When it comes to estimating insurance losses—particularly those not yet reported—actuaries often turn to structured techniques to ensure accuracy and credibility. While the chain ladder method is widely known, the Bornhuetter-Ferguson method (BF Method) is another cornerstone in actuarial science, especially in situations where past data may not fully reflect the expected future outcomes.
If you are not sure what we are talking about, it would be good to first go through our Run off Triangles in Reserving article.
In this article, we’ll break down the Bornhuetter-Ferguson technique, contrast it with the traditional chain ladder actuarial approach, and walk through a detailed example so you can see exactly how the method works in practice.
What is the Bornhuetter-Ferguson Method?
The Bornhuetter-Ferguson method is a widely used actuarial technique for estimating Incurred But Not Reported (IBNR) losses. Originally introduced in 1975 by E.H. Bornhuetter and R.E. Ferguson, this method is particularly helpful in situations where reported claims data alone doesn’t give the full picture—such as with low frequency, high severity losses.
Core Idea
Instead of fully relying on past loss data (as in the chain ladder method), the BF method starts with an a priori estimate of the ultimate loss—often derived using an expected loss ratio (ELR)—and adjusts it based on how much of that loss is expected to have been reported.
The formula is:
BF Ultimate Loss = Reported Loss + (Expected Ultimate Loss × % Unreported)
Or algebraically:
BF = L + ELR × Exposure × (1 – w)
Where:
- L = Reported loss
- ELR = Expected Loss Ratio
- Exposure = Earned premium or sum insured
- w = Percent reported (often 1 / LDF)
Why Use Bornhuetter-Ferguson Over Chain Ladder?
While the chain ladder actuarial method is powerful for well-developed and stable datasets, the Bornhuetter-Ferguson technique is often preferred when:
- Historical data is sparse or volatile
- Reporting delays are unpredictable
- Loss development patterns are unstable
- The insurer wants to incorporate expert judgment or industry-wide expectations
Think of the BF method as a hybrid—it blends the objectivity of the chain ladder development with the stability of expected losses from underwriting or pricing.
Bornhuetter-Ferguson Example
Let’s walk through a simple numerical example.
Step 1: Known Inputs
- Reported Losses to Date (L): ₹1,000,000
- Expected Loss Ratio (ELR): 60%
- Earned Premium (Exposure): ₹2,000,000
- Loss Development Factor (LDF): 1.25
(So, percent reported w = 1 / 1.25 = 0.8 or 80%)
Step 2: Estimate the Ultimate Loss Using BF
We want to calculate the Bornhuetter-Ferguson ultimate loss.
Using the formula:
BF = L + ELR × Exposure × (1 – w)
= ₹1,000,000 + (0.60 × ₹2,000,000 × (1 – 0.8))
= ₹1,000,000 + ₹240,000
= ₹1,240,000
Step 3: Estimate IBNR
Now subtract the reported losses from the BF ultimate:
IBNR = BF – Reported Loss = ₹1,240,000 – ₹1,000,000 = ₹240,000
So, according to the Bornhuetter-Ferguson method, we expect ₹240,000 of losses to still emerge in the future for this period.
Comparison with Chain Ladder Example
If we had used the chain ladder method instead, the ultimate would simply be:
Chain Ladder Ultimate = L × LDF = ₹1,000,000 × 1.25 = ₹1,250,000
And IBNR = ₹250,000
As you can see, the chain ladder example gives slightly higher estimates because it assumes past reporting patterns will continue identically in the future, while BF tempers that assumption by incorporating prior expectations through the ELR.
You can find clm, chain ladder method and example here in our complete guide.
When to Use the Bornhuetter-Ferguson Method
The BF method is ideal when:
- You’re working with new lines of business
- Claims data is incomplete
- You expect claims reporting delays
- You need to incorporate underwriting expectations
It’s especially valuable when you’re unsure if early claims data is predictive of the full picture.
Comparison with the Expected Loss Ratio Method
While the Expected Loss Ratio (ELR) method relies entirely on an a priori estimate—typically derived from underwriting or pricing assumptions—the Bornhuetter-Ferguson method enhances this by blending it with actual reported loss data. The ELR method assumes that historical claims development is either unavailable or unreliable, making it useful for new lines of business or early development periods. However, it ignores emerging loss experience, which may lead to over- or under-estimation. In contrast, Bornhuetter-Ferguson adjusts the expected ultimate loss by incorporating the percentage of losses already reported, offering a more dynamic and responsive reserving approach that still maintains stability where data is sparse. This makes BF a middle ground between purely judgment-based ELR and data-driven methods like the chain ladder.
Final Thoughts
The Bornhuetter-Ferguson technique remains a go-to actuarial tool for loss reserving, especially when claim data is not yet mature. By combining actuarial development techniques with business expectations, it balances data with judgment—a key principle in insurance analytics.
If you’re exploring reserving beyond the standard chain ladder actuarial approach, the BF method offers flexibility and reliability, particularly in uncertain or emerging risk areas.
Learn about another method, which is Expected Loss Ratio Method.