Category / Insurance and Actuarial Practice

The regulation of insurance in the U.S. November 14, 2008 at 9:45 am

The Aleph Blog has a remarkably wrong-headed piece on insurance regulation here, suggesting that federal insurance regulation is a bad thing and that the FED should have let the AIG parent fail.

Some comments. First, the US is the only major economy that does not have a national regulatory framework for insurance. Instead it is regulated at the state level. Some of the states do it well, some less well. Many of them are different. How can it possibly make sense to have over 30 regulatory frameworks for the same product in one country?

Secondly US insurance regulation is a long way behind the curve even in the best states. While the EU is on solvency two, with fairly sophisticated capital modelling, the US framework does not require enough capital for credit risk, which is why the monolines and AIG got into so much trouble in the first place. Their leverage was not effectively constrained by their capital requirements (and in some cases their accounting framework encouraged them to take risks more cheaply than banks would). The U.S. needs to address the arbitrage whereby it is significantly cheaper for some insurance companies to take credit risk than for banks.

Thirdly, letting AIG fail was not a realistic option however much moral hazard its bailout presented. I continue to dislike the bailout. However depriving the banks of hundreds of billions of dollars of protection is simply not sensible at the moment: you would only have to spend the money recapitalising them.

I'm bored of cheap and cheerful

Why AIG must be kept afloat November 10, 2008 at 11:07 pm

It has written an awful lot of CDS protection. If it goes down, the contracts accelerate and the banks who bought protection get recovery on the current MTM. Recovery is unlikely to be more than 50 cents on the dollar, and so the protection buyers would suffer large losses. At least a hundred billion, I would estimate, probably more. So you have the choice between letting AIG fail and putting 100B or more into the protection buyers, or giving it another 50B and trying to keep it afloat. That’s a no brainer.

MBIA sues Countrywide October 4, 2008 at 9:50 am

Confirming the insurance industry habit of substituting claims adjustment for underwriting diligence, MBIA is suing Countrywide according to Housing Wire:

The breach-of-contract lawsuit, filed in New York State’s Supreme Court, suggested that Countrywide developed a “systematic pattern and practice of abandoning its own guidelines for loan origination,” in effort to inflate its market share during the mortgage-lending boom. MBIA accused Countrywide of knowingly negotiating riskier loans “no matter the cost to borrowers, investors or guarantors like MBIA.”…

Overall, the case involves 10 residential mortgage-backed securitizations of more than $14B in mortgage loans.

This is going to be interesting. On the one hand, it seems obvious that mortgage quality did decline in the last years of the Greenspan boom. But can MBIA really prove that Countrywide abandoned its own loan underwriting standards – rather than simply changing them to adjust to `market conditions’ – and that that was a breach of contract of the financial guarantees? If it can, we are going to see a lot more wriggling from the wrappers, and the lesson from Hollywood Funding – that insurers can’t always be trusted to pay when you think they have written protection – will be driven home to a lot more people.

New York really wants London to succeed September 22, 2008 at 9:12 pm

Big TruckAccording to Bloomberg:

New York State will begin to regulate part of the $62 trillion market for credit-default swaps, Governor David Paterson said.

The state will treat contracts in which the buyer also owns the underlying security as insurance, Paterson said today in a news release.

That’s it then. London always was ahead of New York in structured credit: now, provided we do not do something similarly stupid, we can own this market.

It is worth pointing out, en passant, how successful treating credit derivatives as just another insurance contract has been so far. The largest two firms to adopt that paradigm were MBIA and Ambac. Unless you count AIG of course. Still, New York will still have better looking trucks.

That’s something. But it doesn’t produce jobs for the geeks.

Update. The Economist has a nice article, Guilt by suspicion, about the benefits of derivatives and the mud slung at them. I do think it is worth remembering that the cause of all of this mess was not derivatives, it was mortgages.

Ball of steel or brains of lead? August 9, 2008 at 5:31 pm

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?

Fair Value and Insurers July 9, 2008 at 7:06 pm has an excellent post on Fair Value accounting. One quote in particular amused me:

James Tisch, who was effectively the sole voice of dissent on the first panel, complained bitterly that fair value accounting required reams of nearly incomprehensible disclosure information and often forced his company to make poor economic choices.

Tisch … said that if insurance companies had to run mark-to-market accounting through their income statements, “[they] would essentially be out of business”

And that, as we have seen with the financial guarantee insurers, is clearly right. But perhaps if the insurers were forced to use fair value, they might deploy less leverage and pay a little more attention to what the market is telling them.

Blame the actuaries July 2, 2008 at 8:49 am

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.

Bill Ackman I salute you June 5, 2008 at 10:47 pm

S&P lowered Ambac and MBIA to AA today. They are under review from Moody’s. Fitch, only six months late rather than the year or so of the other two agencies, downgraded them in January. Bill Ackman made another big pot of money. And there’s a nice opportunity opening in zombie monoline runoff…

What form of structured finance protection have the monolines written? February 15, 2008 at 9:01 am

Serpentine Pavillion

This is a valid question as we go into any restructuring of the bond insurers, and the answer is more complicated than it appears at first sight. Here are some of the issues.

Many corporate bonds pay interest and final principal – you get coupons for some period, then a return of principal.

A standard CDS on a corporate bond uses a notion of credit event which typically includes default, failure to pay and bankruptcy. If the bond displays a credit event, then the CDS protection buyer stops paying the premium on the CDS and has the right to receive recompense in a short period, perhaps 3 or 5 days. This recompense is either through the right to deliver a bond and receive par (physical settlement) or through the right to receive an estimate of par minus recovery as a cash payment (cash settlement). Some key features include rapid payment, the ability to go short – by purchasing cash settled CDS without owning the bond – and the derivatives (i.e. mark to market) nature of the instrument. Note too that the premium is risky in a standard CDS: if default happens, you stop paying it.

There are insurance policies which behave much like CDS. These are part of a wider class of insurance known as financial guarantee policies. The difference here is that they are legally insurance (and hence have a different legal, accounting, regulatory and tax framework). In particular this is not a mark to market instrument, and in most jurisdictions you have to be an insurance company to write insurance. Note also that insurance typically requires an insurable interest – I cannot profit from buying fire insurance on your house even if it burns down – so if you purchase a financial guarantee policy directly it might not allow you to go short.

The fact that there are two instruments, CDS and financial guarantee policies, which can act much the same way yet have very different accounting should be a matter of shame to the FASB and the IASC.

Another possibility for obtaining protection is a bond wrap. Bond wraps are part of a wider class of insurance policies known as financial guarantee policies. In a bond wrap the policy runs to maturity of the bond, you have to keep paying premium until that date (so the premium is not risky), and the policy writer agrees to make good the scheduled cashflows of the bond should the original bond issuer suffer a credit event. Thus here you get paid on the original schedule, and if there is a credit event you substitute the risk of the issuer for that of the policy writer. Most of the muni policies the monolines have written are in this form. The advantage from their perspective are not only insurance accounting, but also lack of cashflow stress: unlike a CDS you typically have plenty of time to find the cash to make the principal repayment.

With amortising securities the issues become more complex since there is the possibility of a principal and interest payment at each coupon date. You can write standard CDS on amortising securities, but it is also possible to write a pay as you go CDS. This imports bond wrap technology into derivatives, and gives the protection holder the right to demand payments on the original schedule from the CDS writer.

For corporate bonds, amortising or not, matters are fairly straightforward since the failure to receive any cashflow (or at least a material one) is an event of default. For ABS you might not want that feature though: in a typical credit card deal, for instance, there will be a certain level of delinquencies which all parties expect, and if you have a credit event which triggers cash settlement based on default, then many junior ABS would suffer that event in the first month. Moreover in many ABS the collateral prepays, so you do not know when you will get your principal back. This means that to define a CDS or financial guarantee you need to tease out the cashflows each security should get in a given month given the level of prepayments, see what cashflow it actually gets, and define protection based on the difference.

Matters get even more difficult when you have amortising collateral in a CDO but some of the tranches have bullet maturities. Remember too that in some cases the CDO issuance SPV can be technically unable to pay without the CDO collateral having lost value: this can happen in particular due to liquidity risk. Figuring out exactly who pays whom what when something bad happens in a CDO of ABS is sufficiently complex that standard documentation has not been available until recently. Most transactions historically used bespoke documentation, and figuring out exactly which risks were transferred was not a trivial business.

Finally, note that the legal final maturity of ABS is often well beyond the last cashflow date. For a mortgage deal, for instance, it might be 35 years. So a contract which only gives you the right to claim ultimate principal at legal final maturity is like buying protection on a long dated zero coupon bond.

My guess is that most but not all of the monoline’s structured finance business involved taking middle or upper tranche ABS and writing pay as you go style protection on it in the form of a financial guarantee. This has considerable accounting advantages over writing standard bullet CDS, as well as the advantages the monolines enjoy as a result of insurance rather than banking capital. Finally it means that the monolines have relatively little immediate cashflow stress even though their structured finance portfolio would be, on a mark to market basis, highly underwater. None of that means that there is no problem with their business — just that if this is going to be a train wreck, it will be a slow motion one.

In any event we do need to know the answer to this question as it determines the capital needs. If they have written CDS with collateral agreements then the monolines need enough capital to support the mark to market volatility of the trades. If they have just written insurance then they only need enough to support the ultimate realised losses on the portfolio. Those numbers are very different (and it impacts how right Bill Ackman is).

Some people have suggested that one of the villains of the current crisis is mark to market. I don’t agree: mark to market gives one view of the value of a portfolio; insurance accounting another. But certainly having a portfolio of similar risks subject to wildly differing accounting principles in the same legal entity is unhelpful.

Why isn’t Warren stomping on the monolines? January 9, 2008 at 2:00 pm

Bloomberg reports that MBIA is falling again:

MBIA Inc., the giant bond insurer hobbled by the collapse of the subprime market, will cut its dividend 62 percent and raise $1 billion in a sale of notes to boost capital and preserve its AAA credit rating.

The Armonk, New York-based company has declined 81 percent on the New York Stock Exchange in the past 12 months and fell 4.2 percent today after it reported fourth-quarter writedowns and expenses of about $4 billion related to mortgage securities.

Bizarrely Buffett may be willing to help, despite his interest in setting up a competitor:

“We’re looking at multiple ways to participate in the industry,” Ajit Jain, head of Berkshire’s new bond insurer, said today in an interview. Berkshire, based in Omaha, Nebraska, is “looking at ways to support the existing insurers in terms of reinsurance and capital,” he said.

Part of the reason the monolines are in focus is, as Naked Capitalism reports, that Countrywide is rumoured to be close to bankruptcy. If it were to go down, it would trigger a wave of claims on the wraps the monolines have written that they likely could not pay. In this context, why doesn’t Buffett just let his competitors go down? Or has it been gently suggested to him that it would be in the U.S. national interest if he used that spare cash to support the industry? Certainly the NYT’s account of the support Buffett got for setting up his new monoline is bizarre. To pick some of the juicier bits:

Shortly before Thanksgiving, Eric R. Dinallo, the insurance regulator for New York State, did something unusual. He called Warren E. Buffett’s right-hand man on insurance, Ajit Jain, and suggested that he start a new company to insure municipal bonds in New York….

To be a New York company, Berkshire, with its main insurance offices in Stamford, Conn., would technically need to run its new business from offices in New York. But Mr. Dinallo agreed that Berkshire could set up a token office in New York and do most of its work in Connecticut…

For its part, Berkshire agreed to put up $105 million in capital to start, $30 million more than the minimum required by New York. But “to minimize the amount of capital trapped in the entity,” Mr. Jain said, Mr. Dinallo worked out a way for Berkshire to increase its leverage by permitting it to exceed the usual limits on reinsurance, or insurance on the risk the new company acquired.

Wearing a cap January 7, 2008 at 1:18 pm

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 January 5, 2008 at 10:41 am

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…

How muni insurance works January 3, 2008 at 11:08 am

There is a very nice article on Accrued Interest summarising the muni market. It helpfully discusses who the muni issuers are, the difference between general obligations and revenue bonds, muni default rates, and the role of the monolines in wrapping muni bonds. What we need next would be a summary of the tax games in muni land…

Dying for Goldie December 15, 2007 at 4:33 am

Goldie has announced that it will publish a mortality index, presumably to stimulate growth in the mortality swap business. Insurance-linked capital markets products have been around the market for a while without really catching on – I remember being told that mortality swaps were the new credit derivatives – but this might stimulate the market a little. All the same, I’d want to be sure I wasn’t one of the 46,000 odd individuals in the index just in case. Getting between Goldie and an index fixing might just be bad for your health…

Timing risk and finite reinsurance November 21, 2007 at 12:15 pm

One of the murkier parts of the reinsurance world is finite reinsurance. Even finding a good definition is difficult. But here, rather than surveying the whole topic, I want to discuss one particular application, namely hedging timing risk.

The typical situation this arises is where there either may or will certainly be claims on an insurance policy over an extended period, but their timing is uncertain and their maximum size is bounded. Suppose for instance we know that over the next ten years we will very likely have to pay out claims of £10M, but we do not know when these claims will be presented. This risk can cause significant earnings volatility: in years with no claims, our earnings look great, but if £8M or £9M of the £10M arrive all in one year, things will look less good for that year.

This earnings volatility can be hedged (for a price). Typically we transfer some assets, say £8M worth, to a reinsurer: these assets are invested. Simultaneously they write us a reinsurance policy capped at £10M on the risk, and receive a small premium to be thought of as an asset management fee. If claims arrive very early in the policy the reinsurer can lose money as the £8M will probably not have grown to £10M in the first couple of years. If the claims happen late, they make money as the assets will have grown to be worth more than £10M over eight or nine years if prudently managed. The reinsurer therefore takes some timing risk and some investment performance risk, but not much. It is a very large very well capitalised entity so it can handle the earning volatility much better than the ceding insurer.

There is even the possibility of passing some upside of good investment management and/or good claims management back to the ceding insurer via an experience account: for instance if the £8M has grown to £12M before claims of £9M leaving £3M at the end of ten years, then this could be split 50/50 between the reinsurer and the ceding insurer. With careful structuring this can mean that it is possible to transfer very little risk with a finite reinsurance policy yet achieve the desired aim of smoothing earnings, i.e. an accounting arbitrage.

This kind of technology emphasises that insurance can act as a form of capital. Without the policy, the ceding insurer would have to support the earnings volatility with equity. With it in place, capital requirements are reduced. The reinsurer is better placed to take the timing risk than the primary insurer and hence a deal is possible which makes sense for both parties.

Am me up, Pa May 28, 2007 at 7:01 pm

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? April 21, 2007 at 4:25 pm

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 March 7, 2006 at 8:53 am

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 March 6, 2006 at 8:58 am

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.