Principles of Ratemaking

Study guide: Exam 5

Principles of Ratemaking are the four statements in the CAS Statement of Principles Regarding Property and Casualty Insurance Ratemaking that define what makes a rate actuarially sound. Its definitions describe ratemaking as the process of establishing rates, involving considerations such as marketing goals, competition and legal restrictions to the extent they affect the estimation of future costs — and the Statement confines itself to that estimation. The rate itself is defined by Principle 1.

$\text{Rate} = E[\text{Losses} + \text{LAE} + \text{Expenses} + \text{Cost of Capital}]$

Principle 1 — A rate is an estimate of the expected value of future costs. Ratemaking is prospective. Historical data is used only as evidence about the future, which is why losses are developed to ultimate and trended forward, and why premium is put on level. A rate based on what happened, rather than on what is expected to happen, fails this principle regardless of how carefully the history was compiled.

Principle 2 — A rate provides for all costs associated with the transfer of risk. Everything must be in there: incurred losses, ALAE and ULAE, commission and brokerage, other acquisition costs, taxes, licenses and fees, policyholder dividends and general administrative expenses — fixed and variable alike — and the cost of capital, through the underwriting profit and contingency provisions. The effect of reinsurance arrangements is among the Statement's considerations. Omitting a real cost because it is hard to estimate does not make the rate conservative; it makes it inadequate.

Principle 3 — A rate provides for the costs associated with an individual risk transfer. Rates should reflect the risk being transferred, not the average of a heterogeneous pool. This is the actuarial basis for risk classification: the Statement calls for consideration of the risk's own expected costs, allowing for credibility where individual experience is thin.

Principle 4 — A rate is reasonable and not excessive, inadequate, or unfairly discriminatory if it is an actuarially sound estimate of the expected value of all future costs associated with an individual risk transfer. This connects the actuarial standard to the statutory one. Most U.S. states' statutes require rates to be "not excessive, not inadequate, and not unfairly discriminatory"; the Statement's position is that a rate meeting Principles 1–3 satisfies it. Note what follows: a rate differential that reflects a genuine cost difference is not unfair discrimination, and charging the same rate for materially different risks fails Principle 3.

Further points:

The Statement lists considerations that commonly apply — exposure unit, data and its organization, homogeneity, credibility, loss development, trends, catastrophes, individual risk rating, and other influences such as regulatory and legislative changes — and says that informed actuarial judgment can be used effectively and may be applied throughout the process, documented and available for disclosure.
The four principles underlie the whole syllabus: developing and trending is Principle 1, the expense and profit provisions are Principle 2, classification and individual risk rating are Principle 3, and the departure from an indication for competitive or regulatory reasons is precisely where Principle 4 gets tested.

Applying the Principles to a Rate Build-Up An actuary projects a pure premium of $\$250$ , variable expenses of $20\%$ , fixed expenses of $\$38$ per exposure, and a target underwriting profit provision of $5\%$ .

Build the rate and identify which principle each step serves.
Answer
 $\begin{align*} \text{Rate} &= \frac{\$250 + \$38}{1 - 0.20 - 0.05} \\ &= \frac{\$288}{0.75} \\ &= \$384.00 \end{align*}$ 
Step Principle

The $\$250$ is projected — developed to ultimate and trended to the future policy period 1 — expected value of future costs

Expenses and profit are loaded, including the cost of capital 2 — all costs of the risk transfer

The $\$384$ is the rate for this class, derived from its own experience 3 — costs of the individual risk transfer

The rate is neither padded above nor cut below the estimate 4 — not excessive, inadequate or unfairly discriminatory

Step	Principle
The $\$250$ is projected — developed to ultimate and trended to the future policy period	1 — expected value of future costs
Expenses and profit are loaded, including the cost of capital	2 — all costs of the risk transfer
The $\$384$ is the rate for this class, derived from its own experience	3 — costs of the individual risk transfer
The rate is neither padded above nor cut below the estimate	4 — not excessive, inadequate or unfairly discriminatory

Which Principle Is Violated? Evaluate each practice.

(a) An insurer uses a five-year average of raw calendar-year loss ratios, with no development or trend, to set next year's rates. (b) A regulator caps homeowners rates $10\%$ below the indication in coastal territories and allows a $5\%$ increase inland to compensate. (c) An insurer charges the same rate to all commercial auto risks regardless of radius of operation, because splitting them "would be discriminatory". (d) An actuary omits the profit provision, reasoning that investment income will cover the cost of capital.

Answer (a) Principle 1. Raw historical loss ratios are neither developed nor trended, so they are an estimate of past costs, not of expected future costs. Immature years understate; the whole series is at the wrong cost level.

(b) Principle 4 — and it is the regulator's departure, not the actuary's. The coastal rate is inadequate and the inland rate excessive relative to the costs of each risk transfer; inland policyholders are subsidizing coastal ones. The actuary's obligation is to compute and disclose the indication; the constraint is then a documented departure from it (Ratemaking Constraints).

(c) Principle 3, on a misunderstanding of Principle 4. If long-haul risks cost twice what local risks cost, a single rate does not avoid unfairness — it makes local operators pay for long-haul exposure. Under Principle 4, a rate difference that is an actuarially sound reflection of expected cost is not unfairly discriminatory.

(d) Principle 2. Investment income is a legitimate offset and belongs in the derivation of the target underwriting profit provision — a long-tail line can support a lower $Q_T$ for exactly this reason. What it cannot do is justify a zero provision: capital still has a cost, and the rate must provide for it.