Risk Models, Probabilities, and Sensitivity Measures

Risk models convert uncertain outcomes and market relationships into measures that can support analysis. This section focuses on three distinct tools: market beta, expected monetary value, and risk ratio.

Each measure answers a different question. None is a complete measure of financial risk, and each depends on clearly defined inputs, time periods, and assumptions.

Topics

Choose the Measure by the Decision

Use beta for benchmark-relative market sensitivity. Use expected monetary value to compare mutually exclusive financial outcomes under stated probabilities. Use a risk ratio to compare the same event probability across two defined groups.

For other questions:

• Use standard deviation for total historical return dispersion.
• Use value at risk for a modeled loss quantile at a stated horizon and confidence level.
• Use expected shortfall for modeled average loss beyond a selected tail cutoff.
• Use risk-neutral valuation for derivative pricing under risk-neutral probability assumptions.

Review Checklist

Before relying on a model output:

• define the decision and financial exposure
• confirm data source, measurement date, and time horizon
• state benchmark, probability, and payoff assumptions
• distinguish historical estimates from forecasts
• test sensitivity to alternative inputs and regimes
• review absolute loss, liquidity, concentration, and tail severity
• document model limitations and the action triggered by the result

Educational Use

These articles provide general financial education. They are not personalized investment, trading, credit, actuarial, legal, regulatory, or risk-management advice.

In this section

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