Summarizing risk using risk measures and risk indices

Our society is fascinated with risk in many different areas and disciplines. One of the main ways to describe and communicate the level of risk is through risk indices, which summarize risk using numbers or categories such as words, letters, or colors. These indices are used to communicate risks to the public, understand how risk is changing over time, compare among different risks, and support decision making. Given the different methods to construct risk indices, including flawed methods such as risk matrices, this article develops specific steps that analysts can follow to create a risk index. This article emphasizes the importance of describing risk with a probability distribution, developing a numerical risk measure that summarizes the probability distribution, and finally translating the risk measure to an index. Measuring the risk is the most difficult part and requires the analyst to summarize a probability distribution into one or possibly a few numbers. The risk measure can then be transformed to a numerical or categorical index. I apply the method outlined in this article to construct a risk index that compares the risk of fatalities in aviation and highway transportation.