Expected Loss Calculator
Comprehensive risk quantification and insurance optimization
Loss Frequency
Annual probability of loss occurrence (0-1)
Independent exposure units
Severity Distribution
Cost Parameters
Annual Expected Loss
Expected Loss (EL) is the average amount you anticipate losing over a given period, calculated as the product of the probability of a loss event and the severity of that loss when it occurs.
VaR answers: "What is the maximum loss I might face with X% confidence?" It provides a single number summarizing the risk of a portfolio or exposure.
- VaR 95%: Loss exceeded only 5% of the time
- CVaR: Average loss when exceeding VaR threshold
- Use Case: Capital allocation, risk limits
The Total Cost of Risk (TCoR) captures all costs associated with managing risk, not just expected losses.
Normal (Gaussian)
Symmetric bell curve distribution
Use: Moderate, predictable losses with consistent severity
Log-Normal
Right-skewed, always positive values
Use: Insurance losses, financial returns
Exponential
Memoryless, decreasing probability
Use: Time between events, small frequent losses
Pareto
Heavy-tailed, extreme value distribution
Use: Catastrophic losses, natural disasters
When to Retain Risk
- • High frequency, low severity losses
- • Strong financial position to absorb losses
- • Premium exceeds expected loss significantly
- • Losses are predictable and budgetable
- • Want to avoid claim process overhead
When to Transfer Risk
- • Low frequency, high severity losses
- • Catastrophic or ruin potential
- • Regulatory or contractual requirements
- • Access to insurer expertise and services
- • Peace of mind and budget certainty
Optimal Retention Strategy
The optimal retention level minimizes the total cost of risk. Higher retention reduces premiums but increases volatility. Use the Retention Analysis tab to find the sweet spot for your organization based on expected losses and premium savings at different deductible levels.
- •Use historical claims data to calibrate probability and severity
- •Consider multiple severity distributions and compare results
- •Run Monte Carlo simulations for complex risk portfolios
- •Review and update risk parameters annually
- •Consider correlation between different risk exposures
- •Use CVaR (not just VaR) to understand tail risk exposure
- ✗Using only expected loss without considering volatility
- ✗Ignoring tail risk (rare but catastrophic events)
- ✗Assuming normal distribution for heavy-tailed losses
- ✗Not considering administrative costs of risk management
- ✗Over-relying on historical data without adjustments
- ✗Ignoring correlation between exposures
| Risk Category | Probability | Severity | Example | Treatment |
|---|---|---|---|---|
| High Freq / Low Sev | High (>50%) | Low (<$10K) | Minor cargo damage, documentation errors | Retain, self-insure, process improvement |
| Medium / Medium | Med (10-50%) | Med ($10K-$100K) | Equipment failure, delays | Partial transfer, deductible optimization |
| Low Freq / High Sev | Low (1-10%) | High ($100K-$1M) | Major accidents, cargo theft | Full insurance transfer |
| Rare / Catastrophic | <1% | >$1M | Vessel total loss, natural disaster | Essential insurance, contingency plans |