US Tennis Open Updates

With the US Tennis Open now behind us, I found time to update the numbers. 

My mother always says "Ladies first (except up a ladder)" and here the value was on the under-bitches, if you'll pardon the expression.

Backing these from the 4th Round on continued to be profitable. For the past five years, i.e. 20 Grand Slams, profits vary from 45.04 points (Pinnacle prices) to 64.01 points (best prices) from 298 matches.

As for the Men, the results were opposite, with the value on the side of the favourite.

Overall, again the last 20 Grand Slams, and the US Open is best left alone with losses of around 2.65% at Pinnacle prices on both favourites and underdogs.

As always, a big thank you to Joseph Buchdahl and his Tennis Odds, without which none of this would have been possible. 

Fundamentally Flawed

The puzzling Tweet above, apparently triggered by a delayed reading of my excellent and well worth reading Q and A with @Statsbet, before the series took a turn for the worse, appeared in my Notifications this afternoon.

I say puzzling because by James’ own definition**:

a technical trader pays no attention to the past performances of entrants, only considering price movements, market behaviour and structure.

Which is exactly what the systems mentioned on my blog do. 

For the purposes of the Q and A, I used the financial definitions for technical and fundamental analyses as my basis, although the sports and financial markets obviously have big differences.

We all may have our different takes on how these financial market terms should be interpreted when it comes to sports, but to me, fundamental analysis for sports investing means looking at the fundamentals of the individuals or teams competing in the event. So for an NBA game, I might consider injury reports, previous results, days of rest, time zones, individual match ups and so on.

I don’t do this. It might give me an edge if I were travelling with the team and knew they’d been out for a massive session the night before or that Barrow’s star striker Byron Harrison had again slipped in the shower and would be missing the next game, but I don’t have access to private information like this.

Incidentally, although James’ Tweet implies otherwise, the difference between technical analysis and fundamental analysis has nothing to do with whether the data is public or not. Or at least not that I am aware.

Under the ‘fundamental’ heading, I also include silly ideas such as looking at previous results between two clubs, or thinking that because a team has been involved in recent high scoring games, that this is significant or can give me an edge. Others, with far more resources and time than myself, will have already analysed these things far more efficiently than me and my spreadsheet ever could, and it would be delusional of me to think I could ever gain an edge this way.

By ‘technical analysis’ I mean that I look solely at market data, looking for areas where the market may be inefficient. What the sport is, who the teams are, where they play, who plays for them etc. is all irrelevant in my opinion, all a waste of time without private information. Yes, the market data is publicly available, but that doesn’t change the nature of the analysis from technical to fundamental.

Thanks to Tony Stephens for pointing out a rare typo (now corrected) in my last post:

Feeed? Is this some kind of test?

No test - just a rare error to show that I am human.

** For more on this subject, reference p4 of James Butler’s Betfair Trading Techniques.

On The Same Page - i.e. p65

A couple of comments on my post yesterday. Dr. Tsouts asked:

Speaking of banks and staking what do you suggest to those who follow many tipsters? Keeping a common bank or an individual for every tipster? I guess the second is better but we all have a life eventually...

I'd definitely keep discrete banks, for a couple of reasons -

1) So that you can easily compare tipsters

2) Tipsters often suggest specific bank sizes and staking strategies

If you're organised, I'm not sure there would be much of a time saving from maintaining a single bank.

Someone named James also had a comment on my post, specifically related to my comments on staking, writing:

If Master Cassini had actually read Betfair Trading Techniques he would have access to a spreadsheet and simulator to test level stakes against other money management systems.

Even a fractional Kelly kicks sand in the face of level stakes. Whilst useful for testing a strategy, level stakes is woeful for building wealth.

If Master James had actually read my post, he would have seen that that was exactly what I was saying:

About level stakes, I would say that this is the only way to validate whether or not a system is profitable, and for comparing one strategy against another, but for building a bank, it's far too passive. My approach is to increase stakes as the bank builds.

In Betfair Trading Techniques, I read on page 65:

Level stakes is okay for the initial evaluation of a trading model but level stakes won't increase wealth at the optimal rate.

Exactly. On the subject of building banks, I was asked via Twitter:

"what is a good figure to get to, to start using some winnings?" 

My advice was:

As for withdrawing money, I'd say only do this when you have more than you can use. Your betting bank is your capital, and should be used to build your 'business', not to pay for your lifestyle.

I added a link to a 2011 post on the topic. Part of the discipline to be a long term winner is that winning or losing doesn't make a difference to your daily life. If you get excited about a win or depressed about a loss, you're staking too much. And if you think it's a good idea to pull money out to buy a new sports car, or another foreign holiday, well that's short-sighted at best, and probably a bit of a fib at worst.  

Coincidentally, I then came across this advice on my Twitter feed, courtesy of Stephen Burns: 

Before you can trade you have to get your personal finances in order so you can build up enough capital to open a trading account. Before you can trade you must first develop the self control and discipline to earn, save, and grow enough capital to enter the game in the first place….. – Steve

Botters and Spotters

In my always humble opinion, the Q and A series from @Statsbet reached a peak a couple of weeks ago, and further evidence that it is now on the decline came yesterday with the disappointing news that the latest in the series was to be with an unknown - someone called Betfair Pro Trader. 

Talk about desperation and scraping the barrel, and rarely has the expression 'jumping the shark' been more apt.

Long time readers will know that I have never heard of James Butler of Betfair Pro Trader before, nor have I ever bought any of his books called Betfair Trading Techniques: Trading Models, Machine Learning, Money Management, Monte Carlo Methods & Algorithmic Trading.

But I'm always ready to learn something, in fact I have a saying that a day is lost if I haven't learned something new, so I took a look at the thoughts of this previously unknown trader who specialises in automated betting.

Number 2 blog! What a great question. I wonder why I wasn't asked the same one? 

The question of staking plans was asked, with James' reply below:

James could be accused of selecting Kelly because of the Irish connection, but it's a mathematical fact that the Kelly Criterion is the optimal staking method for maximising profits. However, in the real world of sports betting, Kelly has a couple of shortcomings, specifically that the precise edge is seldom known and the size of stakes and thus draw-downs using full Kelly means that most people will abandon it sooner rather than later. My 2008 post on the topic holds true, although the final paragraph's conclusion that:

 Increasing this [2% stake] to 3%, or occasionally 4% on an especially good play, is reasonable

was written in the days when many markets were still free of courtsiders, (or 'spotters' as James calls them), and opportunities were more plentiful for the skilled trader.

About level stakes, I would say that this is the only way to validate whether or not a system is profitable, and for comparing one strategy against another, but for building a bank, it's far too passive. My approach is to increase stakes as the bank builds. 

R J Miller uses a similar method to me, but with a plateau system to determine when he increases his stakes:

I bet 2% of my bank and continue to flat bet until my bank grows by at least 25%. Then I recalculate the 2%. Thus, if I started with $10,000, I would bet $200 a game until my bank grows to at least $12,500. At that point, I would refigure my unit to $250. I bet flat until I reach at least $15,625. My actual risk-reward ratio doesn't get too high. The other thing that I do that is unique and rather arguable is that I never lower my bet. Remember, if you vary the bet, your breakeven goes up. At a 2% unit and three decades of experience, I am comfortable that I can ride through a losing streak. If you lose 10 games at $200 a bet and lower the bet to $180, you must win 12.2 bets to get back to even. This is how I get my 100% annual ROI. My actual bet goes up during the year as my bankroll reaches higher plateaus.

I really don't see the point of the plateau system here. We all have spreadsheets these days, and 2% of $10,000 is as easy to calculate as 2% of $10,123, so why slow down the bank growth unnecessarily? Each time the bank hits a high, increase your stakes.

It's also neither unique nor arguable to never lower the stake once it's reset.

If you're curious about the example on the left, and why the stake size is static despite wins, it's because many games are played on the same day, not necessarily simultaneously, and I (hopefully) raise the stakes at the end of the day for consistency. Some days I might be home and in a position to raise the stake, but more often than not, I am having a life. I'm generally past the stage of checking results in real-time.

I jest about Mr. Butler of course. His expressed opinions about the realities of betting match my own, and he's always worth a read. You might not like what you read, and indeed James writes:

My wish is either to point people in the right direction or to frighten them off. I regard putting someone off betting/trading as of equal merit to teaching people useful skills.

How many fortune seekers are actually dissuaded from pursuing betting is debatable, but close to zero I would say. The nature of a gambler is to pay far more heed to the "winning is easy" garbage churned out from easily discredited sources if you really want to check, than to more rational thoughts and the logical conclusion that:
It's not impossible to make a profit, but it's hard work, and requires a certain disciplined mindset to achieve.

A jump in the number of hits to this blog over the past couple of days, and with Tweets like this one below, today could be an "enormous" one too.

Over Thinking in the NBA

The 2017-18 NBA pre-season is less than a week away, and it's probable that the apparently inexorable increase in 3-point shooting and scoring will continue.

The 3-point line was added for the NBA in 1979, and in the 1980-81 season, there were an average of four attempts per game. With a success rate of 24.5%, the resulting points came to a less than stellar 3 points per game.  

Last season (2016-17), there were a record 54 3-point attempts per game, with an average of 58 points scored per game.  

It's a good example of how a game changes over the years, and how statistics become redundant after significant changes to rules and / or scoring. It's why I typically don't go back more than five seasons when looking at trends.

Another interesting observation is that the pace of the game last season was faster than it has been in recent years. Each team averaged 96.4 possessions per 48 minutes, the highest since 1992-93. No surprise then that there was a record number of points per game last season - the highest since 1990-91. 

No surprise either that the sportsbooks were onto this, with the average points total a record high 210.7.

After six seasons with an average in the 199.4 - 200.9 range, 2015 jumped to 204.9, with 2016 an even larger jump to 210.7. 

This time last year, the previous five seasons had shown an edge in backing Unders when the total was set at less than 189. Knowing the trend was towards higher point totals, I went with sub 184, with a likely more manageable total number of bets.

That would be an understatement, given that had I not died of boredom waiting for a selection, the season total would have been one, and a losing one at that.

There was value backing Overs on high totals, which is logical given that most casual bettors may not be aware of the reasons why they are seeing higher totals, and back the Unders thinking they are getting one over on the sportsbooks. It's not usually that easy.

For the record, backing Overs when the total was 215.5 or higher had a 55.6% strike rate last season. Expect the average totals to increase again this season, and look for profitability on the Overs a little higher than 215.5. 

NCAAF Overtime Overload

When your team is getting points, one of the more annoying ways to lose a bet is when the game goes into overtime. 

Getting points, reaching the end of regulation tied always feels like you have earned the win, but in US sports, overtime counts. Psychologically, your "win" can't be improved upon, but it can always be taken away. The emotions connected to a loss of this type where were written about in this Loss Aversion post earlier this year.  

Prior to this weekend, 123 system matches had gone into overtime, but the good news is that overall, the odds of holding on for the win are in your favour.

Of those 123 matches, 81 (66%) of these games were winners (system winners, not necessarily straight up winners), 6 (5%) resulted in a push, while the other 36 (29%) were losses.

With a total of just 15 games going to more than one overtime in 16 full seasons from 1996, it was unusual that Saturday alone saw three more games added to that total.

I know at least one reader was following these bets at the weekend, and hope that three matches going into overtime didn't cause any unnecessary stress. 

Fortunately, all three double-overtime games were system winners.

The updated overtime records for the system selections are below:

The final game of the weekend was today, and the system made another profit on the Week as East Carolina won straight up to make it a 6-2 weekend with one push. 

Results for the season so far:

Now for the NFL where we have just two selections this weekend. It's been a poor start to the season for the Small Road 'Dogs with a 6-6-1 record, but the New Orleans Saints (+5.5) are leading leading by 21 points with less than five minutes remaining, while the Seattle Seahawks (+2.5) kick-off in a few minutes.  

Loosen the (Mega)Reigns

Thanks to SportsPicksSystem for this recommendation: 

Since you asked. I would advise you the electrum wallet (https://electrum.org/#home) which is a light wallet (no need to download the whole blockchain). This wallet can also be recovered with a 12-word passphrase in case your computer got corrupted (a wallet is just a file).

For an exchange I use Kraken (https://www.kraken.com/) which asks you for personal information (anti-money laundering). The service is working as expected. Fees 0.26%.

At $3,770, I'll not be a buyer, but one of the more interesting markets to keep an eye on. 

One of the blogs on my prestigious blog roll is that of Megarain, who opens his latest post with these words:

I am still here, but, am genuinely getting more enjoyment from non-internet based activities, and have accordingly, greatly reduced my social prescience, and thus the blog has suffered.

The world is still an odd place, we have a President of the United States, whose own biographer, in 'The art of the deal' finds it hard to find more than 2 redeeming qualities in him - yet, the US stock market is at an all-time high, nuclear warheads are tested, with bravado, and the climate appears to have become more severe.

Some of this is just fluff. Gamblers tend to be incredibly narrow-minded .. and consider, just, what can help them, find and develop/mine an edge. This is fair enough, but, at some point, maybe a more balanced approach is needed, and we need to take a more active role, in what is actually happening in the world. But, u probably don't want to hear this .. so, will reign myself in.

I'm not sure how old Megarain is, but that there is far more to life, and that there are far more important things in life, than chasing a small and likely short lasting edge, is an observation from someone with some experience of life. 

As for Trump, I'm surprised that his biographer Tony Schwartz was able to find two redeeming qualities in him. His latest NFL related outbursts are those of an out of touch dotard (new word, learned it this week). 

Suggesting that protecting players from brain injuries and the life long problems they are causing is "ruining the game" simply showing how out of touch he is. Concussions and CTE are serious, life-altering events. The game will cease to exist if this issue isn't addressed, and Rugby will take over, which would actually be a good thing. Trump 's input is ill-informed at best.

More controversial politically were his comments that the NFL should fire players who exercise their right to kneel during the national anthem, and calling them "sons of bitches". Perhaps not the most presidential of speeches. 

Main target Colin Kaepernick's Mum (Mom) had this response:

Interesting and disappointing that at least seven NFL owners donated $1 million to Trump. A perfect opportunity for all NFL teams to express their support for the right to express an opinion and "take a knee" tomorrow, especially those of the New England Patriots, Dallas Cowboys, Los Angeles Rams, Washington Redskins, Jacksonville Jaguars, New York Jets and Houston Texans. OK, so the Rams have already played this 'weekend', and the Cowboys are the Monday Night game, but you get my point.

Also sports related, and after hearing that Steph Curry (of the NBA Champion Golden State Warriors) would not be attending the White House, Trump withdrew the invitation! 

"I quit!". 

"Too late, you're fired!". 

All very childish and pathetic as are many of his Tweets and comments. Aren't there more important things going on in the world than getting peeved because someone doesn't want to come to your party? Perhaps that Russia is known to have hacked into the election systems of 21 states?

LeBron James' response was great:

Megarain says that we probably don't want to hear his views, but I do! The problem is that as much as I enjoy engaging others in person on religion and politics, the two topics we're not meant to discuss in public, as well as other topics such as climate change, which should be based on science but which has become political, I've learned that facts and evidence don't change minds. And that's a real problem. 

Where's the leadership in the UK saying "Listen people - appreciate your input on our non-binding Brexit opinion poll, but we've looked into it, and it's really not a good idea"? Or at least promise a second vote when the terms and conditions of Brexiting are actually known. Check out the excellent Marina Hyde's latest article on the topic. It contains some great lines.

Bitcoin - Boom or Bust?

Rodolfo asked:

What's your take on cryptocurrencies? Bitcoin in particular. From what I've read and heard, blockchain might be a phenomenal technology. I'm following Jeff Berwick from The Dollar Vigilante and few other anarcho-capitalists and libertarians including Doug Casey. Berwick is very optimistic of Bitcoin as in his opinion crash of fiat currencies (especially US dollar) is looming.

My opinion is that the underlying blockchain technology is what Bitcoin will be remembered for, but I have my doubts that first mover or originator Bitcoin will be the ultimate winner in the battle for cryptocurrency supremacy. 

History shows that it is "fast followers" who have a significantly lower rate of failure than first movers, and my limited personal experience with Bitcoin is that it is not easy to use. As for fast followers, this report claims there are 800 and counting!

"The price activity and manic sentiment that led to present prices have dwarfed even the Tulip mania of nearly 400 years ago," he said. "The success of Bitcoin has spawned 800-plus clones (alt-coins) and counting, most of which are high-tech, pump-and-dump schemes."

The hoops you need to jump through to first open a wallet, (one wallet - Airbitz / Gildera - asked me for my bank account username and password, which seemed like a recipe for disaster, so I stopped there), and the charges to purchase Bitcoin (at least those via Coinbase) were not cheap. If any readers can suggest less invasive and cheaper options, please let me know.

Bitcoin (XBT) is also incredibly volatile, which is not good for the heart for someone of my vintage. In just the past week it has closed at $3,014.65 (on Friday 15th September), and then on Monday 18th, closed up more than 36% at $4,109.57. A fun speculation and diversification if you have money you can afford to lose.

When considering Jeff Berwick's published opinions on Bitcoin, it should be remembered that he is an investor so has a bias towards espousing positive views about its future prospects. I'm also curious as to how long he has been warning of a $USD crash? At some point he will be right, but no one can time these things. Looking at the web site, and it appears to have been since at least 2009, and coincidentally I found an unrelated Forbes article from March of that year, where the author was predicting another bear market: 

Thus, most likely, we can brace ourselves for new lows on U.S. and global equities in the next 12 to 18 months. Eventually, a more sustained recovery will occur once we are closer to clear signals that this ugly global U-shaped recession is not turning into an L-shaped near-depression, and that the global economic recovery is clear and sustained. Until then, expect very volatile and choppy U.S. and global equity markets–with new lows reached in the next months and the year ahead.

We're still waiting, eight and a half years later. The S and P 500 Index closed on 11th March 2009 (the date the article was published) at 721.36. Yesterday, that index closed at 2,502.22, up 247%. 

To his credit, Doug Casey is an atheist, and the ability to think independently and logically is always a positive, but his newsletters are out of my price range. 

It's always interesting (amusing?) to read contrarian views, but don't get swept up in the dramatic headlines since most of the articles are full of 'coulds' and 'mights' and rather light on substance.

Reclusive Millionaire Warns: “Get Out of Cash Now”

80% Stock Market Crash To Strike in 2017, Economist Warns  

Team Trump losing Gary Cohn could crash the stock market, warns Yale professor

Baldrick: I think he looks like a bird who's swallowed a plate, my Lord.

Blackadder: No, that's what I think. What do you think? Try to have a thought of your own; thinking is so important. What do you think?

Baldrick: I think thinking is so important, my Lord. 

Upper-Deckers, Unders Bettors

The start of a new season, whatever the sport, is always something of a reset, with changes often made in regard to not only players and coaches, but sometimes also to rules, equipment and venues.

This season, as many of you will doubtless be aware, there have been a record number of home runs in MLB. The previous high for the regular season was 5,693 set in 2000. Already this season there have been at least 5,753 and there are still 10 days to go.

Some reasons for the increase are explored in this New York Times article but no one knows the reason for sure, or if they do, they're keeping it to themselves.

Regardless, one might be excused for thinking that such an increase in recent years might mean there's some money to be made backing Overs. 

In general, no. For years, the value has been on the Under side of the Totals bet, or at least you'd have lost your money at a much slower rate than you would have done on Overs if blindly backing them. 

The database I use goes back to 2004, and the numbers to date since then are:

Blindly backing Overs has not been profitable in any season, but there is hope with Unders, where the "white stick" approach would have made you money in six of the 14 seasons. Unders was the better bet in 11 of the 14 seasons.

Knowing which bets to ignore is always a good thing, and a little effort looking at Unders shows that the profits are to be found when the Total line is set on the low side. This shouldn't come as a huge surprise to regular readers, as the profitability of backing Overs when the Total was set high has been previously discussed. 

Until the 2016 season, backing Under the 7.0 Total was generally profitable, although the trend really started in 2010, but presumably in response to the the jump in Home Runs last season, the profitable Total moved to 7.5, and this season up again to 8.0. 

In stark contrast to 2014 and 2915, only 16 games this year to date have seen the Total set below 7.0 runs, and no fewer than 11 of these games were with our old friend Clayton Kershaw pitching. 

Eight of those games went Over - it's almost as if the sportsbooks think we're stupid enough to back Unders with Kershaw pitching at any price...

He does have a 100% record of Under when the Total is greater than 8 runs. 

The table above shows the total Home Runs in every season since MLB expanded to 30 teams in 1998, and Over / Under results back to 2004, as far back as the database I reference has records.   

Dow Jones One Million

Buffett expects the Dow to be 'over 1 million' in 100 years

As sensational a headline as that one seems, an annual return of an historically low 3.87% will see the DJIA reach one million 100 years from now. 

Over the last 96 years, including the Great Depression when the index lost 80% of its value, the index has averaged an annual increase of 8.35% with a median of 8.01%.

If that 8.35% is maintained, DJIA 1,000,000 will be reached in less than 50 years.

Warren Buffett is being too cautious!  

The best ten years were those from 1989-1998 (an average increase of 16.12% per year). 

47 years saw a double digit percentage gain, while another 19 were up by less than 10%. 

The 96 years is evenly split with 48 Republican and Democrat presidents in office.

The stock market historically does far better under the Democrats, averaging 9.85% annual increases, than under Republicans, with an average of just 5.78%. So much for the myth of Republican fiscal responsibility! 

24 of the 30 down years were overseen by a Republican president, including five of the six where the loss was greater than 20%. 

Of the most recent presidents, Clinton averaged 16.64% (median 19.37%) with one (of eight) down years, Bush Jr. averaged an annual loss of -0.89% (median 1.27%) with four (of eight) down years including the disastrous 2008's -33.84%, (all, it should be remembered, after inheriting an $86 billion surplus from Bill Clinton) while Obama averaged 10.98% (median 9.27%) with one down year. Not bad after the huge mess he inherited in 2009. 

The current White House incumbent has been gifted a growing economy, and thanks to Obama and his policies, the market is at record highs right now, with record low volatility as I've written about earlier this year. Whether the 3% promised can be achieved remains to be seen, but if the world can survive the next 1,139 days, Dow Jones One Million should be a cinch - if they can keep electing Democrats.  

One Damp Squib and Catastrophe Risk

While the game itself wasn't the most exciting game of rugby I have ever seen, the event was personally a lot of fun although from the perspective of Premiership Rugby, it was described by the Guardian as a 'damp squib' for reasons detailed in this article here. 

The beers for the day easily went over the 10.5 line, which in hindsight was probably set unrealistically low, in no small part due to several Saracens players joining us in the Irish bar I wrote about in July after the game. 

It was perhaps a little disturbing that the highlight of the day for one of my son's friends was reportedly finding himself taking a leak while standing next to Billy Vunipola. 

Outside of the toilet, my son became best friends with England and British Lions star Maro Itoje, while I had the pleasure of talking with opening try scorer Chris Wyles as he admiringly watched himself cross the line on TV as the match was replayed later that night.

A day to remember, or so I was told next morning.

Thanks to @Statsbet who published a Tweet featuring a Q and A with myself which generated a lot of interest and comments, all positive so far as I saw, including these two, much appreciated: 

A couple of emails while I was away that I shall get to once I am settled back to relative normality and my kidneys and liver have stabilised, and also two comments on my last post about NFL Small Road 'Dogs, although neither were specifically on that post's topic. The second was from Trader 247 who asked:

Do you spend a lot of time applying your strategies? Is it something that could be fully or partially automated?

The answers to both are no, although I'm sure a computer genius could probably turn the second no into a yes. Since Trader 247's by-line is Automated Sports Trading, perhaps he'll shortly be offering advice on this.

Once a strategy is developed, the beauty of betting rather than trading is that at a time convenient to myself, and ideally as close to the event start time as possible, I run a few queries manually, and am presented with the selections. A few minutes a day at most, certainly far less time than I spend blogging or researching new angles for an edge.

Some sports (e.g. the NFL and NCAAF) have a relatively short season; others (e.g. baseball) are longer, but most days there are very few selections. The T-Bone system for example has had 120 bets since early April which is less than one a day, and if I miss a few days because of work or holidays, it's no big deal. This is a hobby, and not the reason I get up in the morning.


The first comment was from Tattoo / Grega, who sent me a link to a very interesting, and currently relevant given yesterday's earthquake in Mexico and ongoing hurricanes, New York Times Magazine article on risk, specifically catastrophe risk, management, which was written in 2007. 

As soon as I saw that the author was Michael Lewis, I knew it would be a good read. I'm not sure how I'd missed this article. The author has a great talent for writing about complex subjects in a way that even I can understand them. Thank you for the link Grega. It'll be interesting to see what impact the 2017 hurricane season will have on this industry.  

Here is the article in full, In Nature's Casino by Michael Lewis:

It was Aug. 24, 2005, and New Orleans was still charming. Tropical Depression 12 was spinning from the Bahamas toward Florida, but the chances of an American city’s being destroyed by nature were remote, even for one below sea level. An entire industry of weather bookies — scientists who calculate the likelihood of various natural disasters — had in effect set the odds: a storm that destroys $70 billion of insured property should strike the United States only once every 100 years. New Orleanians had made an art form of ignoring threats far more likely than this; indeed, their carelessness was a big reason they were supposedly more charming than other Americans. And it was true: New Orleanians found pleasure even in oblivion. But in their blindness to certain threats, they could not have been more typically American. From Miami to San Francisco, the nation’s priciest real estate now faced beaches and straddled fault lines; its most vibrant cities occupied its most hazardous land. If, after World War II, you had set out to redistribute wealth to maximize the sums that might be lost to nature, you couldn’t have done much better than Americans had done. And virtually no one — not even the weather bookies — fully understood the true odds.

But there was an exception: an American so improbably prepared for the havoc Tropical Depression 12 was about to wreak that he might as well have planned it. His name was John Seo, he was 39 years old and he ran a hedge fund in Westport, Conn., whose chief purpose was to persuade investors to think about catastrophe in the same peculiar way that he did. He had invested nearly a billion dollars of other people’s money in buying what are known as “cat bonds.” The buyer of a catastrophe bond is effectively selling catastrophe insurance. He puts down his money and will lose it all if some specified bad thing happens within a predetermined number of years: a big hurricane hitting Miami, say, or some insurance company losing more than $1 billion on any single natural disaster. In exchange, the cat-bond seller — an insurance company looking to insure itself against extreme losses — pays the buyer a high rate of interest.

Whatever image pops to mind when you hear the phrase “hedge fund manager,” Seo (pronounced so) undermines it. On one hand, he’s the embodiment of what Wall Street has become: quantitative. But he’s quirky. Less interested in money and more interested in ideas than a Wall Street person is meant to be. He inherited not money but math. At the age of 14, in 1950, his mother fled North Korea on foot, walked through live combat, reached the United States and proceeded to become, reportedly, the first Korean woman ever to earn a Ph.D. in mathematics. His father, a South Korean, also came to the United States for his Ph.D. in math and became a professor of economic theory. Two of his three brothers received Ph.D.’s — one in biology, the other in electrical engineering. John took a physics degree from M.I.T. and applied to Harvard to study for his Ph.D. As a boy, he says, he conceived the idea that he would be a biophysicist, even though he didn’t really know what that meant, because, as he puts it, “I wanted to solve a big problem about life.” He earned his doctorate in biophysics from Harvard in three years, a department record.

His parents had raised him to think, but his thoughts were interrupted once he left Harvard. His wife was pregnant with their second child, and the health plan at Brandeis University, where he had accepted a job, declared her pregnancy a pre-existing condition. He had no money, his parents had no money, and so to cover the costs of childbirth, he accepted a temp job with a Chicago trading firm called O’Connor and Associates. O’Connor had turned a small army of M.I.T. scientists into options traders and made them rich. Seo didn’t want to be rich; he just wanted health insurance. To get it, he agreed to spend eight weeks helping O’Connor price esoteric financial options. When he was done, O’Connor offered him 40 grand and asked him to stay, at a starting salary of $250,000, 27 times his post-doc teaching salary. “Biophysics was starved for resources,” Seo says. “Finance was hurling resources at problems. It was almost as if I was taking it as a price signal. It was society’s way of saying, Please, will you start solving problems over here?”

His parents, he suspected, would be appalled. They had sacrificed a lot for his academic career. In the late 1980s, if you walked into the Daylight Donuts shop in Dallas, you would have found a sweet-natured Korean woman in her early 50s cheerfully serving up honey-glazed crullers: John’s mom. She had abandoned math for motherhood, and then motherhood for doughnuts, after her most promising son insisted on attending M.I.T. instead of S.M.U., where his tuition would have been free. She needed money, and she got it by buying this doughnut shop and changing the recipe so the glaze didn’t turn soggy. (Revenues tripled.) Whatever frustration she may have felt, she hid, as she did most of her emotions. But when John told her that he was leaving the university for Wall Street, she wept. His father, a hard man to annoy, said, “The devil has come to you as a prostitute and has asked you to lie down with her.”

A willingness to upset one’s mother is usually a promising first step to a conventional Wall Street career. But Seo soon turned Wall Street into his own private science lab, and his continued interest in deep questions mollified even his father. “Before he got into it, I strongly objected,” Tae Kun Seo says. “But now I think he’s not just grabbing money.” He has watched his son quit one firm to go to work for another, but never for a simple promotion; instead, John has moved to learn something new. Still, everywhere he goes, he has been drawn to a similar thorny problem: the right price to charge to insure against potential losses from extremely unlikely financial events. “Tail risk,” as it is known to quantitative traders, for where it falls in a bell-shaped probability curve. Tail risk, broadly speaking, is whatever financial cataclysm is believed by markets to have a 1 percent chance or less of happening. In the foreign-exchange market, the tail event might be the dollar falling by one-third in a year; in the bond market, it might be interest rates moving 3 percent in six months; in the stock market, it might be a 30 percent crash. “If there’s been a theme to John’s life,” says his brother Nelson, “it’s pricing tail.”

And if there has been a theme of modern Wall Street, it’s that young men with Ph.D.’s who approach money as science can cause more trouble than a hurricane. John Seo is oddly sympathetic to the complaint. He thinks that much of the academic literature about finance is nonsense, for instance. “These academics couldn’t understand the fact that they couldn’t beat the markets,” he says. “So they just said it was efficient. And, ‘Oh, by the way, here’s a ton of math you don’t understand.’ ” He notes that smart risk-takers with no gift for theory often end up with smart solutions to taking extreme financial risk — answers that often violate the academic theories. (“The markets are usually way ahead of the math.”) He prides himself on his ability to square book smarts with horse sense. As one of his former bosses puts it, “John was known as the man who could price anything, and his pricing felt right to people who didn’t understand his math.”

In the mid-1990s, when Wall Street first noticed money to be made covering the financial risks associated with hurricanes and earthquakes, it was inevitable that someone would call John Seo to ask him if he could figure out how to make sense of it. Until then, he had specialized in financial, not natural, disasters. But there was a connection between financial catastrophe and natural catastrophe. Both were extreme, both were improbable and both needed to be insured against. The firm that called him was Lehman Brothers, whose offer enticed Seo to quit his job and spend his first year at Lehman learning all he could about the old-fashioned insurance industry.

Right away, he could see the problem with natural catastrophe. An insurance company could function only if it was able to control its exposure to loss. Geico sells auto insurance to more than seven million Americans. No individual car accident can be foreseen, obviously, but the total number of accidents over a large population is amazingly predictable. The company knows from past experience what percentage of the drivers it insures will file claims and how much those claims will cost. The logic of catastrophe is very different: either no one is affected or vast numbers of people are. After an earthquake flattens Tokyo, a Japanese earthquake insurer is in deep trouble: millions of customers file claims. If there were a great number of rich cities scattered across the planet that might plausibly be destroyed by an earthquake, the insurer could spread its exposure to the losses by selling earthquake insurance to all of them. The losses it suffered in Tokyo would be offset by the gains it made from the cities not destroyed by an earthquake. But the financial risk from earthquakes — and hurricanes — is highly concentrated in a few places.

There were insurance problems that were beyond the insurance industry’s means. Yet insurers continued to cover them, sometimes unenthusiastically, sometimes recklessly. Why didn’t insurance companies see this? Seo wondered, and then found the answer: They hadn’t listened closely enough to Karen Clark.

Thirteen years before what would become Tropical Storm Katrina churned toward Florida — on Monday, Aug. 24, 1992 — Karen Clark walked from her Boston office to a nearby Au Bon Pain. Several hours earlier, Hurricane Andrew had struck Florida, and she knew immediately that the event could define her career. Back in 1985, while working for an insurance company, Clark wrote a paper with the unpromising title “A Formal Approach to Catastrophe Risk Assessment in Management.” In it, she made the simple point that insurance companies had no idea how much money they might lose in a single storm. For decades Americans had been lurching toward catastrophe. The 1970s and ’80s were unusually free of major storms. At the same time, Americans were cramming themselves and their wealth onto the beach. The insurance industry had been oblivious to the trends and continued to price catastrophic risk just as it always had, by the seat of its pants. The big insurance companies ran up and down the Gulf Coast selling as many policies as they could. No one — not even the supposed experts at Lloyd’s of London — had any idea of the scope of new development and the exposure that the insurance industry now had.

To better judge the potential cost of catastrophe, Clark gathered very long-term historical data on hurricanes. “There was all this data that wasn’t being used,” she says. “You could take it, and take all the science that also wasn’t being used, and you could package it in a model that could spit out numbers companies could use to make decisions. It just seemed like such an obvious thing to do.” She combined the long-term hurricane record with new data on property exposure — building-replacement costs by ZIP code, engineering reports, local building codes, etc. — and wound up with a crude but powerful tool, both for judging the probability of a catastrophe striking any one area and for predicting the losses it might inflict. Then she wrote her paper about it.

The attention Clark’s paper attracted was mostly polite. Two years later, she visited Lloyd’s — pregnant with her first child, hauling a Stone Age laptop — and gave a speech to actual risk-takers. In nature’s casino, they had set themselves up as the house, and yet they didn’t know the odds. They assumed that even the worst catastrophe could generate no more than a few billion dollars in losses, but her model was generating insured losses of more than $30 billion for a single storm — and these losses were far more likely to occur than they had been in the previous few decades. She projected catastrophic storms from the distant past onto the present-day population and storms from the more recent past onto richer and more populated areas than they had actually hit. (If you reran today the hurricane that struck Miami in 1926, for instance, it would take out not the few hundred million dollars of property it destroyed at the time but $60 billion to $100 billion.) “But,” she says, “from their point of view, all of this was just in this computer.”

She spoke for 45 minutes but had no sense that she had been heard. “The room was very quiet,” she says. “No one got up and left. But no one asked questions either. People thought they had already figured it out. They were comfortable with their own subjective judgment.” Of course they were; they had made pots of money the past 20 years insuring against catastrophic storms. But — and this was her real point — there hadn’t been any catastrophic storms! The insurers hadn’t been smart. They had been lucky.

Clark soon found herself in a role for which she was, on the surface at least, ill suited: fanatic. “I became obsessed with it,” she says. One big player in the insurance industry took closer notice of her work and paid her enough to start a business. Applied Insurance Research, she called it, or A.I.R. Clark hired a few scientists and engineers, and she set to work acquiring more and better data and building better models. But what she really was doing — without quite realizing it — was waiting, waiting for a storm.

Hurricane Andrew made landfall at 5 on a Monday morning. By 9 she knew only the path of the storm and its intensity, but the information enabled her to estimate the losses: $13 billion, give or take. If builders in South Florida had ignored the building codes and built houses to lower standards, the losses might come in even higher. She faxed the numbers to insurers, then walked to Au Bon Pain. Everything was suddenly more vivid and memorable. She ordered a smoked-turkey and Boursin cheese sandwich on French bread, with lettuce and tomato, and a large Diet Coke. It was a nice sunny day in Boston. She sat outside at a small black table, alone. “It was too stressful to be with other people,” she says. “I didn’t want to even risk a conversation.” She ate in what she describes as “a catatonic state.” The scuttlebutt from Lloyd’s already had it that losses couldn’t possibly exceed $6 billion, and some thought they were looking at a loss of just a few hundred million. “No one believed it,” she says of her estimate. “No one thought it was right. No one said, ‘Yeah, $13 billion sounds like a reasonable number.’ ” As she ate, she wondered what $13 billion in losses looked like.

When she returned to the office, her phones were ringing. “People were outraged,” she says. “They thought I was crazy.” One insurance guy called her, chortling. “A few mobile homes and an Air Force base — how much could it be?” he said.

It took months for the insurers to tote up their losses: $15.5 billion. (Building codes in South Florida had not been strictly enforced.) Fifteen and a half billion dollars exceeded all of the insurance premiums ever collected in Dade County. Eleven insurance companies went bust. And this wasn’t anything like the perfect storm. If it had gone into Miami, it could have bankrupted the whole industry. Clark had been right: the potential financial losses from various catastrophes were too great, and too complicated, to be judged by human intuition. “No one ever called to congratulate me,” Clark says, laughing. “But I had a lot of people call and ask to buy the model.”

After Hurricane Andrew came a shift in the culture of catastrophe. “This one woman really created the method for valuing this risk,” says John Seo. Clark’s firm, A.I.R., soon had more than 25 Ph.D.’s on staff and two competitors, Eqecat and Risk Management Solutions. In its Bay Area offices, R.M.S. now houses more than 100 meteorologists, seismologists, oceanographers, physicists, engineers and statisticians, and they didn’t stop at hurricanes and earthquakes but moved on to flash floods, wildfires, extreme winter storms, tornadoes, tsunamis and an unpleasant phenomenon delicately known as “extreme mortality,” which, more roughly speaking, is the possibility that huge numbers of insured human beings will be killed off by something like a global pandemic.

The models these companies created differed from peril to peril, but they all had one thing in common: they accepted that the past was an imperfect guide to the future. No hurricane has hit the coast of Georgia, for instance, since detailed records have been kept. And so if you relied solely on the past, you would predict that no hurricane ever will hit the Georgia coast. But that makes no sense: the coastline above, in South Carolina, and below, in Florida, has been ravaged by storms. “You are dealing with a physical process,” says Robert Muir-Wood, the chief scientist for R.M.S. “There is no physical reason why Georgia has not been hit. Georgia’s just been lucky.” To evaluate the threat to a Georgia beach house, you need to see through Georgia’s luck. To do this, the R.M.S. modeler creates a history that never happened: he uses what he knows about actual hurricanes, plus what he knows about the forces that create and fuel hurricanes, to invent a 100,000-year history of hurricanes. Real history serves as a guide — it enables him to see, for instance, that the odds of big hurricanes making landfall north of Cape Hatteras are far below the odds of them striking south of Cape Hatteras. It allows him to assign different odds to different stretches of coastline without making the random distinctions that actual hurricanes have made in the last 100 years. Generate a few hundred thousand hurricanes, and you generate not only dozens of massive hurricanes that hit Georgia but also a few that hit, say, Rhode Island.

The companies’ models disagreed here and there, but on one point they spoke with a single voice: four natural perils had outgrown the insurers’ ability to insure them — U.S. hurricane, California earthquake, European winter storm and Japanese earthquake. The insurance industry was prepared to lose $30 billion in a single event, once every 10 years. The models showed that a sole hurricane in Florida wouldn’t have to work too hard to create $100 billion in losses. There were concentrations of wealth in the world that defied the logic of insurance. And most of them were in America.

The more John Seo looked into the insurance industry, the more it seemed to be teetering at the edge of ruin. This had happened once before, in 1842, when the city of Hamburg burned to the ground and bankrupted the entire German insurance industry many times over. Out of the ashes was born a new industry, called reinsurance. The point of reinsurance was to take on the risk that the insurance industry couldn’t dilute through diversification — say, the risk of an entire city burning to the ground or being wiped off the map by a storm. The old insurance companies would still sell policies to the individual residents of Hamburg. But they would turn around and hand some of the premiums they collected to Cologne Re (short for reinsurance) in exchange for taking on losses over a certain amount. Cologne Re would protect itself by diversifying at a higher level — by selling catastrophic fire insurance to lots of other towns.

But by their very nature, the big catastrophic risks of the early 21st century couldn’t be diversified away. Wealth had become far too concentrated in a handful of extraordinarily treacherous places. The only way to handle them was to spread them widely, and the only way to do that was to get them out of the insurance industry and onto Wall Street. Today, the global stock markets are estimated at $59 trillion. A 1 percent drop in the markets — not an unusual event — causes $590 billion in losses. The losses caused by even the biggest natural disaster would be a drop in the bucket to the broader capital markets. “If you could take a Magnitude 8 earthquake and distribute its shock across the planet, no one would feel it,” Seo says. “The same principle applies here.” That’s where catastrophe bonds came in: they were the ideal mechanism for dissipating the potential losses to State Farm, Allstate and the other insurers by extending them to the broader markets.

Karen Clark’s model was, for Seo, the starting point. When he first stumbled upon it and the other companies’ models, he found them “guilty until proven innocent,” as he puts it. “I could see the uncertainty in them,” he says, “just by looking at the different numbers they generated for the same storm.” When they run numbers to see what would happen if the 1926 Miami hurricane hit the city today, A.I.R. puts the losses at $80 billion, R.M.S. at $106 billion and Eqecat at $63 billion. They can’t all be right. But they didn’t need to be exactly right, just sort of right, and the more he poked around inside them, the more he felt they were better than good enough to underpin financial decisions. They enabled you to get a handle on the risk as best you could while acknowledging that you would never know it exactly. And after all, how accurate were the models that forecast the likelihood that Enron would collapse? Next to what Wall Street investors tried to predict every day, natural disasters seemed almost stable. “In the financial markets, you have to care what other people think, even if what they think is screwed up,” Seo says. “Crowd dynamics build on each other. But these things — hurricanes, earthquakes — don’t exhibit crowd behavior. There’s a real underlying risk you have to understand. You have to be a value investor.”

The models were necessary but insufficient. True, they gave you a rough sense of the expected financial losses, but they said nothing about the rewards. Financial markets exist only as long as investors feel the odds are stacked in their favor. Investors — unlike roulette players — can honestly expect to make a gain (their share in the profits of productive enterprise). But how big a gain? How should the payout vary, from government bonds to blue-chip stocks to subprime mortgages? The rewards in each market tended to vary with investors’ moods, but those in catastrophe insurance were just incredibly volatile. Hurricane insurance rates would skyrocket after a big storm, then settle back down. This wouldn’t do: if big investors were going to be persuaded to take billions of dollars in catastrophic risk, they would need to feel there was some reason in the pricing of that risk. “The market,” as Seo puts it, “needs an acceptable mode of failure.”

In the spring of 2001, to the surprise of his colleagues, Seo left his big Wall Street firm and opened a hedge fund — which, he announced, wouldn’t charge its investors the standard 2 percent of assets and 20 percent of returns but a lower, flat fee. “It was quixotic,” says Paul Puleo, a former executive at Lehman who worked with Seo. “He quits this high-paying job to basically open a business in his garage in a market that doesn’t exist.” Seo opened his new shop with his younger brother Nelson and then brought in their older brother, Michael. (His third brother, Scott, had studied astrophysics but decided that “there was no future in astrophysics” and eventually turned himself into an ophthalmologist.) Seo named his firm Fermat Capital Management, after one of his intellectual heroes. “I had once read the letters between Pierre de Fermat and Blaise Pascal,” he wrote in a recent e-mail message. “From my father I had learned that most great mathematicians were nasty guys and total jerks (check out Isaac Newton . . . extra nasty guy), but when I read the Fermat-Pascal letters, you could see that Fermat was an exception to the stereotype . . . truly a noble person. I loved his character and found that his way of analyzing profitless games of chance (probability theory) was the key to understanding how to analyze profitable games of chance (investment theory).”

Four years later, Seo’s hedge fund still faced two problems. The smaller one was that investors were occasionally slow to see the appeal of an investment whose first name was catastrophe. As one investor put it, “My boss won’t let me buy bonds that I have to watch the Weather Channel to follow.” That objection doesn’t worry Seo much. “Investors who object to cat-bond investing usually say that it’s just gambling,” he says. “But the more mature guys say: ‘That’s what investing is. But it’s gambling with the odds in your favor.’ ”

His bigger problem was that insurance companies still didn’t fully understand their predicament: they had $500 billion in exposure to catastrophe but had sold only about $5 billion of cat bonds — a fifth of them to him. Still, he could see their unease in their prices: hurricane- and earthquake-insurance premiums bounced around madly from year to year. Right after Andrew, the entire industry quintupled its prices; a few tranquil years later, prices were back down nearly to where they had been before the storm. Financial markets bounced around wildly too, of course, but in the financial markets, the underlying risks (corporate earnings, people’s moods) were volatile. The risk in natural-disaster insurance was real, physical and, in principle, quantifiable, and from year to year it did not change much, if at all. In effect, the insurers weren’t insuring against disaster; they were only pretending to take the risk, without actually doing so, and billing their customers retroactively for whatever losses they incurred. At the same time, they were quietly sneaking away from catastrophe. Before the 1994 Northridge earthquake, more than a third of California homeowners had quake insurance; right after, the insurers fled the market, so that fewer than 15 percent of California homeowners have earthquakes in their policies today.

The market was broken: people on fault lines and beachfronts were stuck either paying far too much for their insurance or with no real coverage except the vague and corrupting hope that, in a crisis, the government would bail them out. A potentially huge, socially beneficial market was moments from birth. All it needed was a push from nature. And so on Aug. 24, 2005, John Seo was waiting, waiting for a storm. And here it came.

Wall Street is a machine for turning information nobody cares about into information people can get rich from. Back when banks lent people money to buy homes and then sat around waiting for interest payments, no one thought to explore how quickly homeowners would refinance their mortgages if interest rates fell. But then Wall Street created a market in mortgage bonds, and the trader with better information about how and when people refinance made a killing. There’s now a giant subindustry to analyze the inner financial life of the American homeowner.

Catastrophe bonds do something even odder: they financialize storms. Once there’s a market for cat bonds, there’s money to be made, even as a storm strikes, in marginally better weathermen. For instance, before the 2005 hurricane season, a Bermuda cat-bond hedge fund called Nephila found a team of oceanographers in Rhode Island called Accurate Environmental Forecasting, whose forecasts of hurricane seasons had been surprisingly good. Nephila rented the company’s services and traded bonds on the back of its reports. “They kind of chuckle at what we do,” says a Nephila founder, Frank Majors. “The fact that we’re making $10 million bets on whether Charley is going to hit Tampa or not. It made them a little nervous at first. We told them not to worry about what we’re going to do with the information. Just give it to us.”

As Katrina bore down on New Orleans, a cat bond named Kamp Re, issued by the insurance company Zurich, was suddenly at risk. If Zurich lost more than $1.2 billion on a single hurricane in about a two-year period, investors would lose all their money. If Zurich represented about 3 percent of the U.S. insurance market — that is, it was on the hook for about 3 percent of the losses — a hurricane would need to inflict about $40 billion in damage to trigger the default. Since no event as big as this had ever happened, it was hard to say just how likely it was to happen. According to R.M.S., there was a 1.08 percent chance that Kamp Re bond holders would lose all their money — assuming the scientists really understood the odds. The deal had been a success. One of its biggest buyers was John Seo.

As Katrina spun, the players in nature’s casino gathered around the table. When the storm jogged east and struck not New Orleans directly but the less populated, and less wealthy, coastline between Louisiana and Mississippi, they all had the same reaction — relief — but Hemant Shah felt a special relief. Shah is one of the founders of R.M.S., and he was at that moment driving to catch a flight from San Francisco to New York, where he hoped to speak at a conference devoted to predicting terrorism. When he saw Katrina miss New Orleans, he said to himself, O.K., it’s big, but it’s not catastrophic, and he boarded his plane.

As he flew across the country, R.M.S. and its competitors replicated Katrina inside their computers in much the same way that Karen Clark had once replicated Hurricane Andrew. Just hours after landfall, all three firms sent clients in the insurance industry their best estimates of financial losses: R.M.S. put them at $10 billion to $25 billion; Eqecat called for a range between $9 billion and $16 billion; Clark’s A.I.R. had a range of $12.7 billion to $26.5 billion. Big, as Shah said, but not catastrophic. Traders who had underwritten Kamp Re took calls from an investor at a Japanese bank in London. Cheered by Katrina’s path, the fellow was looking to buy some Kamp Re bonds. The traders found another investor eager to unload his Kamp Re holdings. The London investor bought $10 million of Kamp Re at a price of $94.

John Seo just watched. For the past four years, he and his brothers had made money at such moments as this: “live” cat trading, it’s called. A few investors would inevitably become jittery and sell their cat bonds at big discounts, what with the Weather Channel all hysteria all the time. (“The worst place to go if you’re taking risks,” says one cat-bond investor, “is the Weather Channel. They’re just screaming all the time.”) But entering the 2005 hurricane season, the Seo brothers had reconsidered their habit of buying in a storm. “The word had gotten out that buying in the storm was the smart thing to do,” Seo says. “And we were afraid our past successes would give us an irrational interest in buying. Everything’s all fuzzy in these events. And when things are fuzzy, your brain gives you an excuse to push the envelope. So we adopted a policy, before the season, of staying out of the market.”

A few hours later, Hemant Shah’s plane landed in New York. Shah turned on his BlackBerry and discovered that the New Orleans levees had broken: much of the city would soon be underwater. “My first reaction,” Shah says, “was, Uh-oh, we have a problem.” In the imaginary 100,000-year history of hurricanes that R.M.S. had in its computers, no hypothetical storm that struck so far from New Orleans had ever caused the levees to fail. The models, like the intuition they replaced, had a blind spot.

The Kamp Re bonds collapsed, the price dropping from the mid-90s to the low 20s. A few weeks later, an announcement from Zurich American made it clear that the investors in Kamp Re wouldn’t be getting any money back, and Kamp Re’s price fell from $20 to 10 cents. But then the real trouble started: R.M.S., the modeling company, declared that it was rethinking the whole subject of hurricane risk. Since 1995, scientists had noted a distinct uptick in hurricane activity in the North Atlantic Basin. The uptick had been ignorable because the storms had not been making landfall. But between July 2004 and the end of 2005, seven of history’s most expensive hurricanes had struck the American coast, leaving behind 5.5 million insurance claims and $81 billion in insured losses. The rise in hurricane size and frequency was no longer ignorable. R.M.S. convened a panel of scientists. The scientists agreed that unusually warm sea-surface temperatures were causing unusually ferocious and frequent storms. The root cause might be global warming or merely the routine ups and downs of temperatures in the North Atlantic Basin. On cause they failed to agree. On consequence they were united. At the beginning of August 2005, R.M.S. had judged a Katrina-size catastrophe to be a once-in-40-years event. Seven months later, the company pegged it as a once-in-20-years event. The risk had doubled.

It had been just 13 years since Karen Clark’s model swept the industry, but the entire catastrophe risk-taking industry now lived at the mercy of these modelers. The scientists were, in effect, the new odds-makers. It was as if the casino owner had walked up to his roulette table, seen a pile of chips on 00 and announced that 00 would no longer pay 36:1 but would henceforth pay only 18:1. The agencies that rated the insurance companies — S & P, Moodys, etc. — relied on the scientists to evaluate their exposure. When the scientists increased the likelihood of catastrophic storms, S & P and Moodys demanded that the insurance companies raise more capital to cover their suddenly more probable losses. And so in addition to the more than $40 billion they had lost in Katrina, the insurance companies, by edict of the ratings agencies, needed to raise $82 billion from their shareholders just to keep their investment-grade rating. And suddenly they weren’t so eager to expose themselves to losses from hurricanes.

John Seo felt differently. Katrina had cost him millions. But at the same time, in a funny way, it had vindicated his ideas about catastrophe. He had lost only what he had expected to lose. He had found an acceptable mode of failure.

As a boy, John Seo learned everything he could about the Titanic. “It was considered unsinkable because it had a hull of 16 chambers,” he says. The chambers were stacked back to front. If the ship hit something head on, the object might puncture the front chamber, but it would likely have to puncture at least three more to sink the ship. “They probably said, What are the odds of four chambers going?” he says. “There might have been a one-in-a-hundred chance of puncturing a single chamber, but the odds of puncturing four chambers, they probably thought of as one in a million. That’s because they thought of them as independent chambers. And the chambers might have been independent if the first officer hadn’t gambled at the last minute and swerved. By swerving, the iceberg went down the side of the ship. If the officer had taken it head on, he might have killed a passenger or two, but the ship might not have sunk. The mistake was to turn. Often people associate action with lowering risk or controlling risk, but experience shows more often than not that by taking action you only make the risk worse.”

The Titanic offered another lesson for the investor in catastrophe: the threats that seem to us the most remote are those we know the least about. Catastrophe risk is fundamentally different from normal risk. It deals with events so rare that experience doesn’t help you much to predict them. How do you use history to judge the likelihood of a pandemic killing off 1 in every 200 Americans? You can’t. It has happened only once. (The Spanish flu epidemic of 1918.) You lack information. You don’t know what you don’t know. The further out into the tail you go — the less probable the event — the greater the uncertainty. The greater the uncertainty, the more an investor should be paid to live with it.

The financial markets, or, at any rate, the arcane corner of Wall Street that dealt exclusively with highly unlikely financial events, had figured this out. The traders who sold insurance against extreme market collapses — the tail risks — all tended to charge exactly the same price, between four and five times their expected losses. Expected loss could be defined like this: Say an investor wanted to buy $1 billion of insurance for a year against a once-in-100-years stock-market crash. The expected loss would be 1 in 100, 1 percent of $1 billion: $10 million. The insurance would thus cost $40 million to $50 million. The pattern held across Wall Street. The trader at Lehman Brothers who priced stock-market-crash insurance didn’t know the trader at Harvard Management who priced the insurance against drastic interest-rate changes, and he didn’t know the trader at O’Connor and Associates who priced the insurance against the dollar’s losing a third of its value. But their idea of a fair premium for insurance against financial disaster suggested they were reading the same books on the subject — only there were no books. “The reigning theory is that the taste for risk is as arbitrary as the value of a painting,” Seo says. “But if this is so, why are these preferences so consistent across markets?”

Seo thought, Maybe risk is not like art. Maybe there is some deep rule that governs it. And maybe the market is groping its way to that rule all by itself.

Intuitively what the market was doing made sense. Highly improbable events were especially unsettling. The person who insured others against an unlikely event faced not only the problem of judging its likelihood; even if he knew how often it would occur, he didn’t know when it would occur. Even if you had complete certainty that a U.S. stock-market crash happened just once every 25 years, you still didn’t know which year. If you had set up a business to sell crash insurance in January 1987, you would have been bankrupted by the crash in October; on the other hand, if you had gone into the business in 1988, you would have gotten rich. There was no justice in it. The catastrophic risk-taker was a bit like a card counter at the blackjack table allowed to play only a few hands: yes, the odds are in his favor, but he doesn’t always get to play long enough for the odds to determine the outcome.

The uncertainty in these extreme, remote market risks meant that the person who took them should be paid more to do so. But how much more? Extreme events were treated on Wall Street as freak outliers that bore no relation to other, more normal events. There was a striking consistency in the pricing of these risks across Wall Street, but there was no hard logic under them: it was all being done by feel.

The logic is what Seo stumbled upon back in 2000 at Lehman Brothers after someone handed him a weird option to price. An industrial company had called Lehman with a problem. It operated factories in Japan and California, both near fault lines. It could handle one of the two being shut down by an earthquake, but not both at the same time. Could Lehman Brothers quote a price for an option that would pay the company $10 million if both Japan and California suffered earthquakes in the same year? Lehman turned to its employee with a reputation for being able to price anything. And Seo thought it over. The earthquakes that the industrial company was worried about were not all that improbable: roughly once-a-decade events. A sloppy solution would be simply to call an insurance company and buy $10 million in coverage for the Japanese quake and then another $10 million in coverage for the California quake; the going rate was $2 million for each policy. “If I had been lazy, I could have just quoted $4 million for the premium,” he says. “It would have been obnoxious to do so, but traders have been known to do it.” If either quake happened, but not both, he would have a windfall gain of $10 million. (One of his policies would pay him $10 million, but he would not be required to pay anything to the quake-fearing corporation, since it would get paid only if both earthquakes occurred.)

But there was a better solution. He needed to buy the California quake insurance for $2 million, its market price, but only if the Japanese quake happened in the same year. All Seo had to do, then, was buy enough Japanese quake insurance so that if the Japanese quake occurred, he could afford to pay the insurance company for his $10 million California insurance policy: $2 million. In other words, he didn’t need $10 million of Japanese quake insurance; he needed only $2 million. The cost of that was a mere $400,000. For that sum, he could insure the manufacturing company against its strange risk at little risk to himself. Anything he charged above $400,000 was pure profit for Lehman Brothers.

And that was that, except it wasn’t. He saw something. Each risk by itself was not unusual: the quakes being insured against were once-a-decade events. But since each earthquake had a 1-in-10 chance of happening in a year, the chances that both of them would occur were far more remote: 1 in 100 (10 percent of 10 percent). When you combined these more ordinary risks, you simulated extremely unlikely ones. “What I noticed, after the fact, is that this exotic option’s price was special,” he says. “It was related to tail pricing.” The risk of catastrophe wasn’t some freak outlier with no connection to more mainstream risks. It bore a fixed relationship to those risks. Indeed, one way of thinking about natural catastrophes was as a combination of more likely events.

Thus the hunches of Wall Street professionals found vindication in Seo’s arithmetic. The expected loss of the more ordinary risk of a single earthquake was $1 million (a 10 percent chance of a $10 million loss). The insurance cost $2 million, or twice the expected loss. The expected loss of the remote combined risk was $100,000 (a 1 percent chance of a $10 million loss). But the insurance cost $400,000: four times the expected loss. All those practical traders who were pricing tail risk at roughly four times the expected losses had been on to something. “Here I saw the beginnings of a market mechanism that directly links 1-in-10-year risk pricing to 1-in-100-year risk pricing,” Seo says. The intuitive reason that extreme, remote risk should be more highly priced than normal everyday risk was “a happy agreement between human psychological perception and hard mathematical logic.”

Seo’s math — which soon left middle school for graduate school — served two purposes: to describe this universal rule about the pricing of risk and to persuade investors that there was a deeper, hidden logic to investing in catastrophe. They could have some sense of what the price of the risk should be. It was an extraordinary idea: that catastrophe might be fair.

Then came Katrina. The reaction to the storm has put a fine point on Americans’ risk disorientation. The single biggest issue in Florida’s 2006 governor’s race, for instance, was the price of insurance. The Republican, Charlie Crist, got himself elected on the strength of his promise to reduce Floridians’ home-insurance rates by creating a state-subsidized pool of $28 billion in catastrophe insurance coverage. “Florida took this notion of spreading this risk and turned it on its head,” says one former state insurance commissioner. “They said, ‘We’re going to take all this risk ourselves.’ ” The state sold its citizens catastrophe insurance at roughly one-sixth the market rates, thus encouraging them to live in riskier places than they would if they had to pay what the market charged (and in the bargain, the state subsidized the well-to-do who live near the beach at the expense of the less-well-to-do who don’t). But if all the models are correct, $28 billion might not cover even one serious storm. The disaster waiting to happen in Florida grows bigger by the day, but for a man running for governor of Florida, ignoring it is a political no-brainer. If he’s lucky — if no big storms hit in his term — he looks like the genius who saved Floridians billions in catastrophic-risk premiums. If he’s unlucky, he bankrupts Florida and all hell breaks loose, but he can shake down the federal government to cover some of the losses.

Louisiana’s politicians are usually quicker than most to seize upon shrewd politics that generate terrible social policy, but in this case they could not afford to. Louisiana cannot generate and preserve wealth without insurance, and it cannot obtain insurance except at the market price. But that price remains a mystery. Billions of dollars in insurance settlements — received by local businesses and homeowners as payouts on their pre-Katrina policies — bloat New Orleans banks and brokerage houses. The money isn’t moving because the people are paralyzed. It’s as if they have been forced to shoot craps without knowing the odds. Businesses are finding it harder than ever to buy insurance, and homeowners are getting letters from Allstate, State Farm and the others telling them that their long relationship must now come to an end. “I’ve been in the business 45 years,” says a New Orleans insurance broker named Happy Crusel, “and I’ve never seen anything remotely like this.” An entire city is now being reshaped by an invisible force: the price of catastrophic risk. But it’s the wrong price.

Insurance companies, John Seo says, are charging customers too much — or avoiding their customers altogether — instead of sharing their risk with others, like himself, who would be glad to take it. New Orleans, as a result, is slower than it otherwise would be to rebuild. “The insurance companies are basically running away from society,” he says. “What they need to do is take the risk and kick it up to us.” They need to spread it as widely as possible across the investment world and, in the process, minimize the cost of insuring potential losses from catastrophes.

But this, too, is happening. The people on Wall Street who specialize in cat bonds now view Katrina as the single most important thing that ever happened to their business: overnight it went from a tiny backwater to a $14 billion market, and it is now stretching and straining to grow. In March of this year, a single insurer, Allstate, announced its intention to sell $4 billion in catastrophe bonds. A $14 billion market is a trivial sum next to the half-trillion or so dollars that the insurance industry stands to lose from megacatastrophes and next to the additional trillions of dollars worth of property that has gone uninsured in the places most likely to be destroyed by nature, like California, because the insurance is so expensive. But there are all around John Seo signs of a shift in the culture of catastrophe. “It has all the features of providential action,” he says. “It’s like all the actions of man and nature serve to grow the cat-bond market.”

When Katrina struck and his Kamp Re bonds collapsed — from $100 to 0 — Seo was able to view his loss with detachment. The models had badly underestimated the risk, but it was in the nature of extreme risk that the prediction of it would sometimes be mistaken. “The important thing is that the money wasn’t lost in an unearned manner,” he says, by which he means that it wasn’t lost dishonestly or even unwisely or in what his community of investors would consider a professionally unacceptable manner. Investors will endure losses as long as they come in the context of a game they perceive as basically fair, which is why they don’t abandon the stock market after a crash. “That’s all I need to know,” Seo says. “That’s all my clients need to know.” Actually, he goes even further: “I would be embarrassed if we had a big event and our loss wasn’t commensurate with it. It would mean that we didn’t serve society. We failed society.”

Seo’s returns in 2005 were only slightly positive, compared with the roughly 10 to 12 percent he had been delivering, but the demand for his services boomed. He now controls $2 billion, or more than twice what he had before the most costly natural disaster in history. Big investors weren’t scared off by Katrina. Just the reverse. It has led many of them to turn to Seo and others like him to make money from catastrophe. And they probably will. But what interests Seo more is what might happen in the bargain, that the financial consequences of catastrophe will be turned into something they have never been: boringly normal.