Difference between revisions of "Formulas - Pricing"
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Refer ''[[Notation - Pricing]]'' for the list of symbols used in the pricing text. The link is also in the sidebar under ''Miscellaneous Battle Reports'', but just as a quick reminder: | Refer ''[[Notation - Pricing]]'' for the list of symbols used in the pricing text. The link is also in the sidebar under ''Miscellaneous Battle Reports'', but just as a quick reminder: | ||
| − | : '''X''' = | + | : '''X''' = Exposures ''(number of exposures)'', '''P''' = Premium ''(dollars), '''L''' = Losses ''(dollars)'' |
: '''EP''' = Earned Premium ''(dollars)'', '''WP''' = Written Premium ''(dollars) | : '''EP''' = Earned Premium ''(dollars)'', '''WP''' = Written Premium ''(dollars) | ||
| + | * ''Note that '''P''' can refer to either EP or WP, although in the formulas below it's more common to use EP. | ||
In the table below I also use: | In the table below I also use: | ||
: '''F''' = Frequency, '''S''' = Severity, '''LR''' = Loss Ratio, | : '''F''' = Frequency, '''S''' = Severity, '''LR''' = Loss Ratio, | ||
| − | : '''U/W''' as an abbreviation for Underwriting ''(so U/W | + | : '''U/W''' as an abbreviation for Underwriting ''(so U/W should <u>not</u> be interpreted as a formula U divided by W)'' |
{| class='wikitable' | {| class='wikitable' | ||
| Line 15: | Line 16: | ||
|| Frequency || ''counts / X'' || counts-per-exposure | || Frequency || ''counts / X'' || counts-per-exposure | ||
|- | |- | ||
| − | || Severity || L / counts || dollars-per-count | + | || Severity || ''L / counts'' || dollars-per-count |
|- style="border-bottom: 2px solid;" | |- style="border-bottom: 2px solid;" | ||
| − | || Pure Premium || <span style="color: red;">'''L / X'''</span> || = <span style="color: red;">'''F x S'''</span> | + | || Pure Premium || <span style="color: red;">'''''L / X'''''</span> || = <span style="color: red;">'''''F x S'''''</span> |
|- | |- | ||
| − | || Loss Ratio (LR) || L / P || P is usually EP ''(Earned Premium)'' | + | || Loss Ratio (LR) || ''L / P'' || P is usually EP ''(Earned Premium)'' |
|- | |- | ||
| − | || LAE Ratio || LAE / L || LAE includes ''[[Friedland16.ALAE | ALAE]]'' and ''[[Friedland17.ULAE | ULAE]]'' | + | || LAE Ratio || ''LAE / L'' || LAE includes ''[[Friedland16.ALAE | ALAE]]'' and ''[[Friedland17.ULAE | ULAE]]'' |
|- | |- | ||
| − | || Loss & LAE Ratio || <span style="color: red;">'''(L + LAE) / P'''</span> || = <span style="color: red;">'''LR x (1 + LAE Ratio)'''</span> | + | || Loss & LAE Ratio || <span style="color: red;">'''''(L + LAE) / P'''''</span> || = <span style="color: red;">'''''LR x (1 + LAE Ratio)'''''</span> |
|- | |- | ||
| − | || U/W Expense Ratio (UWER)<span style="color: red;"><sup>1</sup></span> || (Comm + Other + TLF) / WP + General / EP || uses both WP and EP | + | || U/W Expense Ratio (UWER)<span style="color: red;"><sup>'''1'''</sup></span> || ''(Comm + Other + TLF) / WP + General / EP'' || uses both WP and EP |
|- | |- | ||
| − | || Operating Expense Ratio (OER) || U/W Expense Ratio + LAE / EP || monitors operational expenditures | + | || Operating Expense Ratio (OER) || ''U/W Expense Ratio + LAE / EP'' || monitors operational expenditures |
|- style="border-bottom: 2px solid; background-color: palegreen; font-weight: 700;" | |- style="border-bottom: 2px solid; background-color: palegreen; font-weight: 700;" | ||
|| Combined Operating Ratio (COR) || LR + LAE / EP + U/W Expense Ratio || primary measure of profitability | || Combined Operating Ratio (COR) || LR + LAE / EP + U/W Expense Ratio || primary measure of profitability | ||
|- | |- | ||
| − | || Retention Ratio || ( # of policies renewed ) / ( # of potential renewal policies ) || measures loyalty | + | || Retention Ratio || ''( # of policies renewed ) / ( # of potential renewal policies )'' || measures loyalty |
|- | |- | ||
| − | || Close Ratio || ( # of accepted quotes ) / ( # of quotes ) || measures product attractiveness | + | || Close Ratio || ''( # of accepted quotes ) / ( # of quotes )'' || measures product attractiveness |
|} | |} | ||
| − | <span style="color: red;"><sup>1</sup></span> (Comm + Other + TLF) = Commissions & Brokerage + Other Acquisition Expenses + | + | <span style="color: red;"><sup>'''1'''</sup></span> ''(Comm + Other + TLF) = Commissions & Brokerage + Other Acquisition Expenses + Taxes, Licenses and Fees'' |
Latest revision as of 20:13, 8 April 2021
Refer Notation - Pricing for the list of symbols used in the pricing text. The link is also in the sidebar under Miscellaneous Battle Reports, but just as a quick reminder:
- X = Exposures (number of exposures), P = Premium (dollars), L = Losses (dollars)
- EP = Earned Premium (dollars), WP = Written Premium (dollars)
- Note that P can refer to either EP or WP, although in the formulas below it's more common to use EP.
In the table below I also use:
- F = Frequency, S = Severity, LR = Loss Ratio,
- U/W as an abbreviation for Underwriting (so U/W should not be interpreted as a formula U divided by W)
| Ratio | Formula | Alternate Term/Formula or Comment |
|---|---|---|
| Frequency | counts / X | counts-per-exposure |
| Severity | L / counts | dollars-per-count |
| Pure Premium | L / X | = F x S |
| Loss Ratio (LR) | L / P | P is usually EP (Earned Premium) |
| LAE Ratio | LAE / L | LAE includes ALAE and ULAE |
| Loss & LAE Ratio | (L + LAE) / P | = LR x (1 + LAE Ratio) |
| U/W Expense Ratio (UWER)1 | (Comm + Other + TLF) / WP + General / EP | uses both WP and EP |
| Operating Expense Ratio (OER) | U/W Expense Ratio + LAE / EP | monitors operational expenditures |
| Combined Operating Ratio (COR) | LR + LAE / EP + U/W Expense Ratio | primary measure of profitability |
| Retention Ratio | ( # of policies renewed ) / ( # of potential renewal policies ) | measures loyalty |
| Close Ratio | ( # of accepted quotes ) / ( # of quotes ) | measures product attractiveness |
1 (Comm + Other + TLF) = Commissions & Brokerage + Other Acquisition Expenses + Taxes, Licenses and Fees
