ABSTRACT
The concept of risk is fundamental to many fields of study. Risk appears in numerous guises, from theoretical modeling of financial decisions to determining the social consequences of expanded nuclear power usage. Despite this importance, the precise definition of risk depends on the context and application. Common usage is derived from insurance applications where risk represents the possibility of loss, injury or peril. This definition is reflected in various risk assessment and some risk management applications, ranging from social and psychological risk to environmental and bio-hazard risk. Units of measurement for risk vary with context. In contrast, risk in financial economics is associated with the possibility that the actual return for a real asset or security will differ from the expected return. There is a fundamental tradeoff between risk and return. This financial risk is typically measured using the variance or standard deviation of historical return from the mean return, a definition of risk that includes both positive and negative outcomes. Where only the possibility of financial loss is of concern, as in value-at-risk applications, measurements are evaluated using the left tail of the probability distribution for return or profit.
