Actuaries and other scams

I think that someone tried to scam me yesterday. I had gone out for a pint of milk, around 8 in the evening, when a man came up to me. At first glance he seemed well dressed - although the suit wasn't hand-made and the tie wasn't silk - and he had a sob story. His wallet had been stolen. He had no money. Could I lend him a tenner to get the train home? Sadly he rather ruined the spiel by clutching a mobile phone, with which he could have presumably have called a friend or work-mate. And the script was rather similar to one I have heard several times before. But what completely ruined it for me was that he claimed to be an actuary. He even showed me his business card, presumably in an attempt to establish his credentials as a trustworthy person. Now, dear reader, if you know what I think of actuaries, you will know that this back-fired.

What happened next? Well, I didn't steal his mobile. Although I was tempted. But he didn't get the cash. So the lesson, scam artists of E1, is when you are trying a con, pick a profession that your interlocutor doesn't think is fundamentally mis-guided.

Ball of steel or brains of lead?

In what is either a strong buy signal for the market or a strong sell signal on the stock, MBIA has announcing that it was not changing its projection of losses on its mortgage-related exposures. The FT story is here. Yes, they had some bizarre FAS 159 gains (CNN is here and my take on the rules is here): yes, they resumed a share buy-back programme. But ignoring all that, if their actuarial loss estimates for RMBS have not changed, either that is a very useful datapoint on where realised default losses actually will be, or their actuaries are fools and it is time to short the stock again. It will be interesting to see which.

Update. John Dizard has pointed out the possible value in the monolines as a vulture play on the eventual losses on RMBS. I can see the idea, but I'd like to know more about the implied residual value of the monolines given the current equity price. Are they really cheap yet?

Blame the actuaries

Yet another story about the travails of the monolines - this time on guaranteed investment contracts - made me think about who is really to blame for the mess these companies are in. It's the people who made their underwriting decisions: their actuaries. They decided that there was little risk in guaranteeing investment returns for extended periods. They decided writing hundreds of billions of dollars of financial guarantees on ABS was a good risk return tradeoff. For that matter their colleagues in the life companies decided that variable annuity life policies were a good idea. (These policies, like a GIC, guarantee a return on a risky investments so they act a lot like long dated written puts: needless to say, the actuaries did not price them that way. Now that the equity markets are tumbling you can expect to see some life companies getting into distress...)

So perhaps one lesson that shines out of this mess is do not let an actuary price or risk manage a financial contract without help from a professional. They are not certain to screw it up. But the evidence of the last few years suggests that there is a real risk that they might get it very wrong indeed.

Wearing a cap

Further to the discussion on Saturday, here are some more thoughts on risks in pensions and who should bear them.

Pensions are complicated things. Consider a typical defined benefit scheme. Here the pensioner has a right to a certain level of pension - often index linked - and the employer has an obligation to provide it. The pension is simply collateral against that obligation.

The first risk, then, is that the employer cannot meet that obligation, typically because they have defaulted, and the pension fund is not adequate. It is this risk that pensions protection legislation is meant to address.

The second risk is that the fund is not judged be adequate to meet the employer's liability, causing the need to 'top up' the fund. I say 'is not judged to be' rather than 'is not' because the law requires an assessment of the future likelihood of adequacy to be made rather than a spot assessment. Ignoring for a moment the veracity of the assessment - which is questionable - let's look at how a fund might fail to be sufficient to meet an employer's liabilities.

There are two moving parts here: the fund assets, and the fund liabilities. Funds are typically invested in some or all of corporate bonds, equities, and inflation linked bonds, plus perhaps other asset classes. Therefore they are typically:

• Short credit spreads (if credit spreads increase, the fund loses money on a MTM basis);
  
• Short nominal rates (because if rates increase, fixed rate bonds are worth less);
  
• Long equities; and
  
• Long CPI inflation (to the extent that they hold inflation-linked assets).
  

On the liability side the fund is:

• Short longevity (if people live longer it has to pay a pension for longer and hence loses money);
  
• Short wage inflation (if final salaries increase, so do pensions);
  
• Short CPI inflation (if inflation increases, so do index-linked pensions);
  
• Long nominal rates (because future liabilities are discounted back to today along some interest rate curve).
  

The risk is then that the spread assets - liabilities goes negative. In a DB scheme then the employer has to top up a fund if this spread falls beneath some threshold value, and hence they are short an option on the spread. In a defined contribution ('DC') scheme the pensioner bears all the risk and hence they are short this complicated spread cap: if their funds don't meet their pension expectations, then they have to find the cash for their retirement from somewhere else.

The details of the cap in any particular situation of course depend on how funds are invested, but typically it will have some elements of equity risk, interest rate risk, corporate credit spread risk, and both wage and CPI inflation risk, together with the risk of the comovement of these factors (which you can simplistically think of as correlation risk). Given it is a very long dated instrument - perhaps as much as ninety years for someone entering the workforce now - and very complicated, it is hardly a surprise that it is difficult to know what it is worth.

Note in particular that because we have a long-dated problem, the details of the dynamics of each component of the spread are crucial. It might be reasonable to assume that some of them, such as corporate credit spreads, are mean reverting. This makes the problem easier. For others, notably inflation and equity returns, there seems no reason at all to assume long term mean reversion. This means there is an awful lot of model risk in pensions analysis.

Some dimensions of pensions risk can be minimised: for instance if the scheme holds inflation linked gilts then it can hedged inflation risk and bears no equity risk. However it still have longevity risk, and (absent a liquid longevity swap market anyway) contingent inflation risk (since if longevity increases the fund is mismatched on the duration of its assets vs. its liabilities and hence has inflation term structure risk). Moreover, of course, a low risk pension fund has to be much more comprehensively funded than one that is taking market risk in multiple dimensions (equities, corporate credit, property, alternative investments, ...) Finally note that longevity risk is remarked considerably less often than other risk components so it is less visible - but that does not mean that it is not there.

The key policy question, then, in pension is who should bear the risk of underfunding, i.e. who should write the spread cap. Recently, there has been a suggestion that rather than one party bearing all of the risk as in current DB and DC schemes, perhaps it should be shared between employers, employees, perhaps with a far out of the money state backstop*. (See here for a further discussion.)

This is certainly a policy option that could be considered. Pensions policy is bedeviled by a failure to address risk issues openly, not least because most pensioners do not want to face the harsh reality that either a pension has significant risk or it is extremely costly to fund. Education is needed to address this point. Once we are ready for the debate, though, I would suggest there is room for a creative sharing of risk. There are no easy options here, not least because of the considerable uncertainty in estimating the size of the risk. But the problem is hard enough without artificially restricting the domain of possible solutions.

*One issue not addressed here is the use of DC schemes to reduce employer contributions. DC does not imply lesser employer contributions and legislation could (and probably should) stop employers using DC as a way of reducing their funding obligations.

Actuaries confirm inductive hypothesis shock

Here's what an actuary used to do.

Look at the markets. Assume the future will continue to be like the average of the past. Take massive amounts of hugely long dated risk on that basis.

Unsurprisingly that strategy didn't work that well which is why we have a pensions crisis (as I discussed earlier: see here or here). The latest in this slow motion train wreck is that UK life insurers have finally woken up to the continuing improvements in longevity and are now shoring up their reserves, again, to account for this.

Over the past hundred years, life expectancy in the UK has increased by four months every 10 years. Now all we need is for insurers to start to appreciate that they are not just short longevity but they are also short longevity vol...

Am me up, Pa

There is a lovely post today on the often insightful Calculated Risk on reverse mortgages. Here's the issue. Older people, particularly retired people, might have a valuable house but a low income. If they sell the house they take the risk that the funds raised run out before they die. What they need is an annuity like stream of income.

A reverse mortgage involves a bank making regularly monthly payments to a borrower as long as they live in exchange for a first lien on their property. The bank takes a combination of house price risk and mortality risk: if house prices go down then the eventual sale of the collateral will be lower than the value of the cash advanced; similarly if the borrower lives a long time then the interest payments create a substantial loss for the bank. Typically these products are structured as true mortgages so any excess of the eventual sale price over the amount needed to repay the loan belongs to the borrower's estate: the bank has the downside of higher longevity but not the upside of lower. Usually the notional principal of the loan is a fraction of the assessed value of the property so if mortality is high then the product is fairly safe. A combination of low mortality (increasing the duration of the loan) and falling house prices (decreasing the collateral value) can however be dangerous. There is also mortality dependent interest rate risk as you don't know how long to hedge rates for.

Note that combined asset price and longevity risk is one of the things that is causing problems in life insurance companies who have written annuities (or worst guaranteed return annuities) based on outdated actuarial tables and dud assumptions about asset returns. They too assumed that prices wouldn't go down and that people wouldn't live too much longer. Still, there's nothing like losing money in exactly the same way as the last guy, is there?
As Keynes put it:

A sound banker, alas, is not one who foresees danger and avoids it, but one who, when he is ruined, is ruined in a conventional and orthodox way along with his fellows, so that no one can really blame him.

Did Gordon really screw up our pensions?

Given Gordon is soon (one hopes, anyway) to ascend to the throne, one cannot help think that the timing of the recent objections to his abolition of tax credits for pension funds is partly political. Still, it is worth examining whether the objectors have a point: is Gordon partially responsible for the pensions crisis? Clearly the answer is no: if scheme actuaries had thought that reduced dividend income would have caused a problem, they should have increased contributions when it happened in 1997. Broadly, they didn't: some even gave employers a contributions holiday. With tax credits the holidays would have been longer and more widespread. The only people then who would have profited had El Gordo been less aggressive would have been employers. But I guess 'It was the actuaries wot dunnit' doesn't make for such a good headline.

Actuarial Advice, Part II

Now my point in Part I was not to be the latest in a long line of people to point out how foolish the actuarial assumption of equity returns being 10% forever are.

Rather, it is that the rules of the system have produced the behaviour.

If you set things up so that you are given advice where the 'best' thing to do today is purely defined by what happened in the past, you run a lot of risk that the future will be different to the past and hence that the advice will be misleading. One of the pieces of information missing in the old actuarial advice was some measure of the probability of things going sufficiently differently that pension obligations could not be met: perhaps if trustees had had that, they might have invested differently?

In the absence of any theory which we have reason to believe governs the behaviour of a variable, didn't David Hume point out the error of thinking the past behaves like the future? For the financial markets this is even more clearly silly than elsewhere: the global economy is obviously very different now from the one we had in the 80s, let alone the 50s. So why should stock prices follow paths characterised by statistics from long ago? That is not to say that we should not pay any attention to the statistics: just that we should be aware that there is model risk in how we use the past to predict the future, and for the sake of the next generation of pensioners, perhaps that risk should be considered along with all the others involved in running a long term investment portfolio.

When we use mathematics to model the world, as in fitting a return distribution of some financial asset, there is the danger that we use the maths that is convenient rather than the maths that captures the essential features of the problem. In finance, for instance, we are so obsessed with normal distributions that we use them whereever possible. Part of the reason for this is that so much is known about them -- we have a lot of tools to hand. Also, the errors made by using a normal distribution are often small for typical financial applications (especially once we hack in the implied volatility smile). That doesn't mean that the assumption that (log) returns are normally distributed is always good, though.

Phillipe Jorion has a insight into the dangers here in his paper on the fall of LTCM ( then search for Long Term Capital Management): he shows how making an modelling assumption, that correlation is stable and the return distribution is normal, leads to a dramatic understatement of risk. Sometimes, which tool you pick makes a lot of difference, and familiar tools can be the riskiest ones, not least because everyone else is using them too.

This is an education issue: the next generation of mathematical modellers needs to be taught how to model, but also about the dangers of modelling, about the need to look at a problem through the prisms of different models.

Turning back to actuarial advice, we have people trying to model the future using the past but without a theory that explains the dynamics, a system that encourages them to give their best guess with quantifying how wrong that guess might be, and a predilection for using tools that have nice mathematical properties but fail to capture significant features of the real world. Is it any wonder we have a pensions crisis?

There, I managed to talk about actuarial advice without mentioning the Ljung Box statistic once...

Actuarial Advice & How It Serves Us, Part I

Pensions are hot, possibly for the first time ever. There is a lot of press comment about underfunded pension funds and many people are becoming aware that their retirement may not be as comfortable as they had hoped. So it is not a bad time to look at one of the systems which underlies pensions, that of actuarial advice, and what it does.

Now what pensions actuaries do is rather complicated and any attempt to summarise it in blog length is at best vainglorious. But here goes. Firstly the problem. A pension fund takes money from people over some fraction of their working lives. The cash is invested. The fund has the liability of providing a pension, either based on pensioner's final salary (defined benefit, or DB) or on how the investments have done (defined contribution, or DC). In the absence of free money (aka a government guarantee) the amount a fund can pay in a pension depends on how much has been contributed and what the investment performance has been.

In a DB scheme, a individual's pension is determined by how the whole scheme has done; more recently for most DC policies, individual pensioner's assets are ring fenced.

So where do the actuaries come in? For a DB scheme, they advise on the investment strategy and the contributions needed to meet the liabilities. I'll concentrate on this kind of scheme, as they are the most interesting and the most problematic.

An aside on the individual versus the collective: In a DC scheme the typical member chooses how to make his contributions. If they do well, the member has a great retirement income. If they do badly, forget about that villa on the Riviera. The problem is that many people, myself included, find managing investments fundamentally boring. Most also have little or no education in it. So the growth of DC schemes combined with low education in investment fundamentals is likely to result in a significant number of pensions which will not provide their beneficiaries with a good standard of retirement income. This is hardly good for society. In a DB scheme, in contrast, short term mistakes in investment performance can be corrected by higher contributions by everyone: the scheme is a pool with money always coming in from current contributions and (after an initial delay) always going out to pensioners. In this setting, if more goes out than comes in, everyone suffers. So we have a classic prisoner's dilemma: to what extent should the individual subsidise the collective, and to what extent should he or she be able to rely on them for support in the event that things go badly?

Next, actuarial advice. A range of assets - different equities, bonds and so on - are available for the pension fund to buy. Which ones should they pick? In the very long term, it seems so far, investing in equities has resulted in higher capital appreciation than investing in safer assets like good quality bonds. On the other hand, in the very long term we are all dead, and in the shorter term there have been several extended periods where equities have underperformed bonds. DB pension fund trustees have to invest members contributions in order to have enough assets to meet the required pension liabilities. The advice they receive from actuaries in the past has often highlighted the historical outperformance of equities and hence influenced trustees to pick higher risk investments (the mean of the return distributions). What it sometimes did not highlight was the risk that equity markets might not outperform (some measure of the sample variance*).

What some actuaries did, in other words, was to build a model based on the past to predict the future. This is not a model in the sense of Newtonian mechanics or Relativity: extrapolation might be more accurate than model as there is very little theory underlying the idea that if something has grown at 10% for the last ten years it will carry on growing at the same rate for the next ten. The risk of doing this is obvious: if the world does not behave as your prediction suggests it should, decisions taken on the basis of the prediction can seem to be rather bad ones. And of course this is what happened with DB pension funds: investment decisions were made on the basis of the outperformance of equities, then when equity markets fell in 2001-2002, many of those funds did not have enough cash to meet the promises they had to keep. Hence the pensions crisis.

In part II, why the way actuarial advice was framed made this more or less inevitable.

* Assuming there is a process rather than just a sample variance is another modelling choice which might or might not be sound.