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TECHNICAL NOTES

## Tips for Interpreting Risk Profiles

A risk profile is a graphical display of the range of outcomes possible under a particular alternative or strategy. It is most commonly displayed as a cumulative probability distribution. A single profile is useful to show how risky a particular course of action is. Multiple profiles on the same graph are useful to compare the riskiness of several alternatives or policies.

The horizontal axis shows the range over which the variable of interest varies. This variable may be the objective function, such as Profit (or Total Cost) or a single component of the objective function (attribute) such as Cost (or Acres of Wetlands).

The vertical axis shows the cumulative probability. A value for the cumulative probability can be interpreted as the probability that the outcome of the alternative will be less than or equal to the corresponding value on the x-axis.

Point A is read as “there is a 60% chance that Profit will be 1000 or less.” Point B is interpreted as “the probability that Profit will be 2000 or less is 1.0 — therefore, 2000 is the maximum profit we can achieve with this decision policy.”

The probability that Profit will be between 1,000 and 2,000 is 0.4 (40%). This is calculated by taking the probability that Profit will be 2000 or less (1.0) and subtracting the probability that Profit will be 1000 or less (0.6): 1.0 – 0.6 = 0.4.

In the above graph, risk profile for alternative A of the decision (abbreviated Decision: A) deterministically dominates distribution the risk profile for alternative B because the lowest possible value for A is higher than the highest possible value for B. One would always prefer alternative A to B because there is no scenario in which B has a better outcome than A. The technical term for this is “no-brainer.”

Risk profile for alternative C probabilistically dominates the risk profile for D because it lies entirely below and to the right of D without crossing it. Probabilistic dominance means that, for any Profit value, the risk profile of C has a lower probability than the risk profile of D. That is good because the probability is the likelihood of being at or below that Profit — so alternative C (which may represent not only an upfront decision alternative but a set of of downstream alternatives) has a greater probability of higher profit than D does. Another way to look at it is to say that for any cumulative probability, the risk profile for C has a higher cap value than the risk profile for D. For example, at the 0.5 point, the risk profile for alternative D is at or below 800, but for alternative C it is at or below 1100, which is better.

Although probabilistic dominance is good, it does not guarantee that alternative C is better in every scenario than D. For any particular scenario (i.e. combination of chance event outcomes), it is possible for alternative D to have a better outcome than C. On the whole, however, alternative C is better. The best way to identify scenarios where D would be better than C is to look at the policy tree.

When two risk profiles cross, it becomes much harder to make strong statements about which alternative is better. For example, risk profiles for alternatives E and F show a common situation — F has much less downside potential, but also less upside. In this case, we would say that alternative E is riskier than F.

In such a situation, your first step is to look at the expected values of the two policies. If one policy has a much higher expected value, you may wish to choose it. If the expected values are very similar, you should consider whether your organization would prefer to choose the alternative with less risk or the alternative with the possibility of greater upside outcomes or if an alternative exists that offers the downside of the first and the upside of the second.