ce.

e e e e e e e e

20. A method as defined in any one of claims 1 to 19, said method calculating and presenting financial returns for said business or said decision.

21. In a method for predicting future performance of at least one activity of a business enterprise, the steps comprising: generating a probability distribution representing future performance of the at least one activity; computing a mean value of the said probability distribution above a predetermined threshold; computing a probability of the future performance being above said predetermined threshold from the said probability distribution; and multiplying the said mean value by the said probability to obtain a value indicative of future performance.

22. The method according to claim 21, the steps further comprising: computing a mean value of the said probability distribution below the predetermined threshold; computing a probability of the future performance being below said predetermined threshold from the said probability distribution; and e # a multiplying the same mean value of the said probability distribution below the predetermined threshold by the said probability of future performance being below said predetermined threshold to obtain a further value indicative of future performance.

23. The method according to claim 22, wherein the said metric and the said further metric are combined to create a combined value indicative of predicted future performance.

24. In a method for assessing the risk and returns of a business activity or decision presented as a risk balance sheet, the method steps characterized by: (a) identifying and recording primary conditions which determine a return generated by the business activities or decisions; (b) estimating and recording both a range of values for the identified conditions and probabilities that the conditions will assume for each value within the said range; (c) estimating and recording risks and returns for said business activities or decisions for possible combinations of the conditions identified; (d) estimating and recording the likelihood of each possible combination of conditions to thereby provide graphic representation and recording of the likelihood of the risks and returns as risk profile data in which the risk profile data À . c.

e À À À eee a e. À provides a representation of a likelihood distribution characterizing both favourable outcomes and risks, forming non-favourable outcomes to obtain data representing the likelihood of risk.