Retrospective Rating

Study guides: Exam 5, Exam 8, Exam GI-301

Retrospective Rating adjusts a policy's premium after the period, based on the insured's own losses during that period, within a guaranteed minimum and maximum. Unlike experience rating, which uses past years to price the coming one, a retro plan charges the insured for its own current-year experience.

$R = \left(\text{BP} + L \times \text{LCF}\right) \times \text{TM}$

$\text{Retro Premium} = \min\!\left(\max(R,\, R_{\min}),\, R_{\max}\right)$

Basic premium (BP) covers the insurer's non-LAE expenses, profit, and the net insurance charge — the cost of the maximum and minimum guarantees. It is expressed as a basic premium factor times standard premium.
Converted losses $(L \times \text{LCF})$ are the insured's reported losses $L$ , limited by any per-accident limit, multiplied by the loss conversion factor, which loads them for the ALAE not already in the losses plus ULAE.
Tax multiplier (TM) grosses the whole thing up for premium taxes and related assessments.
When the plan limits individual losses (a per-accident loss limitation), the insured pays for that limit too: its cost is either built into the table of insurance charges or, in some plans, computed as a separate additional charge.
The maximum protects the insured against a bad year, the minimum protects the insurer against a good one. Together they define how much risk is actually transferred; a plan with a tight max/min band is close to guaranteed cost, a wide one close to self-insurance. The net insurance charge in the basic premium — the insurance charge for the maximum less the insurance savings for the minimum — is the price of that band; the charge and savings come from a table of values, expressed as a percentage of expected unlimited losses (deriving the table is beyond Werner's scope).
Retro plans suit large accounts with credible volume, and they align incentives directly: every dollar of loss inside the band costs the insured $\text{LCF} \times \text{TM}$ dollars of premium. Conceptually a retro plan is close to self-insurance, except that its loss limits and its maximum and minimum leave some risk with the insurer.

Computing a Retrospective Premium A workers compensation policy has standard premium of $\$500{,}000$ , basic premium $\$100{,}000$ , loss conversion factor $1.10$ , tax multiplier $1.03$ , minimum retro premium $\$300{,}000$ and maximum $\$800{,}000$ . Actual limited losses are $\$350{,}000$ .

Compute the retro premium.
Answer
 $\begin{align*} R &= \left(\$100{,}000 + \$350{,}000 \times 1.10\right) \times 1.03 \\ &= \left(\$100{,}000 + \$385{,}000\right) \times 1.03 \\ &= \$485{,}000 \times 1.03 \\ &= \$499{,}550 \end{align*}$ 
This lies between the $\$300{,}000$ minimum and the $\$800{,}000$ maximum, so the final premium is $\$499{,}550$ — slightly below the $\$500{,}000$ standard premium, reflecting losses close to but a little better than expected.

How the Band Changes the Risk Transfer Using the same plan parameters, compute the retro premium at limited losses of $\$100{,}000$ , $\$350{,}000$ and $\$900{,}000$ , and describe what the insured is actually buying.
Answer
 $\begin{align*} \text{Losses } \$100\text{K}: \; R &= (100 + 110) \times 1.03 = \$216{,}300 \\ &\Rightarrow \text{floored at } \$300{,}000 \\[6pt] \text{Losses } \$350\text{K}: \; R &= \$499{,}550 \\[6pt] \text{Losses } \$900\text{K}: \; R &= (100 + 990) \times 1.03 = \$1{,}122{,}700 \\ &\Rightarrow \text{capped at } \$800{,}000 \end{align*}$ 
Inside the band, each extra dollar of loss costs the insured

$1.10 \times 1.03 = \$1.133$

Outside it, nothing. So the insured is buying:

Full retention of losses between roughly $\$174$ K and $\$615$ K — the loss levels that map to the minimum and maximum, from $(100 + 1.10L)(1.03) = 300$ and $= 800$ ,

Insurance above $\$615$ K — the insurer absorbs the $\$322{,}700$ excess in the third scenario,

and it gives up the benefit of results better than $\$174$ K, which is what pays for that protection.

The net insurance charge inside the basic premium is precisely the expected value of that asymmetry. Widen the max and the charge falls; tighten it and the plan converges to a guaranteed-cost policy at a guaranteed-cost price.