A risk is an uncertain event, classified as either a pure risk or a speculative risk. A pure risk involves two possible outcomes, either a loss occurs or no loss occurs. A speculative risk offers not only a loss or no-loss outcome, but also the possibility of a gain.

Another way to view risk in a qualitative sense is as a positive or negative unit which depends on the most likely outcome upon which the event is based.

Starting a business venture which could prove to be profitable with a particular probability, weathering a storm without having insurance in place, both of these are scenarios involving risk. The first situation has both positive risk and negative risk associated with it, and the second has only negative risk.

Risk is commonly viewed in quantitative terms as the following:

  • A measure of dispersion of returns of investments in a portfolio about the mean return of the portfolio, i.e. standard deviation σ, where the square of σ is the volatility, σ2.
  • The range of possible outcomes of a project based on an analysis of possible future events.
  • VAR (Value at Risk), e.g. in a stress test, sensitivity analysis, or scenario analysis.
  • The degree of financial leverage of a company, i.e. how much debt they have issued.
  • A credit risk premium, this is a component of a discount rate used by investors to discount a future value of an investment back to the present, where the discount rate, r, is decomposed as the sum of the risk-free rate, rf, plus the credit risk premium, rcr, in r = rf + rcr. The credit risk premium could also be viewed as the risk of default on a company’s bonds and may be reflected in a credit rating on the company’s bonds or on the company itself.
  • Duration measures for bonds.
  • Delta measures for options.
  • Risk factors in multifactor models using arbitrage pricing theory (APT) in the context of modern portfolio theory (MPT).
  • Market risk, operational risk, economic risks