PRE-READING 4 TYPES OF MODEL STRUCTURES

Transcription

1 LEARNING OBJECTIVES Types of Model Structures PRE-READING 4 TYPES OF MODEL STRUCTURES Appreciate the different structural characteristics that may be incorporated within financial models. Recognise how these structural characteristics can be usefully employed in financial models to provide decision support. Determine the type of model structure to be employed within a particular model. KEY Data Table Decision tree Forecast Pro Forecasting model Goalseeking Model structures Monte Carlo risk analysis Optimising model Precision tree Probabilistic modelling Risk Scenario (what-if) analysis Sensitivity analysis Simulation model Spider graph Tools/Solver command TopRank Add-in Tornado graph Uncertainty Visual Basic Applications (VBA) What-if solver 1

2 Pre-Reading 4 INTRODUCTION Financial models may be classified according to their structural characteristics. This Pre-Reading examines the following commonly used types of financial model structures: simulation models optimising models forecasting models SIMULATION MODELS A simulation model uses a series of model statements to describe the organisation's activities. By varying these statements or their associated values (otherwise known as scenarios ), the user is able to simulate a range of alternative actions and assumptions. A simulation model can support the decision process by helping users to generate pay offs from various strategies and states of nature. Simulation models may be useful for examining the possible outcomes of all feasible actions prior to implementing any one of them. By using a simulation model, it is relatively easy for the user to change input values or formulas to search for what he or she considers to be a "near-optimal" course of action. It needs to be emphasised that a simulation model does not automatically produce an "optimal" solution. However, repeated scenario (what-if) simulations can help to produce a solution as close as practical to optimal. Simulation models are the most commonly used and simple type of financial model. Many accounting spreadsheet applications can be classified as simulation models. Simulation models may be used to perform: Scenario ("What-if") analysis; Sensitivity analysis; Goal seeking; Modelling incorporating risk and uncertainty (probabilistic modelling). Scenario (What-if) Analysis Scenario or what-if analysis enables the user to simulate what might happen to a given situation if one or more input values were changed. Typically, the user starts with a base model which represents the 2

3 Types of Model Structures user's most realistic estimate of what might happen. Input values can then be changed by the user to investigate various scenarios. The user will continue to change input values, searching for a near-optimal or satisfying solution. Some examples of scenario (what-if) analysis models include: a loan amortisation model, where the user is able to investigate the effect of changing data values such as the interest rate, principal advanced, length of the loan or repayment amount; a "lease or buy" analysis model, where the user is able to investigate the economic feasibility of leasing as against buying a new capital item; a "cash flow" model to investigate potential cash flows as changes are made to data items such as the sales volume, selling price, or the timing of receivables and payables. Sensitivity Analysis Sensitivity analysis involves determining the impact on a model s results of changes made to only one input variable (or data factor), while holding all other variables constant. Small changes to this input variable may result in dramatic changes to the results. In this case, the results are said to exhibit high sensitivity to this input variable. Alternatively, a change in this input variable may produce little overall change in the results; thus, low sensitivity. Sensitivity analysis allows the decision maker to determine which input variables have the most impact on the organisation s bottom line. The decision maker may then decide whether it is appropriate to concentrate on those variables. As well as allowing the decision maker to determine the key variables in a decision, sensitivity analysis can be used to determine the margin of error in decisions involving those variables. Sensitivity analysis can be performed using either a spreadsheet package, a financial modelling language, a decision support package, or an add-in to spreadsheet package. The least efficient, but probably most common approach, is to use a spreadsheet package to repeat the scenario (what-if) analysis process over and over again. For each repetition of this process, the value of one input variable is changed and the results recorded. This process is repeated for a range of values for that input variable, and then the whole scenario (what-if) process is repeated for any other input variable that the decision maker wishes to vary. By comparing the relative differences in the results as each of these input variables are varied, the decision maker is able to identify those input variables that cause the largest change in the output result; that is, the high sensitivity or critical variables in that decision situation. Microsoft Excel allows the decision maker to semi-automate the process of varying the values assigned to input variables. Excel s Data Table command allows the decision maker to vary one (or two) input variable/s to identify the effect that this change has on one (or more) formulas (ie. output results) of interest. The table output from this command shows the decision maker the sensitivity of the results to 3

4 Pre-Reading 4 one (or two) input variables. The dialogue box for Excel s Data Table command is shown in Figure 4.1. The operation of this command is examined in the tutorial exercises for Pre-Reading 6. Figure 4.1 Excel's Data Table Dialogue Box Most financial modelling languages also include a vary statement, or similar command, to allow the decision maker to easily substitute a range of values through an input variable. The repeated application of this vary statement, along with the graphic facility of the modelling language, enables the decision maker to perform sensitivity analysis. Irrespective of the method used to run sensitivity analysis in a spreadsheet package or financial modelling language, the output from the sensitivity analysis will only be meaningful if the changes made to each of the input variables are consistent. For example, the decision maker may choose to apply a two percent growth and discount rate, within the range of positive ten percent to negative ten percent, to all the base (or original) values for the input variables of interest. This consistency makes it possible to compare the output results for each of these input variables using either tabular (numeric) output or graphic output (such as a spider graph - see discussion below). Specialist financial modelling tools (such as Optimist) and spreadsheet add-in packages (such and TopRank) incorporate dedicated sensitivity analysis routines. For example, Optimist s sensitivity analysis facility allows the decision maker to nominate an output result of interest and then lists, in decreasing sensitivity order, the input variables that affect the output result. Optimist also displays an ease to target ratio (ETR) for each of these input variables. This ETR value can be within the range 1-999; the higher the value, the greater the sensitivity of the output result to that input variable. The sensitivity analysis facility in spreadsheet add-in package displays the sensitivity of the input variables using a tornado graph. A tornado graph uses a horizontal bar for each input variable that has an effect on the output result; the longer the bar, the greater the sensitivity of the output result to that input variable. The input variables that have the greatest affect on the output result have their bars displayed towards the top of the tornado graph. The further down the tornado graph an input 4

5 Types of Model Structures variable is displayed, the shorter the length of the bar, and the less sensitive the output result is to that input variable. The overall shape of the bars on a tornado graph are similar to the shape of a tornado, hence the name given to this type of graph. The TopRank spreadsheet add-in package is specifically designed to perform sensitivity analysis on spreadsheet models. TopRank allows the decision maker to nominate an output result of interest and then scans the entire model to determine the input variables that affect the output result. The package does this by varying values for each of the input variables and then displays results using three types of graphs: Tornado, Spider and Sensitivity. The tornado graph is similar to the tornado graph facility in package. The spider graph displays a series of lines for the output values as a result of varying the input variables. Each line on the spider graph represents one input variable, and the slope of each line indicating how the rate of change in that particular input variable affects the rate of change in the output result. For example, a spider graph could be used in a profitability model to display the net profit values when several base expenses are varied. Each line on the resulting spider graph would show the net profit values at the varying levels of that expense. The decision maker is then able to interpret, from the slope of each line, the sensitivity of the net profit to these expenses. An example of a spider graph is generated in the tutorial exercise for Pre-Reading 6. A sensitivity graph is similar to a spider graph, except that it can be used to display the effects of varying one input variable on values generated for one or more output results (such as contribution margin, gross profit, or net profit etc.). Some examples of the use of sensitivity analysis include examining the effect of: Interest rate changes on monthly loan repayments; Exchange rate fluctuations on the profitability of an importer or exporter; Interest rate fluctuations on building construction projects; Product selling price changes on demand levels and overall profitability. Goal Seeking Goal seeking involves instructing a model to work backwards from a desired quantified outcome, known as a "goal", to determine the specified changes that would be needed in one or more input variables in order to achieve that goal. In order to determine the value required for that input variable in order to achieve the goal, the model will perform iterative recalculations. These iterative recalculations will continue until the model eventually finds a value for the input variable that achieves the goal, or stops trying to solve for the goal after exceeding an "maximum iteration" limit or time limit. For this reason, goal seeking is also known as backward iteration. Until fairly recently, if you wished to perform a goal seeking routine, you either had to use: 5

6 Pre-Reading 4 a financial modelling language; a spreadsheet package in conjunction with an "add-in" product, such as What-if Solver; a program that you had written in either a general purpose programming language or in the macro language of a spreadsheet package. Most spreadsheet packages now provide an built-in facility to perform goal seeking. For example, Excel s Tools Goal Seek command allows the user to vary a single input variable in order to solve for a specified goal. Figure 4.2 shows Excel s dialogue box for this command. The user is able to set a goal by specifying the first two items on this dialogue box (ie. set cell and to value ), and nominate the input cell that can be varied to achieve this goal by specifying the third item (ie. by changing cell ). This facility is certainly much easier to use than writing even a simple goal seeking routine, using a technique such as a binary search, in a general purpose programming language or spreadsheet macro. If the user wishes to vary more than one input variable when goal seeking, Excel s Tools Solver command, which is discussed later in this Pre-Reading under the section Optimising Models, allows the user to set the goal to a value (rather than to max or min, as used for optimisation). Figure 4.2 Excel's Tools Goal Seek Dialogue Box Possible examples of the application of goal seeking techniques include: Determining the pension plan contributions required to achieve a desired lump sum at retirement, given an assumed average investment rate of return; Determining the product unit sales volume needed to achieve a desired net profit, given a particular selling price and cost structure; Determining the home loan principal that can be borrowed given the current mortgage interest rate, the dollar amount that can be repaid each period, and the number of repayment periods in that mortgage. This home loan calculation is the reverse of a typical loan repayment calculation, where the principle, interest rate and number of repayment periods are input values, and the 6

7 Types of Model Structures spreadsheet model uses an Excel function such as pmt to calculate the repayment amount to be made each period. Probabilistic Modelling The data that is used in financial models can be classified as being either deterministic or probabilistic in nature. Deterministic data is input that has only a single value for each input variable. Probabilistic data is input which requires the user to specify a probability distribution for each uncertain input variable. A probability distribution lists a range of possible values for that input variable, along with their associated probability of occurrence. Probabilistic data is used in models that have been constructed to incorporate risk and uncertainty directly into their logic. These models contain logic, such as monte carlo risk analysis, to allow the decision maker to determine a range of possible output results for the model, and their likelihood of occurrence. The probability distributions used in these models can be classified as either discrete or continuous. A discrete distribution lists a finite number of possible values for an uncertain input variable, along with their associated probability of occurrence. Figure 4.3 illustrates an example of a discrete probability distribution; in total, there are nine possible combinations of cash flows for each investment. These uncertain future net cash flows are based upon three state of the world conditions. For example, there is a 20% chance of a poor state of the world, with a net cash flow for Investment A of $100 in year 1; and if the state of the world remains poor in year 2, a further $300 net cash flow in year 2. Likewise, the probability of a moderate or good state of the world, and their associated net cash flows, are also listed for Investment A and Investment B. A continuous distribution uses a probability function to represent an unlimited number of possible values for an uncertain input variable, along with their associated probability of occurrence. A normal, or bell-shaped curve, is probably the most well known type of continuous probability distribution. For example, an uncertain input variable could be specified as a normal distribution with a mean of 25 and a standard deviation of 6. Many other types of continuous distributions may be used to specify probabilistic data, including exponential distributions, triangular distributions, truncated normal distributions and lognormal distributions. These probability distributions will be examined in further detail in the Pre-Reading covering risk analysis and product (ie. Pre-Reading 19). Most probabilistic models have been built using, as their basis, an existing simulation or optimising model. In these cases, the model builder has simply included probabilistic data in the model, and utilised a decision tree or a monte carlo risk analysis facility in a financial modelling language or spreadsheet add-in package, to incorporate risk and uncertainty into their model. 7

8 Pre-Reading 4 Historically, most large probabilistic models have been built using financial modelling languages, such as such as FCS-EPS, IFPS or Visual DSS, rather than with spreadsheet packages. The development of spreadsheet add-in packages, such have allowed spreadsheet users to incorporate probabilistic data into moderately complex financial models. However, extremely complex probabilistic models are still best developed using specialist financial modelling languages or associated probabilistic DSS tools. The extra facilities in these modelling languages, their speed of recalculation, and the rigour required of the model developer in using these languages, tends to improve the decision support provided by the resulting probabilistic financial models. Probabilistic data can be incorporated into spreadsheet models using either decision trees, for simple discrete probability distributions, or spreadsheet add-in products for more complex discrete or continuous probabilistic distributions. Decision trees provide a profile of the possible inputs and outcomes in a decision situation, along with their associated probabilities of occurrence. A decision tree for a capital investment spreadsheet model is shown in Figure 4.3. Whilst decision trees may be used within spreadsheets for relatively simple probabilistic models, even a small number of uncertain variables can make the spreadsheet model difficult to construct and use. Probabilistic data also increases the recalculation time for the model by an order of magnitude. However, it is possible to build more complex decision trees into spreadsheet models using add-in packages such as PrecisionTree. This add-in package allows the spreadsheet user to build influence diagrams and decision trees into their models. An influence diagram allows the user to see the relationships between components of a problem, while a decision tree allows the user to attach risk values to the options or the sequence of events involved in a decision. More complex models incorporating risk and uncertainty are best built with a software product that directly supports risk analysis, rather than with a standard spreadsheet package. Even though it is possible to use a macro routine generated in Excel s Visual Basic Applications (VBA) programming language to develop a monte carlo risk analysis routine, it is much easier to develop spreadsheet-based probabilistic models using add-in packages such These add-ins support both discrete and continuous data distributions, and incorporate various iterative processing techniques, such as "monte carlo risk analysis", to generate results that show a range of possible output values, and their associated probability of occurrence. A flow chart of the "monte carlo risk analysis" processing logic is shown in Figure 4.4. This logic iteratively generates input data based on the specified probability distributions of the uncertain data variables supplied to the model, and then runs this generated data through a simulation or optimising model. With each iteration of the processing loop, the model generates a new set of data from the probability distributions, and then accumulates or summarises the output from the current "run". Once 8

9 Types of Model Structures the number of iterations exceeds the iteration limit (ie. "N" in Figure 4.4), the loop terminates and the output is summarised, analysed, and presented as a series of tables and graphics. This output represents a range of possible outcomes for the output variable of interest, such as net cash flow, and the associated probability of occurrence for each of these outcomes. Although there have been many successful models developed using probabilistic data, many probabilistic modelling attempts have been frustrated by the difficulties in estimating probabilities, due to a lack of relevant data. If relevant historical data is not available, the model user may have to substitute "hunches". By way of compromise, many model builders wishing to directly incorporate risk and uncertainty into their models have adopted a "Quasi-probabilistic" approach to the probabilistic data. This approach only requires the user to specify the most optimistic, most likely and most pessimistic values, and their associated probability, for each uncertain input variable. For reasons of practicality, many models involving probabilistic data have been simplified to use only "quasi-probabilistic" data or have reverted back to using only deterministic data. 9

10 Pre-Reading 4 Figure 4.3 Using a Decision Tree to Incorporate Risk and Uncertainty into a Spreadsheet Model Decision Tree for Investment Projects Investment A Investment B State of the World Probability Year 1 Year 2 Year 1 Year 2 Poor Moderate , Good , ,500 Discounted Cash Flows present value Expected Year 1 Year 2 Probability a (PV) b PV c , , , , , , , , , A 0.2 1, , , B , , , , , , , , , ,198.5 a Probability in year 1 x probability c Probability x discounted in year 2 present value b Cash Flow Year 1 + Cash Flow Year (1.10) 2 10

11 Types of Model Structures Figure 4.4 The Processing Logic in Monte Carlo Risk Analysis FLOW CHART OF MONTE CARLO SIMULATION START Initialise Counter and Output Variables Input Number of Iterations: N Input Values of CERTAIN Variables Input Distribution for each UNCERTAIN Variable Is Counter < = N? Yes No Generate Values for UNCERTAIN Variables from specified Distributions Analyse Distributions of Output Variables RUN MODEL END STORE OUTPUT DATA ADD 1 TO COUNTER 11

12 Pre-Reading 4 OPTIMISING MODELS Optimising models go one step further than simulation models by incorporating advanced mathematical logic to select a unique, optimal course of action automatically. This output is generated within certain constraints specified for the reality being modelled. Optimising models can usually be developed, using as their basis, existing simulation models. Optimising models require the model builder or user to specify in measurable terms: an objective function, such as profit maximisation, sales maximisation or cost minimisation; constraints that exist in achieving that objective. These constraints could include limitations over resource availability, and product or service demand. These resource limitations need to be expressed in terms of resource units used per unit of product or service. Resource constraints could include limitations over items such as various raw materials, direct labour hours, machinery capacity or finance availability; and the variables that can be changed to achieve that objective function. Mathematical optimisation techniques such as linear and nonlinear programming are commonly used to generate the highest value for the objective function. Mathematical optimising models tell you how best to allocate resources to various products, projects or services. Linear programming can be used where the variables in the model are either simply added or subtracted from each other, or multiplied or divided by constants and then added or subtracted. Nonlinear programming is used in models where the variables are multiplied together or divided by each other, or subjected to exponential calculations before being added or subtracted from each other. Other more complex mathematical techniques may be used in optimising models, including: goal programming, dynamic programming, stochastic programming, chance-constrained programming and quadratic programming. These more complex programming techniques are beyond the scope of this book. If you wish to find out more about these techniques, many operations research or management science books have Pre-Readings devoted to these techniques. In practice, the use of optimising models is limited by: the complexity of the mathematical principles used in optimising models. These principles make the models relatively difficult to build and use. Many accountants and managers are reluctant to use optimising models because they do not fully understand the mathematical principles involved in their construction and use; the software that has typically been used to develop these models has been both expensive and difficult to use. These models have traditionally been developed using general purpose programming languages or specialised modelling languages. These languages require extensive 12

13 Types of Model Structures skills to be used effectively. However, improvements in these languages, along with built-in Solver facilities in spreadsheet packages (for simple problems) and spreadsheet add-ins for more complex problems, have made relatively "easy to use" software more widely available at a comparatively low cost; the complexity inherent in optimising models makes many optimising models relatively timeconsuming, and thus expensive, to develop; unrealistic assumptions may need to be incorporated into many optimising models to help simplify their development. A modelling language which enables optimisation techniques to be employed must at least have the mathematical power to solve simultaneous equations. It also needs sufficient logical power to allow conditional branching and looping to be undertaken. A mathematically efficient "simplex" technique is often used to compare alternatives within the feasible set and to choose the optimal solution, measured in terms of the objective function. Optimisation provides a conceptually neater method of solving problems than does simulation, provided that it is used in decision situations for which it is appropriate. The solution is found by analytical calculation, rather than by the rather clumsy trial-and-error experimental method of simulation. Further, it is more economical in terms of computer time and cost to use an optimisation technique rather than a Monte Carlo simulation method. In practice, the two techniques are appropriate for solving different types of problems and should be regarded as complementary rather than conflicting options. To use an optimisation technique, it is necessary to make a number of restrictive assumptions which are seldom more than approximately true. When these assumptions are clearly too unrealistic, or the problem to be solved is too complex to fit the precise and narrow framework of an optimising model, then simulation is more appropriate. Microsoft Excel incorporates built-in routines to handle simple optimising problems. For example, Excel incorporates linear and nonlinear programming facilities in its "Solver" facility. This facility is able to solve simple optimisation problems, and being relatively simple to use, is ideal for introducing spreadsheet model builders to the concept of optimisation. Figure 4.5 illustrates the Solver dialogue box that can be accessed using the Tools Solver command. This command allows the user to optimise a target cell (as indicated in the Set Target Cell item and the Max or Min radio buttons), by changing a range of cells (as indicated in the By Changing Cells item), but subject to the constraints specified (in the Subject to the Constraints item). This command will be examined in more detail in Pre-Reading 18, which covers the use of linear programming techniques to solve accounting problems. 13

14 Pre-Reading 4 Figure 4.5 Excel s Solver Dialogue Box The solver facility built into Excel is only capable of solving relatively small and simple optimising problems. Larger or more complex problems are best solved using a specialist financial modelling language, an optimisation language, or a spreadsheet add-in package such as What sbest!, Evolver or Premium Solver. Basically, these tools are able to handle many more variables than built-in spreadsheet solvers, and have solver engines (ie. logic) that support a range of additional calculation methods, such as quadratic programming and genetic algorithms, to more quickly and accurately solve optimising problems. Some examples of optimising model applications include: A product mix model to determine the optimum sales mix of several products, each with its own demand schedule and profit margin, and all straining for a share of the scarce resources (eg. raw materials, labour supply and factory time etc.); A portfolio management model to determine the optimum portfolio of investments. The portfolio model aims to maximise the income stream and capital growth from the investments, given the projected returns from the individual investments and the desired risk profile of the investor; A capital resource budgeting model to determine the optimum allocation of available capital to different projects; A personnel planning model to allocate staff with various skills to a number of projects based upon the availability and skills of the staff, and the timetable for completion of the various tasks in each project; 14

15 Types of Model Structures An input blending model to determine the optimum blend of ingredients to be used in a production process. For example, the model may be used to determine the optimum blend of ingredients for livestock feed. The objective in this case would be to produce livestock feed which optimises the livestock growth rates, but within the constraint of an acceptable maximum cost price per kilogram; A transportation model to determine the best routes to be followed by delivery trucks in order to deliver the maximum amount of goods using a minimum quantity of resources such as driver s time, fuel and kilometres travelled. Other common optimising applications involving transportation systems include scheduling truck arrival and departure times between two points to optimise product movement efficiencies; and determining air routes for a domestic airline to maximise aircraft seat allocation or load percentages; A project scheduling model to determine the optimum sequence of events to be performed in order to complete a project in a minimum amount of time or with minimum resource usage. The model aims to identify the critical path through the project tasks and determine the other tasks that have some "slack" time associated with them; and An inventory model to determine the optimum order quantity and re-order point for one or more products. The model aims to minimise the overall cost of the products, including their ordering and holding costs, whist still maintaining a satisfactory service level for customer orders. FORECASTING MODELS Forecasting models aim to produce accurate estimates of future values for specific variables. These estimates may be an end in themselves for decision making, or may then be used as input to simulation or optimising models. Two general types of forecasting models are commonly used: Time series analysis, which develops forecasts by observing past values of a single variable. The forecasting techniques associated with time series analysis include: linear regression, Box- Jenkins, moving averages and exponential smoothing. Causal forecasting, which seeks to identify a theoretical relationship between the forecast variable, known as the dependent variable, and one or more explanatory or independent variables. The most common forecasting technique associated with causal forecasting is multiple regression. If historical data is relevant and available, it is possible to use a computer-based "analysis and forecasting routine" to generate the input data needed in a model. The forecasting sub-routines may be contained within the modelling language, which is very convenient, or a separate "applications" package may be 15

16 Pre-Reading 4 used which can be interfaced with the modelling software. Alternatively, forecasts can be generated externally by another model and entered manually into the model by the user. Statistical forecasting facilities may be used in two ways; to analyse the pattern of past data or to use the past data behaviour pattern to predict future values. By analysing the pattern of past data, decision makers can gain a better understanding of the variables in the problem they are trying to solve. For instance, in an accounting environment, they may wish to determine: The trend in the value of variables. If trends have changed in recent periods, indicating a break or turning point. How much a cost factor is likely to vary because of random fluctuations. The relative fixed and variable proportion of costs. What seasonal or cyclical fluctuations occur in sales levels; and The extent to which variables are correlated with one another. This sort of information provides useful evidence of the behavioural relationships existing in the environment being modelled. These behavioural relationships can then be built into the logic statements of a model built with a financial modelling language, or into the formulas used in a spreadsheet model. The forecasting facility may be used to predict future values in one of two ways. The user may specify the behavioural pattern of the variable being forecast (using a behavioural equation), and the forecasting facility then uses this information to forecast the variable of interest. However, the forecasting facility is more commonly used to determine the relationship between variables, and it then uses this information to extrapolate future values for the variable of interest. Certain conditions must be satisfied for this method of prediction to be appropriate: The historical data must be relevant. Conditions must be sufficiently stable for the past to be an appropriate basis for predicting the future; There must be sufficient periods of data available in the time series for the proposed forecasting technique; The accuracy of the historical data must match the precision required in the forecast; and The error and other statistics, which are automatically generated with the forecast, must indicate that the forecast method used is appropriate. 16

17 Types of Model Structures Although it is usually better to base simulation and optimising models on data that has been generated from forecasting models, rather than from mere "guesses", the usefulness of forecasting models may be limited by: its cost/benefit ratio. The cost of generating data using a forecasting model may outweigh the benefit likely to be derived from the more accurate forecast data generated by that model; a lack of relevant data. The past data may be so erratic, or exhibit a stochastic or random walk pattern, that the time series techniques may be inappropriate. Other relevant data on which to base the forecast may not be available. Pre-Reading 14 in this book covers an example of time series forecasting; namely, the use of classical time series decomposition analysis. The logic used in this type of model may be constructed totally by the model builder, using any of Excel s built-in statistical functions (of which there are approximately 70, including median, average, slope, linest etc.). Alternately, the model builder may choose to use the forecasting facilities of a financial modelling language, a statistical forecasting package, or a spreadsheet add-in package such as Forecast Pro. Forecast Pro includes a number of time series forecasting techniques, including moving averages, exponential smoothing, Box-Jenkins and dynamic regression, to allow the model builder to uncover meaningful patterns in historical data. If a statistical pattern seems to exist, the expert system component of this add-in can assist the decision maker to decide which forecasting method will provide the best forecast, and to support this choice, provides a diagnostic summary indicating why the chosen technique is best. However, ultimately it is the personal judgement and expertise of the decision maker (or model builder) that must be relied upon in deciding if the future will behave in a sufficiently similar manner to the past, and therefore, whether reliance can be placed upon this time series forecasting tool. CHOOSING A MODEL S STRUCTURE Many factors combine together to determine the type of model structure to be employed within a particular model. These factors include the: Mathematical nature of the relationships between variables. For example, these relationships may be based upon deterministic data; that is, input values that are known with certainty. Alternatively, these relationships may be based on a level of uncertainty, requiring the model builder to incorporate various risk analysis techniques. 17

18 Pre-Reading 4 Objectives of the decision maker. The decision maker may only be interested in achieving a satisfactory result, rather than spending extra time attempting to identify the optimum solution for an objective function. For example, the problem being modelled may not lend itself to easily being solved using linear or nonlinear programming, and the constraints limiting the achievement of that objective function may be difficult, if not impossible, to specify accurately. The model builder may simply require a what-if simulation model, rather than attempt to build a more demanding and expensive optimising model. Level of knowledge and skill of both the decision maker and model builder. This factor obviously determines the level of sophistication that the model builder will incorporate within a financial model. Budget available to develop the model. In terms of both cost and timeliness, the model builder must ensure that the resources allocated to the construction of the model are appropriate to the likely benefit, in the form of improved decisions, that will potentially flow from the model. Extent of control existing over the decision variables. For example, the model builder may attempt to use techniques such as sensitivity analysis to identify those decision variables that will have the greatest effect on results, and which can be manipulated by the decision maker. Level of uncertainty associated with the decision environment. Once again, this will determine whether the logic of the model incorporates deterministic or probabilistic data, and the types of information that may be generated by the model. For example, the model output may be a distribution table showing a range of possible results, or a graph illustrating possible results and their probability of occurrence. 18

19 Types of Model Structures SUMMARY Financial models can be classified according to three types of structural characteristics: simulation models, optimising models, and forecasting models. Simulation models use a series of model statements to describe the organisation's activities. By varying these statements or their associated values (otherwise known as scenarios ), the user is able to simulate a range of alternative actions and assumptions. Simulation models may be used to perform scenario (what-if) analysis, sensitivity analysis, goal seeking, or probabilistic modelling. Scenario (what-if) analysis enables the user to simulate what might happen to a given situation if one or more input values were changed. Sensitivity analysis involves determining the impact on a model s results of changes made to only one input variable (or data factor), while holding all other variables constant. Goal seeking involves instructing a model to work backwards from a desired quantified outcome, known as a "goal", to determine the specified changes that would be needed in one or more input variables in order to achieve that goal. Probabilistic modelling allows the decision maker to incorporate risk and uncertainty directly into their financial models. These probabilistic models contain probability distributions for each uncertain input variable and logic, such as monte carlo risk analysis, to allow the decision maker to determine a range of possible output results for the model, and their likelihood of occurrence. Optimising models go one step further than simulation models by incorporating advanced mathematical logic to select a unique, optimal course of action automatically. This optimum or best solution is generated by the model after the decision maker has specified the objective to be achieved, the cell/s that can be adjusted to achieve that objective, and the constraints that limit the achievement of that objective. Forecasting models aim to produce accurate estimates of future values for specific variables. Two general types of forecasting models are commonly used: time series analysis and causal forecasting. Time series analysis develops forecasts by observing past values of a single variable. Causal forecasting seeks to identify a theoretical relationship between the forecast variable, known as the dependent variable, and one or more explanatory or independent variables. Many factors determine the type of model structure to be employed within a particular model. These factors include the relationships between variables in that environment, the objectives, skill and knowledge of the decision maker, the budget and time available to develop the model, the control that the decision maker exerts over the variables in the decision environment, and the level of uncertainty in that environment. 19

20 Pre-Reading 4 REVIEW QUESTIONS Review Question 4.1 Draw up a table showing for each type of model structure (i.e. simulation, optimisation and forecasting), the advantages, disadvantages and possible examples. Review Question 4.2 Under what circumstances may it be appropriate to use decision trees within models incorporating probabilistic data? Briefly describe an example of an application using a decision tree within a spreadsheet. 20