The combined ratio is one of the most important metrics in insurance, used to assess an insurer’s profitability and efficiency. But what exactly does it measure, and why does it matter? Let’s break it down in simple terms.

Recently, I was studying materials from the CAS DISC RM online course. It focuses on risk management and the insurance industry. I learned a lot about writing different types of insurance, how insurers operate in the USA, and how to measure the financial profitability of insurance companies.

One of the key metrics used to measure an insurance company's success in underwriting is the combined ratio. It is the sum of the loss ratio and the expense ratio. Although I was already familiar with this ratio, my understanding has significantly improved after studying these materials.

One interesting thing I learned is that the CAS DISC RM materials present a different formula for the combined ratio compared to other online sources. While the results are similar, there are still some differences.

In this Actuarial Concepts post, I will go through both formulas, explain the elements of the combined ratio, and show why it is such a useful metric.

What Is the Combined Ratio?

The combined ratio is a key financial metric used in the insurance industry to evaluate underwriting performance. It can be calculated as:

where incurred losses are claims payments and loss adjustment expenses such as court fees, and underwriting expenses are administrative costs, commissions, and other operational expenses.

Earned premiums represent the revenue an insurer earns from policies during a given period.

But also, combined ratio can be calculated as:

where the loss ratio is:

(LAE stands for loss adjustment expenses), and the expense ratio is:

As you may see, the denominators differ in loss ratio and expense ratio.

Earned premiums usually are not equal to written premiums, which are the total amount of premiums an insurance company records on its books for policies issued during a specific period, regardless of whether the premium has been received in full or whether the policy period has begun.

Therefore, calculating combined ratio using these two methods can produce different outcomes.

A combined ratio below 100% means the insurer is making an underwriting profit, while a ratio above 100% indicates an underwriting loss.

Why Does It Matter?

There are many ways combined ratio matters in insurance companies:

Measures underwriting profitability – A combined ratio below 100% indicates an underwriting profit, while a ratio above 100% means the insurer is losing money on underwriting alone.
Evaluates operational efficiency – It shows how well an insurer manages losses and expenses relative to the premiums collected or written.
Helps assess financial stability – A consistently high combined ratio may indicate wrongly priced policies, high claim costs, or excessive operational expenses, all of which can threaten an insurer’s profitability.
Provides insight for decision-making – Insurers can use this metric to improve pricing, risk selection, and expense management to improve financial performance.
Monitored by investors and regulators – A key metric for analysts, investors, and regulators to evaluate an insurer’s long-term financial stability and competitive position in the market.

Example

If an insurer has:

$70 million in losses
$5 million in loss adjustment expenses
$2.5 million in underwriting expenses
$200 million in premiums written
$100 million in premiums earned

What is the combined ratio of this insurer?

We will use both methods presented in this post.

Solution 1

The combined ratio is the sum of incurred losses, loss adjustment expenses, and underwriting expenses divided by earned premiums. Taking values from the example, we have:

Since the ratio is below 100%, the insurer is making an underwriting profit.

Solution 2

The combined ratio is the sum of loss ratio and expense ratio. Taking values from the example, we have loss ratio equal to:

expense ratio equal to:

and the combined ratio, which is equal to:

Since the ratio is below 100%, the insurer is making an underwriting profit.

Using both methods, we see that insight is the same, but values are a little bit different.

Summary

The combined ratio is a simple yet highly insightful metric in the insurance industry. However, to get a full view of an insurance company’s underwriting activities, additional financial metrics should also be considered.

I presented two different methods for calculating this metric. While they differ slightly, insurance companies should have strict guidelines on which calculation method to use—especially when dealing with large volumes of losses, expenses, and premiums.

Unfortunately, I did not pass the CAS DISC RM exam and will need to retake it (more on this in the Actuarial Journey Updates!). However, I still learned a lot and can highly recommend this online course—not just for aspiring actuaries but for anyone interested in risk management and insurance.

I hope this short introduction to the combined ratio was helpful or sparked your interest. If you’d like to learn more, I’ve included a few links below. Enjoy!

Combined Ratio: Definition, What It Measures, Formula, Examples - https://www.investopedia.com/terms/c/combinedratio.asp

Understanding Combined Ratio - https://insurancetrainingcenter.com/resource/understanding-combined-ratio/

Combined Ratio: The Key Insurance Performance Metric