## Risk assessment in Open Design

Once the constraints allow a positive solution space, the question arises how to utilise the available financial margin. For instance, should we use it for a prestigious entrance and a large parking lot or should we keep the investment as low as possible? The former - the expensive option - is more risky in the sense that users may not be prepared to pay extra rent for the nice entrance and the parking area. There is also a reasonable chance, however, that they will be prepared to pay more for it than its (discounted) cost. In that case the financial return will be higher than for the inexpensive option (no prestigious entrance and only a limited parking lot).

The probability curves for the financial return of the inexpensive and the expensive options are typically as shown in Figure 4.1.

The (cumulative) probability P that the return will be above a minimum threshold R is:

This gives us the risk profiles of the two options (Fig. 4.2).

If the investor prefers a moderate but sure return, he should choose option 'X'. Conversely, if he wishes to go for a more ambitious return and is willing to accept the associated higher risk, then he should choose option 'Y'. The difference between the two risk profiles is caused by the associated probability curves of the rent users will be prepared to pay.

Risk assessment by introducing probability distributions for variables entailing risk was already proposed by Hertz (1969) in the late sixties. The probability distributions of the variables determining the return on investment are the basis of Monte Carlo simulations as shown in Figure 4.3.

Return on investment (%)

Figure 4.2 Risk profiles (cumulative probability) of two investment options

Return on investment (%)

Figure 4.2 Risk profiles (cumulative probability) of two investment options

Process Stochastic variables

Process Stochastic variables

As mentioned before, instead of making one estimate for each variable that affects the return of investment, three estimates are made:

1. A pessimistic estimate, defined as having a probability of 10% that reality will be worse than that;

3. An optimistic estimate, defined as having a probability of 10% that reality will be better than that.

These three points determine the probability distribution for the variable concerned. With these distribution curves, Monte Carlo simulation finally gives the probability distribution for the return on investment.

The arithmetic of the Monte Carlo simulation is simple: whenever a risk variable enters into the calculation, a random number generated by the computer is corrected with the (skewed) distribution of the variable concerned. The calculation is done, say, 2 000 times. The resulting 2 000 different outcomes for the return on investment provide the probability distribution of the return on investment.

This approach has two important advantages compared to conventional investment analyses based on single values:

1. It allows trading-off moderate return-low risk investments against high return-high risk investments. The decision support information provided by the two different risk profiles is extremely relevant for an investor.

2. As already mentioned before, by asking experts a range instead of a single estimate, they tend to be genuine. When people are asked to give only one estimate, they tend to give their pessimistic guess without saying so.

An underlying assumption of the Monte Carlo simulation is that de variables involved are stochastically independent (see also Section 8.4).

It should be noted that the three estimates asked from experts for risk assessment of the investment are of a different nature than the three values asked from stakeholders for the constraints in the LP calculations. The former give the range in which a variable, such as construction cost, must be expected. The latter determine the uncertainty related to stakeholder negotiations.

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