The Efficient Frontier of Shoes

In financial economics, there is a concept called the efficient frontier of investing. You can combine a portfolio of shares and other investments in many ways. In theory, there is one line which consists of the intersection of the best return for each level of risk (or alternatively, the lowest risk for each level of return),

While I was futilely trying to convince myself that the shoes I was trying on would become more comfortable with a bit more wear, in my annual shoe buying expedition, I realised that it’s quite a useful concept for shoes, as well.

In buying shoes, there is generally an optimal level of comfort for a given level of dagginess. So in buying shoes, I try to optimise comfort at the least stylish point on the curve I think I can get away with for a given occasion. Others will choose comfort, and optimise fashion, but either way we will end up in the same place.

In putting together the efficient frontier graph, I realised something else. Changing gender from female to male moves the line upwards AND makes it much flatter. The only place the two lines intersect is at runners, and the dagginess factor at that point is MUCH higher for me than women.

Cross posted at actuarialeye.

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Missing girls

Crossing the Nile to go to school - But how many girls live to go to school in Africa?

Last year I read a fascinating book, Unnatural Selection: Choosing Boys Over Girls, and the Consequences of a World Full of Men, by Mara Hvistendahl. She talks about the issue of missing women, how demographically, there should be more women than there are in many different countries of the world. The issue was the subject of an Economist cover nearly two years ago.

Tyler Cowen has alerted me to a fascinating paper on the subject, soberly entitled, Missing women: age and disease, by Siwan Anderson and Debraj Ray.

The authors, instead of doing a fairly high level comparison of ratios between men and women at birth, and men and women in the population as a whole, look at projections of the relative proportions of men and women given the same relative birth and death ratios between genders that happen in the first world. They readily point out that there are many different ways to work out what the “appropriate” relative birth and death rates are, but nevertheless they come up with some fascinating conclusions.

Our study of excess female deaths by age yields two key findings. First, once we control for natural variations in the sex ratio at birth, sub-Saharan Africa has as many missing women as India and China: significantly more as a percentage of the female population. Second, the majority of missing women are of adult age. Sub-Saharan Africa has no missing females at birth, while the corresponding proportion for India is under 11%. China’s missing females, in contrast, are largely prenatal. About 37–45% of them may be classified as missing at birth. But all these regions display missing women at a variety of ages. For instance, excess female mortality up to age 15 does not account for more than a third of the total in India or sub-Saharan Africa.

So the fascinating thing about this study for me is the complexity it adds to the story. While the standard story of why there are “missing women” is sex specific abortion and female infanticide, that is only really the explanation in China. In other countries, the story is much more complex, with relative female death rates much higher than males at a variety of ages, and in sub-Saharan Africa, particularly because of maternal death rates and deaths from HIV-AIDS.

Ultimately, the conclusion of the paper is not that different from the Economist’s attention grabbing “100 million missing women”. But the reasons are far more interesting.

We find approximately 20 million missing women in India, 58 million missing women in China, and 8 million missing women in sub-Saharan Africa. Look at the enormous difference between China and the other two regions (in flows all three regions were about the same). This comes from the fact that excess female deaths in China are clustered at age 0. We reiterate, though, that these estimates must be treated with a great deal of caution.

The missing women in India and sub-Saharan Africa are largely because a variety of causes (injury, suicide, various diseases) disproportionately kill the women there.  That’s a reason to worry, and potentially an easier issue to fix, if the will and the resources are available.

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Cross posted at my new blog actuarial eye.

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The cost of living longer

This article, from the US smart money magazine, is a fascinating look at the latest thinking on how long we are likely to live. You really should read it in full.

It looks at the latest thinking on longevity, and what that means for retirement planning. Some US life insurers are providing insurance older and older, even for people who have had brushes with cancer and other nasty diseases, on the basis that modern medicine really is getting much better. Some of the underwriters interviewed for the article suggest that you really should plan on living to age 95.

Many Australian financial plans tend to look at the average life expectancy and save on that basis. On average, a 65 year old Australian man should expect to live to 83, and a 65 year old woman should expect to live to 86. So if you are likely to live to 86 (based on your current age) you should make sure you have enough capital and income to last that long. If you die sooner, at least you can pass on the left over money to your heirs.

But what if you live longer? Most Australians would assume they will live off the aged pension in that case. And it is generally enough so that you won’t starve (although if you don’t own your own house you’ll find it tougher). But the aged pension is not a huge amount of money. The maximum rate for a single pensioner is $748.80 per fortnight, and $564.50 per person for one half of a couple. That’s $19,536 for a year for the single pensioner.

Longevity is a real risk, but not one that most people are willing to insure against. It feels like a bet that you lose twice. If you die too soon, you’ve missed out of years of life, and an insurance company got to keep your money. I blogged about this years ago. I don’t believe the longevity insurance (generally annuities) will ever be more than a tiny niche product in Australia. But it is still a risk most people should think about.

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Cross posted at my new blog actuarial eye.

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Fertility update

Last month, the annual fertility rates were released by the ABS. I last did a post on this two years ago, so it is time for an update.

My broad conclusion was that fertility rates are pretty stable in Australia, with the very important caveat that that stability is in the number of children the average woman has in her lifetime, not necessarily how old she is when she has them.

So first, the headline. In the last two years, the total fertility rate for Australia (which represents the average number of babies that a woman could expect to bear during her reproductive lifetime, assuming current age-specific fertility rates apply) has dropped from 1.97 in 2008 to 1.89 in 2010. That is a reasonably significant drop (nearly 0.1 of a child!).

But the movement in the headline fertility rate is always much more than the movement in the average fertility for a woman over her lifetime. Below, you can see that the lifetime fertility rate for women this century has stayed quite stable.

Source: ABS, my own analysis

Women born in 1933 had the most children, on average – 3.1 in total. But women born in 1966 (the most recent date for whom lifetime projection is reasonable) are expected to have 2.05 babies, on average, over their life.

So why does the headline rate move around so much? It is all to do with when women have their babies. Those women born in 1933 had already had two of their children by the age of 28.  In another three years, on average, they’d had another half a child. In contrast, the woman born in 1966 had had one child by the time she got to 28. And it took her until the age of 33 to have the next half a child (on average). But she was still having children in her late 30s and 40s – she was having 50% more children then than her mother’s generation 30 years earlier.

This graph shows that effect.

Source: ABS and my own analysis

Interestingly, the generation from 1906 shown in this graph is much more similar to that woman born in 1966. While the woman born in 1906 had more children in her twenties than her granddaughter’s generation, she kept having them well into her late 30s and 40s, even more than women who are that age now.

Every year the news of the latest statistics gives rise to articles like this one, pointing out that Australia is in danger of not reproducing its population. But while we do seem to be dropping under replacement rate slightly, the bigger news is the change in the age of most parents – that’s the main message from this year’s statistics.

Cross posted at my new blog actuarial eye.

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Travelling Feminist: Women on Boards

This is a departure from my usual Travelling Feminist post. But I’m in Norway, and Norway, in the 21st century, is proud of its position as one of the most equal countries (by gender roles) in the world.  Statistics Norway has a special gender equality index, and 40% of the parliament (the Storting) is female. Norway has gone further than most in one particular respect – they have legislated for approximately equal gender representation on listed Boards:

Companies are required to have at least 33% to 50% of each gender depending on the size of the board (see details in the document attached). The 40% requirement applies to boards of over 10 members. These percentages are for the shareholder representatives. And for those who wonder, yes, one company did have to search for a male board member to reach the target! (Source: Europeanpwn)

The process the Norwegians went through was two fold. In 2003 (when the percentage of women on listed company Boards was 9%), they introduced the concept, with a deadline of 2005, but no sanctions for non compliance. And then in 2006, they went further, and said that by 2008, those companies that were not complying would be delisted. And now Norway has more than 40% women on its listed Boards. The effect has trickled into non listed companies, as well, with the percentage of women there rising as well, to 17%. The change has been studied by a few different people.

The only quantitative study, by Amy Dittmar and Kenneth Ahern of the Ross School of Business at the University of Michigan found that the companies with the smallest proportion of women at the beginning of the period of compulsion lost the most value compared with their peers – their hypothesis is that they were most likely to be forced to appoint unsuitable candidates. They found that female directors were significantly different from their male peers – they were better educated (more likely to have an MBA), younger (around 8 years on average) and less likely to have been a CEO. They also found that the proportion of listed companies out of Norway’s total seemed to have reduced (with a reduction in the number of listed companies, and an increase in the number of listed).

Although their study did try and correct for the possibility that the companies with more women on Boards at the beginning were better companies to start with (which is a reasonable hypothesis, given several studies showing statistically better performances from companies with more diversity at Executive level), by comparing with similar US and Scandinavian firms to see if the performance gap was similar, and by correcting for industry differences, it still seems to have relied fairly heavily on market capitalisation at a particular point in time (compared with net assets – the Tobin Q) as a measure of which companies performed, which makes me suspicious, given that the point was in the middle of the global financial crisis. The measurements were relative, rather than absolute, but the strongest argument that comes from this study for me, is that compulsion should be more gradually introduced.

Kate Sweetman spent some time interviewing directorsof Norwegian companies who went through the change. She interviewed men and women, all of whom were already directors, and almost all of whom opposed the change. Two years later, in a series of one-on-one interviews, every single person said that the boards were measurably improved with the addition of the women…some direct quotes:

* “If I had to generalize about the differences between men and women on boards? Women are more interested in getting the facts. Much more prepared; ask many more questions. Men tend to shoot from the hip.

* “What do women bring? We used to be a fraternity of men sitting on each others’ boards. The real issue is the fraternity of men. It is necessary to break up the in-breeding. It is unhealthy how the men protect each other. They are unwilling to go up against the CEO, for example.”

* “Think about the difference between an evening out with 3 of your girlfriends, or a guy and 3 of his guy friends, or two couple friends going out. It is always more interesting when the couples go out. Very different dynamics. The group dynamics totally change. More civilized. Less swearing, less jockeying for position. The problem with jockeying is that jockeying is about the individual’s position, not about the company.”

And Aagoth Storvik and Mari Teigen, both senior researchers at the Institute for Social Research in Oslo, released a study that argued that without both the compulsory quotas and the accompanying sanctions for non-compliance, it would be next to impossible to increase the number of female board members. This articlein Der Spiegel quotes from the study, and the researcher, pointing out that 7 years after the concept was introduced, nobody in Oslo is worried about it any more.

“But after the reform went into force almost nobody seemed to object, hardly anybody is writing about it in the newspapers any more or telling us about negative experiences.”

Australia, where the percentage of women on listed boards was 8% in 2010, recently went through a period of soul searching about this issue. The same arguments as were used in Norway (here outlined by Kate Sweetman) were used as to why quotas are a bad idea:

Quotas are wrong because they are about diversity and business is about meritocracy; quotas are simply a form of institutionalized reverse discrimination–what about the men?; government has no business interfering with the workings of business; quotas on boards flew in the face of shareholder rights; if qualified women existed, we would already have them on the boards; women don’t really want this anyway.

After several people publicly called for quotas, the proportion of women changed faster than it ever has – reaching 10% in less than a year. But 10% is still a long way from 40%. Should there be quotas? The Economist recently argued strongly that this was the wrong way to change the proportion. They ultimately viewed the financial study as more powerful than any other arguments. Although their piece made powerful points that women are consistently underestimated by men (based on a study by INSEAD) and that women are less likely to have a powerful mentor than men – often key to making it to the very top of a corporate, they seem to end up with the view that the main reason that women don’t make it to the top is that old saw – work life balance – they don’t just get the experience needed to get to the very top, and they don’t want to put in the hours.

But a much bigger obstacle to putting more women in boardrooms is that so many struggle to balance work and a family….Partly because it is so tricky to juggle kids and a career, many highly able women opt for jobs with predictable hours, such as human resources or accounting*. They also gravitate towards fields where their skills are less likely to become obsolete if they take a career break, which is perhaps one reason why nearly two-thirds of new American law graduates are female but only 18% of engineers.

I once would have agreed with them, being very cautious about the concept of quotas. Quotas can lead to adverse consequences in many different situations – just those that the Norwegian directors were fearful of. The thought of being regarded as the “token” – not there on merit, but because of a rule, is appalling. But the Norwegian experience suggests to me that it is not just a matter of lack of experience. Unless they are forced to, companies will fall back into comfortable habits when hiring people, particularly those, like board members, for whom it is difficult to define competence or success objectively.

Once more women are let into the boardroom, astonishingly enough, they add value just as they are. Quotas had the effect of forcing companies to hire women who were already capable of adding value to the companies that recruited them.  The last word should go to Hilde Tonne, an executive vice president and head of communications at Telenor, a global telecommunications company based in Oslo, from the NY Times:

“We have excluded women for 1,000 years,” she said, with a smile. “So we have already had quotas — it’s just that they were for men.”

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* This is a minor point, but one that has to be made. Most articles you read about women on boards say that not enough women take the hard operational jobs – running an operational division, or being the CFO, rather than HR and marketing. Yet the Economist is talking about women going into easy jobs like accounting and suggesting that is why they aren’t Board members! Really, we can’t win.

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Is honesty the best policy?

As we missed yet another u-bahn train laboriously putting €2.80 in a ticket machine yesterday for the boys’ train tickets, I pondered the various approaches taken to honesty by all the public transport systems we have tried.

Singapore, China, Israel, and the Netherlands share a common characteristic. It is nigh on impossible to get on a train without a valid ticket (just like most of Sydney’s public transport system). While most of the continental European trains so far in our trip(Germany, Austria, Poland and the Czech Republic) rely on honesty, plus monitoring – you can get on and off a train however you please, but there are big signs everywhere warning that if you are caught without a ticket, the ticket price will be expensive (and then there will also be the hassle factor of potential criminal proceedings…).

For the record, in our month or so so far in public transport systems relying on honesty, we’ve had our tickets checked once.

When I was a backpacker, there was a thriving gossip network comparing notes on how likely you were to be caught on the various public transport systems. German trains, in particular, were seen as a soft touch. I’m sure the same discussions take place in youth hostels around the world today.

For the slightly less impecunious traveller, the decision to take your chances also depends on the hassle of buying a ticket. Probably not coincidentally, all of the honesty countries have various travel passes (starting at a day and moving up to a week or so) which are very good deals compared with single tickets if you’re doing much more than two trips in a day. So if you have any chance of buying a ticket, you are pretty likely to have one when checked.

I’d love to know how the authorities make the decision to go for an honesty based system. Is it a reflection on the society generally, that most people are pretty honest, so the occasional threat of a ticket inspector is enough to keep them in line? Or is it that they see public transport as a public good anyway, so the revenue raised is not the most important aspect? What is the probability that they target in deciding how many ticket inspectors to employ? And do they know how much leakage they have in their total ticket take? How much do you save when you don’t have to bother with ticket gates and all the associated paraphernalia (particularly if you have a complex ticketing system – don’t get me started on Sydney’s fare structure)?

In Berlin, at least, they targeted us right. Our week long ticket cost as much as 10 single tickets, so was clearly a sensible purchase (for the adults, at least). And so we would have felt smugly virtuous if we met a ticket inspector.

I’m inclined to think that the Germans have got it right – take the hassle out of ticket buying, and everyone will have one. While there is bound to be leakage, the utility for all the virtuous ticket buyers is quite substantial. And ticket inspectors can target the times and lines that are most likely to have free riders.

 

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Civilized travel

What’s the most pleasant form of public transport? Bar none it has to be the long distance train. We’re sitting on a train from Salzburg to Munich, having a very relaxing morning. We got up slowly this morning, did a bit of school work, packed ourselves up, and walked to the station.

And we’ve just whiled away the last two hours very pleasantly. Chatterboy and Hungry Boy have watched a bit of educational television, and are now playing a game and reading a book respectively. Mr Penguin and I have been reading our current books. We had a nice lunch of filled rolls, which I picked up at the train station before the train left, and at each end we have an absolute maximum of half an hour between the station and where we are staying.

Hard to imagine a trip that nice involving a car, even if you aren’t the driver.

To make that work, you do need a high population density. Even in rural areas, we can almost always see a village. That’s certainly not true when we drive to Canberra from Sydney (a trip that is nearly twice as far).

And part of the reason our train journey was so pleasant was that the train was practically empty, as it was around the middle of a working day. I imagine that the German train system gets a fair degree of subsidy from the government, and certainly the amount we paid for this trip (€29 for around 150km) didn’t pay for our share of the deserted carriage.

Ryan Avent, the Economist’s economics online editor, had a fascinating post a while ago describing the flawed analysis that means that even in parts of the US where long distance travel makes sense, the established economic discourse means that road subsidies and rail subsidies are measured completely differently.

There is a similar discourse in Australia, too, and from everything I’ve read, the NSW Treasury, in particular, had an ideological objection to trains for many years, since they weren’t enough of a market solution to transport issues.

So I can’t see the Australian train system getting significantly better any time soon. A shame, since trains are such a civilized way to travel.

 

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Riskiness

A few weeks ago, the Penguin family had a very enjoyable time at Rocket Car Day, in inner-city Sydney. Our car, the Silver Surfer, won its heat, and was a respectable third place in its repechage final (also in the SMH here). The day was very enjoyable. It was entirely frequented by inner-west geeks (or those who were inner-west geeks at heart, like us). Each new rocket car that was unveiled was admired by the spectators, particularly those (like the R2D2 car) which had clearly had some decorative effort put in, or some careful design effort.

The organisers had put on a barbecue, in best Australian tradition, and the lightheartedness of the event was summed up by the visual joke of the trigger mechanism

Acme Rocket Car launcher

Also at the event, all of us, wearing sandals, were about two metres away from the person who had a one centimetre diameter hole burnt in her foot by one of the more streamlined entries. She was wearing an enclosed shoe.

The organiser was quoted in the SMH:

‘Last year we drew some blood, there’s a variety of things that go wrong.”

But despite the dangers of stray projectiles, tempered by the rule ”too light, won’t race”, lots of children are apparently part of the elated crowd.

”I’ve always tried to keep the spirit of it very community-based … and very relaxed,” Mook said.

I imagine that this event will be quite different in a few years time. Despite the very strong disclaimers at the beginning (you are watching at your own risk, please stay out of the path of the cars), someone is bound to sue for injuries after a while. And then there will be fences, an entry fee, compulsory enclosed shoes, and the wonderful community spirit will be diminished.

Here in Australia, we have a mixture of ways of compensating for accidents that cause injury. They start from the legal view that if the accident was someone’s fault other than your own, you should be compensated by the person at fault. But they’ve changed a lot over the years, as that view became too expensive, in some cases.

If there is clearly no-one at fault but yourself – bad luck – no compensation. But that group of injuries is getting smaller and smaller. At rocket car day, I imagine the woman with the hole burnt in her foot would have a reasonable case against the person who made the rocket car that hit her, or against the organisers, despite the disclaimers.

And then there are a variety of possible organisations or persons who could be at fault:

• your employer – in which case there are very defined limits as to how much you get per injury
• the person driving the car that hits you – again very defined limits per injury
• someone who can be sued for negligence (for example a council), which relies on the courts deciding how much you get per injury)
• the doctor who caused your injury (which also relies on the courts)
• Nobody (which is what the organisers were hoping in this case)

And, of course, if your injury comes from illness, then there is no-one to sue.

But in New Zealand, they have an Accident Compensation Commission, which gives you the same amount per permanent injury regardless of who was at fault (even no-one, or yourself). The key to this, is that nobody can be sued for causing personal injury. The laws in New Zealand have been changed to stop that.

This approach does seem to genuinely lead to a different attitude to risk. The ACC is funded through employment, car insurance, and general taxation. Which means that community organisations, councils and other people organising events do not have any financial consequences in the event of an accident.

Here in Australia, some laws (notably workers compensation and motor accident laws) have been changed (in different ways in different states), to take away that right to sue. But not for all injuries.The Productivity Commission has recently set up an inquiry into a national disability care and support scheme. This is looking at, among other things, whether there should be a social insurance scheme for all disabilities. On the face of it, that seems like a great idea – the long term disabled in this country mostly get a raw deal, but a very variable one, depending on whether there is anyone to sue. But substantial legal reform would be needed to make that work – providing the funding to make disability compensation a more level playing field by type of injury.

We do get a benefit we get in this country from the risk avoidance that comes from people being scared of being sued. But we also get a cost in that many moderately risky activities just don’t happen. That rocket car day was probably very close to that boundary, and may not stay on the do-able side for long. I’d rather not lose it. But that is much easier to say if you’ve never suffered one of those catastrophic, possibly preventable injuries that our legal system tries to stop.

I hope the productivity commission comes up with something more like NZ. But I doubt if it will happen. It seems too old-fashioned some how.

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Nearly there, Dad

My dad, who isn’t competitive at all, asked me recently how old he would have to be before he had outlived 50% of his contemporaries. He suspects he may have passed that age sometime in the past few years. So I’ve been exploring the ABS mortality statistics.

If you look at the most recently produced life table, the answer is that a man must make it about four months past his 82nd birthday (The life expectancy at birth on current rates is 79.2 years – the difference is the difference between a mean and a median).

But that doesn’t tell the whole story. The most recently produced life table uses mortality rates from 2006-2008. So it overstates the chances of living that long, for my dad’s contemporaries, who have lived through a time where mortality rates were worse than they are now. So I had to go and see what I could reconstruct about mortality rates, to reflect the actual experience of my dad’s contemporaries. I’ve cheated, and used Australian statistics for the whole period (my dad didn’t move to Australia until his late 30s, but he lived in New Zealand and the US, mostly, until then).

The difference is actually less than I thought it would be. He has to live to almost exactly 78 years old to outlast half his contemporaries. But his life expectancy at birth (based on the actual experience to now) was only 70 years.

One of the striking improvements in mortality was at birth. 4.5% of babies born back in the 30s didn’t make it to their first birthday (including my dad’s older sister). In 2006-2008 table, 0.5% of babies didn’t make it. Another measure of general improvement is that back when Dad was born, his life expectancy based on mortality rates for the population then was only 63 years. Improvements in medicine, nutrition, and public health have added 7 years to the lifespans of babies born back then.

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The insurance cycle

The insurance cycle is something that is well known to general insurers (property and casualty, if you are in the US). For many classes of business, the price of insurance fluctuates much more than the underlying cost. The general consensus is that it is about availability of capital. If the insurance market as a whole has suffered substantial losses recently (think 2005 and the nightmare Hurricane year in the US) then all the capital that is generally available for insurance companies will have been used up paying claims. So companies will have to pay much more for capital, reinsurers will charge higher premiums, and the market as a whole will charge much higher premiums for the next few years. This is, of course, completely contrary to the Efficient Market Hypothesis that would suggest that the premium should reflect the best forward looking view of the risk, but it is a well known phenomenom.

But in my view, there is a different (closely related) reason. Insurance cycles generally happen in “long tail” business – that is business where the claims are paid a long time after the premium is received. Think workers compensation insurance, or (for an extreme) asbestos insurance. And this means that the company is deciding on the premium rate to charge a long time before they know what the ultimate claims will be. Of course, they will get it wrong (that is the only certain thing about insurance). If the insurance companies charge too high a premium for that year’s risk, capital will come flooding into the market because there are superprofits to be made.  And the price will come down substantially.  And if they charge a premium that is too low, the opposite occurs. The problem with this approach is that it is happening a long time later. So inevitably there is an overcorrection – hey presto – an insurance cycle where insurance companies make super profits some of the time, and diabolical losses (if they are still in the market) the rest of the time.

If you know what you are doing, the way to make good profits on this kind of business this is to hold your nerve on price. You need to charge the higher prices that the market generally is charging just after a disastrous year, but when the prices start going too low, you need to be able to hold your nerve and refuse to participate. That takes a long term, patient, shareholder, and a company where the pricing power is nowhere near the marketing team (which will have sales targets they are expected to meet). Of course, you won’t know whether you were right until many years later.

A colleague of mine recently described the group life insurance market as a commoditised business – low margin high volume. It would be, if the ultimate cost of the product was known up front. But the insurance cycle (group life claims, particularly for  disability are paid up to 10-15 years after the premium) changes this dynamic. Instead, I think it is a business where the way to make money is through disciplined and very superior pricing. Which is not very common in any financial services business, and may be the reason not much money has been made in this business historically.

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This is the season for industry events, so I’m musing on what I’ve seen on this blog. It feels quite strange to be doing professional blogging here, but that’s why I originally started this blog after all!

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