Why Compare Indicated and Current Factors?
A class factor in a rating plan translates a base rate into a class-specific rate. An indicated factor summarizes the relative level suggested by an analysis of class experience; a current factor is the factor presently used in the rating plan. Comparing them helps identify classes where the existing plan may not reflect the experience-based indication. The comparison is a diagnostic, not an instruction to change a factor automatically.
A factor comparison is meaningful only when both factors use the same reference. For example, an indicated set expressed relative to one base class cannot be compared directly with current factors expressed relative to another. The earlier material on rebasing relativities establishes how to put both sets on the same base. Here, the emphasis is on measuring and interpreting their differences once that alignment is made.
Factor-point differences and percentage differences answer different questions. A difference of 0.10 does not mean a 10% difference in every case: moving from 0.50 to 0.60 is a 20% increase, while moving from 1.00 to 1.10 is a 10% increase. State the comparison measure and its reference clearly.
Align the Basis Before Comparing
Factors are relative quantities. Suppose a model produces unscaled values \(q_j\). If class \(b\) is chosen as the base, the base-class indicated factor is \(I_b=1\), and the other indicated factors are \(I_j=q_j/q_b\). Current factors must be expressed relative to that same base before comparing. If the indicated and current sets already share a common normalization, use that common basis rather than rebasing again.
A consistent multiplicative rescaling of every factor in a set does not change the relationships within that set, but it can change a direct comparison with a differently scaled set. Therefore, a ratio of two factors is interpretable as a class-level comparison only after their bases or normalization conventions agree.
Check that indicated and current factors use the same base class or the same stated normalization.
For each class, calculate \(I_j-C_j\), \(I_j/C_j\), and, when useful, \(100(I_j-C_j)/C_j\%\).
Examine the class experience and exposure volume behind the indication. A discrepancy identifies a review question; it does not, by itself, establish that a factor should change.
Why the Percentage Formula Uses the Current Factor
The requested percentage is the change from the factor currently in use to the indicated factor. In the usual definition of percentage change, the starting value is the denominator. The change is \(I_j-C_j\), and the starting value is \(C_j\). Thus:
This calculation is directional: it asks how far the indicated value is from the current one, measured as a proportion of the current value. Reversing the denominator instead answers a different question—how far the current value is below or above the indicated value, relative to the indication. Do not switch denominators without stating the reference.
Worked Example: Comparing Factors on a Common Base
A hypothetical repair-coverage plan uses class A as its base. An experience analysis gives loss costs of $200, $250, and $180 per exposure for classes A, B, and C. The current factors are 1.00, 1.15, and 1.00. Calculate the indicated factors from the loss costs and compare each class with its current factor.
Method and assumptions. Use class A as the base and calculate each indicated factor as its class loss cost divided by class A’s loss cost. The supplied loss costs are treated as the indications for this example. This is a deterministic hypothetical comparison: no interest rate or mortality assumption is used, and no probability distribution is assumed.
Indicated factors. Class A is the base, so \(I_A=200/200=1.00\). For class B, \(I_B=250/200=1.25\). For class C, \(I_C=180/200=0.90\).
Class A. The factor-point difference is \(1.00-1.00=0.00\). The ratio is \(1.00/1.00=1.00\), so the percentage difference is \(1.00-1=0\%\).
Class B. The difference is \(1.25-1.15=0.10\). The ratio is \(1.25/1.15=1.0869565\ldots\). The percentage difference is \(1.0869565\ldots-1=0.0869565\ldots\), or \(8.70\%\) rounded to two decimal places. The indication is above the current factor.
Class C. The difference is \(0.90-1.00=-0.10\). The ratio is \(0.90/1.00=0.90\), so the percentage difference is \(-10.00\%\). The indication is below the current factor.
Check and trap avoided. Multiplying each indicated factor by the base loss cost returns the supplied loss costs: \(1.00(200)=200\), \(1.25(200)=250\), and \(0.90(200)=180\). The 0.10 factor-point difference for class B is not a 10% change; using the current factor as the denominator gives \(0.10/1.15=8.70\%\).
Interpretation: Size, Direction, and Supporting Experience
A useful comparison table shows at least the indicated factor, current factor, factor-point difference, and percentage difference. The sign shows direction; the magnitude shows the size of the discrepancy on the chosen scale. Neither measure alone tells whether a revision is appropriate.
Review the experience that produced the indicated factor. The earlier material on class loss costs and model-based class relativities supplies ways to construct indications; this comparison step asks whether the resulting indication differs from the current plan and whether the observed experience warrants further attention. Exposure volume matters because a factor based on limited experience may be less persuasive than one supported by more experience. A large percentage difference based on sparse data should not be treated as conclusive evidence.
It is also useful to look for a coherent pattern. If multiple related classes have indications consistently above their current factors, that pattern may justify examining the existing class structure or the underlying data. If one class differs sharply while nearby classes do not, check the classification assignment, experience allocation, and modeling basis before drawing a conclusion. These checks identify questions for review; they do not replace a formal assessment of uncertainty or other rating constraints.
Worked Example: Rebasing Before Comparing
A hypothetical equipment insurer’s model reports raw indicated values of 0.80, 1.00, and 1.20 for classes A, B, and C. The current plan uses A as the base, with current factors 1.00, 1.20, and 1.40. Rebase the indications to A and compare classes B and C.
Method and assumptions. Divide every raw indicated value by the raw value for base class A, 0.80. Then compare the rebased indications with current factors on the same A-base scale. Values are deterministic and hypothetical; no interest rate, mortality assumption, or probability distribution is used.
Rebase class A. \(I_A=0.80/0.80=1.00\).
Rebase class B. \(I_B=1.00/0.80=1.25\).
Rebase class C. \(I_C=1.20/0.80=1.50\).
Compare class B. Its factor-point difference is \(1.25-1.20=0.05\). Its ratio is \(1.25/1.20=1.0416667\ldots\), so the percentage difference is \(4.17\%\) rounded to two decimal places.
Compare class C. Its factor-point difference is \(1.50-1.40=0.10\). Its ratio is \(1.50/1.40=1.0714286\ldots\), so the percentage difference is \(7.14\%\) rounded to two decimal places.
Check and trap avoided. The rebased base factor is exactly 1.00, consistent with the current base. Directly comparing the raw model value 1.00 for B with the current factor 1.20 would incorrectly suggest a \(-16.67\%\) discrepancy. Those values use different references; rebasing first gives the correct comparison of \(+4.17\%\).
Use Exposure and Loss Experience to Prioritize Review
The class-level percentage difference describes a relative factor gap, not the number of dollars affected. To assess how much observed class experience supports review, inspect the underlying exposure and loss amounts as well as the indicated factor. For a simple pure-premium indication, class loss cost is losses divided by exposures; the indicated factor relative to a base class is the class loss cost divided by the base-class loss cost. The next example carries out these calculations and checks the comparison.
Worked Example: Identifying a Class for Further Review
A hypothetical service-contract portfolio has the following earned exposures and losses for a consistent experience period. Current factors are shown on a base-A scale. Calculate indicated factors from class loss costs, compare them with current factors, and identify what the results support reviewing.
| Class | Exposures | Losses | Current factor |
|---|---|---|---|
| A | 1,000 | $200,000 | 1.00 |
| B | 600 | $150,000 | 1.15 |
| C | 400 | $72,000 | 1.00 |
Method and assumptions. Calculate loss cost as losses divided by exposures, and use class A’s loss cost as the base. Treat the hypothetical losses and exposures as the data supplied for this deterministic illustration; no interest rate, mortality assumption, or probability distribution is used.
Class A loss cost. \(200{,}000/1{,}000=\$200\) per exposure. Therefore, \(I_A=200/200=1.00\).
Class B loss cost. \(150{,}000/600=\$250\) per exposure. Therefore, \(I_B=250/200=1.25\). Its difference from the current factor is \(1.25-1.15=0.10\), and its percentage difference is \(0.10/1.15=0.0869565\ldots=8.70\%\), rounded to two decimal places.
Class C loss cost. \(72{,}000/400=\$180\) per exposure. Therefore, \(I_C=180/200=0.90\). Its difference from the current factor is \(0.90-1.00=-0.10\), and its percentage difference is \(-0.10/1.00=-10.00\%\).
Interpretation and check. Class B’s indication is above its current factor, while class C’s is below. The loss-cost check is \(1.25(\$200)=\$250\) for B and \(0.90(\$200)=\$180\) for C, matching the calculated values. Class B has 600 exposures and a positive factor discrepancy; this supports examining its experience and data basis. It does not prove that the factor should be changed. Class C’s difference also merits review, but its 400 exposures and observed loss cost should be considered before treating the indication as decisive.
Common Mistakes and Practical Checks
- Comparing factors on different bases. Rebase or otherwise align the factor sets before calculating a difference or ratio.
- Using the wrong denominator. For a percentage change from the current factor, divide by \(C_j\), not \(I_j\).
- Confusing factor points with percentages. Report \(I_j-C_j\) as a factor-point difference and \((I_j-C_j)/C_j\) as a percentage difference.
- Treating an indication as a decision. A difference is a signal for analysis. It does not, on its own, account for data limitations, uncertainty, or other rating considerations.
- Ignoring experience volume. A large discrepancy based on limited exposure may call for investigation rather than immediate action.
Check Your Understanding
For each problem, use the current factor as the denominator when a percentage difference is requested. Treat the scenarios as hypothetical.
- A base class has an indicated factor of 1.00 and a current factor of 1.00. Another class has an indicated factor of 1.32 and a current factor of 1.20. Find its factor-point and percentage differences. (Answer: \(+0.12\) factor points; \(+10.00\%\).)
- A model gives raw indicated values of 0.75 for base class A and 1.05 for class B. Current factors are 1.00 for A and 1.30 for B. Rebase the indication to A and calculate B’s percentage difference. (Answer: rebased indication \(1.40\); difference \(+7.69\%\).)
- Class P has 800 exposures and $160,000 of losses; base class Q has 1,000 exposures and $200,000 of losses. Current factors are 1.00 for Q and 0.90 for P. Using class loss costs, find P’s indicated factor and percentage difference. (Answer: indicated factor \(1.00\); percentage difference \(+11.11\%\).)
- A class has current factor 0.80 and indicated factor 0.72. Calculate the factor-point difference and the percentage difference relative to current. State the direction. (Answer: \(-0.08\) factor points; \(-10.00\%\); indication below current.)
- Two classes have indicated factors 1.10 and 1.20 and current factors 1.00 and 1.10, respectively. Which has the larger percentage difference relative to current, and by how much? (Answer: the first class, \(10.00\%\) versus \(9.09\%\), a difference of \(0.91\) percentage points when rounded to two decimals.)