Insurance theory · page 6 of 10

Measuring a portfolio

Frequency, severity, loss ratio, combined ratio and retention.

A portfolio is a group of policies: a product, a line, a country, a broker's book. A handful of ratios tell whether it works.

How often, and how much

\text{frequency} = \frac{\text{number of claims}}{\text{exposure (policy-years)}}

\text{severity} = \frac{\text{incurred claims}}{\text{number of claims}}

Frequency is how often claims happen; severity, how much each costs on average. Their product is the pure premium, the claims cost per policy-year before expenses. Motor claims are frequent and mostly moderate; home fires are rare and very expensive: the same pure premium can hide very different risks.

Does it make money?

\text{loss ratio} = \frac{\text{incurred claims}}{\text{earned premium}}

A loss ratio of 0.65 means 65 cents of every euro earned went on claims. Add the expense ratio, expenses (including commission) divided by premium, and you get the combined ratio:

\text{combined ratio} = \text{loss ratio} + \text{expense ratio}

A combined ratio below 100% means the insurance itself made a profit, before any investment income; above 100%, it lost money.

Do customers stay?

\text{retention rate} = \frac{\text{policies renewed}}{\text{policies due for renewal}}

Retaining a customer is far cheaper than winning a new one, so retention is watched as closely as the loss ratio. Its opposite, policies not renewed, is the lapse or churn rate.

At Harbour Mutual

You will reproduce these on Day 4.
Line	Claims for losses in 2025	Average incurred
Home	164	€3,711.61
Motor	431	€3,539.11
Travel	39	€1,036.23

Practise it on Day 4

Check your understanding

Answer every question, then check.

1. Home Contents has incurred claims of €114,000 on earned premium of €100,000. What is its loss ratio?

0.88

1.14

0.14

2. A portfolio has a loss ratio of 70% and an expense ratio of 25%. Is the insurance itself profitable?

Yes: the combined ratio is 95%

No: 70% is too high

It cannot be told

3. Which measure is claims divided by exposure?

Severity

Frequency

Loss ratio