## The ins and outs of bulk annuities

The UK has a well developed and highly competitive market in bulk annuities. These typically arise when a defined-benefit pension scheme wants to insure its liabilities. The most obvious scenario is when a pension scheme is being wound up and benefits have to be secured with an insurance company.  Since the pension scheme is ceasing to exist, individual policies are purchased for each member. The now-former pension-scheme member owns his or her own annuity policy, which cannot be surrendered or transferred once annuity payments start.  All risks such as longevity and investment are transferred to the insurer in a transaction known as a buy-out.

However, there is another option called a buy-in — the scheme continues to exist and pay pensions, but with a single insurance policy covering the risks from many pensioners.  Here the policy is owned by the pension scheme, not the individual members, and the pension scheme then acts as a conduit for payments from the insurer to the pensioners.  As with the buy-out policy, the insurer bears the longevity and investment risks.

Both kinds of bulk annuity have their place, and each pension scheme will decide on its own strategy.  This includes partial buy-outs or buy-ins, i.e. covering only part of the scheme's liabilities, although there are some points to beware about selective buy-outs based on health.  However, buy-ins throw up some interesting challenges for an insurer's mortality investigations.  Buy-outs are like ordinary annuities — once payment starts, the only event which can happen to the policy is mortality.  With only one mode of exit, this leads to what actuaries call a single decrement analysis, and it can be done using either the force of mortality, μx, or the rate of mortality, qx.  In contrast, buy-ins are additionally at risk of surrender or transfer: it can and does happen that the owning pension scheme wants to cancel the policy.  This complicates mortality analysis involving buy-in annuities, as they are obviously at risk of two competing decrements: mortality and transfer.

Analysing mortality when there are competing decrements is problematic for a qx-style investigation.  For this reason, analysts performing a qx-style analysis will sometimes just exclude the data for buy-in annuities.  This is far from satisfactory, however, as ignoring data is an inefficient use of available resources.  However, additional assumptions have to be made if buy-in annuities are to be included in a qx model.  These assumptions are not always realistic, but they will always complicate the mathematics and sometimes cause errors.

Fortunately, there is a simple solution to including buy-in annuities in the mortality investigation: use a survival model for the force of mortality, μx.  For a mortality study, the surrender of a buy-in policy is simply a kind of censoring (the surrender event is unrelated to an individual's risk of mortality, so it is called uninformative censoring).  This has no impact on the model structure for μx-style analysis, whereas two or more decrements cause headaches for qx models.  In addition, survival models easily handle fractional years of exposure. By allowing a bulk-annuity insurer to use all of its available information, survival models deliver clear business benefits over qx-style analysis.

Jim O'Connor
(Feb 28, 2016)
Hi Thank you for your article, I work and live in the US and have been a licenced agent for 32 years, to understand your article can I conceptually think of "Buy Out"Bulk Annuities" used for ending Defined Benefit plans- as similar to a "terminal funded annuity". We also need approval from the Pension Benefit Guaranty Corporation "PBGC" and the IRS.

It is often used because the employer is concerned that they will not be able to fund the plan correctly, (under funded plans) and the cost to bring the plan whole is prohibitive for that employer so the employer will request to end the DB Plan. And hopefully, the terminal funded annuity will cost the least additional out of pocket cost for the employer to satisfy the IRS and the PBGC that the plan participants will recieve the benefits that were part of their contract at retirement.

If there is a similarty, (I appologise if my premise of similarity is incorect),then, are such products like Bulk annuities that you call 'Buy out Bulk annuities' used by employers similar to our terminal funded annuity plans?

Second question,just a few years ago in the US the immedite annuity market place created a new product, for the US that is, called a deferred immediate annuity, You purchase it today but it does not start until some distant time in the future, and because of this the actual rate of income stream is substantially larger than an immediate annuity Payment purchased at the time the person requests, or needs this product in retirement.

Does Scotand or the UK in general offer a deferred immediate annuity, similar to what I have suggested.
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