The fundamental basis for the value of risk could be curvature in agents utility functions.
If the utility of $0 is 0, then there are three basic possibilities.

The log function would be an interesting choice, but we will use the square root function this semester.

The basic diagram showing the value of the risk inherent in an asset with two possible values.

We will study
1. Utility-Based Valuation of Risk
2. Mean-Variance Analysis
These are two views that are not entirely contradictory. The first emphasizes fundamental economics. The second emphasizes objective measures that might be obtained from historical statistics.