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

  1. 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
  2. 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
  3. 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?
  4. 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.

Practical Example / Solution Capacity / $
An insurer has arranged a five line surplus treaty and a two line 2nd surplus treaty. A risk with a sum insured of $10 million is offered of which the insurer only intends to retain only $1 500 000 for its own account. Reinsurer X takes 10% of the 1st surplus and 25% of the 2nd surplus treaty. What sum is reinsurer X liable for? / Retention
1st surplus (five times retention)
2nd surplus (twice retention) / 1 500 000
7 500 000
3 000 000

Treaty capacity $12 million

Risk apportionment as follows

  • Retention$1 500 000
  • 1st surplus$7 500 000
  • 2nd surplus treaty$1 000 000
  • Total$10 000 000

Reinsurer X has (10% of $7 500 000)$750 000

(25% of $3 000 000)$750 000

Total$1 500 000

  1. 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 / Sum Insured ($) / Premium
3rd / 3 000 000 / 75 000
2nd / 1 000 000 / 500 000
1st / 900 000 / 3 000 000
Retension / 100 000 / 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 / Sum Insured ($) / Comment
3rd / Nil / Loss did not exceed $2 000 000
2nd / 750 000 / Paid by reinsurers
1st / 900 000 / 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.

  1. The insurer has issued apolicy 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 / Amount
3rd layer / $40million / Reinsurer
2nd layer / $30 million / Reinsurer
1st layer / $20 million / Reinsurer
retention / $10 million / Insurer
  1. 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.
  2. 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$40million x 150% = $60million

Claim to layer$60million-$40million = $20million x 90%=$18million

2nd layer$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

  1. 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 reinsurerx 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 reinsurersXannual premiumx9 months

security12 months

500 000x$200 0009= $37 500 payable

2000 00012