Combining Manual and Experience Rate Indications

Why the Basis of an Indication Matters

A manual indication and an experience indication can describe different views of expected losses: one based on a manual rating plan, the other on adjusted loss experience. Combining them is meaningful only after confirming that both refer to the same prospective risk, exposure, coverage, and rate level. A credibility weight cannot repair mismatched inputs.

The experience estimate may already have been adjusted for development, trend, and rate level. The manual estimate must refer to that same prospective period and current rate level. The earlier material on matching loss, exposure, and premium bases is useful here: amounts that cover different exposures or different terms must first be made comparable.

Definition: Let $L_E$ be projected experience losses and $L_M$ be manual expected losses, both evaluated on the same target exposure base. Given an experience credibility weight $Z$, where $0\leq Z\leq 1$, the blended expected losses are $$ L_B=ZL_E+(1-Z)L_M. $$ The weight $Z$ applies to the experience estimate; $1-Z$ applies to the manual estimate. It is not automatically an exposure share or a claim-count share.

This formulation treats the manual estimate as the complement of the experience weight. It assumes the supplied estimates are comparable expected losses, not raw amounts from different exposure volumes. If the components are expected loss costs per exposure rather than totals, blend those costs after defining the same exposure unit.

From Blended Losses to an Indicated Rate Change

Under a simple loss-ratio pricing structure, let $P_0$ be the current premium on the target exposure base and let $r$ be the permissible loss ratio: the portion of premium available for losses. Assume the same $r$ applies to the indication being calculated and that fixed expenses do not require a separate adjustment. Then the indicated premium is $L_B/r$, and the rate-change factor compares that premium with $P_0$.

P_{\mathrm{ind}}=\frac{L_B}{r}, \qquad \text{indicated rate change} =\frac{P_{\mathrm{ind}}}{P_0}-1 =\frac{L_B}{rP_0}-1.

The units must agree: $L_B$ and $P_0$ must cover the same target exposures. If the pricing structure has fixed expenses per exposure, or if its permissible loss ratio differs between components, this simple conversion may not apply unchanged. Calculate the components under the appropriate premium formula before combining them.

Why Blending on a Common Basis Works

Suppose the experience and manual estimates are each projected losses for the same target set of exposures. Credibility assigns a proportion $Z$ to one estimate and $1-Z$ to the other, so the combined expected loss is their weighted sum. Under a common permissible loss ratio $r$, converting that loss estimate to premium divides the entire sum by $r$:

\frac{L_B}{r} =\frac{ZL_E+(1-Z)L_M}{r} =Z\frac{L_E}{r}+(1-Z)\frac{L_M}{r}.

Thus, when both component premiums use the same exposure base and the same loss-ratio conversion, blending their indicated premiums gives the same result as blending losses first. The equivalence depends on those shared conditions. In particular, a total loss amount observed on fewer exposures cannot be substituted directly for a total on the full target portfolio.

Worked Indications

Worked Example: Blending Two Estimates on One Exposure Base

A hypothetical insurer is reviewing a block with 1,000 exposure units and current premium $P_0=\$600{,}000$. For those same 1,000 units, adjusted experience indicates expected losses of $L_E=\$462{,}000$, while the manual plan indicates $L_M=\$430{,}000$. The experience credibility is $Z=0.40$, and the permissible loss ratio is $r=0.70$. Calculate the indicated rate change. No interest or mortality assumption is involved; the loss amounts are supplied prospective estimates, not random observations to be fitted to a distribution.

Method. Blend the expected loss estimates on their common 1,000-unit basis, then convert the blended amount to premium using the permissible loss ratio.

First calculate the credibility weights: the experience weight is $0.40$, and the manual weight is $1-0.40=0.60$.

L_B=0.40(\$462{,}000)+0.60(\$430{,}000) =\$184{,}800+\$258{,}000 =\$442{,}800.

The indicated premium is

P_{\mathrm{ind}}=\frac{\$442{,}800}{0.70} =\$632{,}571.43.

Relative to current premium, the indicated rate change is

\frac{\$632{,}571.43}{\$600{,}000}-1 =1.0542857-1 =0.0542857.

Rounded to two decimal places, the indicated change is +5.43%. Check: $0.70(\$632{,}571.43)=\$442{,}800$, the blended loss estimate. The common mistake avoided is reversing the credibility weights or applying the weights to incompatible amounts.

Worked Example: Standardizing Experience to the Target Exposure

A hypothetical specialty portfolio has 1,000 target exposure units and current premium of $\$700{,}000$. Experience losses of $\$480{,}000$ are projected for only 800 exposure units. The manual estimate is $\$500$ per exposure unit for the target portfolio. Use $Z=0.40$ and a permissible loss ratio of $0.75$. Find the indicated rate change. No interest or mortality assumption is involved; no parametric loss distribution is assumed.

Method. First convert the experience amount to a loss cost per exposure and project it to the same 1,000-unit base as the manual estimate. Only then blend.

Experience loss cost is

\frac{\$480{,}000}{800}=\$600\text{ per exposure}.

On the 1,000-unit target base, that is $\$600(1{,}000)=\$600{,}000$. The manual estimate on the same base is $\$500(1{,}000)=\$500{,}000$. Therefore,

L_B=0.40(\$600{,}000)+0.60(\$500{,}000) =\$240{,}000+\$300{,}000 =\$540{,}000.

The indicated premium and rate change are

P_{\mathrm{ind}}=\frac{\$540{,}000}{0.75}=\$720{,}000, \qquad \frac{\$720{,}000}{\$700{,}000}-1 =0.0285714.

Rounded to two decimal places, the indication is +2.86%. Check: the indicated premium provides a loss provision of $0.75(\$720{,}000)=\$540{,}000$. A tempting but incorrect calculation blends $\$480{,}000$ directly with $\$500{,}000$, giving $\$492{,}000$. That treats losses on 800 exposures as though they covered 1,000, and would produce a materially different, invalid indication.

When an Indication Percentage Can Be Blended

Sometimes the manual and experience results are already expressed as indicated premium factors rather than loss totals. Blending those factors is valid when each factor is defined relative to the same current premium base and uses the same premium and expense structure. For example, if both factors apply to $P_0$, then their blended factor is $Zf_E+(1-Z)f_M$. If they use different denominators, the percentages do not represent comparable quantities; return to common-basis loss or premium amounts first.

A separate weighting issue arises when combining indications for multiple classes into one portfolio change. Class factors must be applied to each class's current premium, then the indicated premiums added. A simple average of class percentage changes gives equal influence to classes regardless of their premium size.

Worked Example: Aggregating Class Indications by Current Premium

A hypothetical insurer has two classes. Class A has current premium $\$400{,}000$, manual factor $1.04$, experience factor $1.16$, and experience credibility $Z_A=0.25$. Class B has current premium $\$600{,}000$, manual factor $1.02$, experience factor $0.90$, and $Z_B=0.50$. Within each class, both factors use that class's same current premium and rate basis. Find the portfolio rate change. There is no assumed interest rate, mortality model, or fitted loss distribution.

Method. Blend the factors within each class, apply each blended factor to its current premium, and aggregate the indicated premiums.

For Class A, the blended factor is

$$ f_A=0.25(1.16)+0.75(1.04)=0.29+0.78=1.07. $$

Its indicated premium is $\$400{,}000(1.07)=\$428{,}000$. For Class B,

$$ f_B=0.50(0.90)+0.50(1.02)=0.45+0.51=0.96, $$

so its indicated premium is $\$600{,}000(0.96)=\$576{,}000$. The total current premium is $\$400{,}000+\$600{,}000=\$1{,}000{,}000$, while the total indicated premium is $\$428{,}000+\$576{,}000=\$1{,}004{,}000$. Thus the portfolio factor is $1{,}004{,}000/1{,}000{,}000=1.004$, or +0.40%. Check: the class premium changes are $+\$28{,}000$ and $-\$24{,}000$, netting to $+\$4{,}000$. The unweighted average of $+7\%$ and $-4\%$, or $+1.5\%$, is wrong because it gives both classes equal portfolio weight.

Common Basis Checks and Exam Traps

Before accepting a combined indication, check what each input covers and how it was produced. A compact audit is often more useful than immediately calculating a weighted average.

Identify the target.
Specify the prospective policy period, exposure unit, coverage, limits, deductibles, and class mix represented by the indication.

Standardize each estimate.
Confirm experience and manual expected losses are on the same exposure base and rate level. If necessary, convert totals to loss costs per exposure before projecting to the target exposures.

Apply the stated blend.
Use $Z$ for experience and $1-Z$ for manual. Do not substitute an exposure count or premium share for $Z$ unless the problem explicitly defines it that way.

Convert to an indicated premium.
Use the specified permissible loss ratio or other pricing structure, and check that the resulting loss provision agrees with the blended loss estimate.

Aggregate only after class calculations.
For a portfolio factor, add indicated class premiums and divide by total current premium. Do not average class rate changes without appropriate weights.

A weighted average is not inherently wrong. It is wrong when the quantities being averaged have different denominators, different exposure bases, or different meanings. Credibility blending combines estimates of the same prospective quantity; portfolio aggregation combines premium dollars from the classes actually in the portfolio. Keeping those operations distinct prevents many rate indication errors.

Key takeaway: Standardize first, blend second, and convert to a rate change last. Use the credibility weights only on comparable manual and experience estimates, and use current premium weights when aggregating class indications.

Check Your Understanding

For each problem, identify the common basis before calculating. Round rate changes to two decimal places.

A hypothetical block has 500 exposure units, current premium $\$250{,}000$, and permissible loss ratio $0.70$. Manual losses are $\$320$ per exposure; experience losses are $\$350$ per exposure on those same units. With $Z=0.60$, find the rate change. (Answer: $-3.43\%$)
A hypothetical target has 800 exposures and current premium $\$480{,}000$. Experience losses of $\$270{,}000$ cover 600 exposures; manual losses are $\$420$ per exposure on the target base. With $Z=0.25$ and permissible loss ratio $0.75$, find the rate change. (Answer: $-5.00\%$)
Manual and experience factors of $1.03$ and $1.11$ both apply to the same current premium base. If $Z=0.40$, find the blended rate change. (Answer: $+6.20\%$)
Two hypothetical classes have current premiums of $\$300{,}000$ and $\$700{,}000$, with indicated factors $1.08$ and $0.97$. Find the portfolio rate change. (Answer: $+0.30\%$)
An experience indication is based on 400 exposure units and a manual indication on 600 exposure units. Is it valid to blend their total loss amounts directly when the target has 1,000 exposures? State the necessary correction. (Answer: No; convert each to a loss cost per exposure and project both to the same 1,000-exposure base before blending.)

What You'll Learn