Expense Ratio

Study guide: Exam 5

Expense Ratio is underwriting expenses as a share of premium — the non-claim cost of writing and servicing business. Together with the loss and LAE ratio it makes up the combined ratio.

\text{UW Expense Ratio} = \frac{\text{Underwriting Expenses}}{\text{Premium}}

\text{Operating Expense Ratio} = \text{UW Expense Ratio} + \frac{\text{LAE}}{\text{Earned Premium}}

• The historical combined ratio puts all underwriting expenses over written premium. For the underwriting expense ratio itself, Werner splits the categories by when they are incurred: those incurred at the onset of the policy (commissions, other acquisition, taxes, licenses and fees) are measured against written premium, those incurred throughout the policy (general expenses) against earned premium, and the category ratios are added.
• The operating expense ratio adds all loss adjustment expense — allocated and unallocated — to the underwriting expense ratio, as a ratio to earned premium: it is the share of each premium dollar spent on loss adjustment and underwriting expenses. Companies may also put LAE in the loss ratio (a loss and LAE ratio); whichever is done, LAE must be counted once, so a loss ratio combined with the OER must exclude it.
• For ratemaking, where both kinds are material, the ratio is split into fixed and variable components, because they enter the rate formula in different places — see Expense Provisions.
• The mix of expenses depends on distribution. A national direct writer may incur significant other acquisition costs for advertising; an agency-based company relies more on its agents to generate new business, so its other acquisition costs are lower, but at least partially offset by higher commissions.
• The choice of denominator matters little when volume is stable, since written and earned premium are then about equal. In a growing (or shrinking) book, written premium runs proportionately above (or below) earned, and so do acquisition costs — which is why expenses incurred at the onset of the policy are matched to written premium.

Underwriting, Operating and Combined Ratios An insurer reports: written premium \$46{,}000{,}000; earned premium \$40{,}000{,}000; commissions \$6{,}900{,}000; premium taxes \$1{,}150{,}000; other acquisition \$1{,}840{,}000; general expenses \$2{,}530{,}000; losses \$25{,}600{,}000; ALAE \$2{,}000{,}000; ULAE \$1{,}600{,}000.

Compute the expense ratio, operating expense ratio and combined ratio.

Answer Underwriting expenses total

\$6{,}900{,}000 + \$1{,}150{,}000 + \$1{,}840{,}000 + \$2{,}530{,}000 = \$12{,}420{,}000

\begin{align*}
\text{UW expense ratio (all to written)} &= \frac{\$12{,}420{,}000}{\$46{,}000{,}000} = 27.0\% \\[6pt]
\text{LAE ratio to earned} &= \frac{\$2{,}000{,}000 + \$1{,}600{,}000}{\$40{,}000{,}000} = 9.0\% \\[4pt]
\text{Operating expense ratio} &= 27.0\% + 9.0\% = 36.0\% \\[6pt]
\text{Loss ratio} &= \frac{\$25{,}600{,}000}{\$40{,}000{,}000} = 64.0\% \\[4pt]
\text{Combined ratio} &= 64.0\% + 9.0\% + 27.0\% = 100.0\%
\end{align*}

The book breaks even on underwriting. The combined ratio is also the loss ratio plus the OER, 64.0\% + 36.0\% = 100.0\% — which is why the loss ratio in it must exclude LAE: both ALAE and ULAE are already in the OER, and counting either in the loss ratio as well would double count it.

Splitting the Ratio for Ratemaking Using the same expenses, the insurer judges general expenses to be 75\% fixed and other acquisition 50\% fixed; commissions and taxes are fully variable. Projected average premium is \$800.

Derive V and the fixed expense per exposure.

Answer As percentages of the appropriate premium base (written for commissions, taxes and acquisition; earned for general):

\begin{align*}
\text{Commissions} &= 15.0\% \text{ (written)} \\
\text{Taxes} &= 2.5\% \text{ (written)} \\
\text{Other acquisition} &= 4.0\% \text{ (written)} \\
\text{General} &= 6.3\% \text{ (earned)}
\end{align*}

\begin{align*}
V &= 15.0 + 2.5 + (4.0 \times 0.5) + (6.3 \times 0.25) \\
&= 15.0 + 2.5 + 2.0 + 1.6 \\
&= 21.1\% \\[6pt]
F\% &= (4.0 \times 0.5) + (6.3 \times 0.75) \\
&= 2.0 + 4.7 = 6.7\% \\[4pt]
F &= 0.067 \times \$800 = \$53.60 \text{ per exposure}
\end{align*}

The total, 21.1\% + 6.7\% = 27.8\%, is the underwriting expense ratio with general expenses on earned premium, which is why it differs from the 27.0\% of the first example, where every category is over written premium. The split into 21.1\% variable and \$53.60 fixed is what the rate formula needs. Only the split tells you how the cost should be distributed across a \$300 policy and a \$3{,}000 one.