Category Archives: Actuarial and Risk

What is best practice for matching annuities in Greece in 2012?

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Best practice for matching non-profit annuities in most countries, certainly from a risk perspective, is still to cash flow match (or at the very least, match key durations) using government bonds.

The theory is that the insurer isn’t then exposed to changes in the term structure on interest rates, only exposed to illiqudity/reinvestment risk to the extent of mortality fluctuations, isn’t exposed to currency risk and certainly isn’t exposed to credit risk. Without complex margining requirements like some swaps and without the need to roll cash investments over, government bonds should allow ALM teams to sleep well.

Now, Solvency II is likely to adopt a swap yield curve rather than bond yield curve. There are some good reasons here, including arguably fewer distortions from temporary supply and demand imbalances, improved liquidity and so on. The same yield curve is used for liquid liabilities so the allowance for an illiquidity premium over and above the swap curve at some times, in some ways and for some products is still under debate.

But what should Greek insurers do in the meantime?

Frankly, Greek government bonds don’t remove credit risk and the huge credit spreads on these instruments will create huge funding gaps and variability in earnings unless a Greek govi yield curve is used to value liabilities as well. It’s not clear at all that Greece will stay part of the Euro, so German government bonds don’t remove currency risk. German government bonds in any case are show signs of nervousness as yields creep up.

The swap market is exposed to the same Euro break-up risks as bonds. Which banks will survive, what happens to currencies in the meantime and what does that do to long-term Euro swaps? What about Euro-Sterling swaps issued by Greek banks (I’m not sure if these even exist though).

All in all, it’s good to be involved in ALM in South Africa, and even the Middle East just at the moment.

Nearer the edge than ever before

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Great piece outlining the very real, very possible and very very awful possibilities and implications of Italian default.

I wouldn’t want anything to do with any bank that has much at all to do with European banks or European sovereign debt. The old South African Rand is seeming like a safer relative bet than at pretty much any other time in the last decade.

JPBIBNR – Just Plain Bad Incurred But Not Reported

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Nigerian GAAP, soon to be replaced by IFRS at least in the financial services sector, requires IBNR liabilities to be set equal to 10% of the Outstanding Claims Reserve. This is a terrible estimate of IBNR and there really are other, also very simple, better measures available.

As an aside, the use of IFRS balance sheet figures for regulatory reporting is also an unusual idea. There is no particular reason to believe that a shareholder financial reporting basis is appropriate as a regulatory measure. It can be, with specific capital rules perhaps, but it’s not automatically so.

Why the 10% of OCR rule for IBNR liabilities is so bad:

  1. For very long-tailed business with no or low claims reported in the first year, the IBNR will be massively understated
  2. as claims are reported (and before they are paid), the OCR will increase. The IBNR should decrease as the claims have now been reported, but given the 10% rule it will actually increase.
  3. The reconciliation of opening to closing IBNR and the comparison of actual vs expected IBNR claims over time is not useful since there are no explicit expectations built into the methodology
  4. Clearly the method is not sensitive to risks and delays of product lines or processes.

So what’s better? Well aside from the range of standard but fairly complex techniques (including Ultimate Loss methods, Basic Chain Ladder, Bornhuetter-Fergusson, Average Cost Per Claim and a whole range of stochastic methods) there are better simpler measures.

A starting point, although also very far from ideal, is the current (soon to be changed) South African statutory requirement of 7% of net written premiums. It also isn’t sensitive to different delay patterns and will give poor results if net written premium is growing or shrinking rapidly.

Really, the ideal simplification requires a little more complexity, but as a reward for this effort is a far more robust, more accurate measure that behaves sensibly in a far wider set of scenarios.

For each line of business for each delay year, we use a specified percentage of gross earned premium for the gross IBNR. Reinsurers’ share can be calculated similarly. The information relating to earned premium per line of business going back several years should be trivial to obtain and ensures we get a sensible pattern taking into account the growth in the business, the mix of business as well as change in mix of business. The method works well for start-up, mature or declining books.

The fundamental drawback of not reflecting a particular insurer’s patterns remains, but aside from using actual delay data this is about as good as one can hope for.

Frankly, why more regulators don’t prescribe this method is a mystery. The information is available, it’s trivial to calculate and verify and the results are robust.

Somehow, somewhere

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National Treasury is mulling Deposit Insurance with an explicit charge on the banks.

This is not a new idea, and has historically been resisted by the major banks since they feel, generally rightly, that they are less likely to have a problem of confidence and therefore less likely to benefit from deposit insurance. Smaller banks, on the other hand, are certainly more at risk of a run on the bank arising due to perceptions thus causing a liquidity problem when a solvency problem doesn’t exist.

Determining the appropriate mechanism to charge for deposit insurance is not straightforward. Clearly the charge can’t be the same fixed amount for all banks as the exposure will be very different between banks. The large banks would lobby hard to pay a lower rate (even if a higher overall amount) for the insurance given that they should be less subject to those confidence issues.

But how to determine that difference? One could take cue from the market by looking at credit ratings and, even more market-oriented, the spreads on debt issued by the banks. Three immediate problems come to mind:

  1. Credit quality of long-term debt isn’t the same as protection for depositors
  2. Probability of default is an input into confidence issues but certainly isn’t the entire story
  3. Does anybody seriously still believe in the Efficient Market Hypothesis and trust that we can believe what the market offers as an impartial, objective and balanced view of reality?

So there are some fascinating technical problems to solve when implementing deposit insurance, not least of which is deciding how much gets protected.

What caught my eye was Moneyweb columnist, Phakamisa Ndzamela, demonstrating his disbelief at how deposit insurance could create a moral hazard and ultimately increase risk within the banking system.

some senior bank executives have cautioned that this could push the cost of banking higher and somehow encourage risky lending. [emphasis added]

Obviously Ndzamela hasn’t heard of the Savings and Loan crisis in the US in the 1980s, or, I don’t know, the Global Financial Crisis that we are still in, which was massively exacerbated (if perhaps not quite caused) through risk being accepted without due care because it was being passed off immediately to someone else.

Why S&P downgraded

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I don’t think many serious investors care that S&P downgraded US debt. Bond yields are down (more on this in my next post), which means prices are up. US stocks are down, but that’s more about concerns about US and global economic prospects than the credit of the US government.

Nevertheless, S&P did downgrade. Why? I don’t think it is primarily to do with a materially increased estimated probability of default. It has more to do with a change in the payoffs in a ‘game’ (as in game theory) S&P is playíng.

Consider the quadrant of options. S&P downgrades or doesn’t and the US defaults or doesn’t. I’ve constructed totally hypothetically, but perhaps plausible scenarios below, for the S&P’s potential assessment of losses under each possibility given their views and external perceptions of them before and after 2008.

Before 2008, the fallout that would come from downgrading the US and the US not defaulting would be significant and cries of “un-American” might be heard again. Even if the US were downgraded, default would still be a blow for S&P since anything above a BBB rating really shouldn’t ever default if there models are “correct”. I’ve thrown in another hypothetical, a 0.01% probability of default – in other words very low, and as you’ll see in the next scenario, not necessarily higher now for S&P to change their view.

Now, either on a traditional minimax (minimizing the maximum cost) or an expected value basis, before 20008 S&P wouldn’t downgrade the US. This is an important calibration, since S&P didn’t downgrade the US.

After 2008, even if we leave the assessed probability of default unchanged, the world is different and therefore we have different costs.  If S&P doesn’t downgrade the US – even if the US doesn’t default, there will be a cost to S&P since might share the view that the US could default now. The dent in credibility since 2008 means that S&P has to try harder to convince the skeptics that they don’t rate risky instruments as AAA. Along with this goes a massive hit if the US does default and S&P hasn’t downgraded the US. The good news is that at least now a downgrade is viewed more with more understanding even if the US doesn’t default (although be sure Obama’s White House is not happy at the moment).

After 2008, even if the assessed probability of default is unchanged, the minimax and expected value rules both suggested a downgrade is the better option for S&P.

Before 2008

 Don’t downgrade

 Downgrade

 PD

0.0001
Default

-500.0

-50.0
No Default

0.0

-1,000.0
Expected

-0.1

-999.9
After 2008

 Don’t downgrade

 Downgrade

 PD

0.0001
Default

-10,000.0

-50.0
No Default

-10.0

-10.0
Expected

-11.0

-10.0

Now the example is contrived – I chose a set of parameters that demonstrates the point I’m trying to make. This isn’t a problem since I’m not saying this is what happened. I‘m saying it is plausible that S&P made a perfectly rationale (for them) decision to downgrade even if they didn’t think the US was more likely to default now than before.

In truth, the US might be more likely to default now than before, although the change is probability not sufficient on its own to merit a downgrade at this point. Especially since S&P have their maths wrong.


Medical Schemes, discrimination and the CPA

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The Consumer Protection Act (CPA) protects consumers from abuse by enforcing fair practices, improved disclosure and added minimum warranties etc,

It’s a good piece of legislation, even if at times some aspects of it may result in greater costs than benefits.

TimesLive has a story about the alleged noncompliance of medical schemes with the CPA.

Some of the issues may have merit, but this struck me as particularly troubling:

According to the act, it is unfair when a consumer is discriminated against on the grounds of age.

Our constitution explicitly allows discrimination on actuarially sound rating factors that have both a statistical and causal link. This is how insurance is South Africa still uses underwriting to select homogenous groups of risks and to limit anti-selection by policyholders. If widespread anti-selection were to occur, then life insurance would not be viable.

Medical Schemes in South Africa have only very limited underwriting options in order to provide as many citizens as possible with fair health coverage. “Late joiners” are charged a premium since they haven’t contributed to the societal risk pool since they were most healthy and therefore haven’t paid “their fair share”. This has to do with a specifically identified risk rather than general discrimination based on age. These restrictions are important to maintain the solvency and viability of medical schemes.

Some schemes prevent women who fall pregnant within nine months of joining the scheme from claiming for the pregnancy even though they pay full premiums

This point is more tricky, but it does again reflect a misunderstanding. “Full premiums” on an actuarial sound basis have probably not been paid, since the fair premium for a member who joins just to get pregnancy benefits and hasn’t contributed at other times would be much higher than the premium that is charged. This one is a little more grey and while I feel the rules are entirely fair, they may not be viewed that way by a particular judge on a particular day.

Some schemes require that members give three months’ notice when terminating their membership, whereas the act deems 20 business days to be reasonable

This might reflect the desire to not have members leave a scheme immediately after having utilized the maximum benefit available to them before joining another scheme. I don’t know how much of this behavior would ever happen, so this might also ultimately be changed.

Many schemes don’t enforce the allowed waiting periods for members joining. If some of these other changes were to be made, I would expect these provisions would be more regularly used. Of course, that is another of the problems cited with medical schemes arising from the CPA.

All in all, we may see some changes, but by and large these comments reflect a lack of appreciation for the actuarial realities of managing a health scheme with community rating.

Gaining new insight into insurer profitability through New Business Margin on Revenue

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The Value of New Business written by an insurers is a good measure of the value created through sales activity over a certain period. It’s not the easiest number to interpret in terms of profitability though.

New Business Margin, which is the Value of New Business (VNB) as a percentage of the Present Value of New Business Premiums (PVNBP) is a common measure of profitability of that news business.

But it’s a flawed measure, especially when it comes to comparing product lines and insurers or even to understand the change in profitability from one period to the next. It uses and unequal yardstick to measure business.

New Business Margin on Revenue (NBMR) provides a significantly improved measure of profitability that can be used to compare margins across products, across insurers and across time. Further, it leads easily to a component analysis of the margin, adding additional insights to shareholders, brokers and regulators.

If you haven’t read my introductory post on New Business Margin on Revenue, it would be worthwhile doing so now – this post is going to illustrate the sort of results it provides in a practical, numerical example.

Example 1 considers how NBMR clarifies distortions from a change in mix of business.

Example 2 shows how more complex dynamics can be understood through a component analysis of NBMR. The spreadsheet showing the underlying calcs is attached at the end of this post. Continue reading →

New thoughts on renewal rates for Embedded Values

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Embedded Values (EVs) are widely used to measure value for life insurers. In the context of long-term contracts such as individual life, it reflects the value embedded in prudent regulatory provisions (or “actuarial reserves”).

For short-term business (group risk, health insurance, health administration, general insurance etc.) it is something different since these lines don’t have long-term prudent provisions. In these cases it reflects the present value of future profits expected to be earned out of the existing business.

The inclusion of these short term types of business within EV is widespread. It seemingly increases consistency between different types of contracts since we are considering the long-term expected profitability in all cases. More on this apparent consistency in a moment.

What do we include in the EV and VIF?

EV is not a complete economic measure of the value of an insurer, since it ignores future profits arising from future new business. This is by design. An Appraisal Value incorporates the Value of Future New Business (VFNB) as well, although there is always subjectivity over how many years of future new business should be included. (More on this in a separate post.)

Existing Business vs Future Business

The idea of “existing business” and “future new business” is clear in the individual life context. It’s existing business if you have a contract, and future new business if not. Premium increases and slight benefit modifications can usually be accommodated within the existing contract and so should ideally be included in the Value of In Force (VIF) based on the expected probabilities of these changes. Continue reading →