Actuarial Notes

Non-Pricing Solutions

Study guide: Exam 5

Non-Pricing Solutions are actions that bring the fundamental insurance equation back into balance by reducing costs — expenses or expected losses — rather than by raising rates. Werner & Modlin present them in Implementation, alongside the pricing solutions, as a response to an indication the company cannot or will not take in full — see Considerations for Implementing Rates.

\bar{P}_I = \frac{\bar{L} + \bar{E}_F}{1 - V - Q_T}

  • \bar{P}_I is the indicated average premium, \bar{L} the expected loss and LAE per exposure, \bar{E}_F the fixed expense per exposure, V the variable expense provision and Q_T the target profit provision (the pure premium form of the indication). A pricing solution raises the current average premium toward \bar{P}_I; a non-pricing solution lowers \bar{P}_I toward the current premium.
  • Reduce expenses — underwriting or LAE: a smaller marketing budget, lower staffing, lower acquisition cost. This lowers \bar{E}_F or V.
  • Reduce expected losses in three ways:
    • Change the portfolio — tighten underwriting criteria, or non-renew policies whose premium is grossly inadequate. Premium leaves along with the losses, so it helps only if the loss reduction exceeds the premium reduction.
    • Reduce coverage — a coverage level change such as excluding mold from homeowners. Removing previously covered loss without lowering the rate is equivalent to a rate increase.
    • Better loss control — for example, medical management and return-to-work programs that stop workers compensation disability claims escalating.
  • When they are used: where rates are promulgated or increases are hard to obtain, companies often run the indication but act on it through non-pricing levers; where a full increase would damage retention and new business (see Ratemaking Constraints, Lifetime Value), they supplement a partial increase. Catastrophe concentration is managed the same way — restricting new business in exposed areas, requiring higher catastrophe deductibles, buying reinsurance.
  • After any such action the losses, expenses and premium are re-projected and the indication recomputed. Underwriting and coverage changes act only as policies renew, so they take a full term to earn in.

Closing a Capped Indication Expected loss and LAE are \$420 per exposure, fixed expenses \$35, variable expenses 22\% of premium and the target profit 5\%. The current average premium is \$580 and the regulator will approve at most +3\%.

Find the indication, and what non-pricing action alone would close the gap at +3\%.

Answer

\begin{align*}
\bar{P}_I &= \frac{\$420 + \$35}{1 - 0.22 - 0.05} = \frac{\$455}{0.73} \\
&= \$623.29 \quad (+7.5\%) \\
\text{Approved premium} &= \$580 \times 1.03 = \$597.40
\end{align*}

Solve for each lever with the others fixed:

\begin{align*}
V &= 1 - 0.05 - \frac{\$455}{\$597.40} = 18.8\% \\
\bar{L} &= \$597.40 \times 0.73 - \$35 = \$401.10
\end{align*}

Either variable expenses fall by 3.2 points (a commission cut, say) or expected losses fall 4.5\% (a coverage restriction or loss control program). A mix — losses -2\% and fixed expenses down to \$30 — gives \bar{P}_I = (\$411.60 + \$30)/0.73 = \$604.93, still 1.3\% above the approved level; the remaining shortfall is accepted as a lower profit until the next filing.

Non-Renewing an Inadequate Segment The book has 10{,}000 policies at an average premium of \$580 and expected loss of \$420 (same expense and profit assumptions). A segment of 800 policies averages \$700 of premium and \$900 of expected loss. The company non-renews the segment. Recompute the indication, first with fixed expenses per policy unchanged, then with total fixed expenses of \$350{,}000 unchanged.

Answer

\begin{align*}
\bar{L} &= \frac{\$4{,}200{,}000 - \$720{,}000}{9{,}200} = \$378.26 \\
\bar{P} &= \frac{\$5{,}800{,}000 - \$560{,}000}{9{,}200} = \$569.57 \\
\bar{P}_I &= \frac{\$378.26 + \$35}{0.73} = \$566.11
\end{align*}

The indication moves from +7.5\% to -0.6\%: a segment running a 129\% loss ratio was absorbing the whole gap.

But fixed costs do not leave with the policies. Spreading \$350{,}000 over 9{,}200 policies gives \$38.04 each:

\bar{P}_I = \frac{\$378.26 + \$38.04}{0.73} = \$570.27

which is +0.1\%. The action still works, but part of its benefit is given back as the fixed expense load rises. Werner's caution is that a portfolio change moves premium as well as losses; fixed costs, being fixed in total rather than per policy, move the per-exposure load too.