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A Case for Stochastic Budgeting

by Stephen W. Philbrick

I've managed to work in the insurance industry for a quarter century without spending any appreciable time in a company's budgeting process, but I'm not going to let that lack of experience dispel me from talking about budgeting. If you haven't yet fallen asleep, there is an actuarial aspect to the process.

Most budgets are deterministic, despite the fact that actual outcomes generally form a distribution (very, very few budget items are truly fixed). Given the stochastic nature of outcomes, the people generating the budget have to "collapse" this distribution into a single point. An obvious question is which single point is used or should be used.

Experience shows that most companies fail to achieve their budget. Usually, this is for an obvious reason. Some CEOs deliberately want a "stretch" budget, for motivational purposes. Others are simply overly ambitious, discounting last year's problems as solved or nonrepeatable, and failing to account for next year's unanticipated problem because, well, it is unanticipated. In either case, we can say the budget has been established at an aggressive percentile of the distribution.

The simple mathematical answer is that most companies will fail to meet their budgets if the budgets are more aggressive than the true expectations. Some companies may decide that stretch or optimistic budgets are legitimate management tools, but may also want more realistic budgets. In terms of a stochastic budget, a company can generate both on a consistent basis. One advantage of a formal stochastic approach to budgeting is that the stretch in the stretch budget can be comparable among divisions, by selecting a common percentile for each division. However, one must be cognizant of the fact that percentiles do not "add." For example, the 75th percentile of each business unit does not aggregate to the 75th percentile of the total company.

For many budget items, the distribution of possible outcomes is reasonably close to normal, so the mean, median, and modes are identical. (For the statistically minded, we can relax this to uni-modal, symmetric distributions.) Insurance losses are notoriously skewed. Should a line manager budget for mean losses, median losses, or some other level? This situation is probably most extreme in catastrophe-exposed business. Actual catastrophe losses will fall below the mean level most years. If a budget is linked to performance bonuses, this could lead to odd results. In the case of catastrophe losses, the phenomenon is so well recognized that any decent performance bonus system will account for it, possibly by capping or excluding catastrophe losses from the calculation and setting a target consistent with the capping.

In other areas, the difference between mean and median results may be closer and, paradoxically, more of a problem because the company may not specifically address it. Many expense items may have a distribution that looks close to normal over most of its range. Yet the potential for an extraordinary expense exceeds the likelihood of an extraordinary expense savings. Lest this be dismissed as rounding error, it amounts to tens of millions of dollars for some of the larger insurance companies.

It may be reasonable to assume a company estimating its upcoming costs produces numbers that are more in line with median results than mean results. Again, a seeming paradox is that this may be less true when results are seriously skewed (as in the case of catastrophe losses) because companies will formally model the results in these cases. However, in expense categories, it might be reasonable to assume numbers are median results. A formal approach to budgeting from a stochastic point of view will help identify the potential for outliers, ensure management is aware of the aggregate exposure to extreme events, yet still budget to achievable results.

Ironically, the existence of insurance may help explain why this issue doesn't come up in general budgeting for other industries. The prototypical widget factory, in the absence of insurance, would have to budget for the possibility that their building might burn to the ground. The odds are against this happening, so the modal value is zero. The median value may well be zero. But any company that budgets zero for this contingency will, in the long run, not budget enough to cover its costs. In the real world, the company insures the building, converting a highly skewed distribution into a fixed point (the cost of the insurance protection), and budgets accordingly. Other potentially skewed exposures to a widget factory—the cost of liability claims, the cost of raw materials—are addressed through risk management techniques, such as the purchase of insurance or the use of commodity futures contracts. These have the effect of converting potentially skewed results into point estimates or costs more resembling normal distributions.

In conclusion, whenever one works with a budget, one needs to ask the purpose and then determine whether the metrics used to produce the values match that purpose. A stochastic budgeting process forces one to think about issues such as mean versus median levels, and helps ensure transparency and consistency of results.

(Thanks to Rob Painter, who helped improve this discussion.)