Cryptocurrency exchanges are frequently targeted and compromised by cyber-attacks, which may lead to significant losses for the depositors and closure of the affected exchanges. These risks threaten the viability of the entire public blockchain ecosystem since exchanges serve as major gateways for participation in public blockchain technologies. In this paper, we develop an economic model to capture the short-term incentives of cryptocurrency exchanges with respect to making security investments and establishing transaction fees. Using the model, we derive conclusions regarding an exchange's optimal economic decisions, and illustrate key features of these conclusions using graphs based on real-world data. Our security investment model exhibits horizontal scaling properties with respect to reducing exposure to losses, and may be of special interest to exchanges operating in markets with high price volatility.