5 Factored Value Technique for Risks and Opportunities

In some organisations they take a ‘swings and roundabouts’ approach to Risk Contingency … that everything will work itself out on average. A technique in popular use is that of the ‘Factored Value’ or ‘Expected Value’, in which we simply multiply the ‘central value’ of the Risk variables’ 3-point range by the corresponding Probability of Occurrence. This includes Baseline Uncertainty with a probability of 100%. However, the popularity of a technique is probably more of an indicator of its simplicity than its appropriateness.

Depending on what the ‘central value’ represents, there are two ways we can do this … the ‘wrong way’, and the ‘slightly better way’. (Did you notice that I didn’t say ‘right way’? Does that make it sound too much like I’m biased against this technique altogether?)

Note that any factoring technique will inherently exclude any Unknown Unknowns and will therefore understate reality just as with Monte Carlo Simulation. The only possible exception to this might be the Factoring of the Maximum Values (but even then we should expect some sleepless nights).

5.1 The wrong way

As we commented previously, the ‘central value’ in a 3-Point Estimate is often the Most Likely (or Modal) value. Using the example that we created in Chapter 3, Table 3.19, and followed up in Chapter 4, Table 4.3, if we were to multiply the Mode of each Risk and Opportunity by its corresponding Probability of Occurrence, we would get a value of £ 68.2 k as illustrated in Table 5.1. To illustrate why this is an inherently misguided technique to use, let’s consider the natural extension of this and apply the same logic to the Baseline Uncertainties. This then requires us to multiply the Most Likely Values by 100% and aggregate them (in other words, just add them together) as we have in the same table.

Now some of us may already be shaking their heads saying, ‘No, we shouldn’t do that!’ (which is true) so why should we condone the practice for Risks and Opportunities?

However, setting that aside for a moment, let’s follow the logic through, and compare the results with the Monte Carlo Output.

We might wonder if Warren Buffett was referring to the blind use of this technique when he expressed his views on the source of risk (Miles, 2004, p.85) ... It would have been nice if he had been referring to this, but in reality he was talking in a more general sense of not investing in things we don’t understand, if you read the full context. This can be read across here.

Table 5.1 Factored Most Likely Value Technique for Baseline and Risk Contingency

We may recall that from our previous Monte Carlo Model (Chapter 3 Table 3.16), that the average or Expected Value for the Baseline tasks with 25% Isometric Correlation was £ 809.5 k, and for the four Risks and one Opportunity, it was £ 71.8 k (Figure 3.47 in Chapter 3 Section 3.3.2), or £ 880.3 k in total. As Table 5.1 shows that in this case the Factored Most Likely Technique understates the true Expected Value or Average of the Baseline by £ 22.9 k or 3.5% and that the Factored Most Likely Value of the assumed Risk and Opportunity Distributions is also understated by £ 3.6 k or some 5% in this example.

Furthermore, as we have just discussed in Chapter 3 Section 3.3.3 a Contingency of £ 64 k is not sufficient to cover Risk 2 should it occur. Nor is £ 68.2 k … unless we get lucky and it comes in at the optimistic end!

Note: If we had had more distributions that were positively skewed rather than symmetrical, then this inadequacy would have been magnified.

Furthermore, if we had also included a Factored Most Likely Value for the Extreme Risk we considered in Chapter 3 Section 3.3.6, then it would have only added an extra £ 11 k (5% x £ 220 k). This also shows the futility of assigning Risk Contingency based on the Factored Most Likely Value (a regrettably not uncommon practice in some areas) … we either have £ 11 k more than we need if it does not occur, or we’re between £ 189 k and £ 259 k short if it does occur (based on at a Minimum Value of £ 200 k and a Maximum Value of £ 270 k).

Where has Rambo gone when you need him?

5.2 A slightly better way

If instead of taking the Factored Most Likely Value, what would happen if we were to take the Factored Mean Value? Table 5.2 summarises the results and compares it with the Factored Most Likely Value. (If the Mean values of each distribution are not readily available, we could assume that they were all Triangular or Symmetrical Distributions and take the average of the Minimum, Most Likely and Maximum Values; see Volume II Chapters 3 and 4.)

In this particular case the Factored Mean for the Baseline Uncertainty is now in line with our Monte Carlo Model Output, and the Factored Mean of the Risks and Opportunity is some 3.7% higher than the Factored Most Likely. However, despite being a better and more logical technique than factoring the Most Likely Value, the value it gives is still less than the minimum for Risk 2 should it occur.

Table 5.2 Factored Mean Value Technique for Baseline and Risk Contingency

Note that if we were to take the Factored Maximum Values of the Risks and Opportunity in this case, then we would get a value that would indeed cover off this largest Impact Risk if it were to occur. However, we cannot generalise and say that would always be the case, but it may be an indication that the better value for unmitigated Risk Contingency is at least the Factored Input Means and potentially nearer to the Factored Input Maxima Values … which might make one or two of us a little uncomfortable, and potentially it may make us uncompetitive. If nothing else, it gives us a strong indication of the true size of the problem to be managed. Figure 5.1 illustrates the range of values in comparison with the Monte Carlo Output. In this case the Confidence Level of the Factored Input Means is around 60%.

Even then, for a High Impact, Low Probability Risk, the contribution to Risk Contingency made by Factoring even a maximum value, fails the Credibility element of our TRACEability objective

5.3 The best way

If in doubt, don’t do it!

Don’t Factor Risk values by their Probabilities of Occurrence except as a means of validating a more analytical review of the data, such as the approach suggested in Chapter 3 Section 3.4.

If we have no alternative, i.e. we do not have access to suitable Monte Carlo Simulation software, then we should consider using the Factored Maxima of the Risks (not Opportunities) as this will at least provide some provision for a higher Confidence

Level that may help to alleviate some the pain we will feel in the event of the inevitable Unknown Unknowns. To this we need to add the Means of the Baseline Uncertainty (not the Modes or the Medians!).

Figure 5.1 Example Monte Carlo Simulation with Four Independent Risks and One Opportunity (Excluding the Baseline Costs) - Range and Likelihood of Potential Cost Outcomes

In the case of this example from Table 5.2 we would get £ 97.85 k + £ 809 k or £ 906.85 k … which is still less than the £ 933 k that we compiled using the Slipping and Sliding Technique supported by two different approaches, and it is equivalent to around 61% Confidence Level on the Bottom-up Monte Carlo Simulation, or the 41% Confidence Level on our pseudo Top-down profile.

Factoring …. use it only as a last resort, but if you can avoid it, then avoid it by all means!

5.4 Chapter review

We recognised that some organisations like to use the very simplistic Factoring Technique for developing a view of Risk Contingency. Many simply take the sum of the product of each Risk’s Most Likely Value multiplied by its Probability of Occurrence. This will understate the true Expected Value of the identified Risks; we really should use their Mean values not their Most Likely ones. Factoring the maximum values is equivalent to taking a higher Confidence Level from a Monte Carlo Simulation, but may still be less than the value indicated by the Slipping and Sliding Technique in Chapter 4. Furthermore, whichever factoring technique we use it will suffer even more acutely from the same problem as Bottom-up Monte Carlo Simulation … in that it does not include any provision whatsoever for Unknown Unknowns. At least Monte Carlo allows us to err on the cautious side with a higher Confidence Level.

Does it pass the TRACEability test? Hardly! It may be a technique that is Transparent, certainly Repeatable, and is often used by experienced people, but where it falls down is on whether it is Appropriate, and it often fails the Credibility test in that it gives next to nothing as a contribution towards Low Probability, High Impact Risks.