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What Is Risk?

Risk is the possibility that an outcome differs from what was expected, and in finance the outcomes that matter are losses. A disciplined definition, due to Kaplan and Garrick (1981), treats risk as the joint answer to three questions: what can go wrong, how likely is it, and how bad is the consequence. Risk is therefore not a single number but a set of scenarios paired with probabilities and severities. This framing separates risk (which has a probability distribution we can describe) from a mere hazard or a one-off bad event.

Why it matters

Think of risk as a list, not a feeling. Each row says "here is a thing that could go wrong, here is roughly how often it happens, here is how much it would hurt." A storm is a hazard; the chance of the storm flooding your warehouse and the dollar damage it would do is the risk. The whole field of risk management is just building that list carefully and then deciding what to do about each row.

Formulas

Kaplan-Garrick risk triplet
R={⟨si, pi, xi⟩},i=1,…,NR = \{ \langle s_i,\, p_i,\, x_i \rangle \}, \quad i = 1, \dots, N
Risk is the full set of triplets: scenario sis_i (what can go wrong), its probability pip_i (how likely), and its consequence xix_i (how bad). No single triplet is "the risk"; the whole set is.
Expected loss of a scenario set
E[L]=∑i=1Npi xiE[L] = \sum_{i=1}^{N} p_i \, x_i
A common one-number summary multiplies each consequence by its probability and sums. Useful, but it hides the tail: two risk sets can share the same E[L]E[L] yet differ wildly in their worst cases.

Worked examples

Scenario

A trading desk holds a US$10M equity position. Identify the risk in Kaplan-Garrick terms rather than as a single number.

Solution

List scenarios: a 1% daily drop (consequence US$100k) with probability ~16%, a 5% drop (US$500k) with probability ~2%, a 10% crash (US$1M) with probability ~0.3%. The risk is that whole table of scenario, probability, and consequence. The expected daily loss is the probability-weighted sum, but management also cares about the rare US$1M row, which is why VaR and expected shortfall later focus on the tail of this list.

Common mistakes

  • ✗Risk means the same thing as a bad outcome. A bad outcome is a realized loss; risk is the forward-looking distribution of possible outcomes and their probabilities before anything happens.
  • ✗Risk is always a single number. A single number such as expected loss or VaR is a summary of the underlying scenario set, and any summary discards information about the rest of the distribution.
  • ✗More risk always means a higher expected loss. Two positions can have the same expected loss but very different tail risk; risk is about the whole distribution, not just its mean.
  • ✗Only downside counts, so risk and volatility are identical. Volatility measures dispersion in both directions, while financial risk usually emphasizes the loss tail; the two coincide only under symmetric distributions.

Revision bullets

  • •Risk = possibility actual outcome differs from expected, focused on losses
  • •Kaplan-Garrick (1981): risk is the set of {scenario, probability, consequence} triplets
  • •Risk is a distribution of outcomes, not one realized bad event
  • •Expected loss summarizes the set but hides the tail
  • •A hazard is a source; risk pairs it with likelihood and severity

Quick check

Under the Kaplan-Garrick (1981) definition, "risk" is best described as

Two portfolios have an identical expected loss. What can you still NOT conclude?

Connected topics

Risk vs UncertaintyRM ProcessRisk TaxonomyVaR Definition

Sources

  1. Kaplan & Garrick (1981)
    Kaplan, S., & Garrick, B. J. "On the Quantitative Definition of Risk." Risk Analysis, 1(1), 11-27, 1981.
    Origin of the risk-as-triplet definition: {scenario, likelihood, consequence}.
  2. Jorion (2007), Ch. 1
    Jorion, P. Value at Risk: The New Benchmark for Managing Financial Risk. 3rd ed. McGraw-Hill, 2007.
    Frames financial risk as the dispersion of unexpected outcomes, with losses as the focus of measurement.
How to cite this page
Dr. Phil's Quant Lab. (2026). What Is Risk?. Derivatives Atlas. https://phucnguyenvan.com/concept/frm-what-is-risk
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