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in BUS 4027W - Actuarial Risk Management by

Please explain the statement:

"A company exposed to 100% of 5 risks faces greater claims volatility than one exposed to 50% of 10 risks." what is the process behind a company passing its risks to another? 

2 Answers

+1 vote
by (950 points)
edited by
On the statement:
It goes back to the old idea of 'not putting all your eggs in one basket.' The very aim of a reciprocal quota share is to diversify the risks you have on your books. This is because the factors that may make the claims experience on one sort of risk adverse may have little to no influence on another risk. An insurer that insured 1000 houses all in one town would be bankrupt if there was a hurricane that swooped through the town, whereas an insurer that insured 100 houses in 10 different towns (1000 in total) would be less likely to suffer the same risk

A simple example would be if you imagined two South African companies:
  • Company A is a small insurer which just entered the life space, they are currently selling term assurance cover. They conduct a claims analysis and find that they are experiencing more claims than expected. They find out that 80% of their policyholders live in Gauteng. 
  • Company B is a well-established life insurer.
  • Company A used standard South African mortality tables to come up with their rates. They realize that they are overexposed to GP specific risk and want to diversify their risk so that their experience more closely mimics the national experience. 
  • Company A would go to company B and enter into a treaty where they will pass over 40% of their term assurance business to the company B in exchange for an equal share of company B's term assurance business. 
  • Now company A's exposure to GP specific mortality risk has been reduced considerable. 
 
+1 vote
by (780 points)

My first response it to think about the law of large numbers. Generally speaking, as the number of risks gets larger, even if the exposure to them is lower, the insurer can more accurately estimate their total claims for a period and thus improve the predictability of their experience.

However: the aim of reciprocal quote share reinsurance is to diversify your risks, like Akani said. Two insurers would enter into an agreement to share their claims - they may be sharing the same insured risk (e.g. motor insurance - see Rowan's answer from last year here) but just now across a more diverse group of policyholders, e.g. geographically or by other factors. They could also be sharing different risks - exchanging a portion of a life insurance book for a portion of a motor insurance book.

The amount of capital the insurer needs to hold also decreases as diversification increases.

You asked about the process that takes place:

The two companies entering into the agreement will come up with their own terms -  they would swap a portion of the book such that the size of the risk ceded and the risk accepted are equal, i.e. the expected liabilities are the same for both parties. (See Landi's answer from 2017 here - she says that alternatively, both could decide on a premium to charge each other for taking on a portion of the other's risk.)


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