The possibility to use hedging strategies is an often neglected aspect in the literature on prediction/betting markets, as most papers assume that bettors will bet according to their beliefs about the probability of the outcome of the event, as opposed to the direction in which the odds will move. This ignores strategies that try to buy low and sell high through exploiting price changes, which is an important aspect to incorporate to fully understand market pricing. In this paper, we derive the key mathematical results in using hedging strategies through taking opposite positions to an initial bet after the market odds have changed and show that a profit can be made without explicitly speculating on the probability of the outcomes. We also discuss two sources of inefficiency that can arise when using hedging strategies in practice: (i) the need to pay a fee when using a betting exchange and (ii) the lack of a lay option (the possibility to bet against outcomes) on some markets, and we analyze how they affect the possibilities to hedge. Many of the results have interesting properties when expressed in terms of the naive probabilities implied by the odds.