The implementation of a centralized transmission expansion plan is a complex task when several investors compete and bid to build a new transmission asset, as is the case now in Chile. The assessment of a transmission project depends on the number of competitors, where the project is subject to risks, such as delays, penalties, and cost overruns. The risk faced by an investor is measured using the Conditional Value at Risk (CVaR), which can be interpreted as the risk of not reaching an expected return on investment, depending on the tolerance to risk and the real income obtained with the investor's portfolio. This risk comes from the difference between the regulated income (investor's bid) and the real cost during the implementation and operation of the transmission project. The difference is the "surplus" profit that the investor obtains by participating in the tender, considering their risk tolerance. The goal is to determine the optimal value of a risky investor's portfolio made up of several transmission projects. The optimal portfolio may allow the central planner to improve the efficiency of the project allocation process. To test the methodology, two case studies are analyzed: the IEEE 24-bus Reliability Test System and a predefined expansion plan of Chile's Central Interconnected System (SIC).