Statistical Risk Modelling

Background

Risk and uncertainty are part and parcel of most businesses and we need to understand these if we are ever to make rational business decisions.   Quantitative Risk Analysis, using Monte Carlo simulation is one way of coming to grips with risk and uncertainty.   It is a powerful and precise method for assimilating the uncertainties of a problem and it produces a realistic appreciation of the problem’s total uncertainty.

Single point modelling, what happens when you put in a “best guess” as a value in a spreadsheet only provides one possible answer, an answer that assumes the case that all the single variables in the spreadsheet are correct.   Rarely if ever is this the case.

Traditionally we attempt to overcome this by selecting various combinations for each input variable.   These various combinations are known as what-if scenarios.   These combinations may include an expected maximum value, an expected minimum value and the best guess.   There are however physical drawbacks for attempting to do this for more than a few variables.   For example giving each of 4 variables a maximum, minimum and best guess would create 81 possible what-if scenarios and if you added one more variable to the mix, it would raise the number of possible scenarios to 243.

There has to be a better way, and there is:

A Better Way

Monte Carlo simulation  and substituting single point deterministic modelled values with probability distributions for each value.   This allows for us to consider whatever output we designate be it cash flow; NPV; EBIT; beta etc as a probability distribution.   A sensitivity analysis which is also derived from the simulation will bring to the fore those variables that need constant monitoring if performance is to be maintained.

For example: would it help to know that you not only have a 95% probability of exceeding an EBIT of $1,000,000 but that you also have a 60% probability of receiving more than $4,000,000.   Then again on a different project would it concern you to know that while you have a 60% probability of exceeding a $2,000,000 EBIT you also had a 20% probability of getting nothing and a 10% probability of showing a $500,000 loss?

Probability distributions: We now substitute either historical data plus predicted data; or maximum, minimum and best guess data; or average value plus a standard deviation; or just maximum and minimum data; or ...... for the single point data that we normally would have used.

For each uncertain input variable (one that has a range of possible values), you with our assistance, define the possible values with a probability distribution. The type of distribution we select is based on the conditions surrounding that variable.