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Forecast modelling – Strategy @ Risk

Strategy @ Risk

Tag: Forecast modelling

  • Forecasting sales and forecasting uncertainty

    Forecasting sales and forecasting uncertainty

    This entry is part 1 of 4 in the series Predictive Analytics

     

    Introduction

    There are a large number of methods used for forecasting ranging from judgmental (expert forecasting etc.) thru expert systems and time series to causal methods (regression analysis etc.).

    Most are used to give single point forecast or at most single point forecasts for a limited number of scenarios.  We will in the following take a look at the un-usefulness of such single point forecasts.

    As example we will use a simple forecast ‘model’ for net sales for a large multinational company. It turns out that there is a good linear relation between the company’s yearly net sales in million euro and growth rates (%) in world GDP:

    with a correlation coefficient R= 0.995. The relation thus accounts for almost 99% of the variation in the sales data. The observed data is given as green dots in the graph below, and the regression as the green line. The ‘model’ explains expected sales as constant equal 1638M and with 53M in increased or decreased sales per percent increase or decrease in world GDP:

    The International Monetary Fund (IMF) that kindly provided the historical GDP growth rates also gives forecasts for expected future change in the World GDP growth rate (WEO, April 2012) – for the next five years. When we put these forecasts into the ‘model’ we ends up with forecasts for net sales for 2012 to 2016 as depicted by the yellow dots in the graph above.

    So mission accomplished!  …  Or is it really?

    We know that the probability for getting a single-point forecast right is zero even when assuming that the forecast of the GDP growth rate is correct – so the forecasts we so far have will certainly be wrong, but how wrong?

    “Some even persist in using forecasts that are manifestly unreliable, an attitude encountered by the future Nobel laureate Kenneth Arrow when he was a young statistician during the Second World War. When Arrow discovered that month-long weather forecasts used by the army were worthless, he warned his superiors against using them. He was rebuffed. “The Commanding General is well aware the forecasts are no good,” he was told. “However, he needs them for planning purposes.” (Gardner & Tetlock, 2011)

    Maybe we should take a closer look at possible forecast errors, input data and the final forecast.

    The prediction band

    Given the regression we can calculate a forecast band for future observations of sales given forecasts of the future GDP growth rate. That is the region where we with a certain probability will expect new values of net sales to fall. In the graph below the green area give the 95% forecast band:

    Since the variance of the predictions increases the further new forecasts for the GDP growth rate lies from the mean of the sample values (used to compute the regression), the band will widen as we move to either side of this mean. The band will also widen with decreasing correlation (R) and sample size (the number of observations the regression is based on).

    So even if the fit to the data is good, our regression is based on a very small sample giving plenty of room for prediction errors. In fact a 95% confidence interval for 2012, with an expected GDP growth rate of 3.5%, is net sales 1824M plus/minus 82M. Even so the interval is still only approx. 9% of the expected value.

    Now we have shown that the model gives good forecasts, calculated the confidence interval(s) and shown that the expected relative error(s) with high probability will be small!

    So the mission is finally accomplished!  …  Or is it really?

    The forecasts we have made is based on forecasts of future world GDP growth rates, but how certain are they?

    The GDP forecasts

    Forecasting the future growth in GDP for any country is at best difficult and much more so for the GDP growth for the entire world. The IMF has therefore supplied the baseline forecasts with a fan chart ((  The Inflation Report Projections: Understanding the Fan Chart By Erik Britton, Paul Fisher and John Whitley, BoE Quarterly Bulletin, February 1998, pages 30-37.)) picturing the uncertainty in their estimates.

    This fan chart ((Figure 1.12. from:, World Economic Outlook (April 2012), International Monetary Fund, Isbn  9781616352462))  shows as blue colored bands the uncertainty around the WEO baseline forecast with 50, 70, and 90 percent confidence intervals ((As shown, the 70 percent confidence interval includes the 50 percent interval, and the 90 percent confidence interval includes the 50 and 70 percent intervals. See Appendix 1.2 in the April 2009 World Economic Outlook for details.)) :

    There is also another band on the chart, implied but un-seen, indicating a 10% chance of something “unpredictable”. The fan chart thus covers only 90% of the IMF’s estimates of the future probable growth rates.

    The table below shows the actual figures for the forecasted GDP growth (%) and the limits of the confidence intervals:

    Lower

    Baseline

    Upper

    90%

    70%

    50%

    50%

    70%

    90%

    2012

    2.5

    2.9

    3.1

    .5

    3.8

    4.0

    4.3

    2013

    2.1

    2.8

    3.3

    4.1

    4.8

    5.2

    5.9

    The IMF has the following comments to the figures:

    “Risks around the WEO projections have diminished, consistent with market indicators, but they remain large and tilted to the downside. The various indicators do not point in a consistent direction. Inflation and oil price indicators suggest downside risks to growth. The term spread and S&P 500 options prices, however, point to upside risks.”

    Our approximation of the distribution that can have produced the fan chart for 2012 as given in the World Economic Outlook for April 2012 is shown below:

    This distribution has:  mean 3.43%, standard deviation 0.54, minimum 1.22 and maximum 4.70 – it is skewed with a left tail. The distribution thus also encompasses the implied but un-seen band in the chart.

    Now we are ready for serious forecasting!

    The final sales forecasts

    By employing the same technique that we used to calculate the forecast band we can by Monte Carlo simulation compute the 2012 distribution of net sales forecasts, given the distribution of GDP growth rates and by using the expected variance for the differences between forecasts using the regression and new observations. The figure below describes the forecast process:

    We however are not only using the 90% interval for The GDP growth rate or the 95% forecast band, but the full range of the distributions. The final forecasts of net sales are given as a histogram in the graph below:

    This distribution of forecasted net sales has:  mean sales 1820M, standard deviation 81, minimum sales 1590M and maximum sales 2055M – and it is slightly skewed with a left tail.

    So what added information have we got from the added effort?

    Well, we now know that there is only a 20% probability for net sales to be lower than 1755 or above 1890. The interval from 1755M to 1890M in net sales will then with 60% probability contain the actual sales in 2012 – see graph below giving the cumulative sales distribution:

    We also know that we with 90% probability will see actual net sales in 2012 between 1720M and 1955M.But most important is that we have visualized the uncertainty in the sales forecasts and that contingency planning for both low and high sales should be performed.

    An uncertain past

    The Bank of England’s fan chart from 2008 showed a wide range of possible futures, but it also showed the uncertainty about where we were then – see that the black line showing National Statistics data for the past has probability bands around it:

    This indicates that the values for past GDP growth rates are uncertain (stochastic) or contains measurement errors. This of course also holds for the IMF historic growth rates, but they are not supplying this type of information.

    If the growth rates can be considered stochastic the results above will still hold, if the conditional distribution for net sales given the GDP growth rate still fulfills the standard assumptions for using regression methods. If not other methods of estimation must be considered.

    Black Swans

    But all this uncertainty was still not enough to contain what was to become reality – shown by the red line in the graph above.

    How wrong can we be? Often more wrong than we like to think. This is good – as in useful – to know.

    “As Donald Rumsfeld once said: it’s not only what we don’t know – the known unknowns – it’s what we don’t know we don’t know.”

    While statistic methods may lead us to a reasonably understanding of some phenomenon that does not always translate into an accurate practical prediction capability. When that is the case, we find ourselves talking about risk, the likelihood that some unfavorable or favorable event will take place. Risk assessment is then necessitated and we are left only with probabilities.

    A final word

    Sales forecast models are an integrated part of our enterprise simulation models – as parts of the models predictive analytics. Predictive analytics can be described as statistic modeling enabling the prediction of future events or results ((in this case the probability distribution of future net sales)) , using present and past information and data.

    In today’s fast moving and highly uncertain markets, forecasting have become the single most important element of the management process. The ability to quickly and accurately detect changes in key external and internal variables and adjust tactics accordingly can make all the difference between success and failure:

    1. Forecasts must integrate both external and internal drivers of business and the financial results.
    2. Absolute forecast accuracy (i.e. small confidence intervals) is less important than the insight about how current decisions and likely future events will interact to form the result.
    3. Detail does not equal accuracy with respect to forecasts.
    4. The forecast is often less important than the assumptions and variables that underpin it – those are the things that should be traced to provide advance warning.
    5. Never relay on single point or scenario forecasting.

    The forecasts are usually done in three stages, first by forecasting the market for that particular product(s), then the firm’s market share(s) ending up with a sales forecast. If the firm has activities in different geographic markets then the exercise has to be repeated in each market, having in mind the correlation between markets:

    1. All uncertainty about the different market sizes, market shares and their correlation will finally end up contributing to the uncertainty in the forecast for the firm’s total sales.
    2. This uncertainty combined with the uncertainty from other forecasted variables like interest rates, exchange rates, taxes etc. will eventually be manifested in the probability distribution for the firm’s equity value.

    The ‘model’ we have been using in the example have never been tested out of sample. Its usefulness as a forecast model is therefore still debatable.

    References

    Gardner, D & Tetlock, P., (2011), Overcoming Our Aversion to Acknowledging Our Ignorance, http://www.cato-unbound.org/2011/07/11/dan-gardner-and-philip-tetlock/overcoming-our-aversion-to-acknowledging-our-ignorance/

    World Economic Outlook Database, April 2012 Edition; http://www.imf.org/external/pubs/ft/weo/2012/01/weodata/index.aspx

    Endnotes

     

     

  • Uncertainty modeling

    Uncertainty modeling

    This entry is part 2 of 3 in the series What We Do

    Prediction is very difficult, especially about the future.
    Niels Bohr. Danish physicist (1885 – 1962)

    Strategy @ Risks models provide the possibility to study risk and uncertainties related to operational activities;  cost, prices, suppliers,  markets, sales channels etc. financial issues like; interest rates risk, exchange rates risks, translation risk , taxes etc., strategic issues like investments in new or existing activities, valuation and M&As’ etc and for a wide range of budgeting purposes.

    All economic activities have an inherent volatility that is an integrated part of its operations. This means that whatever you do some uncertainty will always remain.

    The aim is to estimate the economic impact that such critical uncertainty may have on corporate earnings at risk. This will add a third dimension – probability – to all forecasts, give new insight: the ability to deal with uncertainties in an informed way and thus benefits above ordinary spread-sheet exercises.

    The results from these analyzes can be presented in form of B/S and P&L looking at the coming one to five (short term) or five to fifteen years (long term); showing the impacts to e.g. equity value, company value, operating income etc. With the purpose of:

    • Improve predictability in operating earnings and its’ expected volatility
    • Improve budgeting processes, predicting budget deviations and its’ probabilities
    • Evaluate alternative strategic investment options at risk
    • Identify and benchmark investment portfolios and their uncertainty
    • Identify and benchmark individual business units’ risk profiles
    • Evaluate equity values and enterprise values and their uncertainty in M&A processes, etc.

    Methods

    To be able to add uncertainty to financial models, we also have to add more complexity. This complexity is inevitable, but in our case, it is desirable and it will be well managed inside our models.

    People say they want models that are simple, but what they really want is models with the necessary features – that are easy to use. If something is complex but well designed, it will be easy to use – and this holds for our models.

    Most companies have some sort of model describing the company’s operations. They are mostly used for budgeting, but in some cases also for forecasting cash flow and other important performance measures. Almost all are deterministic models based on expected or average values of input data; sales, cost, interest and currency rates etc.

    We know however that forecasts based on average values are on average wrong. In addition will deterministic models miss the important uncertainty dimension that gives both the different risks facing the company and the opportunities they bring forth.

    S@R has set out to create models that can give answers to both deterministic and stochastic questions, by linking dedicated Ebitda models to holistic balance simulation taking into account all important factors describing the company. The basis is a real balance simulation model – not a simple cash flow forecast model.

    Both the deterministic and stochastic balance simulation can be set about in two different alternatives:

    1. by a using a EBITDA model to describe the companies operations or
    2. by using coefficients of fabrications (e.g. kg flour pr 1000 bread etc.) as direct input to the balance model – the ‘short cut’ method.

    The first approach implies setting up a dedicated Ebitda subroutine to the balance model. This will give detailed answers to a broad range of questions about markets, capacity driven investments, operational performance and uncertainty, but entails a higher degree of effort from both the company and S@R. This is a tool for long term planning and strategy development.

    The second (‘the short cut’) uses coefficients of fabrications and their variations, and is a low effort (cost) alternative, usually using the internal accounting as basis. This will in many cases give a ‘good enough’ description of the company – its risks and opportunities. It can be based on existing investment and market plans.  The data needed for the company’s economic environment (taxes, interest rates etc) will be the same in both alternatives:

    The ‘short cut’ approach is especially suited for quick appraisals of M&A cases where time and data is limited and where one wishes to limit efforts in an initial stage. Later the data and assumptions can be augmented to much more sophisticated analysis within the same ‘short cut’ framework. In this way analysis can be successively built in the direction the previous studies suggested.

    This also makes it a good tool for short-term (3-5 years) analysis and even for budget assessment. Since it will use a limited number of variables – usually less than twenty – describing the operations, it is easy to maintain and operate. The variables describing financial strategy and the economic environment come in addition, but will be easy to obtain.

    Used in budgeting it will give the opportunity to evaluate budget targets, their probable deviation from expected result and the probable upside or down side given the budget target (Upside/downside ratio).

    Done this way analysis can be run for subsidiaries across countries translating the P&L and Balance to any currency for benchmarking, investment appraisals, risk and opportunity assessments etc. The final uncertainty distributions can then be “aggregated’ to show global risk for the mother company.

    An interesting feature is the models ability to start simulations with an empty opening balance. This can be used to assess divisions that do not have an independent balance since the model will call for equity/debt etc. based on a target ratio, according to the simulated production and sales and the necessary investments. Questions about further investment in divisions or product lines can be studied this way.

    Since all runs (500 to 1000) in the simulation produces a complete P&L and Balance the uncertainty curve (distribution) for any financial metric like ‘Yearly result’, ‘free cash flow’, economic profit’, ‘equity value’, ‘IRR’ or’ translation gain/loss’ etc. can be produced.

    In some cases we have used both approaches for the same client, using the last approach for smaller daughter companies with production structures differing from the main companies.
    The second approach can also be considered as an introduction and stepping stone to a more holistic Ebitda model.

    Time and effort

    The work load for the client is usually limited to a small team of people ( 1 to 3 persons) acting as project leaders and principal contacts, assuring that all necessary information, describing value and risks for the clients’ operations can be collected as basis for modeling and calculations. However the type of data will have to be agreed upon depending on the scope of analysis.

    Very often will key people from the controller group be adequate for this work and if they don’t have the direct knowledge they usually know who to ask. The work for this team, depending on the scope and choice of method (see above) can vary in effective time from a few days to a couple of weeks, but this can be stretched from three to four weeks to the same number of months.

    For S&R the time frame will depend on the availability of key personnel from the client and the availability of data. For the second alternative it can take from one to three weeks of normal work to three to six months for the first alternative for more complex models. The total time will also depend on the number of analysis that needs to be run and the type of reports that has to be delivered.

    S@R_ValueSim

    Selecting strategy

    Models like this are excellent for selection and assessment of strategies. Since we can find the probability distribution for equity value, changes in this brought by different strategies will form a basis for selection or adjustment of current strategy. Models including real option strategies are a natural extension of these simulation models:

    If there is a strategy with a curve to the right and under all other feasible strategies this will be the stochastic dominant one. If the curves crosses further calculations needs to be done before a stochastic dominant or preferable strategy can be found:

    Types of problems we aim to address:

    The effects of uncertainties on the P&L and Balance and the effects of the Boards strategies (market, hedging etc.) on future P&L and Balance sheets evaluating:

    • Market position and potential for growth
    • Effects of tax and capital cost
    • Strategies
    • Business units, country units or product lines –  capital allocation – compare risk, opportunity and expected profitability
    • Valuations, capital cost and debt requirements, individually and effect on company
    • The future cash-flow volatility of company and the individual BU’s
    • Investments, M&A actions, their individual value, necessary commitments and impact on company
    • Etc.

    The aim regardless of approach is to quantify not only the company’s single and aggregated risks, but also the potential, thus making the company capable to perform detailed planning and of executing earlier and more apt actions against uncertain factors.

    Used in budgeting, this will improve budget stability through higher insight in cost side risks and income-side potentials. This is achieved by an active budget-forecast process; the control-adjustment cycle will teach the company to better target realistic budgets – with better stability and increased company value as a result.

    This is most clearly seen when effort is put into correctly evaluating strategies-projects and investments effects on the enterprise. The best way to do this is by comparing and Choosing strategies by analyzing the individual strategies risks and potential – and select the alternative that is dominant (stochastic) given the company’s chosen risk-profile.

    A severe depression like that of 1920-1921 is outside the range of probability. –The Harvard Economic Society, 16 November 1929

  • Concession Revenue Modelling and Forecasting

    Concession Revenue Modelling and Forecasting

    This entry is part 2 of 4 in the series Airports

     

    Concessions are an important source of revenue for all airports. An airport simulation model should therefore be able to give a good forecast of revenue from different types of concessions -given a small set of assumptions about local future price levels and income development for its international Pax. Since we already have a good forecast model for the expected number of international Pax (and its variation) we will attempt to forecast the airports revenue pr Pax from one type of concession and use both forecasts to estimate the airports revenue from that concession.

    The theory behind is simple; the concessionaires sales is a function of product price and the customers (Pax) income level. Some other airport specific variables also enter the equation however they will not be discussed here. As a proxy for change in Pax income we will use the individual countries change in GDP.  The price movement is represented by the corresponding movements of a price index.

    We assume that changes in the trend for the airports revenue is a function of the changes in the general income level and that the seasonal variance is caused by the seasonal changes in the passenger mix (business/leisure travel).

    It is of course impossible to forecast the exact level of revenue, but that is as we shall see where Monte Carlo simulation proves its worth.

    The fist step is a time series analysis of the observed revenue pr Pax, decomposing the series in trend and seasonal factors:

    Concession-revenue

    The time series fit turns out to be very good explaining more than 90 % of the series variation. At this point however our only interest is the trend movements and its relation to change in prices, income and a few other airport specific variables. We will however here only look at income – the most important of the variable.

    Step two, is a time series analysis of income (weighted average of GDP development in countries with majority of Pax) separating trend and seasonal factors. This trend is what we are looking for; we want to use it to explain the trend movements in the revenue.

    Step three, is then a regression of the revenue trend on the income trend as shown in the graph below. The revenue trend was estimated assuming a quadratic relation over time and we can see that the fit is good. In fact 98 % of the variance in the revenue trend can be explained by the change in income (+) trend:

    Concession-trend

    Now the model will be as follows – step four:

    1. We will collect the central banks GDP forecasts (base line scenario) and use this to forecast the most likely change in income trend
    2. More and more central banks are now producing fan charts giving the possible event space (with probabilities) for their forecasts. We will use this to establish a probability distribution for our income proxy

    Below is given an example of a fan chart taken from the Bank of England’s inflation report November 2009. (Bank of England, 2009) ((The fan chart depicts the probability of various outcomes for GDP growth.  It has been conditioned on the assumption that the stock of purchased assets financed by the issuance of central bank reserves reaches £200 billion and remains there throughout the forecast period.  To the left of the first vertical dashed line, the distribution reflects the likelihood of revisions to the data over the past; to the right, it reflects uncertainty over the evolution of GDP growth in the future.  If economic circumstances identical to today’s were to prevail on 100 occasions, the MPC’s best collective judgement is that the mature estimate of GDP growth would lie within the darkest central band on only 10 of those occasions.  The fan chart is constructed so that outturns are also expected to lie within each pair of the lighter green areas on 10 occasions.  In any particular quarter of the forecast period, GDP is therefore expected to lie somewhere within the fan on 90 out of 100 occasions.  The bands widen as the time horizon is extended, indicating the increasing uncertainty about outcomes.  See the box on page 39 of the November 2007 Inflation Report for a fuller description of the fan chart and what it represents.  The second dashed line is drawn at the two-year point of the projection.))

    Bilde1

    3. We will then use the relation between historic revenue and income trend to forecast the revenue trend
    4. Adding the seasonal variation using the estimated seasonal factors – give us a forecast of the periodic revenue.

    For our historic data the result is shown in the graph below:

    Concession-revenue-estimate

    The calculated revenue series have a very high correlation with the observed revenue series (R=0.95) explaining approximately 90% of the series variation.

    Step five, now we can forecast the revenue from concession pr Pax figures for the next periods (month, quarters or years), using Monte Carlo simulation:

    1. From the income proxy distribution we draw a possible change in yearly income and calculates the new trend
    2. Using the estimated relation between historic revenue and income trend we forecast the most likely revenue trend and calculate the 95% confidence interval. We then use this to establish a probability distribution for the period’s trend level and draws a value. This value is adjusted with the period’s seasonal factor and becomes our forecasted value for the airports revenue from the concession – for this period.

    Running thru this a thousand times we get a distribution as given below:

    Concession-revenue-distribuIn the airport EBITDA model this only a small but important part for forecasting future airport revenue. As the models data are updated (monthly) all the time series analysis and regressions are redone dynamically to capture changes in trends and seasonal factors.

    The level of monthly revenue from the concession is obviously more complex than can be described with a small set of variable and assumptions. Our model has with high probability specification errors and we may or may not have violated some of the statistical methods assumptions (the model produces output to monitor this). But we feel that we are far better of than having put all our money on a single figure as a forecast. At least we know something about the forecasts uncertainty.

    References

    Bank of England. (2009, November). Inflation Report November 2009 . Retrieved from http://www.bankofengland.co.uk/publications/inflationreport/ir09nov5.ppt

  • What we do; Predictive and Prescriptive Analytics

    What we do; Predictive and Prescriptive Analytics

    This entry is part 1 of 3 in the series What We Do

     

    Analytics is the discovery and communication of meaningful patterns in data. It is especially valuable in areas rich with recorded information – as in all economic activities. Analytics relies on the simultaneous application of statistical methods, simulation modeling and operations research to quantify performance.

    Prescriptive analytics goes beyond descriptive, diagnostic and predictive analytics; by being able to recommend specific courses of action and show the likely outcome of each decision.

    Predictive analytics will tell what probably will happen, but will leave it up to the client to figure out what to do with it.

    Prescriptive analytics will also tell what probably will happen, but in addition:  when it probably will happen and why it likely will happen, thus how to take advantage of this predictive future. Since there are always more than one course of action prescriptive analytics have to include: predicted consequences of actions, assessment of the value of the consequences and suggestions of the actions giving highest equity value for the company.

    By employing simulation modeling (Monte Carlo methods) we can give answers – by probability statements – to the critical question at the top of the value staircase.

     

    Prescriptive-analytics

     

    This feature is a basic element of the S@R balance simulation model, where the Monte Carlo simulation can be stopped at any point on the probability distribution for company value  (i.e. very high or very low value of company) giving full set of reports: P&L and balance sheet etc. – enabling a full postmortem analysis: what it was that happened and why it did happen.

    Different courses of actions to repeat or avoid the result with high probability can then be researched and assessed. The EBITDA client specific model will capture relationships among many factors to allow simultaneous assessment of risk or potential associated with a particular set of conditions, guiding decision making for candidate transactions. Even the language we use to write the models are specially developed for making decision support systems.

    Our methods will as well include data and information visualization to clearly and effectively communicate both information and acquired knowledge – to reinforce comprehension and cognition.

    Firms may thus fruitfully apply analytics to business data, to describe, predict, and improve its business performance.

     

  • Projects we have done

    Projects we have done

    Consultancy, in contrast to selling software products, is quite a delicate process. Trust is the most important asset to successfully completing a project, and S@R customers consider discretion to be important. That’s why we have decided to publish relevant contents – which provide insight into our methods of operation – only accessible in anonymous form and often collected from different projects.

    The same applies to naming customers, but large projects has been performed in

    • Finance
    • Banking
    • Pulp & Paper
    • Airport Operations
    • Brewery
    • Aquaculture
    • Mining & Quarrying
    • Car parts
    • Rail coach production

    etc. –  all for multinational companies.