06/02/2012. Market Shocks! Week 2. Proportional Reinsurance: Operation & Application

Size: px

Start display at page:

Download "06/02/2012. Market Shocks! Week 2. Proportional Reinsurance: Operation & Application"

Randolph Lyons
5 years ago
Views:

1 Week 2 Proportional Reinsurance: Operation & Application Market Shocks! 1

2 What is the function of reinsurance? Methods of Reinsurance Facultative v Treaty also facultative obligatory arrangements and open covers Forms of Reinsurance Proportional Non-Proportional Quota Share Surplus Excessof-Loss Stop Loss 2

3 Reinsurer agrees fixed-quota (%) of all insurances policies. Quota determines how liability, premiums & losses are distributed. Simple & cost effective. Suitable for limiting the risk of random fluctuations and risk of change across an entire portfolio. young developing companies Reinsurer takes the risk of any incorrect estimates. Example 1 Direct insurer s retention 70% Reinsurance quota share 30% Sum insured (SI) of the insured object 10 million Direct insurer retains 70% of the exposure 7 million Reinsurer assumes 30% of the exposure 3 million Premium rate is 2% 0 of the SI Direct insurer retains 70% Reinsurer receives 30% 6000 Loss 6 million Direct insurer pays 70% 4.2 million Reinsurer pays 30% 1.8 million Motor quota share treaties normally cover: Motor third party liability (TPL); and Motor own damage (MOD). Pricing procedure The technical premium is the premium the reinsurer needs to charge in order to carry on its business. The commercial premium is the premium that is actually charged for a specific treaty in a given instance. Dependent on market conditions. 9 3

4 Technical premium is the sum of: Risk premium; Fluctuation loading; and Expense loading. Reinsurance premium is always expressed indirectly via a commission. Price quoted in terms of reinsurance commission. Intended to compensate the direct insurer for his agent s commissions, internal administration expenses & loss adjustment costs. Example 2 Direct Insurer (DI) expects losses of 60m,. operating costs of 30m, & expects profits of 10m, Required original premium is 100m. Cedes 25% (under a quota share) to a RE. Reinsurer receives a premium = 25m - Expects to pay out 25% of 60m = 15m -Profit Margin (10%) = 2.5m Reinsurance commission = 7.5m It is dependent on claims experience over the life of the treaty, e.g. it is possible that actual claims are higher than expected claims. 4

5 Lets say actual claims are 64m Reinsurer receives a premium = 25m - Actually pays out 25% of 64m = 16m -Profit Margin (10%) = 2.5m Reinsurance commission = 6.5m Commission is paid retrospectively. Reinsurer does not participate in all risks. Direct insurer retains all risks up to a certain amount of liability. Upper limit on reinsurer s obligation to accept risk. That limit is defined as a multiple of the direct insurer s retention (lines). 14 According to the terms of the treaty, the cedent has a limit of on any risk and the reinsurer s liability is limited to 9 lines. Example 1: The cedent s original liability amounts to 3m; the premium is 0.15% (of the sum insured) and the loss is 1.5 million. Example 1 Total Cedent s (1 line) Reinsurer s surplus Sum insured/liability = 10% = 90% (9 lines) Premium = 10% = 90% Loss = 10% = 90% 5

6 Example 2: The cedent s original liability is , the premium is 0.15% and the loss is Example 2 Total Cedent s Reinsurer s (1 line) surplus Sum insured/liability = 100% 0 =0% Premium = 100% 0 = 0% Loss = 100% 0 = 0% Example 3: The cedent s original liability is , the premium is 0.15% and the loss is Example 3 Total Cedent s (1 line) Reinsurer s surplus Sum insured/liability = 8.57% = 14.29% =77.14% (9 lines) Premium = 22.86% = 77.14% Loss = 22.86% = 77.14% Quota Share Quota share treaty is agreed at the start of the insurance period. Expected losses = 55m, Operating costs = 20m, and Profit = 25m Required premium = 100m The Quote Share Treaty identifies a 75:25 split between the cedent (direct insurer) and the reinsurer respectively. 6

7 Why would the DI opt for quota share re.? Gives freedom to write business, Part of the actuarial risk is transferred to the RI, A fixed percentage of expected losses (25%) will be paid by RI. Assuming market conditions remain constant, what will be the value of the RI commission? RI receives premium = 25m (25% of 100m), RI expected profit margin is 25% ( 25m x 0.25 = 6.25m), Expected RI losses 13.5m (25% of 55m). RI Commission = 25m- 13.5m = 11.5m m = 5.25m 19 Quota Share What is the outcome if direct premiums are reduced by 15% ( 15m)? RI now receives 25% of 85m over the life of the treaty ( 21.25m). Expected losses remain the same: 13.5m. RI Commission is now reduced: ( m) = 7.75m, RI profit margin = 6.25m. Commission = 1.5m Thus the DI would absorb the entire discount of 15m which he granted to policyholders to keep the business. 20 Quota Share As part of a surplus treaty, the following is agreed: Cedent s (Direct Insurer) retention 1m Reinsurer s liability is limited to 3 lines What is the allocation of losses in the following examples? A: SI 2.3m Loss 1.8m, B: SI Loss 800,000m, C: SI 5m Loss 4.79m. 21 7

8 Risk 1: SI = 2.3m, Loss 1.8m Cedent (Direct Insurer) 1m Retention as a proportion of entire risk 2.3m 43.47% x 1.8m = 782, % Reinsurer Retention as a proportion of entire risk 56.52% x 1.8m = 1,017, m 2.3m 56.52% 22 Risk 2. SI = 850,000, Loss 800,000m DI pay out = 100% x 800,000 = 800,000m. Risk 3. SI = 5m, Loss 4.79m Cedant (Direct Insurer) 1m Retention as a proportion of entire risk 20.00% 5m 1m + outside terms of treaty 20.00% 5m 40% x 4.79m = 1.916m Reinsurer 3m Retention as a proportion of entire risk 60.00% 5m 60% x 4.79m = 2.874m 8

Rating and Ratemaking

Rating and Ratemaking Ratemaking refers to the pricing of insurance and the calculation of insurance premiums A rate is the price per unit of insurance An exposure unit is the unit of measurement used