Reinsurance tutorials
1. Makaza pays a premium of $120 for her car insurance to Bhachi Insurance Company. The
sum insured is $12 000. Bhachi Insurance Company retains $4 000 and cedes the rest. If it is
a proportional insurance arrangement, how much premium will Bhachi Insurance pay to the
reinsurer?
Answer. 2/3 of $120
2. A cedant has an 80% quota share applying to a risk of $50 000. What is the monetary value
of the retention? Answer, 20% of $50 000 =$10 000
3. A ceding company has a 40% quota share treaty. It accepts a risk and receives a premium of
$6 000. How much premiums do the reinsurers receive. Answer, 40% of $6 000
4. If a claim occurs on the risk described in 3 above, the company has to pay $10 000. How
much will they recover from its quota share reinsurance?
5. As an insurer, you have a six line surplus treaty with a retention of $200 000. You are not
very happy with the risk so you lower you retention to $100 000. How much can you pass on
to reinsurers on this risk and what will be your gross acceptance? Answer $700 000.
6.
Practical Example
Solution Capacity
$
An insurer has arranged a
Retention
1 500 000
five line surplus treaty and a
two line 2nd surplus treaty. A 1st surplus (five times
7 500 000
risk with a sum insured of
retention)
$10 million is offered of
which the insurer only
intends to retain only $1 500
000 for its own account.
2nd surplus (twice retention)
3 000 000
Reinsurer X takes 10% of the
1st surplus and 25% of the 2nd
surplus treaty. What sum is
reinsurer X liable for?
Treaty capacity $12 million
Risk apportionment as follows
 Retention
 1st surplus
 2nd surplus treaty
 Total
Reinsurer X has (10% of $7 500 000)
(25% of $3 000 000)
Total
$1 500 000
$7 500 000
$1 000 000
$10 000 000
$750 000
$750 000
$1 500 000
7. An insurance company has a 10 line surplus treaty for its theft account. A theft policy is
issued to a client for a theft account for $200 000. The insurer retains 40 000. A CLAIMED IS
AGREED FOR $20 000. Explain what recovery if any the insurer could make from reinsurers.
Answer = [1 – (40/200)] *20 000 = $16 000
Reinsurance Commission.
This is paid by reinsurers to a cedant for the costs the cedant incurs in acquiring business. It
is paid only in proportional business.
Profit commission
Profit commission is extra commission paid to cedant over and above the flat rate
commission, based on the net profit made by the reinsurer from the treaty.
Sliding scale commission
Sliding scale commission is another technique which attempts to maintain a reasonable
relationship between cedant and reinsurer as far as the payment of equitable commission is
concerned.
Loss participation
Loss participation, also known as MALUS clause, is a form of reverse profit commission.
Under this arrangement a share of losses under a proportional treaty must be borne by the
cedant in the event of a loss ratio exceeding an agreed percentage.
Non Proportional treaties
1. The insurer has a working excess of loss treaty. He wants to retain $100 000 any one loss for
its own account. The maximum valued vehicle in the account is $5 000 000. The working
excess of loss treaty could be structured as follows:
Layer
3rd
2nd
1st
Retension
Sum Insured ($)
3 000 000
1 000 000
900 000
100 000
Premium
75 000
500 000
3 000 000
8 000 000
The premium for each layer varies as the reinsurers in the third layer, for example only
become involved if the loss exceeds $2 000 000. A vehicle valued at $4 500 000 is damaged
and the cost payable is assessed at $1 750 000.
The loss will be calculated as follows:
Layer
3rd
Sum Insured ($)
Nil
2nd
1st
750 000
900 000
Comment
Loss did not exceed $2 000
000
Paid by reinsurers
Paid by reinsurers
Retension
100 000
Paid by the insurer
The insurer may decide that he cannot afford to pay more than 50 times the amount of $100
000. Therefore he will purchase catastrophe excess of loss. That is the retention will be $100
000 times 50 = $5 million.
2. The insurer has issued a policy covering a very large building valued at $100 million. The
insurer has the financial strength to be able to retain for his own account $10 million. He
therefore arrange catastrophe reinsurance as follow:
Layer
3rd layer
2nd layer
1st layer
retention
Amount
$40million
$30 million
$20 million
$10 million
Reinsurer
Reinsurer
Reinsurer
Insurer
3. The insurer has the stop loss treaty protecting his growth account. The stop loss treaty cover
will pay 90% of all claims which exceed 100% of the premium up to maximum of 150% of the
premiums. the annual premium income for 2009 was $30million. The losses are $36 million
the loss ratio is therefore 120%. Total loss is $36million - $30 million = $6million.treaty pays
90% of $6million which $5,4million.
4. Estimated premium income $30 million
1st layer to pay 90% of all claims which exceed 100% of premiums up to 150% of premiums
subject to a maximum amount of $18million, whichever is the lesser.
2nd layer to pay 100% of all claims which exceed 150% of premiums up to 200% subject to a
maximum amount of $16million, whichever is the lesser.
Let us assume that the premium income reaches $40 million, but claims amount to
$70million, resulting in a loss ratio of 175%. The loss would, in this instance, be allocated
over the two layers as follows:
Total loss $70million
1st layer
Claim to layer
2nd layer
$40million x 150% = $60million
$60million-$40million = $20million x 90%=$18million
$70million -1st layer limit $60million = $10million
100% x$10million =$10million which is less than the maximum of
$16million.
So the end result or allocation of payments looks like this;
Insured
$40 million
Plus
$2 million (10% of layer)
Total
$42 million
1st layer
$18 million
2nd layer
$10 million
Total
$70 million
5. A cover is for $2 million in excess of $1 million per event. It runs for 12 months from 1
January at a premium of $200 000. An event in 31 March causes an aggregate loss of $1 500
000. Calculate the premium required for reinstatement.
 The reinstatement provision is prorate to as to amount only.
 The reinstatement provision is pro rata as to both amount and time.
Solution
Cover $2 million and excess per event $1 million with premium of $200 000. Loss to
reinsurers: $500 000
Pro rata as to amount
Loss to reinsurer x annual premium
Security
500 000 x 200 000
=
$50 000
2 000 000
Pro rata as to amount and time
The loss happened on 31 March leaving nine months of the reinsurance cover to run after
reinstatement.
Loss to reinsurers
X
annual premium
security
500 000
2000 000
x
9 months
12 months
x
$200 000
9
12
= $37 500 payable