Formulae

Question 1

Earned premiums

Answer 1

Written premiums
- Change in UPR (end-begin)

Question 2

Claims incurred

Answer 2

Paid claims
+ change in reserves (end-begin)

Question 3

Expenses incurred

Answer 3

Paid expenses
+ change in reserves (end-begin)

Question 4

Underwriting profit

Answer 4

= earned premiums
- claims incurred
- expenses incurred

Question 5

Benefit payment after the principle of average

Answer 5

(sum insured) / (value of risk)
x
(loss amount)

Question 6

Proportion reinsured

Answer 6

(Net WP) / (Gross WP)

Or

(Net claims incurred) / (Gross claims incurred)

Question 7

Expense ratio

Answer 7

(Expenses paid) / (Net written premium)

Question 8

Loss ratio (claim ratio)

Answer 8

(Incurred claims) / (Earned premiums)

Or

(Claims paid from WP) / (Written premiums)

Question 9

Commission rate

Answer 9

(Commission paid) / (Net written premiums)

Question 10

Combined ratio (operating ratio or underwriting ratio)

Answer 10

Loss ratio + expense ratio

Question 11

Investment return ratio

Answer 11

(Investment return amount) / (Average assets held)

Question 12

Profit margin

Answer 12

(Insurance profit) / (NEP)

Question 13

Return on Capital

Answer 13

(Profit after tax) / (Reserves at the start of the period)

Question 14

Solvency ratio

Answer 14

(A - L) / (NWP)

Question 15

Assets to liabilities

Answer 15

A:L

Question 16

Claims settlement pattern

Answer 16

(Total outstanding claims reserve) / (Claims paid)

Question 17

The technical account (the revenue account)

Answer 17

Premiums earned
(Claims incurred)
(Expenses incurred)
Change in DAC

= Underwriting profit

+ Investment income

= Insurance profit

Question 18

Net premiums earned

Answer 18

Gross premiums written
(Reinsurance premiums paid)
(Change in UPR)

= Premiums earned

Question 19

Net claims incurred

Answer 19

Gross claims paid
(Reinsurance and other recoveries)
Change in RBNS

= claims incurred

Question 20

Net expenses incurred

Answer 20

Expenses paid
Change in expense provision
(Reinsurance commissions received)

= net expenses incurred

Question 21

The Profit and Loss account

Answer 21

Insurance profit
Other investment income
Profits from other activities
(Interest on loans)

= Profit before tax

(Tax)

= Profit attributable to shareholders

(Dividends)

= Retained profits

Question 22

The Balance Sheet

Answer 22

Fixed assets
Investments
Other current assets
= Total Assets

(Current liabilities)
(Deferred tax)
(Unearned premium reserve)
Deferred acquisition costs
(RBNS)
= (Total Liabilities)

= Shareholders’ Net Assets

Share capital
Share premium account
Profit and loss account
Revaluation reserve
= Shareholders’ funds

Question 23

Amount of return commission

Answer 23

= (return commission %)(proportion ceded).(premium)

Question 24

Ceding commission

Answer 24

= return commission + override commission

Question 25

Proportion retained under surplus reinsurance

Answer 25

a = (retention amount) / (total amount) for every risk ceded

Question 26

Largest risk the company can take on under surplus reinsurance

Answer 26

(maximum retention).(maximum number of lines)

= R.(1+L)

Question 27

When we want to cede the maximum amount of a risk under a surplus treaty

Answer 27

(EML)/(k+1) = size of each line.

Cede k and retain 1

Question 28

Rate on line (for XoL)

Answer 28

(total reinsurance premium charged, ignoring reinstatement premiums) / (width of layer)

Question 29

UPR

Answer 29

(Premium - Acquisition costs).(Proportion of risk period unexpired)

Question 30

AURR

Answer 30

Max(0, URR - UPR)

Question 31

Premium liability

Answer 31

The larger of (aggregate of UPR for all lines of business) and (best estimate of URR)

Question 32

Prediction variance

Answer 32

Process variance + Estimation variance

Question 33

Premium rate

Answer 33

1) premium income/expected loss

2) premium income/limit

3) premium income/exposure

4) premium income/risk-adjusted exposure

Question 34

Premium rate change

Answer 34

(Premium rate @T2 / Premium rate @ T1) - 1

Question 35

Lapse rate

Answer 35

(# lapses) / (# renewals invited)

Question 36

Renewal rate

Answer 36

(# renewals) / (# renewals invited)

Question 37

New business rate

Answer 37

(# new policies) / (# renewals invited)

Question 38

Strike rate

Answer 38

(# policies written) / (# quotes given)

Question 39

Not-take-up rate

Answer 39

(# policies not struck) / (# quotes given)

Question 40

Cancellation rate

Answer 40

1) (# policies cancelled) / (# policies exposed)
Gives a central rate

2) (# cancellations) / (# renewals invited)
Gives an initial rate

Question 41

Endorsement rate

Answer 41

(# endorsements) / (# policies exposed)

Question 42

Credibility-weighted estimate

Answer 42

Estimate of future claims =
Z.(observations) + (1-Z).(other information)

Z = credibility
1-Z = complement of credibility

Question 43

Burning cost premium

Answer 43

(total claims) / ( total exposed to risk)

Question 44

Effective burning cost premium

Answer 44

Burning cost using unadjusted data

Question 45

Indexed burning cost

Answer 45

Burning cost using adjusted data

Question 46

Pure risk premium

Answer 46

(expected claim frequency).(expected cost per claim)

[(#claims)/(#policies) ÷
(exposure)/(#policies)] x (total claim amount)/(#claims)

Question 47

Relative loss severity

Answer 47

Y = X/M

Relative loss severity = size of loss / size of risk

Question 48

Liability outgo

Answer 48

Total gross claim payments
(Reinsurance and other recoveries)
Expenses
(Outstanding premiums received)
Tax and dividend payments