In-Force

Study guides: Exam 5, Exam GI-101

In-Force describes the policies, exposures or premium that are actively providing coverage at a single point in time — a stock measured at a date, as opposed to the flows of written and earned business measured over a period.

$\text{In-force at date } t = \sum_{\text{policies}} \mathbf{1}\{\text{effective} \le t < \text{expiration}\}$

$\text{In-force premium} = \sum \text{full-term premium of policies in force}$

Written, earned and in-force answer three different questions. Written counts what was sold during the period, earned counts the coverage actually provided during the period, and in-force counts what is on the books right now — see Written Premium and Earned Premium.
In-force premium is the full-term premium of each policy in effect at the date — the policy's own term, not an annualized one — so a six-month policy carrying $\$400$ of premium contributes $\$400$ . Books written on different terms are therefore not directly comparable: of two insurers writing the same written premium, one on annual and one on semi-annual policies, the semi-annual writer's in-force premium is half the other's. After a mid-term change, in-force premium is the full-term premium applicable on the date.
In-force exposures count the insured units exposed to loss at the date — a snapshot with no regard to the duration of the exposure. Companies define the insured unit differently: items such as cars (a three-car policy is three in-force exposures), policies, or written exposures.
As the best estimate of the company's mix of business at a date, the latest in-force premium is used to measure the impact of a rate change on the existing portfolio, and the latest in-force distribution is normally the estimate of the distribution expected while new rates are in effect. Where earned premium by territory is unavailable, in-force premium by territory may stand in for it.
Changes in average premium, once adjusted for rate changes, show changes in the mix of business written; comparing successive in-force snapshots separates the change in volume (policy count) from the change in average premium.
Renewal analysis works on the in-force book too: the retention ratio is policies renewed $\div$ potential renewal policies, and rate scenarios for the renewal portfolio are tested on the in-force distribution — see also lifetime value analysis, which allows for the fact that not all insureds renew.

Reading an In-Force Snapshot At $6/30/2024$ an insurer's auto book contains:

Policy Term Premium

A $1/1/2024$ – $12/31/2024$ $\$1{,}200$ (annual)

B $3/1/2024$ – $2/28/2025$ $\$900$ (annual)

C $7/1/2024$ – $6/30/2025$ $\$1{,}000$ (annual)

D $4/1/2024$ – $9/30/2024$ $\$500$ (six-month)

Compute the in-force policy count and in-force premium at $6/30/2024$ .

Answer A policy is in force if its effective date is on or before $6/30/2024$ and its expiration is after it.

A — in force ( $1/1$ to $12/31$ ) ✓

B — in force ( $3/1$ to $2/28/2025$ ) ✓

C — not in force; coverage begins $7/1/2024$ ✗

D — in force ( $4/1$ to $9/30$ ) ✓

$\text{In-force count} = 3$

Each policy in force contributes its full-term premium — D its six-month $\$500$ , not an annualized $\$1{,}000$ :

$\text{In-force premium} = 1{,}200 + 900 + 500 = \$2{,}600$

Note that C will count in CY 2024 written premium (its effective date is in 2024) even though it is not in force on $6/30$ , and D is earning premium right now — three different answers from the same four policies.

Policy	Term	Premium
A	$1/1/2024$ – $12/31/2024$	$\$1{,}200$ (annual)
B	$3/1/2024$ – $2/28/2025$	$\$900$ (annual)
C	$7/1/2024$ – $6/30/2025$	$\$1{,}000$ (annual)
D	$4/1/2024$ – $9/30/2024$	$\$500$ (six-month)

Separating Growth from Rate An insurer reports the following homeowners in-force figures:

Date Policies in force In-force premium

$12/31/2023$ $40{,}000$ $\$52{,}000{,}000$

$12/31/2024$ $42{,}000$ $\$58{,}800{,}000$

Decompose the $13.1\%$ premium growth.
Answer
 $\begin{align*} \text{Avg premium 2023} &= \frac{\$52{,}000{,}000}{40{,}000} = \$1{,}300 \\[4pt] \text{Avg premium 2024} &= \frac{\$58{,}800{,}000}{42{,}000} = \$1{,}400 \end{align*}$ 
 $\begin{align*} \text{Exposure growth} &= \frac{42{,}000}{40{,}000} - 1 = +5.0\% \\[4pt] \text{Average premium growth} &= \frac{1{,}400}{1{,}300} - 1 = +7.7\% \end{align*}$ 
Check: $1.050 \times 1.077 = 1.131$ , the $+13.1\%$ total.

The $+7.7\%$ is not all rate. It is rate change plus premium trend from shifts in mix such as amounts of insurance. Only once the premium is restated at current rate level does the change in average premium show the change in mix; attributing all of it to rate would assume the book is $7.7\%$ better priced than it is.

Date	Policies in force	In-force premium
$12/31/2023$	$40{,}000$	$\$52{,}000{,}000$
$12/31/2024$	$42{,}000$	$\$58{,}800{,}000$