This entry is part 1 of 2 in the series Budgeting


Budgeting is one area that is well suited for Monte Carlo Simulation. Budgeting involves personal judgments about future values of large number of variables like; sales, prices, wages, down- time, error rates, exchange rates etc. – variables that describes the nature of the business.

Everyone that has been involved in a budgeting process knows that it is an exercise in uncertainty; however it is seldom described in this way and even more seldom is uncertainty actually calculated as an integrated part of the budget.

Admittedly a number of large public building projects are calculated this way, but more often than not is the aim only to calculate some percentile (usually 85%) as expected budget cost.

Most managers and their staff have, based on experience, a good grasp of the range in which the values of their variables will fall.  A manager’s subjective probability describes his personal judgement ebitabout how likely a particular event is to occur. It is not based on any precise computation but is a reasonable assessment by a knowledgeable person. Selecting the budget value however is more difficult. Should it be the “mean” or the “most likely value” or should the manager just delegate fixing of the values to the responsible departments?

Now we know that the budget values might be biased by a number of reasons – simplest by bonus schemes etc. – and that budgets based on average assumptions are wrong on average1

When judging probability, people can locate the source of the uncertainty either in their environment or in their own imperfect knowledge2. When assessing uncertainty, people tend to underestimate it – often called overconfidence and hindsight bias.

Overconfidence bias concerns the fact that people overestimate how much they actually know: when they are p percent sure that they have predicted correctly, they are in fact right on average less than p percent of the time3.

Hindsight bias concerns the fact that people overestimate how much they would have known had they not possessed the correct answer: events which are given an average probability of p percent before they have occurred, are given, in hindsight, probabilities higher than p percent4.

We will however not endeavor to ask for the managers subjective probabilities only ask for the range of possible values (5-95%) and their best guess of the most likely value. We will then use this to generate an appropriate log-normal distribution for sales, prices etc. For investments we will use triangular distributions to avoid long tails. Where, most likely values are hard to guesstimate we will use rectangular distributions.

We will then proceed as if the distributions where known (Keynes):

[Under uncertainty] there is no scientific basis on which to form any calculable probability whatever. We simply do not know. Nevertheless, the necessity for action and for decision compels us as practical men to do our best to overlook this awkward fact and to behave exactly as we should if we had behind us a good Benthamite calculation of a series of prospective advantages and disadvantages, each multiplied by its appropriate probability waiting to be summed. 5


The data collection can easily be embedded in the ordinary budget process, by asking the managers to set the lower and upper 5% values for all variables demining the budget, and assuming that the budget figures are the most likely values.

This gives us the opportunity to simulate (Monte Carlo) a number of possible outcomes – usually 1000 – of net revenue, operating expenses and finally EBIT (DA).

In this case the budget was optimistic with ca 84% probability of having an outcome below and only with 26% probability of having an outcome above. The accounts also proved it to be high (actual) with final EBIT falling closer to the expected value. In our experience expected value is a better estimator for final result than the budget  EBIT.

However, the most important part of this exercise is the shape of the cumulative distribution curve for EBIT. The shape gives a good picture of the uncertainty the company faces in the year to come, a flat curve indicates more uncertainty both in the budget forecast and the final result than a steeper curve.

Wisely used the curve (distribution) can be used both to inform stakeholders about risk being faced and to make contingency plans foreseeing adverse events.percieved-uncertainty-in-ne

Having the probability distributions for net revenue and operating expenses we can calculate and plot the manager’s perceived uncertainty by using coefficients of variation.

In our material we find on average twice as much uncertainty in the forecasts for net revenue than for operating expenses.

As many often have budget values above expected value they are exposing a downward risk. We can measure this risk by the Upside Potential Ratio, which is the expected return above budget value per unit of downside risk. It can be found using the upper and lower moments calculated at budget value.


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  1. Savage, Sam L. “The Flaw of Averages”, Harvard Business Review, November (2002): 20-21. []
  2. Kahneman D, Tversky A . ” On the psychology of prediction.” Psychological Review 80(1973): 237-251 []
  3. Keren G.  “Calibration and probability judgments: Conceptual and methodological issues”. Acta Psychologica 77(1991): 217-273. []
  4. Fischhoff B.  “Hindsight=foresight: The effect of outcome knowledge on judgment under uncertainty”. Journal of Experimental Psychology: Human Perception and Performance 1(1975) 288-299. []
  5. John Maynard Keynes. ” General Theory of Employment, Quarterly Journal of Economics (1937 []


About the Author

S@R develops models for support of decision making under uncertainty. Taking advantage of recognized financial and economic theory, we customize simulation models to fit specific industries, situations and needs.

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