« Resolving the U.S. Fiscal Crisis | Main | A preliminary estimate for Canadian 2011Q1 GDP growth »


Feed You can follow this conversation by subscribing to the comment feed for this post.

In the videos I saw of the tsunami swallowing whole towns, it was amazing just how little damage the earthquake itself had caused. The last numbers I saw had almost 30K people dead or missing. I wonder how many of the people who own(ed) destroyed homes and businesses are also also mostly dead? No point in rebuilding homes and businesses if most everyone is dead. If a critical mass of people are obliterated, there's probably no point in rebuilding. Better to move.

Patrick: "Better to move."

On this one I think the big unanswered question is how much damage to the fishing/farming industry will result from the tsunami/radiation. Everything was flooded with dirty, oily, salt water - will the land ever be arable again?

Here too is where the fact that there's recourse mortgages in Japan becomes so important - it's harder just to walk away from property when one has a $80,000 loan against it already.

Another question is the value of the land that people own would be enough to pay for the cost of rebuilding - i.e. one could finance the cost of rebuilding by taking out a loan with the land as collatoral. It seems that the answer might be no. This is what Yasu Sawada wrote to me (quoted with permission):

A quick internet search tells me that the land value of Rikuzen Takada
is around 40,000 Yen per Tsubo (1 Tsubo=3.3 m^2), i.e., 500 USD per 3.3
m^2. According to the Census, the median "home floor size" of Rikuzen
Takada is between 150-199 m^2. Assuming that the floor size and the
land size are the same, then a predicted median land value is 500 USD *
175 m^2 /3.3= 26,500 USD. If people own a large home garden, which is
likely, and the size of the land is 3 times as large as the home floor,
the land value would be 79,500 USD. This may indicate that the value
the land be insufficient indeed.

Frances - Given the age profile you mention, and the high savings rate in Japan, I wonder how many of the destroyed properties where paid off, or at least mostly paid off? Also, I wonder how much of people's retirement savings are protected from seizure in case of bankruptcy/default in Japan? In Canada it's not much. Something like 40K.

It wouldn't surprise me at all if most of the destroyed towns where simply never rebuilt. Especially when so many of the former inhabitants are now dead. There's nobody left to live there.

Ugh: *were* paid off ... were never rebuilt. Geez.

The damn 'h' gremlin won't stop jumping on my keyboard.

Re Insurance:

1) In an efficient market insurance is supposed to be available for any risk an individual does not control (no moral hazard).
2) Rational, risk averse individuals are supposed to insure all risk they can't diversify.

Re Land value:

It wont be worth anything unless most everyone commits to rebuild (Land value is a positive externality). 

It could have hit anywhere. The least they can do is socialize the financial losses.

To the extent that many of the displaced people were pensioners, they will continue to receive meagre social security (or whatever the Japanese equivalent is called) benefits. They likely also have savings. They may not desire to rebuild destroyed houses anyways. It may be more rational to simply rent elsewhere, which ought to increase demand for housing, and indirectly drive rebuilding by homebuilders.

Also, I doubt poor people who lost their homes had much real wealth tied up in their houses, assuming that the housing in the Tohoku region were generally built during the boom in the 1980s. The secondary market for houses in Japan is tiny. Historically, houses in Japan have lasted an average of 25 years, compared to 44 years for houses in North America. The houses built during the boom period were built rather hastily and with relatively poor quality building materials (historically green timber was used instead of kiln-dried timber). Normally home buyers in Japan are only willing pay for the land, since they intend to destroy the old house and replace it with a new one.


"1) In an efficient market insurance is supposed to be available for any risk an individual does not control (no moral hazard).
2) Rational, risk averse individuals are supposed to insure all risk they can't diversify."

Insurance works because of the possibility of risk pooling - you and I can put money into an insurance pool, and if a random unfortunate event happens to one of us, then that person collects.

But if people face highly correlated risks - whenever you suffer an unfortunate event I also suffer an unfortunate event - then it's not possible for us to pool risks. An earthquake is that kind of a highly correlated risk - as is a war or a tsunami.

One thing that is really striking about Yasuyuki Sawada and Satoshi Shimizutani's finding is that people weren't able to consumption smooth after the Kobe earthquake - they weren't able to use insurance to cover their earthquake-related losses.

Frances: I agree. But Japan has lost, what, a few % of GDP mostly all focused on a small minority of the population. So it doesn't look, to me, like a very systemic loss. And anyways, reinsurance is a global, not local, industry. Earthquake risk seems like a perfect insurance candidate on a global scale. Tsunamis and small wars seem in the same category, though the latter is probably fraught with moral hazard.

Hi, Frances. I'm surprised to read that earthquake is highly correlated risk. As K observes, the insurance pool is surely broader than a particular location. Even if it were confined to Japan, surely the loss could be shared through insurance with other Japanese residents?

In any event, if there is a market failure, the government should insure by spreading the loss across different generations. I'd go further and suggest that the government makes it compulsory to acquire natural disaster insurance, and offer a "public option" if private insurers have market power on setting insurance premiums. In many countries, it is compulsory for vehicles to have third party insurance.

K: "Earthquake risk seems like a perfect insurance candidate on a global scale." The amount a risk-neutral person would charge for bearing earthquake risk is probability of a catastrophic earthquake occurring*loss if such an earthquake occurs+administrative costs. Unfortunately it's extremely difficult to estimate precisely the extreme tails of any distribution, including the probability-of-catastrophic-earthquake distribution. But if you can't price something, you can't buy and sell it.

Kien - "the government should insure by spreading the loss across different generations."

This is a crucial difference between government and private insurance companies. A private insurance company can inter-temporarily insure against a Kobe 1995 or East Japan 2011 magnitude earthquake by carrying a reserve equal to the loss associated with such a disaster, or having an appropriate ability to borrow. I just don't see insurance companies wanting to carry around billions of dollars worth of reserves. Governments, however, have much greater ability to carry out such intergenerational transfers.

So, yes, there is scope for government risk-spreading - when people don't have the option of avoiding disaster by not doing stupid things. I'm less sympathetic to people who live up-river from me in Ottawa, choose to build on a flood plain ("the land was so cheap! and it's waterfront!") and then complain when their houses are flooded. "But the insurance company wouldn't sell us flood insurance so what could we do?"

That's another limitation of insurance: the inability to insure against certainty.

Frances: "But if you can't price something, you can't buy and sell it."

I don't agree with you there. All markets are just a consensus of divergent educated guesses. That's how we get markets in things like catastrophe bonds for hurricanes and earthquakes.

K - here's where I"m coming from. There's some stylized facts to explain, namely, the way that people financed rebuilding of homes after Kobe 1995 was through borrowing; they financed replacement of furnishings etc by dissaving.

They didn't finance rebuilding through insurance.

From what I can discover, much of the loss this time wasn't covered by insurance either (though the figures in that article look like they might be applying to Kobe).

I'm trying to find ways to explaining the observation that people did not, in fact, have insurance coverage that paid for their loss.

On catastrophe bonds, this is what the ever-authoritative NY Times has to say:
Cat bonds are set off only by events that are specified in great detail in advance. Moody’s said it had identified four rated bonds linked to some form of earthquake coverage in Japan.

The initial estimate, by AIR Worldwide, of insured losses from the earthquake was very narrow. Issued on Sunday, that estimate, of $15 billion to $35 billion, included only damage caused by the earthquake and the subsequent fires, not the tsunami, landslides or nuclear accidents.

Frances, I agree that the reason the tsunami victims were not insured for there losses is that they would not have been willing to pay what market providers would have charged, which is what I think you are saying. Conceding that, however:

1. The reason Cat bonds, like all financial contracts, are specified in such great detail is to maximize the likelihood that both sides will agree when an event has been triggered. The mechanisms of financial markets require such questions to be settled quickly. This is one of the problems that comes up when insurance companies dabble in OTC derivatives trading; their culture of delaying, litigating, dragging out payment causes chaos when carried over to financial markets.
2. Note that unlike insurance, Cat bonds are written against events, not losses. This is important because it cuts the feedback loop created by the moral hazard of insurance. On the other hand, it creates a significant basis risk for insurance companies that want to use Cat bonds as reinsurance.
3. The Cat bonds written on Japanese earthquakes are mostly linked to the Tokyo area, because such earthquakes are the most likely to cause losses greater than insurance companies can support. Earthquakes in the hinterlands were not expected to be too expensive. Your quotations demonstrate that this calculation was correct.
4. Whether the Cat bond market can indeed rebound and grow significantly (as many expect) depends on whether investors are able to write protection more cheaply than traditional reinsurance companies. This is not inconceivable, but because of the basis risk mentioned earlier they will never completely displace reinsurance. Perhaps Cat bonds could provide a base level of reinsurance, with the basis reinsured by traditional means.

And finally, a little off-topic:

5. Although I understand what you and Nick mean when you write "risk-neutral", it is distracting because it is already a term of art in finance, where it means something close to the opposite. In this case, it is doubly distracting because a red herring: the price of risk is the dominating consideration.

I have a premonition that you are about to object that there is a difference between "risk" and "uncertainty." While this is obviously true, I wouldn't be so confident that earthquakes are radically different from financial assets in that respect; consider how many papers have been published arguing over the value of the "equity premium."

Here's a case against buying Tsunami insurance:  why would I buy insurance against a contingency in which there is a high probability that I, and my whole family, is dead? At the very least I would only pay for the contingency of my being alive, which ought to reduce the premium significantly. Maybe insurance companies aren't very creative.

On a more general note, this does in fact go back to the discussion about risk and uncertainty (sorry Phil).  Asteroid impact and alien invasion is also unanticipated by insurance contracts, as is anything else that happens *not to be anticipated*. E.g. impossible nuclear reactor melt down.  But I do agree with Phil that markets *can* handle this kind of risk: stocks and bonds (like Tepco's) assume this risk all the time.  Actual tail risk is probably a significant part what is commonly ascribed to "equity risk premium", and may explain the "anomalously" high level of that premium.  But insurance contracts probably cannot handle such risk.  This leaves an obvious role for governments to help out.

On "risk neutral": I don't have an issue with your use of the term, Frances. Risk neutral "probability", or "measure" is "art." But "risk neutral investor" is both common sense *and* not inconsistent with the meaning of risk neutral measure.  The risk neutral measure is the measure that would have to apply to the dynamics of the market if the observed market prices were, in fact, the expectations of a risk neutral investor.  I'm OK with that.

"Here's a case against buying Tsunami insurance: why would I buy insurance against a contingency in which there is a high probability that I, and my whole family, is dead?"

Yes. And the reverse of the medal: why would I by insurance from someone who is highly likely to be bankrupt if the insured contingency eventuates? But I'm not sure that either of these factors is what is going on in the tsunami insurance (non-)market.

No, I agree the risk of death is probably not the reason, Phil. Just a curious aside.

On the contingent credit risk of the insurer: if the whole exposed world insures against earthquakes, tsunamis and hurricanes, I don't see why the insurers wouldn't be diversified and big enough to be relatively secure against an event or two.  But perhaps most people just don't want to pay for it in which case there might be insufficient capital to cover a large event (especially an unlikely, i.e. low premium, one).  In that case, there's a chicken and egg problem:  insurers will charge excessive premium for a risk they can't adequately diversify; clients will refuse to buy excessively priced insurance. So we are in a bad equilibrium, i.e. a market failure. I know I turned down earthquake insurance; seemed too expensive.

Seems I've just talked myself into agreeing that you might be right, Frances.   

Here are some more (far fetched?) possible reasons not to have insurance:

1) An event that destroys my neighbourhood is bad; but it's not *as* bad as one that just destroys *my* house.  At least I don't lose social rank (I might gain it!).  So I'm not willing to pay as much premium to insure a large scale disaster.

2) It's the moral obligation of the government to pay the cost of a large scale natural disaster.  It's not my responsibility.

Phil: "the reason the tsunami victims were not insured for their losses is that they would not have been willing to pay what market providers would have charged"

And then the question is - why? Is it because the premium charged is too high relative to the expected loss? Because people aren't able to estimate the benefits of buying insurance (long tails etc)? Because people are liquidity constrained in some respect - that is, they can't afford the premiums? Or because they figure someone else will help out if disaster strikes? The point K makes is interesting - there's no point in buying insurance against an event that will kill you and your family - or buying insurance that will pay for your home to be rebuilt when the local economy is totally destroyed.

"whether investors are able to write protection more cheaply than traditional reinsurance companies" - why would investors be able to write protection more cheaply? I can think of one reason - investors might underestimate the risk of a catastrophic loss.

"why [won't the market for tsunami insurance clear]?"

Since you are the economist, I'll let you answer that one! People like me and K are always mystified by the markets insurance companies won't make. It's not really as simple as "premium too high"; you can't get a quotation. So that might be the right answer, as I contend, but you cannot demonstrate it directly. An explanation for this unobservable is necessarily more tenuous yet.

"why would investors be able to write protection more cheaply?"

Most people who take this position think it is because Cat bonds have low correlations to other financial assets, and that purely financial investors will benefit more from this than reinsurance companies. Yes, the premises of this argument are debatable (and have often been debated.)

"People like me and K are always mystified by the markets insurance companies won't make. "

"I don't agree with you there. All markets are just a consensus of divergent educated guesses."

I'm reminded of the discussion here about Starr's ex-post versus ex-ante optimality results.

If there is *any* divergence of beliefs about states of the world occurring, then the process of maximizing expected utility will always result in ex-post pareto inefficient allocations, regardless of which state actually obtains.

So yes, you can sometimes finagle a bid in out of people for events whose likelihood are unknown, but if there is any divergence in beliefs, then this introduces a lottery aspect. Random redistributions of wealth are welfare reducing.

As you cannot give everyone a premium for bearing this randomness, the rational response may be to refuse to bid, rather than to make a guess about the likelihood of the outcome, and hope that everyone is making the same guess.

RSJ, I see that it was a mistake for me to dodge Frances' question (well, I did feel guilty :-)

The distributions of financial assets are non-stationary, and consequently "uncertain" rather than "risky." It may seem paradoxical, but a consequence of this is that the second moments are easier to estimate empirically than the first. But what happens in a pricing context is that uncertainty over returns is translated to inflation of implied volatility. (Ex-ante implied vols are systematically higher than ex-post realized vols.) This is one reason I don't like the "fat tails" language: it obscures what is going on.

In other words, investors are always uncertain of the real probability measure and there is never agreement about real-world probabilities of states of the world. (This is why one hates to see a pricing model that retains a price of risk parameter.) You may believe this is ex-post Pareto-inefficient, but so what? It is not a way of differentiating earthquakes and tsunamis from equities and precious metals.

Phil: I agree except that it's not uncertainty that makes the first moment tough to measure. This is a property of any semi-martingale. Take just a brownian motion: it is not even *in principle* possible to distinguish a brownian motion from a drifted brownian motion, even given perfect knowledge of the path. The second moment, however, can be calculated perfectly from the knowledge of any arbitrarily short path.

"In other words, investors are always uncertain of the real probability measure and there is never agreement about real-world probabilities of states of the world"

Yup. There isn't agreement that there's any such thing as "real probabilities". Everybody has a subjective measure (and support). That produces a price.


It's not that I "believe" that is inefficient. It *is* inefficient.

It's a theorem.

And is stands to reason that if the market participants are aware of this, they will demand a premium before participating in a market whose outcomes are guaranteed to be inefficient. If you cannot supply them with a premium, then there wont be a market.

With equities or financing of capital more generally, equity investors can demand a premium and firms can supply the premium out of wages. But who is paying the premium for catastrophic bonds?

RSJ: For firms with monopolistic pricing power (basically all of them) it can also come out of the price of goods. That's who ultimately pays the required premium for cat bonds: insurance buyers.

Or a better way to put it: insurance buyers will pay more than the expected loss even though they shouldn't have to if that loss is zero beta. They pay it because they are risk averse and the insurance is variance reducing for them. They can further improve their Sharpe ratio and fully fund their insurance purchase by buying everyone elses cat bonds-ie mutually insuring.

Ex-post, it will may not be variance reducing for them if there is disagreement on the probability distribution. Particularly when you are dealing with unlikely events.

Suppose you have two people, subject to the same (variable) income stream -- e.g. risk of rain.

Person A believes that there is .005% chance of rain tomorrow, and he will lose $1000 if it rains.

Person B believes that there .00005% chance of rain tomorrow, and he will lose $1000 if it rains.

If there is a market for rain bonds, then B will insure A, even though B is not more prepared to withstand rain. He will insure A because he thinks the price is too expensive. Then, if it rains, B loses a lot, and if it doesn't rain, A loses a lot.

What they should do, is shut down the market and instead borrow in case it rains, to smooth their income.

Which is exactly what happens with these unlikely events -- e.g. earthquakes.

If the catastrophe is really not correlated to the asset markets, then their borrowing costs will not rise when there is an earthquake, so there is no point to purchasing insurance.

Insurance markets are successful if there is agreement about the underlying distribution. Say death and injury -- those distributions are known. Distributions of earthquakes are not known.

And you have a similar problem with trying to price deposit insurance. You will increase variance ex-post rather than decrease it.

The contingent claims markets only reduce expected or ex-ante variance. In order to get from an expected reduction in variance to an actual (ex-post) reduction in variance, there must be agreement about the probability distribution. If there is large divergence -- people are guessing -- then it turns into a lottery, and lotteries do not reduce variance, even though everyone *thinks* that they are reducing their variance.

The benefit of insurance is not from trading between people with exposure to the same event. Think of the world divided into eg 100 independent rain areas. The people in each region buy insurance on 99% of their rain risk and sells 1% of the insurance for each of the other 99. The variance is then reduced be a factor of 10=sqrt(100). The price of insurance is irrelevant. The point is for them to all share the worlds rain risk communally.

Borrowing or saving is just a way to self insure over time. That works for things like rain that are sufficiently frequent that you can diversify over a life time. Bit it's useless for earthquakes and tsunamis. For those, global communal insurance would be hugely variance reducing and utility improving for any concave utility under any sane subjective measure and under whatever set of a actually realized events.

Sorry, that was stupid. Forget about variance. Average variance doesn't change no matter how you distribute it. What changes is utility: if it's concave, mutual insurance is utility improving.

Sorry, one more time: if the hundred events are independent, variance per person will drop by a factor of *100*. The width (standard deviation) of each persons distribution will be decreased by a factor of ten. My first comment said "variance" when it should have said "risk". My second one (the one just before this one) was just plain nonsense. Note to self: never panic correct a comment.

The comments to this entry are closed.

Search this site

  • Google

Blog powered by Typepad