Economics and similar, for the sleep-deprived

A subtle change has been made to the comments links, so they no longer pop up. Does this in any way help with the problem about comments not appearing on permalinked posts, readers?

Update: seemingly not

Update: Oh yeah!

Wednesday, October 02, 2002

Come as you are, pay as you go

Hello and welcome to "the Brad DeLong comments section defunct debates annex", or as it used to be known, "D-Squared Digest". If you're not a regular of the BDeL site, then the chances are that you're not confused the difference between defined contribution (DC) pension schemes and defined benefit (DB) schemes. But, for contributors to that site, sufferers from head injuries and anyone who has read a Cato pamphlet in the last two weeks (actually thinking about it, that probably constitutes a head injury), here's my best shot at explaining the matter simply.

The problem is simple; you want your employer to keep paying you after you stop working. I'm now going to offer a menu of alternative ways in which this aim can be satisfied:

1) Every month with your pay packet, your employer gives you an "extra" bit of money (perhaps with a different tax treatment to the rest of your wages) which you invest in a portfolio of bonds and equities. The size of the extra bit of money is determined by the amount which an actuary estimates you would need to invest every month to expect a retirement income equal to (say) half your salary on retiring.

This is a 401(k) style scheme

2) The same as 1), but the employer also offers you a deal; they will guarantee that if the investment return on your portfolio turns out to be not quite enough to give you that income on retiring, they will make up the difference. In return for this, they will probably want to take some of the upside if your portfolio does incredibly well. You have considerable legal protection in this matter; they can't lift any assets at all out of the portfolio without your consent, so you'll be in a decent position to negotiate with them when the time comes.

This is not a scheme which resembles anything in actual use, but it has some defined benefit elements.

OK, right now, before we get into anything more realistic, let's note one thing; it is absolutely clear that 2) is less risky than 1). Plan 2) is just plan 1), plus an arrangement with the company which can only decrease the volatilty of investment returns to you. You might think you could do better in terms of expected return under 1), but it cannot be lower risk than 2), because any portfolio you could have under 1), you can have under 2), and the guarantee can't make that portfolio more risky. Also note that you need to think about your risk/reward tradeoff not right now, but at retirement -- as in, if you make a huge killing on dot com stocks in your Plan 1) pension, you're unlikely to live long enough to spend it.

That's why we know that less of the investment risk is borne by employees under a DB plan than a DC

Just to re-emphasise this, the risk that your employer will go bankrupt and not be able to honour the guarantee is not an additional risk under 2), because if this happens,, 2) just collapses into 1). It would be a risk under this plan, not on the menu ...

minus 1) Your employer just goes on paying you after you retire

A "book reserve" pension scheme, popular in some European countries, albeit usually operated on an industry-wide basis rather than company-specific

... but that's not a DB plan. Anyway ....

The problem with 1) and 2) is that you will be restricted in what you can invest in as you get older, because you will want to be taking less risk. Also, your own personal portfolio is unlikely to be large enough to provide optimal diversification, leaving you bearing risks with no corresponding reward (I'm assuming orthodox finance theory here, give me a break). Because of this, your employer will offer you two other menu items:

3) A "pooled" version of 1). Under this scheme, your extra bit of money is pooled with those of all the other employees, and they are managed on a combined basis. If you leave your employer, you get your contributions to the pool, grossed up to reflect the investment performance of the pool.

This is a DC plan

Since the employees are all of different ages, the cashflow profile of the scheme will be the average of the cashflows of the individual plans, so effectively (simplifying somewhat), it can be invested as if it were being invested on behalf of an employee of the average age of the workforce. Hence, a bigger equity allocation than an individual employee would be able to sustain for most of his working life and (probably/hopefully) higher returns. I'm now going to state a proposition that I can prove mathematically, but won't because it's tedious:

For reasonable assumptions and the same level of contribution, 3) is better than 1)

Basically, unless you believe yourself to be a super ace stock picker (or at least, much better than the pool managers), you face a better risk/return tradeoff under 3). This is basically because big risk pools are better than small ones.

But wait, there's another option ...

4) A pooled version of 2), with the contributions pooled and managed in the manner of 3). You get a guarantee of some minimum level of pension, plus, if investment returns do better than the actuary expected, the windfall is shared between the company and you. The pooled fund is overseen by "trustees" who carry out the negotiations with the company on behalf of pool members, and from time to time, you can expect "pay rises" if you're retired, or improvements in the guaranteed level if you haven't, arising from this negotiation process. If you leave the company before retirement, you receive the actuary's assessment of your "fair share" of the assets of the pool, usually calculated on the basis of assumptions about the return on the pool's investment and the split of that return between you and the company.

This, in all its glory, is a typical DB plan

Again it can be clearly seen that if you stay with the company all your life, 4) is strictly less risky than 3), for the same reason that 2) was less risky than 1). If you assume that the two pooled options follow the same investment policy, then it ought to be the case that 4) is strictly to be preferred to 3) in that it offers a better risk/reward tradeoff, so long as the trustees are doing their job in looking after the pool members. Most of the DB scheme horror stories, like the Halliburton one doing the rounds at the moment, are of this man-bites-dog variety, where the trustees of the scheme have cut a bad deal for pensioners.

Things get a bit more tricky and opaque if you don't stay with the company until retirement. In principle, actuarially fair rules for calculating your asset share under 4) could be developed. However, in actual fact, you are exposed to the problem that a) the trustees and actuary are there to look after the pension fund members, not departing members (lawyers: don't quote me on this), and b) the actuary is always going to use an "expected rate of return" on the fund's investments in calculating your share which errs on the side of caution, because his primary duty is to ensure the soundness of the fund. I personally have moved between a number of DB schemes in my life, and have probably caught the thin end of this economic reality as a result.

So the real question about DB versus DC from workers' point of view is; are workers really so mobile these days that the commmonality of interest presumed by the pooled DB scheme is no longer an appropriate assumption? I've yet to see a serious study which concludes that this is anywhere near being the case in general.

So there you have it. Now, back to the trauma ward ...
0 comments this item posted by the management 10/02/2002 09:16:00 AM

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