Most people associate the term `hedging' exclusively with financial applications, particularly the use of financial derivatives. We argue that hedging is an activity that human and machine agents should engage in more broadly, even when the agent's value is not necessarily in monetary units. In this paper, we propose a decision-theoretic view of hedging based on augmenting a probabilistic graphical model -- specifically a Bayesian network or an influence diagram -- with a reward. Hedging is therefore posed as a particular kind of graph manipulation, and can be viewed as analogous to control/intervention and information gathering related analysis. Effective hedging occurs when a risk-averse agent finds opportunity to balance uncertain rewards in their current situation. We illustrate the concepts with examples and counter-examples, and conduct experiments to demonstrate the properties and applicability of the proposed computational tools that enable agents to proactively identify potential hedging opportunities in real-world situations.