Immediate access to information via the internet is a fantastic thing. I honestly don't know how we used to get along beforehand, for instance how could someone plan a trip to Seattle, to take a ferry to Whidbey island prior to the internet? Now, we just click a couple links, book a couple things online, find out the schedule and head to Seattle... Before the internet/www how did we even know that specific ferry existed?
The larger point is "how did we ever know anything" before yahoo (ok, I'm dating myself here but before google was a verb, the best search engine imho was yahoo (what else did you have, altavista? webcrawler?)). In grad school we used to play games where we would ask random "consultant" type interview questions like: "How many weddings take place in Mexico City every year?" The reason we did this was simple: in physics (the discipline I did my graduate school in) it was crucial to know what to expect from a calculation before you did the actual calculation. Otherwise how would you know if you were right?
But now, if you were asked that same question you'd just google it (ah, there I go, using it as a verb.... as Calvin (of Calvin&Hobbes) said "verbing weirds languages.) This fact -- that we can just google things -- really diminishes the role of trivia in our culture. I remember when it I was young, reading books called "The Straight Dope" where people would write questions about random topics and the author (an authority on random trivia) would respond. We can't even begin to think about that delay! Could you imagine submitting a google request and waiting not only for a person to read your query, but for them to draft a response, and then compile about a hundred or so similar queries and then publish a book compiling the results?!? On the one hand it seem ludicrous in today's standards, but on the other it means...
There is no more trivia. I personally think this is sad. How many times have you sat around and the conversation deteriorated to "ok lets just google it"? That statement is as empowering as it is sad. As we embrace the new information age, we should be cognizant of what we're leaving behind.
Saturday, August 15, 2009
Thursday, June 11, 2009
One Humble Quants' View on the Credit Crunch
Since I work in the finance industry, I have been asked by a number of people what I thought lead to the "credit crunch". So I'm attempting here to put down some ideas on what I think.
The short story is everyone down the line. So let's line up the usual suspects
1. The people who bought mortgages they couldn't afford.
Now, I don't know if I can go so far and say the education system in the United States is to blame, however reports do show a lower than average numeracy rate. People at some level have to take responsibility for knowing whether or not they can afford something.
But that's a bit glib. We all know the powerful persuasion techniques of salespeople, and especially when charts and numbers are bandied about.
2. The banks that sold the mortgage.
Ie, the salespeople.
These people should have had some responsibility to be open and honest with their clients. Especially about the whole term of the mortgage. These salespeople were showing the teaser rates, but somehow not emphasizing the fact that these rates reset after a couple of months or years. The long term affordability should have been made clear.
In regular circumstances, the banks would not want to enter into mortgages where the probability of default was high, they would likely lose the principal of the mortgage. However, this is no longer the case -- the banks that sell the mortgages do not take on the risk of default.
So... let's ask the question: Who takes on the risk of bad mortgages? That brings us to the next suspect.
3. Fannie Mae, but ultimately the federal government.
The answer is that the banks did not hold the risk of the mortgages, they were able to offload all of the risk of mortgage default to Fannie Mae (the Federal National Mortgage Association -- FNMA). Fannie Mae bought the mortgages from the banks, so the banks made money on creating the mortgage and then selling it immediately to Fannie Mae. If the banks hold no risk, then they are transformed into the business of mortgage creation -- the more mortgages they create the more money they make, and are never exposed to the risk of default. Therefore they have no incentive to tell their clients that they cannot possibly afford that mortgage.
The next suspect please.
4. Ronald Reagan and Alan Greenspan.
The federal government enacted policy to encourage home ownership throughout country. The premise -- which sounds plausible -- is that having some stake in ownership increases participation in the economy. To set this up, they mandated that Fannie Mae relieve the banks for the mortgages they sell. This reduces the amount of risk they have in-house and allow them to go again and sell another mortgage.
Now, even if Fannie may were mandated from above to buy mortgages in order to get more of the populous to be homeowners, surely the would be exposed to the risk of default and would therefore mandate policy downward to the banks to limit their risk.
Next question: How was Fannie Mae offloading the risk of the bad mortgages?
5. Financial alchemists on Wall Street. (NB: Not the quants!)
The people responsible for consolidating all of the mortgages into a single financial product. Here's the rationale: a single mortgage isn't always the best investment. It doesn't promise regular payments at regular intervals -- the mortgage can be paid down early, or it could even default. But packaging a large number of mortgages together, and then selling smaller "tranches" (or slices -- a literal french translation) can make the payments more reliable. This is done by partitioning the tranches such that the "lower tier" ones are populated by the mortgages that default first, and then the "mezzanine" and "senior" tranches are populated by the mortgages that haven't defaulted. Thus, the senior tranches have a longer expected lifetime. One would expect that on average some percentage of the mortgages default and some percentage of the mortgages are prepaid, but these are all relegated to the lower tranches and do not affect the senior tranches. This plausible sounding argument is based somewhat on the "law of large numbers", which roughly states that if a large number of events are considered, then things average out and we have a better handle on their aggregate behaviour.
I called this alchemy because people on Wall street took all these individual mortgages that the populous couldn't afford and packaged them into a financial product that investment banks all over the world were clamouring to buy. Why would they want to buy these types of products? The answer is that they were very highly rated -- they appeared to be good a good quality investment. How did these investments get this appearance? They were rated highly by the ratings agencies. The next suspect.
6. Ratings agencies.
The ratings agencies are autonomous corporations whose purpose is to determine credit-worthiness. Examples include Standards&Poors, Moodys etc. They do this for municipalities, institutions but also for the tranches mentioned above.
The problem leading to the credit crunch was that the investment banks who were structuring these MBSs (Mortgage Backed Securities) and CDOs (Consolidated Debt Obligations) described above had full access to the policies of the ratings agencies, and even in some cases, could meet and discuss with the agencies how to achieve top ratings.
So the investment bankers (aka the alchemists) could figure out exactly how to structure the CDOs in order to achieve the highest rating, regardless of their content.
Now, I'm not actually saying these people were being purposefully deceitful, but they certainly believed the numbers and equations much more than they had any right to do. The reason for this is that ever since 1973, mathematicians and physicists have been employed in Wall street. 1973 was the year that Black Scholes and Merton figured out the "exact" pricing of an option using "fancy mathematics". This ushered in a new era on Wall street -- an arms race -- where each bank hired more and more physicists developing more and more mathematical finance tools. The point is that their return was extraordinary. Wall street got addicted to math.
This culture grew where the math was, well, if not king, then let's just go with indispensable. Hidden within the price of a CDO is some pretty severe assumptions on the default rates and correlations of individual mortgages. The physicists on Wall street decided they could bring their mathematical sophistication to bear on this issue... This brings us to the next suspect.
7. Ok, maybe the quants too.
WIRED magazine recently ran a cover story on The Formula that Ruined Wall Street -- the Guassian Copula (here is a very interesting take on the formula). This formula encapsulates a technique for turning marginal probability distributions into joint probability distributions (here is an interesting take on this relationship). The inventor of this formula knew full all of the assumptions and limitations built into the formula, but it did allow for tractable pricing of very intensely complicated financial products -- mortgage backed securities, exactly those espoused above.
Now I personally don't believe we can fault the discoverer/inventor of the Guassian copula formula David Li. He masterfully solved a difficult problem with an elegant solution, one which clearly had limitations -- limitations that Li both knew about and tried to convey. (See the Quant Manifesto).
I'm going out on a limb here, but I believe that "prepayment" modeling is more akin to actuarial work -- financial mathematics is a different game altogether. Financial mathematics concerns itself with "arbitrage freedom" -- the idea of no-free lunch, two parties can agree on a price because any other price will benefit one side of the deal more than the other -- and has some formal mathematics conditions when this can be true. The idea behind this is "replication", that one can replicate derivative contracts by buying and selling the underlying securities. Anyway, the point is that the current price of a derivative does not depend on past history, only today's prices in the market.
You can't play these formal mathematical games with prepayment modeling, this relies heavily on historical statistics and assumptions about how various factors work together (such as how prepayments move with interest rate movements).
Anyway I digress. The point here is that the quants stopped doing financial mathematics when they started entertaining models like prepayment models. The limitations should have been made more clear, however most likely these models had moderate success in the past and had never been tested in declining real estate market conditions.
Conclusions
So in total, I guess there are a couple of specific policies that come out of this.
1) Strengthen education. Keep the population numerate and literate.
2) Don't let the CMHC give interest only mortgages.
3) Set up a firewall between ratings agencies and banks.
4) (this wasn't really addressed here) Don't allow bank mergers.
The short story is everyone down the line. So let's line up the usual suspects
1. The people who bought mortgages they couldn't afford.
Now, I don't know if I can go so far and say the education system in the United States is to blame, however reports do show a lower than average numeracy rate. People at some level have to take responsibility for knowing whether or not they can afford something.
But that's a bit glib. We all know the powerful persuasion techniques of salespeople, and especially when charts and numbers are bandied about.
2. The banks that sold the mortgage.
Ie, the salespeople.
These people should have had some responsibility to be open and honest with their clients. Especially about the whole term of the mortgage. These salespeople were showing the teaser rates, but somehow not emphasizing the fact that these rates reset after a couple of months or years. The long term affordability should have been made clear.
In regular circumstances, the banks would not want to enter into mortgages where the probability of default was high, they would likely lose the principal of the mortgage. However, this is no longer the case -- the banks that sell the mortgages do not take on the risk of default.
So... let's ask the question: Who takes on the risk of bad mortgages? That brings us to the next suspect.
3. Fannie Mae, but ultimately the federal government.
The answer is that the banks did not hold the risk of the mortgages, they were able to offload all of the risk of mortgage default to Fannie Mae (the Federal National Mortgage Association -- FNMA). Fannie Mae bought the mortgages from the banks, so the banks made money on creating the mortgage and then selling it immediately to Fannie Mae. If the banks hold no risk, then they are transformed into the business of mortgage creation -- the more mortgages they create the more money they make, and are never exposed to the risk of default. Therefore they have no incentive to tell their clients that they cannot possibly afford that mortgage.
The next suspect please.
4. Ronald Reagan and Alan Greenspan.
The federal government enacted policy to encourage home ownership throughout country. The premise -- which sounds plausible -- is that having some stake in ownership increases participation in the economy. To set this up, they mandated that Fannie Mae relieve the banks for the mortgages they sell. This reduces the amount of risk they have in-house and allow them to go again and sell another mortgage.
Now, even if Fannie may were mandated from above to buy mortgages in order to get more of the populous to be homeowners, surely the would be exposed to the risk of default and would therefore mandate policy downward to the banks to limit their risk.
Next question: How was Fannie Mae offloading the risk of the bad mortgages?
5. Financial alchemists on Wall Street. (NB: Not the quants!)
The people responsible for consolidating all of the mortgages into a single financial product. Here's the rationale: a single mortgage isn't always the best investment. It doesn't promise regular payments at regular intervals -- the mortgage can be paid down early, or it could even default. But packaging a large number of mortgages together, and then selling smaller "tranches" (or slices -- a literal french translation) can make the payments more reliable. This is done by partitioning the tranches such that the "lower tier" ones are populated by the mortgages that default first, and then the "mezzanine" and "senior" tranches are populated by the mortgages that haven't defaulted. Thus, the senior tranches have a longer expected lifetime. One would expect that on average some percentage of the mortgages default and some percentage of the mortgages are prepaid, but these are all relegated to the lower tranches and do not affect the senior tranches. This plausible sounding argument is based somewhat on the "law of large numbers", which roughly states that if a large number of events are considered, then things average out and we have a better handle on their aggregate behaviour.
I called this alchemy because people on Wall street took all these individual mortgages that the populous couldn't afford and packaged them into a financial product that investment banks all over the world were clamouring to buy. Why would they want to buy these types of products? The answer is that they were very highly rated -- they appeared to be good a good quality investment. How did these investments get this appearance? They were rated highly by the ratings agencies. The next suspect.
6. Ratings agencies.
The ratings agencies are autonomous corporations whose purpose is to determine credit-worthiness. Examples include Standards&Poors, Moodys etc. They do this for municipalities, institutions but also for the tranches mentioned above.
The problem leading to the credit crunch was that the investment banks who were structuring these MBSs (Mortgage Backed Securities) and CDOs (Consolidated Debt Obligations) described above had full access to the policies of the ratings agencies, and even in some cases, could meet and discuss with the agencies how to achieve top ratings.
So the investment bankers (aka the alchemists) could figure out exactly how to structure the CDOs in order to achieve the highest rating, regardless of their content.
Now, I'm not actually saying these people were being purposefully deceitful, but they certainly believed the numbers and equations much more than they had any right to do. The reason for this is that ever since 1973, mathematicians and physicists have been employed in Wall street. 1973 was the year that Black Scholes and Merton figured out the "exact" pricing of an option using "fancy mathematics". This ushered in a new era on Wall street -- an arms race -- where each bank hired more and more physicists developing more and more mathematical finance tools. The point is that their return was extraordinary. Wall street got addicted to math.
This culture grew where the math was, well, if not king, then let's just go with indispensable. Hidden within the price of a CDO is some pretty severe assumptions on the default rates and correlations of individual mortgages. The physicists on Wall street decided they could bring their mathematical sophistication to bear on this issue... This brings us to the next suspect.
7. Ok, maybe the quants too.
WIRED magazine recently ran a cover story on The Formula that Ruined Wall Street -- the Guassian Copula (here is a very interesting take on the formula). This formula encapsulates a technique for turning marginal probability distributions into joint probability distributions (here is an interesting take on this relationship). The inventor of this formula knew full all of the assumptions and limitations built into the formula, but it did allow for tractable pricing of very intensely complicated financial products -- mortgage backed securities, exactly those espoused above.
Now I personally don't believe we can fault the discoverer/inventor of the Guassian copula formula David Li. He masterfully solved a difficult problem with an elegant solution, one which clearly had limitations -- limitations that Li both knew about and tried to convey. (See the Quant Manifesto).
I'm going out on a limb here, but I believe that "prepayment" modeling is more akin to actuarial work -- financial mathematics is a different game altogether. Financial mathematics concerns itself with "arbitrage freedom" -- the idea of no-free lunch, two parties can agree on a price because any other price will benefit one side of the deal more than the other -- and has some formal mathematics conditions when this can be true. The idea behind this is "replication", that one can replicate derivative contracts by buying and selling the underlying securities. Anyway, the point is that the current price of a derivative does not depend on past history, only today's prices in the market.
You can't play these formal mathematical games with prepayment modeling, this relies heavily on historical statistics and assumptions about how various factors work together (such as how prepayments move with interest rate movements).
Anyway I digress. The point here is that the quants stopped doing financial mathematics when they started entertaining models like prepayment models. The limitations should have been made more clear, however most likely these models had moderate success in the past and had never been tested in declining real estate market conditions.
Conclusions
So in total, I guess there are a couple of specific policies that come out of this.
1) Strengthen education. Keep the population numerate and literate.
2) Don't let the CMHC give interest only mortgages.
3) Set up a firewall between ratings agencies and banks.
4) (this wasn't really addressed here) Don't allow bank mergers.
Monday, June 8, 2009
An "old" blog
Here is something I wrote while in grad school in The Graduate magazine. The title is "The snake that swallowed his tale"
I was watching the football playoffs with a beer in my hand, when I started thinking about history. Brett Favre had just completed a forward pass. He owed this completion to Newt Rockne, the coach from Notre Dame who, for all intents and purposes, invented the forward pass. Before him, American football looked more like English rugby.
English rugby was "invented" when a not-so-bright schoolboy at the Rugby School outside of London England was playing soccer and picked up the ball. The ref told him the rules, but by the third time the boy did it, the ref left the game play on, and rugby was born. The boy's name was William Webb Ellis, and the World Cup of Rugby trophy is still named for him.
It's no surprise that American football used to look like rugby, since it is a direct descendant of it. The first recorded game of American football was played between Yale and Harvard in the mid 1800's. These tow schools have tried to mimic everything English since their inception. Harvard was founded in 1636, sixteen ears after pilgrims landed at Plymouth rock. It has graduated seven American presidents, from the famous -- John Fitzgerald Kennedy -- to the infamous -- George W. Bush. It has also housed more than forty faculty members whose international fame has been ensuredby the endowment of Alfred Nobel and the Nobel prizes.
The Nobel prizes came about due to a misprint in a Swedish newspaper. You see, Alfred Nobel had a prother who passed away. Some reporter mistook the two Nobels and printed Alfred Nobel's obituary the next day. when he read his own obituary (a rather frightening thought), he was not pleased with the report: "Only to be remembered from his destructive contribution" of trinitrotoluene, an explosive responsible for many deaths" (not a direct quotation). It was so written because Alfred Nobel had invented dynamite, or trinitrotoluene (TNT).
Nobel disliked his obituary enough that he decided change his will and he established an early prize to be given to those academics that have contributed the most in their field, the fields being physics, chemistry, medicine, literature and peace. Economics came only in 1968 through a donation of a bank in hopes of securing economics as a legitimate scientific field (the reader is left to decide the success).
There were three winners of the Nobel prize in medicine in 2001 -- Leland Hartwell, Tim Hunt and Paul Nurse -- for their discoveries of key regulators of the cell cycle. The cell cycle includes cell division and the creation of energy through the breakdown of glucose (among many other things). In most living cells this is done in the presence of oxygen.
However, there is another pathway available when oxygen is not present. For humans this pathway leads to the creation of lactic acid, which is what aches in your muscles after physical exertion and must be coarsing through Brett Favre's body at the moments, and the corresponding pathway in plants leads to the creation of alcohol, which is responsible for the beer I'm currently enjoying.
I was watching the football playoffs with a beer in my hand, when I started thinking about history. Brett Favre had just completed a forward pass. He owed this completion to Newt Rockne, the coach from Notre Dame who, for all intents and purposes, invented the forward pass. Before him, American football looked more like English rugby.
English rugby was "invented" when a not-so-bright schoolboy at the Rugby School outside of London England was playing soccer and picked up the ball. The ref told him the rules, but by the third time the boy did it, the ref left the game play on, and rugby was born. The boy's name was William Webb Ellis, and the World Cup of Rugby trophy is still named for him.
It's no surprise that American football used to look like rugby, since it is a direct descendant of it. The first recorded game of American football was played between Yale and Harvard in the mid 1800's. These tow schools have tried to mimic everything English since their inception. Harvard was founded in 1636, sixteen ears after pilgrims landed at Plymouth rock. It has graduated seven American presidents, from the famous -- John Fitzgerald Kennedy -- to the infamous -- George W. Bush. It has also housed more than forty faculty members whose international fame has been ensuredby the endowment of Alfred Nobel and the Nobel prizes.
The Nobel prizes came about due to a misprint in a Swedish newspaper. You see, Alfred Nobel had a prother who passed away. Some reporter mistook the two Nobels and printed Alfred Nobel's obituary the next day. when he read his own obituary (a rather frightening thought), he was not pleased with the report: "Only to be remembered from his destructive contribution" of trinitrotoluene, an explosive responsible for many deaths" (not a direct quotation). It was so written because Alfred Nobel had invented dynamite, or trinitrotoluene (TNT).
Nobel disliked his obituary enough that he decided change his will and he established an early prize to be given to those academics that have contributed the most in their field, the fields being physics, chemistry, medicine, literature and peace. Economics came only in 1968 through a donation of a bank in hopes of securing economics as a legitimate scientific field (the reader is left to decide the success).
There were three winners of the Nobel prize in medicine in 2001 -- Leland Hartwell, Tim Hunt and Paul Nurse -- for their discoveries of key regulators of the cell cycle. The cell cycle includes cell division and the creation of energy through the breakdown of glucose (among many other things). In most living cells this is done in the presence of oxygen.
However, there is another pathway available when oxygen is not present. For humans this pathway leads to the creation of lactic acid, which is what aches in your muscles after physical exertion and must be coarsing through Brett Favre's body at the moments, and the corresponding pathway in plants leads to the creation of alcohol, which is responsible for the beer I'm currently enjoying.
Thursday, June 4, 2009
Explanatory Note
So, this is my first blog post. I had a blog with friends a couple of years ago, but it was disabled after a year or so of disuse. The genesis of that blog was a trip to Chicago a year after we all left grad school after we started debating arcane philosophical points on various subjects. We all looked at each other and said "I miss this". So my bright idea was to have a ready-to-go website that we could all post to. Needless to say it lasted all of a couple months (a fate I hope to avoid here!)
Ah, the title... "Explanatory Note". My blog is called "Chaos in oneself" and the website is chaosdancingstar.blogspot.com This is from a Nietzsche quotation:
"One must still have chaos in oneself in order to give birth to a dancing star."
A couple of years ago I received a fridge magnet as a birthday present from my mom with that quotation on it. That same year I got a journal with the same quotation on it for Christmas from a friend! Although I don't believe in fate, this quotation stuck with me. More than one person in the world saw this and thought of me... so I started to wonder why. It's always interesting to think about how others see you, so this "two sigma event" struck me.
I like to think that people see my chaotic tendencies as a necessary predicate to amazing results :) What do I mean by chaotic tendencies? I don't just mean clothes piling up or deadlines being flexed... I like to think of it as the seemingly chaotic jumps my thoughts seem to take. A good friend of mine (who just published a book "The Riverbones", read it it's amazing - it's a travel memoir about his time in Suriname, and I make a cameo as the "mathematician friend") used to describe me as "thinking outside the box", and the connections that he's referring to I think stem from all of the seemingly random connections I make between seemingly disparate thoughts and ideas.
Anyway, this is a bit of background of the blog title and website name. Don't know if anyone's reading, I hope to continue to blog about subjects such as finance, politics, mathematics, economics, sailing, books, current events. With that cross-section of subjects I think I'll be lucky if anyone is reading! Oh well, it'll be cathartic and I can practice oratory.
Ah, the title... "Explanatory Note". My blog is called "Chaos in oneself" and the website is chaosdancingstar.blogspot.com This is from a Nietzsche quotation:
"One must still have chaos in oneself in order to give birth to a dancing star."
A couple of years ago I received a fridge magnet as a birthday present from my mom with that quotation on it. That same year I got a journal with the same quotation on it for Christmas from a friend! Although I don't believe in fate, this quotation stuck with me. More than one person in the world saw this and thought of me... so I started to wonder why. It's always interesting to think about how others see you, so this "two sigma event" struck me.
I like to think that people see my chaotic tendencies as a necessary predicate to amazing results :) What do I mean by chaotic tendencies? I don't just mean clothes piling up or deadlines being flexed... I like to think of it as the seemingly chaotic jumps my thoughts seem to take. A good friend of mine (who just published a book "The Riverbones", read it it's amazing - it's a travel memoir about his time in Suriname, and I make a cameo as the "mathematician friend") used to describe me as "thinking outside the box", and the connections that he's referring to I think stem from all of the seemingly random connections I make between seemingly disparate thoughts and ideas.
Anyway, this is a bit of background of the blog title and website name. Don't know if anyone's reading, I hope to continue to blog about subjects such as finance, politics, mathematics, economics, sailing, books, current events. With that cross-section of subjects I think I'll be lucky if anyone is reading! Oh well, it'll be cathartic and I can practice oratory.
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