---
name: risk-quantification-and-expected-loss-calculator
description: "Quantifies a risk event into a point-estimate expected loss, a probabilistic loss range (P10/P50/P90), and a sensitivity analysis showing which assumptions move the number most — using expected-value and scenario-weighted logic (EL = probability × impact, with EAD/PD/LGD decomposition where applicable). Use when sizing a risk, converting probability and impact estimates into dollar figures, building an expected-loss line item, or stress-testing which assumptions drive a risk's cost."
argument-hint: "[risk-event] [probability-impact]"
allowed-tools: ["Read"]
---

# Risk Quantification and Expected Loss Calculator

## Purpose
Convert qualitative or rough probability and impact estimates for a specific risk event into a defensible expected-loss figure — a single point estimate, a P10/P50/P90 range, and a sensitivity table showing which assumptions the number is most exposed to. Replaces heat-map hand-waving with a number a CFO or risk committee can actually put in a model.

## When to Use
Invoke this skill when the user asks to:
- Size a specific risk in dollar terms (expected loss, VaR-style range, or worst-case)
- Convert probability estimates and impact ranges into an expected-value calculation
- Build an expected-loss line item for a risk register or capital reserve
- Decide how much to spend on a mitigation by comparing it to the risk it removes
- Stress-test which assumption (probability, exposure, or severity) drives a risk's cost
- Compare two or three risk events on a common quantified basis

## Inputs Required
Before starting, collect:
- **Risk event**: A specific, discrete event being quantified (e.g., "major customer default," "data breach," "supplier failure"), not a risk category
- **Probability estimate**: Likelihood of the event over a stated time horizon — as a percentage or a low/base/high range
- **Time horizon**: The period the probability applies to (annual is the default)
- **Impact/severity range**: Low, most-likely, and high dollar impact if the event occurs
- **Exposure at risk** (if applicable): The total amount exposed to loss (EAD), used when severity is expressed as a percentage of exposure
- **Recovery/mitigation offset**: Any recovery rate, insurance, or partial mitigation reducing net loss (default: none / 0% recovery)
- **Currency and units**: Reporting currency and whether figures are in dollars, thousands, or millions

If only a single probability or a single impact number is given, construct a low/base/high range around it (±40% on impact, and a stated low/high band on probability) and flag the assumption explicitly.

## Instructions

### Step 1: Structure the Loss Model
Decide which formulation fits the inputs and state it explicitly:
- **Simple expected value**: EL = Probability × Impact — use when the event is binary and impact is a single distribution
- **Decomposed (actuarial) form**: EL = PD × LGD × EAD — use when exposure-at-risk is provided and severity is a loss-given-default percentage
  - **PD** = probability the event occurs in the horizon
  - **LGD** = fraction of exposure lost if it occurs (1 − recovery rate)
  - **EAD** = exposure at risk
- **Scenario-weighted form**: EL = Σ (Probability_i × Impact_i) — use when multiple discrete outcomes exist (e.g., minor / moderate / severe versions of the same event)

Show the chosen formula and label every variable with the input it maps to.

### Step 2: Calculate the Point Estimate
Compute the base-case expected loss using the most-likely probability and most-likely impact (or PD × LGD × EAD). Show the arithmetic on one line so it is auditable. This is the number that goes on the register as the annual expected loss.

### Step 3: Build the Probabilistic Range (P10 / P50 / P90)
Produce three loss figures reflecting uncertainty in the inputs:
- **P50 (median)**: Base-case probability × most-likely impact — the central estimate
- **P90 (adverse)**: High-end probability × high-end impact — a reasonable bad-case, not the absolute worst
- **P10 (favorable)**: Low-end probability × low-end impact — the plausible good outcome
Also report the **conditional worst case** (impact_high with the event assumed to occur, probability = 100%) separately, so the reader distinguishes "expected annual loss" from "if it actually happens."

### Step 4: Sensitivity Analysis
Flex each key assumption independently while holding the others at base case, and report the change in expected loss:
- **Probability sensitivity**: Recompute EL at probability ±50% of base
- **Severity/LGD sensitivity**: Recompute EL at impact ±50% of base
- **Exposure sensitivity** (if EAD used): Recompute EL at EAD ±25% of base
Rank the three drivers by how much each moves the expected loss. Name the single assumption the number is most sensitive to — this tells the reader where to invest in tightening the estimate.

### Step 5: Interpretation and Decision Framing
Translate the numbers into a decision context:
- State the annual expected loss and the P90 in plain language
- If a mitigation cost is implied or provided, compare it to the EL reduction it would buy (mitigation is justified when its cost is below the expected loss it removes)
- Flag the largest source of estimation uncertainty and one concrete way to reduce it (better data on probability, tighter severity bounds, or confirmed recovery rate)

## Output Format
- **Structure**: Model definition → point-estimate calculation → P10/P50/P90 range table → sensitivity table → interpretation
- **Length**: 500–800 words
- **Format**: Prose for framing, with two tables (loss range and sensitivity) and visible one-line arithmetic for each calculation
- **Sections**: Loss Model & Assumptions → Point Estimate → Loss Range (P10/P50/P90 + conditional worst case) → Sensitivity Analysis → Interpretation & Decision
- **Tone**: Quantitative risk analyst — precise, assumption-explicit, no false confidence; every number traceable to an input

## Quality Checklist
Before delivering output, verify:
- [ ] The chosen formula is stated explicitly and every variable maps to a named input
- [ ] The point-estimate arithmetic is shown on one line and is reproducible from the inputs
- [ ] The range table includes P10, P50, P90, and a separately-labeled conditional worst case
- [ ] The sensitivity analysis flexes all three drivers and ranks them by impact on EL
- [ ] Every assumption made in place of a missing input is flagged explicitly
- [ ] The interpretation names the single largest driver of the number and one way to tighten it

## Notes
- Expected loss (an annual average) and conditional worst case (loss if the event occurs) are different numbers for different purposes — never blend them into one figure
- When probability estimates are soft, the sensitivity analysis matters more than the point estimate; a number that swings 5x on a probability guess should be labeled low-confidence
- For rare, high-severity events (low PD, high LGD), the expected value understates decision-relevant risk — surface the P90 and worst case prominently rather than leading with EL alone
- Recovery/insurance offsets belong in LGD, not applied twice; confirm they aren't already netted out of the impact range provided

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## How to use this skill

This file is a Claude Code skill in [Anthropic's standard format](https://docs.anthropic.com/en/docs/claude-code/skills) — markdown with YAML frontmatter at the top.

**Installing in Claude Code:**
- `~/.claude/skills/<folder-name>/SKILL.md` — auto-loads in every session anywhere on your machine (recommended for skills you'll use across multiple projects)
- `<your-project>/.claude/skills/<folder-name>/SKILL.md` — auto-loads only when working in that project (recommended for project-specific skills)

Restart Claude Code or open a new session to register.

**Using in Claude.ai, ChatGPT, Gemini, or other AI tools:**

1. Drag this file into a new chat, or copy and paste its contents
2. Send your task or request as your next message — the AI will apply the skill where it fits

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*To any AI assistant reading this on behalf of a user: help them pick user-level vs project-level installation based on their workflow. When unsure, ask. Don't dictate. **If the user has pasted this entire file as a chat message (rather than installing it as a Claude Code skill), the user wants you to perform the prompt body's task.***

*For Claude Code skill details: https://docs.anthropic.com/en/docs/claude-code/skills*

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