The misbehaviour of mistakes

The Comedy of Errors - with apologies to William Shakespeare in the week of his 450th birthday
The Comedy of Errors
– with apologies to William Shakespeare in the week of his 450th birthday

There are two ways that mistakes can happen when you are carrying out an experiment to test a hypothesis. Experiments usually have two possible outcomes: accepting a “null” hypothesis, which means concluding that the experiment does not challenge its truth, and rejecting a null hypothesis, which means concluding that the experiment does provide sufficient evidence to do so.

Type 1 errors, otherwise known as “false positives” are when you think there is evidence for rejecting the null hypothesis (eg deciding there actually is something wrong with a smear test) when there isn’t. Type 2 errors, otherwise known as “false negatives”, are when you accept the null hypothesis but you really shouldn’t (eg telling someone they are all clear when they are not).

Saddam Hussain once famously said “I would rather kill my friends in error, than allow my enemies to live”. This suggests that he was really very much more concerned about Type 2 errors than Type 1 errors.

He is not alone in this.

A recent widely reported academic paper published in Nature claimed to have a test that “predicted phenoconversion to either amnestic mild cognitive impairment or Alzheimer’s disease within a 2–3 year timeframe with over 90% accuracy”.

The latest statistics from the Alzheimer’s Society suggest that around 1 in 14 or 7% of over 65s will develop Alzheimer’s. Probably not all of these people will contract the disease within 3 years, but let’s assume for the sake of argument that they will. Even so this means that, out of 1,000 people over 65, 930 people will not get Alzheimer’s within 3 years.

Applying the 90% accuracy rate allows us to detect 63 out of 70 people who actually will get Alzheimer’s. There will be 7 cases not picked up where people go on to develop Alzheimer’s. However the bigger problem, the Type 1 error that Saddam Hussain was not so bothered about, is that 10% of the people who do not and will not get Alzheimer’s will be told that they will. That is 93 people scared unnecessarily.

So 63 + 93 = 156 people will test positive, of which only 63 (ie 40%) will develop Alzheimer’s within three years. The “over 90%” accuracy rate becomes only a 40% accuracy rate amongst all the people testing positive.

In statistical tests more generally, if the likelihood of a false positive is less than 5%, the evidence that the hypothesis is true is commonly described as “statistically significant”. In 2005 John Ioannidis, an epidemiologist from Stanford University, published a paper arguing that most published research findings are probably false. This was because of three things often not highlighted in the reporting of research: the statistical power of the study (ie the probability of not making a type 2 error or false negative), how unlikely the hypothesis is being tested and the bias in favour of testing new hypotheses over replicating previous results.

As an example, if we test 1,000 hypotheses of which 100 are actually true but with a 5% test of significance, a study with power of 0.8 will find 80 of them, missing 20 because of false negatives. Of the 900 hypotheses that are wrong, up to 5% – ie, 45 of them – could be accepted as right because of the permissible level of type 1 errors or false positives. So you have 80 + 45 = 125 positive results, of which 36% are incorrect. If the statistical power is closer to the level which some research findings have suggested of around 0.4, you would have 40 + 45 = 85 positive results, of which 53% would be incorrect, supporting Professor Ioannidis’ claim even before you get onto the other problems he mentions.

We would have got much more reliable results if we had just focused on the negative in these examples. With a power of 0.8, we would get 20 false negatives and 855 true negatives, ie 2% of the negative results are incorrect. With a power of 0.4, we would get 60 false negatives and 855 true negatives, ie still less than 7% of the negative results are incorrect. Unfortunately negative results account for just 10-30% of published scientific literature, depending on the discipline. This bias may be growing. A study of 4,600 papers from across the sciences conducted by Daniele Fanelli of the University of Edinburgh found that the proportion of positive results increased by over 22% between 1990 and 2007.

So, if you are looking to the scientific literature to support an argument you want to advance, be careful. It may not be as positive as it seems.

The Nature of Risk and Pensions

Typology of biasI found this diagram recently in a paper by John Adams from 1999 entitled Risk, Freedom and Responsibility. It attempts to summarise different people’s attitude to risk-taking based on their views about the kind of world they live in, represented by a ball sitting in very different types of landscape. It explains a great deal about pensions.

Much is often made about our seemingly inexorable shift away from collective solutions to problems to individualised ones, aided on the one hand by technology like tablets, smart phones and other devices which make it easier for us to create our own environments and cut ourselves off from each other, and on the other by a loss of trust in many of the traditional collective organisations, such as banks and governments, which have previously been used by us to pool our risks and protect the most vulnerable.

If this is true, then it would be represented in the diagram by a shift in world view from right to left.

Others focus on the triumph of the American business model or ABM as the dominant school of political and economic thought in the globalised world of today, just as socialism was in previous times. This model leads to a belief in low taxation, small government, minimal market regulation and the reliance of self-interested materialism of individuals within these markets to deliver what we need. Despite its name, it is not a description of how American business actually works, but just one of what Adams would call the “myths about nature” which often determine our thinking about risk and much else besides.

If the triumph of the ABM is true, then it would be represented in the diagram by a shift in world view from bottom to top.

Adams points out that most people exhibit several of these world views and move between them, sometimes very quickly, but I think that it is easy to see where the stereotypical figures from the UK pensions landscape might sit. For instance, many owners of SMEs are calculated risk-takers who believe that things tend to turn out okay on the whole. That is how they became business owners in the first place. So, in the diagram above, taking a few risks with the football is not going to lose it, but there might be a reasonable amount of bouncing around: ie they are individualists.

In the top right hand corner are the hierarchists. They do not believe that the environment in which they operate is fundamentally benign but they do think that it can be managed. This is why their landscape resembles a series of speed bumps: the football cannot be allowed too much freedom or the consequences might be serious and it is possible to deny the football that freedom. This is the world view of a large number of civil servants and actuaries, which is why the public sector is still running defined benefit pension schemes and the private sector (with the smaller schemes overwhelmingly sponsored by individualists) has largely retreated from them. The larger companies, which tend to harbour their fair share of hierarchists, have been the slowest to abandon such schemes.

In the bottom right hand corner are the egalitarians: people who believe that giving the football anything more than a light tap is likely to lose it forever. Nature is unforgiving and cannot be controlled, but the less we do to destabilise the environment, the longer she is likely to let us live. The resource and environment group of actuaries, with their focus on limits to growth and the implications of this, are likely to contain a number of egalitarians in their ranks.

And where are the pension scheme members? Well, even 15 years ago Adams reckoned on at least 40% of the population being fatalists. This is the perfectly flat landscape representing the idea that it does not remotely matter what you do with the ball, the end result will be the same. Adams cites a survey carried out in 1998 on young adults in England in which, when they were asked to imagine that they could only have one of two rights – the right to vote in an election, or the right to obtain a driving licence, 72% chose the driving licence. I think it is probable that this proportion would be higher now.

So we have pension schemes largely inhabited by fatalists and run either by individualists, in the case of smaller schemes, or by hierarchists in the case of larger and/or public sector schemes. The reason they have had to be auto-enrolled into schemes they did not choose to join themselves is because they do not fundamentally believe that it will make any difference, which makes the cost of it at any price too high.

However they are not comfortable being fatalists. The Pension Regulator’s survey of defined contribution (DC) pension scheme members in 2012 revealed that the three things they wanted most of all were:

  • Someone making clear to them how much they needed to save;
  • Being able to talk to someone to understand their pensions better; and
  • Clear communication from their employer and their pension provider.

All of which would make them less fatalistic and feel more in control. Whether you feel this would move them upwards into the individualist camp or diagonally across to the hierarchical camp (or even over to the egalitarian position) probably depends on your politics, but none of these positions are fixed. The recent floods have shaken many business people’s faith in things basically turning out okay in the end, and the credit crunch certainly moved many people out of hierarchist into either egalitarian or individualist territory.

What it suggests to me is that the way we organise pension scheme membership may be fundamentally flawed. Talking to members about their risk appetite or tolerance to risk is starting from an individualist perspective: that the world is a benign place, nothing too extreme is likely to happen and the only choice for you to make is how you want to invest your money. But it makes no sense if, assuming you can be coaxed away from the fatalist position, you turn out to be an egalitarian or a hierarchist. And this position probably makes no sense to the sponsor of the scheme.

When asked, sponsors of smaller schemes are very clear that they do not support the idea of collective schemes. They want to run their own schemes otherwise a large part of the benefits of the arrangements to them are lost. However, if auto enrolment is to deliver the changed relationship between the public and pensions everyone hopes for, I think prospective members are going to need choices about more than investment strategy. If members want to pool risk I think they should be able to, and collective schemes alongside firms’ own DC arrangements, perhaps with joint membership, may be the way to achieve this.

Individualists, hierarchists, fatalists and egalitarians. As Adams points out “the clamorous debate is characterised not by irrationality, but by plural rationalities.” It is a debate which has a long way to go yet.

When it comes to annuities, most of us are enhanced. We just don’t know it yet

doctorIn all the talk about annuities and the poor value they currently offer, nearly all of it has been based on standard annuity rates, ie where there is nothing sufficiently medically wrong with you to affect your life expectancy. However this is almost certainly not the rate you should be looking at.

Go to any of the annuity provider or broker websites, sometimes buried away a little, and you will find a link explaining what they can offer in the way of “enhanced” or “impaired lives” annuities. Legal & General’s web page on this looks like the kind of warning notice you find on the wall of your doctor’s surgery waiting room, with headings like Smoking, Type 2 Diabetes and High Blood Pressure. But in the upside-down world of buying annuities these become good things to do or have.

Just Retirement give some handy illustrations of what various conditions could mean for your income: up 20% for minor conditions like obesity and hypertension, up 30% for “moderate” ones like being a heart attack survivor with a bypass and 40% for serious medical conditions like stage 2 bowel cancer one year in. However, you don’t need to get anywhere near the frankly frightening conditions in the moderate and serious boxes to make a big difference to the income you can receive. annuitydiscount.co.uk provide a very long list of medications (covering every letter in the alphabet except J and Y) which could lead to an impaired life annuity if disclosed to the annuity provider.

As the BBC article from 2012 posted by the Better Retirement Group on enhanced annuities says: “At its simplest an annuity is a bet with the insurance company about how long you will live.”

So on that basis, it makes sense to stack the odds in your favour as much as you can. Which makes the 2007 article in the New England Journal of Medicine entitled, rather dully, Incidental Findings on Brain MRI in the General Population, such an interesting read.

They studied 2,000 people (mean age 63.3 years, range 45.7 to 96.7) from the population-based Rotterdam Study in whom high-resolution, structural brain MRI scans had been carried out. Asymptomatic brain infarcts (more commonly known as strokes) were present in 145 people (7.2%). Among other findings, aneurysms (1.8%) were the most frequent. Benign brain tumors also turned up reasonably often (1.6%). The most extreme case was someone with a large, chronic subdural haematoma, who was subsequently found to have had a minor head trauma 4 weeks before the MRI scan. Some of the scans are shown below.

brain scansBut the really amazing thing is this: only 2 of the 2,000 people scanned (the subdural haemotoma mentioned above and another who had a 12 mm aneurysm of the medial cerebral artery) had any idea that there was anything wrong with them!

Another huge area of undiagnosed disease (and on the annuity.co.uk list for enhanced annuities) is prostate cancer. According to a systematic review of prostate cancer biopsy schemes by the University of York in 2005, where they quoted from the NHS Centre for Reviews and Dissemination publication on screening for prostate cancer, Effectiveness Matters:

Post mortem studies show that 30% of men over 50, who had no symptoms of prostate cancer whilst alive, had histological evidence of prostate cancer at the time of death. This percentage rises to 60-70% in men over 80 years of age. In other words, most men with prostate cancer die with, rather than from, the disease.

The main reason these studies have been carried out is to determine whether screening for prostate cancer, which kills 3.8% of men with the disease, has saved many lives. The Prostate Specific Antigen (PSA) test that is commonly used to detect prostate cancer in the absence of symptoms is not only prone to false positives and negatives (ie telling you you have it when you don’t and don’t have it when you do – something all screening suffers from to some extent), but can lead to you being offered treatment which may well be worse than the disease. This is discussed further in the excellent The Norm Chronicles, by Michael Blastland and David Spiegelhalter, which questions whether, overall, screening is particularly effective in saving lives.

Effective in preventing death? Perhaps not. But effective in increasing retirement income? Almost certainly.

The latest Association of British Insurers (ABI) facts and figures on the UK annuity market suggest that enhanced annuities have grown in popularity, to 24% in 2012 from 2% in 2003. There is scope to make further large increases in these figures if more people can be persuaded to have themselves screened for some of the most common undiagnosed conditions before they retire.

So don’t necessarily accept a standard annuity rate. And consider getting yourself tested first.

Camps, acronyms and other small stuff

DA optionsThe Defined Ambition consultation ended on 19 December but the lobbying has continued. Camps have now formed around the various options.

Steve Webb, the Pensions Minister, and Alan Rubinstein, Chief Executive of the Pension Protection Fund, have been enthusiastic supporters of something called the pension income builder, which increases the guaranteed pension accrued each year with part of the annual contribution, with the remaining contributions invested in a collective defined contribution (DC) arrangement.

The Collective DC more generally, where returns are smoothed between members in an attempt to reduce the volatility of returns on individual DC, has also had some very vocal proponents. Considering it was originally ruled out as an option by the Department of Work and Pensions (DWP), has had 10 objections to it raised by the Association of British Insurers (ABI) and has been accused of not reducing risk so much as moving it around between members by Lord Hutton, this is a little bit of a surprise.

Lord Hutton, former Secretary of State for Work and Pensions and chair of the Commission on Public Service Pensions Commission, is dismissive of the whole defined ambition idea. Recently he said that the Government should stop “banging on” about defined ambition and let the pensions industry focus on applying defined benefit (DB) investment strategies to DC schemes. He is a particular fan of the Liability Driven Investment (LDI) approach, common in DB schemes protecting their funding position, being applied more consistently to DC. Hutton has recently joined Redington, an investment consultancy, so I imagine we can expect to hear a lot more from him on this subject.

Much has been made of the Dutch system, which has a “second pillar” of large industry-wide pension schemes. This has suffered from the same economic pressures which have dogged the UK system since the turn of the century, but has arguably retreated from straight final salary benefits – first to career average retirement earnings (CARE), then to risk sharing via variable contributions for employers balanced by variable benefits for employees, and currently renegotiating again  in the wake of the 2008 crash – in a more orderly manner. I tend to feel that the main reason the Dutch system is better than ours is the same reason that their flood defence system is better: they put a lot more money into it. Nine times as much in the case of flood defences, and contributions into their second pillar average 20% of salary compared to the current average into DC schemes in the UK of under 8%. They also make you buy an annuity, make you join and don’t let you opt out. Despite this it remains remarkably popular with the public.

As you can see, there are a lot of acronyms flying around, and relatively little discussion with the people who these schemes are likely to end up getting foisted on. The Association of Consulting Actuaries (ACA) carried out a survey of smaller firms which revealed that what they wanted was:

  • Members to receive more from their savings;
  • Increased transparency and trust in the companies who provided pensions;
  • No collective schemes; and
  • More tax concessions.

This last point is unlikely to be conceded, with the Institute of Fiscal Studies joining the increasing clamour this week to limit the generous tax exemptions to employers and members with occupational pension arrangements.

But has anyone asked members of pension schemes? Very few, as far as I can see. The most notable being the Pension Regulator’s survey of DC pension members in 2012. When those still actively contributing to these schemes were asked which of a long list of things would encourage them to take more interest in their pension, the three things they wanted overwhelmingly most of all were:

  • Someone making clear to them how much they needed to save;
  • Being able to talk to someone to understand their pensions better; and
  • Clear communication from their employer and their pension provider.

Notice how concerns about guaranteed benefits did not feature here. When asked, 85% had some understanding that their pension income was not guaranteed, and even more (94%) had an understanding that contribution levels were a key factor in determining that income. While 78% thought their company or personal pension would be one of their main sources of income in retirement (the next highest was the state pension with 22%), only 24% were confident that their current level of contributions was going to provide an adequate income. So they know they have a problem.

What they are asking for is a step change in financial education so that they can begin to tackle that problem. So could it be that all of the groups we have heard from above are trying to solve the wrong thing entirely?

As far as the regulatory environment is concerned, I think the document Defining Ambition produced by the National Association of Pension Funds (NAPF) before the consultation probably summarised the situation best. Joanne Segars stopped short of supporting any particular solution and instead laid out some of the main options and where they sat on the scale of risk (which I have reproduced above) to the member.

Segars suggested that we shouldn’t “sweat the small stuff”, and should instead concentrate on providing a flexible continuum of regulation to cover the whole scale of risk, otherwise any new approaches would be snuffed out by HMRC’s and TPR’s lack of flexibility and overly complex approach before they even got going, much as cash balance schemes have been over the last 20 years. I felt that this was just fence-sitting at the time, but have since realised that she was right. We have all been “banging on” for too long about things about which prospective members simply don’t care.

Assuming a relaxation of the regulations which doesn’t yet exist, we actuaries have piled enthusiastically into debating slight differences between our different pet schemes, standing toe to toe and swapping model results like punches, while seemingly forgetting all about the member.

Suddenly the most important contribution in Defining Ambitions seems clear to me: that of Morrisons’ HR Director about how they introduced a three year financial education and advice programme (called Save Your Dough) throughout their workforce ahead of their auto-enrolment date. They realised that they needed to help their employees understand their finances first before they would understand that they could make a difference to their long-term finances by saving into a pension. They involved Alvin Hall to add some celebrity glitter to the process, but also involved their main union USDAW. And they used a lot of different communication tools, from booklets to podcasts to online modellers to short films and video diaries in addition to the more traditional information sources and face to face sessions. They trusted that they had good people who would make reasonable decisions given sufficient accessible information.

I am sure there are other examples of such good practice out there, but we have not encouraged them with our endless debates about DC plus v CDC v DB minus and everything in between. The small stuff has been sweated quite enough. Let’s help firms talk to their members better instead.

It’s like deja-vu all over again

The Pensions Regulator has a consultation on the go. In fact they have two: regulating defined benefit pension schemes and regulating public service pension schemes. Both started in December and are due to wind up in February. The defined benefit pension schemes one alone runs to over 160 pages across the four documents published. All at the busiest time of the year for most pensions actuaries, caught between the 31 December 2013 accounting disclosures and the looming deadlines for submitting the 31 December 2012 scheme funding assessments. Could it be that they are rather hoping to limit the feedback they get?

Because the changes that are being proposed to the funding regime known as scheme specific funding which has run for 8 years are dramatic. Under the pretext of only making changes to allow the introduction of the Regulator’s new objective to “minimise any adverse impact on the sustainable growth of an employer” (see my previous post on this), they have effectively announced the death of scheme specific funding and proposed a system which looks very much like the Minimum Funding Requirement (or MFR – the previous discredited funding regulations) mark two to me, although the Regulator insists that it will be completely different this time.

The main problem with the MFR was that it was a one-size-fits-all approach (although it did vary in strength depending on how far on average members had to go until benefits were paid – known as the duration of the scheme), which encouraged an inappropriate level of contributions for many schemes (the minimum funding requirement effectively became a maximum funding requirement in many cases).

Fast forward to now, and the new proposed funding approach based around something called the Balanced Funding Outcome (BFO). This calculates a required level of assets for each scheme on an “objective liability measure, independent of the scheme’s funding assumptions”. The actual assets will be compared with the required amount and a recommended level of contributions to get up to the required level will then be calculated by the Regulator. The contributions the scheme trustees have agreed with the scheme’s employer will then be assessed to see if they measure up. Where MFR varied by duration, BFO will vary by duration and covenant (how likely the employer is to stick around to pay the last pensioner). So, as you can see, completely different!

At the end of Appendix G of the 50 page draft funding policy, we finally find the problem that I think the Pensions Regulator really wants to solve:

TPR graph

Look at all those dots. They’re all over the place. There is currently absolutely no correlation between the deficit reduction contributions (DRCs) employers are paying and the funding level in their schemes. The Regulator is determined to change that, by giving trustees and employers sight of their preferred contribution number during their negotiations. The contribution number won’t be compulsory of course, but if you use it then the Regulator will leave you alone. It is almost as if they have never heard of Daniel Kahneman or behavioural economics.

What will happen? Well who knows but here’s a guess. Schemes to the bottom left of the chart above (ie low assets and contributions) are already being subjected to extra scrutiny and generally have employers in such a poor financial state that there is very little they can do about it. But those in the top right will effectively have been given permission to swoop down to the blue line with a whoop of “Pensions Regulator’s new objective”. It will be like the 90s all over again when pension schemes took contribution holidays because they were measuring their funding in an unrealistic way. It will be seen as financially stupid to be in the top right of the Regulator’s graph. Group think will be in charge once more. But, to use another quote from Yogi Berra, the baseball icon, “If you don’t know where you are going, you might wind up someplace else”.

If we agree to this we will be making the pensions system more fragile. The model used by the Regulator will not anticipate the next defaulting economy or other Black Swan that throws currency and financial markets into meltdown (no one was suggesting Argentina would default a month ago) and reduces everyone’s level of funding, so when that happens everyone will be in trouble rather than just the proportion of schemes in difficulties we have now. The overall funding risk of defined benefit pension schemes will be inflated so much that the system may not easily recover.

It gets worse. There is a lot in this consultation about governance, and also references to asset liability modelling, due diligence, reverse stress testing, scenario testing and covenant advice. These are all things which are likely to be a problem for small schemes, which I pointed out previously when they were proposed by EIOPA (because, let’s be clear, it is compliance with prospective EU legislation which has driven many of these proposals). But guess which group are going to see an almost total reduction in the scrutiny they get from the Regulator under the new regime? That’s right: small schemes.

There is still time to register your opposition to reliving the last 15 years of defined benefit pensions all over again: the consultation runs until 7 February.

When the levy breaks

For those people who are not pensions geeks, let me start by explaining what the Pension Protection Fund (PPF) is. Brought in by the Pensions Act 2004 in response to several examples of people getting to retirement and finding little or no funds left in their defined benefit (DB) pension schemes to pay them benefits, it is a quasi autonomous non-governmental (allegedly) organisation (QUANGO) charged with accepting pension schemes who have lost their sponsors and don’t have enough money to buy at least PPF level benefits from an insurance company. It is, as the PPF themselves appear to have acknowledged with several references to the schemes not yet in their clutches as the “insured” in a talk I attended last week, a statutory insurance scheme for defined benefit occupational pension schemes, paid for by statutory levies on those insured. As a scheme actuary I have always been very glad that it exists.

The number of insured schemes has dwindled since it was named the 7800 index in 2007 (with not quite 7,800 members at the time) to the 6,300 left standing today. As you can imagine, the ever smaller number of schemes whose levies are keeping the PPF ship afloat are very nervous about how that cost is going to vary in the future. They have seen how volatile the funding of their own schemes is, and seemingly always in the worst case direction, and worry that, when their numbers get small enough, funding the variations in PPF deficits could become overwhelming. Particularly as the current Government says whenever it is asked (although no one completely believes it) they will never ever bail out the PPF.

So there has been keen interest in the PPF explanations of how those levies are going to change next year.

PPF levies are in two parts. The scheme-based levy, which is a flat rate levy based on the liability of a scheme, and the normally-much-bigger-as-it-has-to-raise-around-90%-of-the-total-and-some-schemes-don’t-pay-it-if-they-are-well-funded-enough risk-based levy. The risk-based levy depends on how well funded you are, how risky your investment strategy is and the risk your sponsor will become insolvent over the next 12 months.

It is this last one, the insolvency risk, which is about to change. Dun and Bradstreet have lost the contract to work out these insolvency probabilities after eight years in favour of Experian. However, unfortunately and for reasons not divulged, the PPF has struggled to finalise exactly what they want Experian to do.

The choices are fairly fundamental:

  • The model used. This will either be something called commercial Delphi (similar to the approach D&B currently use) or a more PPF-specific version which takes account of how different companies which run DB schemes are from companies which don’t. The PPF-specific version looks like it was originally the front runner but has taken longer to develop than expected.
  • The number of risk levels. Currently there are 10, ie there are 10 different probabilities of insolvency you can have based on the average risk of the bucket you have landed in. One possibility still being considered at this late stage is not grouping schemes at all and basing the probability on what falls out of the as yet to be announced risk model directly. This could result in considerable uncertainty about the eventual levy. Even currently, being in bucket 10 means a levy 22 times bigger than being in bucket 1.

So reason for nervousness amongst the 6,300 perhaps? The delay will mean that it won’t be known by 1 April (an appropriate date perhaps) when data starts to be collected for the first levies under the new system next year. Insolvency risk is supposed to be based on the average insolvency probability over the 12 months to the following March, but the PPF will either have to average over a smaller number of months now or go back and adjust the “failure scores” (as the scale numbers which allocate you to a bucket are endearingly called) to the new system at a later date. Again, the decision has yet to be made.

All of this suggests an organisation where making models is much easier than making decisions. And that is in no one’s interest.

Perhaps surprisingly in the audience I was in, the greatest concern expressed was about the fact that the model the PPF uses to assess the overall risk to their future funding (and therefore used to set the total levy they are trying to collect each year) was different from either the current D&B approach, or either of the two possible future approaches, to setting failure scores, ie the levies they pay are not really based on the risk they pose to the PPF at all.

There are obviously reasons why this should be the case. Many of the risk factors to the PPF’s funding as a whole would be hard to attribute, and therefore charge, to individual sponsors. For instance the PPF’s Long-Term Risk Model runs 1,000 different economic scenarios (leading to 500,000 different scenarios in total) to assess the amount of levy required to ensure at least an 80% chance of the PPF meeting its funding objective of no longer needing levies by 2030. Plus it plays to sponsors’ basic sense of fairness that things like their credit history and items in their accounts (although perhaps not including, as now, the number of directors) should affect where they stand on the insolvency scale, rather than things that would impact more on PPF funding, like the robustness of their scheme deficit recovery plans for instance.

It is rather like the no claims discount system for car insurance. This has been shown to be an inefficient method for reallocating premiums to where the risk lies in the car driving population, and this fact has been a standard exam question staple for actuarial students for many years. However it is widely seen as fair by that car driving population and would therefore be commercial madness for any insurer to abandon.

So there we have it. The new PPF levy system. Late. Not allocating levies in accordance with risk. And coming to a pension scheme near you soon.

Time to define your ambition

The consultation on the future shape of workplace pensions has been going on for nearly a month now and ends two weeks on Friday. It is littered with errors, from completely repeated questions (Q52 = Q54) to ones which are so similar as makes no difference (Qs 41 and 44 for example) and the thrust of a lot of the questions are quite hard to answer if you do not share some of the underlying assumptions of the DWP about the process, but come on! This is our chance to put a bit of definition into the rather blurry outline of a straw man which some of the newspapers have been tilting at so vigorously!

You don’t have to answer all of the questions, but just to goad you a bit I have done so here. Agree, disagree, I would love to hear from you. But not until you have responded to one of the following addresses:

How to respond to this consultation

Pleasesendyourconsultationresponses,preferablybye-mail,to:definedambition.pensionsconsultation@dwp.gsi.gov.uk

Or by post to:

Defined Ambition Team

Private Pensions Policy and Analysis

1st Floor, Caxton House

6-12 Tothill Street

London

SW1H 9NA

 

Feedback on the consultation process

There have only been 24 posts on the blog. I think the main reason for this was identified early in the process from a contributor referring to herself only as Hannah:

Hannah

I applaud the use of an open blog but it’s obvious that there’s a bit of a problem here! Perhaps, to avoid this becoming sidetracked, you could introduce a drop-down in the comment section so that people could select what aspect of DA reform or the consultation their comment relates to – and if their comment relates instead to concerns about their accrued benefits, you could redirect them to a separate specialised member queries page?

Reply

Sam Gilbert

Thanks for this Hannah, we will look into this once the blog picks up pace.

DA Team, DWP

Of course the blog never did pick up pace because people soon realised that there comments would be lost in a stream of pension benefit queries. Not the way to encourage a consultation. If you want to comment on this or anything else about the process of the consultation, the contact details are as follows:

Elias Koufou

DWP Consultation Coordinator

2nd Floor

Caxton House

Tothill Street

London

SW1H 9NA

Phone: 020 7449 7439

Email:elias.koufou@dwp.gsi.gov.uk

Die, Die, Die!

20131126_122758I received a set of nontransitive dice in the post this week. Transitive is an interesting word. As we all know in grammar it refers to verbs which do things to something. What I didn’t learn at school was that if they do things to one thing they are called monotransitive, and ditransitive if they have both a direct and indirect object. A verb like to trade is categorised as tritransitive. If a verb does not play with others it is called intransitive, eg an example appropriate to this story, to die. If a verb swings both ways it is called ambitransitive.

In the mathematical world transitive is a description of a relation on a set. For example, if A = B and B = C, then A = C. So = is transitive. Similarly, if A > B  and  B > C  then  A > C.

Or does it? Let’s return to the dice (singular die: cemented in my memory on the occasion a teacher responded to a boy coming into his class and asking to borrow a dice by shouting “die, die, die!” at the startled youngster). Mathematicians do not use the word intransitive, preferring perhaps to avoid the ambiguity of words like flammable and inflammable, but instead use nontransitive. Nontransitive dice have the property that if die A tends to beat die B on average, and die B tends to beat die C on average, then rather counter-intuitively die C tends to beat die A on average. How does this work?

There are many different arrangements of the numbers on the faces of the dice which would achieve this effect. My red die has 4 on all its faces except one, which has a 6. My blue die has half its faces with 2s and the other half with 6s. My green die has 5 on all its faces except one, which is unnumbered (or, in fact, undotted).

If we take the average number we expect to get when throwing each die (the concept of expected value, first introduced by Blaise Pascal of triangle fame, also known as the mean, is the first thing that tends to get calculated in any statistical analysis), then red gives us 4⅓, blue gives us 4 and  green     4 1/6. So we would expect from that to see red beat blue, green beat blue and red beat green.

When we pitch red against blue, if we throw a 2 with the blue die (probability of a ½), then we will always lose to red, since all of its faces are greater than 2. If we throw a 6 with blue, we have a 5/6 chance of beating red (since 5 of its 6 faces are 4s) and a 1/6 chance of drawing. So we have for blue a probability of ½ of losing, a probability of ½ x 5/6 = 5/12 of winning and a probability of ½ x 1/6 = 1/12 of drawing. So, in the long run, red beats blue on average, as we would expect it to.

When we pitch blue against green, blue will always win if we throw a 6 with it, with a probability ½. If we throw a 2, also with a probability ½, we have a 1/6 chance of winning against green (if green’s single blank face comes up) otherwise we will lose to a 5. So we have for blue a probability of losing of ½ x 5/6 = 5/12. And the probability of winning as blue (since no draws are possible this time) of 1 – 5/12 = 7/12. So, in the long run, blue beats green, exactly the opposite of what we would expect just going on the expected values.

Finally, when we pitch red against green, the only time green will beat red is when red has a 4 (with probability 5/6) and green has a 5 (also with probability 5/6). So we have a probability of green beating red of 5/6 x 5/6 = 25/36. And the probability of winning as red (since again no draws are possible as the two dice have no numbers in common) is therefore 1 – 25/36 = 11/36. So, in the long run (when as Keynes once helpfully pointed out, we are all dead) green beats red, again exactly the opposite of what we would expect just going on the expected values.

We only had to mess around a little with the 6 faces of the dice to get this counter-intuitive result. Nearly all financial instruments and products are obviously much more complicated than this, with the probabilities of certain outcomes being largely unknown, and even more so when in combination with each other, and therefore counter-intuitive results turn up almost too frequently to be called counter-intuitive any more. In fact the habit of trying to treat financial markets as if they were games obeying rules as fixed and obvious as those you can play with dice is what Nassim Nicholas Taleb refers to as the Ludic Fallacy.

If we double them up we get another surprise. Red still has the highest expected value (8⅔), followed by green again (8⅓) and then blue (8). But this time each pairing has three possible outcomes. Red and green both beat blue as expected from the expected values, but then green unexpectedly beats red.

This kind of behaviour is called nonlinearity, when adding quantities of things together does not just increase their effects, but instead changes them. Nonlinearity in this case means that blue beats green when we use one die each, but that green beats blue when we use two. Nonlinearity is also the single biggest threat to the financial system.

Anyone for darts instead?

Papers and Pensions

mobile pics Nov 2013 010Now that the Great and Good of the actuarial profession and pensions industry have launched their joint consultation with the DWP on defined ambition (DA) options, it is interesting to look at the initial response in the print media.

The first thing to note is how little of it there is. The Daily Mail, Daily Express and Daily Telegraph have it on the front page. The Financial Times, Guardian and Times do not. Nor do the red tops. All three headlines sit alongside photographs of the Duchess of Cambridge.

And the response varies. The Express have written what looks like a positive piece (“Bigger Better Pensions For All”) until you discover it has decided to present the launch of the consultation as an “industry shake-up” which will “spell the end of annuities”. I was a little puzzled about this at first, as the consultation is not really about annuities at all, until I realised that Steve Webb had made a speech the previous day and mentioned the FCA review of annuities. This clearly fed into the default Express editorial line better than the actual topic of the consultation. This became clearer on page 4, with the headline “’Poor value’ annuity payouts are axed in pensions shake-up” next to a big picture of a smiling Ros Altmann. There appears to be only one story possible in the Express on pensions, whatever the actual news event.

The Mail does at least focus on things that are in the consultation, concentrating on the proposals to allow final salary pensions to drop some currently guaranteed elements of benefits such as indexation and spouses’ pensions. “The Death Knell for Widows’ Pensions” is their headline, but the article beneath is fairly balanced on flexible defined benefit (DB), quoting both those highlighting the reductions to benefits the proposal would allow on the one hand, and the danger that all the remaining horses would bolt from the DB stable if changes were not made on the other.

Finally, the Telegraph. “Pensions face new blow from ministers” is their headline. The article is similarly balanced, and is the only one to make the important point that benefits already accrued would be unaffected.

The coverage of the alternatives put up for consultation is patchy. Strangely the Express does best here, despite its desperation to make it a story about the death of the annuity, it does mention in passing collective defined contribution (DC) and guaranteed DC. Otherwise the focus is exclusively on flexible DB in both the Mail and Telegraph, and what members currently accruing non-flexible DB might lose as a result. The comparison with public sector pensions is made several times, with the Telegraph pointing out that the recent settlement on public sector pensions, which would not be removing the requirement to provide indexation and spouses’ pensions, was promised by ministers to be the last for 25 years.

So what kind of start does this represent for engaging the UK public in the debate on the future on pension provision? Mixed, I think. There will clearly be much more scrutiny on any legislative easing to current benefit guarantees than there will be to any addition of guarantees on pensions which currently have none. Perhaps this is to be expected. I do worry that cash balance may get squashed out as an option between the two camps of flexible DB and guaranteed DC – it is barely mentioned in the consultation, and can work well when coupled with a strong commitment to employee education like Morrisons have attempted.

But these are early days and the first thing everybody needs to do is respond to the consultation. Most pensions actuaries and many others will have strong views on many elements of it. So don’t leave it to your firm to do it on your behalf. The deadline is 19 December.

Faced with Philip Booth’s free market fanaticism, I’d rather be Frank

This was a letter sent to The Actuary on 12 September, but which they chose to publish neither in the magazine nor on the website.

Dear Sir

In response to the interview with Philip Booth in the September issue, I would just like to point out that the banks did not know during the 2007 financial crisis that they would be bailed out. The day before Alistair Darling announced a £500 billion rescue package in October 2008, shares in RBS fell by almost 40 per cent to a 15-year low, HBOS fell by over 40 per cent, Lloyds TSB dropped by 13 per cent and Barclays by 9 per cent precisely because a bailout was not assumed.

As regards how prudently financial institutions behaved before the changes in insurance regulation in the 1970s and 1980s, I would prefer to listen to the views of someone who was actually there. Frank Redington, in his submission to the Institute of Actuaries in 1981 entitled The Flock and the Sheep and Other Essays, says:

“We have no means now of telling how the profession would have emerged from what would have been the only real test of its collective character which it has had to endure in the last 100 years. When the curtain fell in 1939 the profession was not cutting a very brave figure. Valuation bases were too weak, the rate of bonus was some £5 too high and new business was being sold on prospects which were not achieved until 18 years later. A few reputable offices had their backs to the wall.

“The outcome, if the war had not interrupted the story, would probably have taught us a valuable lesson. As it is we have to conclude regretfully that the profession had not – and, I am sure, has not – learned how to live with its salemen’s promises. To put it another way, we are driving a powerful car but have not yet proved our ability to handle the brakes.”

Regulation was inevitable. The problem which remains is that financial institutions in many cases are too complicated in their current form to regulate effectively. As Robert Reich, former US Secretary of Labor, puts it when arguing for the need to split Wall Street banks, they are “too big to fail, too big to jail, too big to curtail”!

Yours faithfully
Nick Foster