Risk Loading Calculator

Work out risk loading instantly with clear inputs, formula shown and shareable results.

About Risk Loading Calculator

A premium equal to expected losses would leave an insurer insolvent half the time. The standard-deviation principle adds a risk load of k·σ to compensate for volatility, and expenses are then grossed up as a share of premium.

Formula

Standard deviation principle

Premium = (E[L] + k·σ) / (1 - expense ratio)

k: Risk load factor
σ: Loss SD

Worked example

With the default values below, Risk Loading Calculator returns Technical Premium of $1,008,522.73. Change any input above and every figure here is recalculated in your browser.

Inputs used

Expected Lossminimum 0: 800,000
Loss Standard Deviationminimum 0: 250,000
Risk Load Factor (k)accepts 0.01–5: 0.35
Expense Ratioaccepts 0–60 %: 12 %

Results

Technical Premium: $1,008,522.73
Risk Load: $87,500.00
Total Loading Over Expected Loss: 26.065%
Margin Above Expected Loss: $208,522.73

Step by step

1Values used
2Standard deviation principle
3Technical Premium= 1,008,522.73
4Risk Load= 87,500.00
5Total Loading Over Expected Loss= 26.065
6Margin Above Expected Loss= 208,522.73

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax or compounding frequency into account.
Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is k chosen?

From the return required on the capital the volatility ties up, so more volatile lines carry a higher k.

Why divide by (1 − expense ratio)?

Because expenses are quoted as a percentage of premium, not of losses, so grossing up is the consistent treatment.