## 3 ALARP and CAPM. A Model for the Investment Risk Management
### Phases of the Risk Assessment Model
In this case, no risk mitigation measures need to be defined in order to increase the project return (Figure 6a);
* The project initiative is unacceptable to the investor if E(IRR) \(<r_{t}\) or if the expected IRR of the project is lower than the return expected from a project with a high-risk profile. In this case, the project is unsustainable, so that it is necessary to define improvement measures which decrease the risk of failure or increase the profitability of the initiative (Figure 6b);
* The project initiative has a tolerable risk, if \(r_{a}<\) E(IRR) \(<r_{t}\), i.e., if the expected IRR of the project is between the return expected from a project with a medium-risk profile and the return expected from a project with a high-risk profile. In this case, mitigation measures should be implemented that do not have disproportionate costs compared to the achievable benefits (Figure 6c). _Step 3: risk treatment._ If the risk is unacceptable or tolerable for the investor (Figure 6b,c), it is first necessary to define changes to the project, then to assess the residual risk, i.e., the risk which remains despite the containment strategy undertaken. Then, the riskiness of the project is evaluated again in terms of expected IRR (Figure 6). Specifically, consider that the pre-mitigation intervention is in a tolerable condition (represented in Figure 6c). In this case, the following scenarios may occur:  
* The post mitigation design initiative is in a condition of broad acceptability (Figure 6a). The mitigation measures should be implemented;
* The post mitigation project initiative is in an unacceptable or ALARP condition for the investor (Figure 6b,c). The pre-mitigation project is tolerable according to the ALARP principle, i.e., it has been shown that the improvement measures have disproportionate costs compared to the achievable benefits. Consider, on the other hand, the case where the pre-mitigation intervention is in an unacceptable condition (Figure 6b). It may be that:  
* The post mitigation design initiative is in a condition of broad acceptability (Figure 6a). The mitigation measures should be applied;
* The design initiative after mitigation still falls into an unacceptable condition (Figure 6b). The project is still risky, and the planned interventions cannot be realized;
* The project initiative after mitigation is in a tolerable condition (Figure 6c). The investment risk is now tolerable according to the ALARP principle, i.e., if any other improvement intervention does not result in greater benefits at lower costs. It is important to underline that the planning of risk mitigation measures is a crucial step in the analysis model and thus on the outcome of the assessment [45]. Risk mitigation strategies may take the form of structural modifications or changes in the economic and financial management of the project. This entails different costs from those estimated by the initial scenario, as well as different revenues. These changes may also significantly influence the profitability index of the intervention and therefore the value of the Expected Internal Rate of Return. In other words, the implementation of mitigation strategies can lead to a distancing/approaching of the E(IRR) from the thresholds of acceptability and tolerability of the risk. Therefore, in order to prevent the project from failing, it is absolutely necessary that the investor assesses ex-ante all possible mitigation measures to determine the optimal balance between cost reduction, revenue increase, and residual risk containment. To compare two or more mitigation strategies, the risk assessment described above can be combined with the estimation of the net-cost-of-preventing-a-failure (NPAF):  
\[\text{NPAF}= \frac{\Delta C}{\text{AR}}, \tag{6}\]  
Figure 6: Acceptability and tolerability of the investment in terms of E(IRR) (**a**) Widely acceptable condition; (**b**) Unacceptable condition; (**c**) Tolerable condition according to the ALARP principle.