He Xun appointed Ye Wei Kang Lan as the Great Wall.
Since the mid-1980s, Wall Street has been relying on financial engineering elites to create various new ways of making profits. Their method of creating money has been running successfully for so many years until one of them "suddenly" triggered this global economic disaster.
A year ago, people always thought that a mathematical genius like Xianglin Li might win the Nobel Prize one day, because some financial economists and even Wall Street geniuses did win the Nobel Prize in economics before. Xianglin Li's pioneering work is to measure investment risks, but in the financial field, his achievements are more influential than those of scholars who won the Nobel Prize before, and are widely used faster. However, when dazed bankers, politicians, regulators and investors are looking for the root cause in the ruins of the worst financial collapse since the Great Depression, he may be more grateful that he still has a job in the financial industry.
Xianglin Li's research is to determine the correlation between assets, that is, to quantify the correlation between completely different events with mathematical models. This is a big problem in the financial field, but this formula called Gaussian dependence function he constructed can make extremely complex risks more easily and accurately measured by mathematical means than before. Based on this formula, financial institutions can boldly sell all kinds of new securities and financial derivatives, and expand the financial market to an almost incredible extent.
From bond investors to Wall Street banks, from rating agencies to regulators, almost everyone is using the Xianglin Li formula. Soon, the method of using this formula to measure risk has been deeply rooted in the financial field and has helped people make a lot of money, so that any warning about the limitations of this formula has been ignored.
However, all of a sudden, people who use this formula found that the financial market began to change unexpectedly. In 2008, a small crack turned into a huge canyon, which swallowed tens of billions of dollars in an instant, pushing the global banking system to the brink of collapse and triggering this economic crisis that spread to all corners of the world.
To be sure, Xianglin Li will not win the Nobel Prize in Economics in a short time. And this financial tsunami has also made the position of financial economics, which was worshipped and believed by people before, no longer exist.
Why is the influence of mathematical formula so great?
The surprising question is, how can a mathematical formula bring such devastating results to the financial community? The answer lies in the huge bond market, which allows pension funds, insurance companies and hedge funds to lend trillions of dollars to enterprises, countries and home buyers. If a company wants to issue bonds to borrow money, investors will closely examine the company's accounts to confirm that the company can have enough funds to repay the loan. Lenders will charge higher interest rates if they think the loan risk is high.
Bond investors bet on "high probability events". If the probability of a bond default is 1%, they can get an extra 2% interest, and they will flock to buy the bond. It's like a casino. People don't mind losing some money occasionally, as long as they are winning money most of the time.
Bond investors usually invest in a pool of assets consisting of hundreds or even thousands of mortgage loans. The total scale of such activities involved now is staggering: the total debt owed by American buyers has reached 1 1 trillion dollars. However, the mortgage asset pool is more chaotic than the bond market. In this kind of investment, there is no guaranteed interest rate because the amount of cash paid collectively by buyers each month is a function of the number of buyers who have refinanced and failed to repay due to default. Similarly, there is no fixed repayment due date for such loan activities. Because the time for the purchaser to repay the mortgage is unpredictable, such as the purchaser's decision to sell the property, the total repayment amount in the pool is also irregular. The biggest headache is that there is no way to determine a single probability value for the probability of default (that is, the higher the probability, the greater the risk of loan loss).
Wall Street's solution is to grade all kinds of assets in the whole pool through a method called tranching, and create a risk-free security bond with 3A rating. The first-level investors can get the interest on debt repayment first, while other types of investors can charge higher interest, although their ratings are slightly lower due to the higher risk of default.
Rating agencies and investors are comfortable with AAA bonds because they believe that hundreds of loan buyers will not default at the same time. One person may lose his job, and others may get sick. However, these are individual unfortunate events and will not have a significant impact on the overall mortgage asset pool. However, all catastrophic events are not individual, and the hierarchical method cannot solve all the problems of asset pool risk.
The event that house prices may fall will affect a large number of people at the same time. If the value of the house near the buyer's home falls, the net asset value of this person's house will also fall, and it is very likely that his (her) neighbor's property will also fall. Once the buyer defaults on repayment, neighboring neighbors are likely to default. This is the so-called correlation, that is, the relationship between the change of one variable and the change of other variables and the degree of influence. Measuring this relationship and its degree is an important part in determining the risk of mortgage bonds.
As long as investors can price risks, they are willing to take risks. What they hate is uncertainty, that is, the uncertainty of risk. For this reason, bond investors and mortgage lenders are eager to find ways to measure, simulate and price correlation. Before the econometric model was applied to the financial market, the only time investors felt safe about investing in the mortgage asset pool was that there was no risk, that is, such bonds were implicitly guaranteed by the federal government through Freddie Mac and Fannie Mae.
Understand the concept of relevance
In order to better understand the concept of "relevance", let's give a simple example: suppose a child in a primary school is named Alice, and her parents have a 5% chance of divorce this year, 5% chance of getting lice on their heads, 5% chance of seeing the teacher fall on a banana peel, and 5% chance of winning the class reading contest. Suppose investors want to trade a security based on the probability that these events will happen to Alice, and their bids may be similar.
We consider two children, not only Alice, but also her deskmate britney spears. Suppose Britney's parents are divorced. What are the chances of Alice's parents getting divorced? In most cases, it should be 5%, which means that their correlation may be close to 0 in this matter; If britney spears has lice on her head, Alice is much more likely to have lice, perhaps 50%, which means that their correlation is about 0.5; If Britney Spears saw the teacher fall, because they were deskmates, the probability that Alice also saw it may be 95%, and their correlation is close to1; If britney spears wins the class reading contest, Alice has no chance of winning, and their correlation in this matter is-1.
If investors trade securities based on the probability that these events happen to these two children at the same time, their judgments are likely to be very different, because the correlation between the two children in various events is different.
But this is a very imprecise science. Just to determine that the probability of something happening to a person is 5%, it takes a lot of energy to collect historical data for statistics and error analysis, while judging the probability of another person happening to this person is more complicated and lacks relevant historical data, so the possibility of error is even greater.
In the housing mortgage market, it is more difficult to calculate this correlation. First of all, we must calculate the probability of falling house prices in a certain area. You can predict the future by observing the historical trend of house prices, but the macroeconomic situation of a country is also extremely important. On this basis, we have to judge, if the house price in one state falls, what is the probability that the same house price in another state will fall?
Xianglin Li has made a breakthrough.
Xianglin Li, born in rural China in 1960s, obtained a master's degree in economics from Nankai University with honors, and then went to the United States to study and obtained an MBA degree from Laval University in Quebec. After that, he continued his studies and obtained a master's degree in actuarial science and a doctor's degree in statistics from the University of Waterloo in Canada. From 65438 to 0997, he started his financial career in Imperial Commercial Bank of Canada, and later worked for Barclays Capital, and was responsible for rebuilding its quantitative analysis team in 2004.
Xianglin Li's academic background is very typical among Wall Street elites. Since the income from academic research is far less than the salaries paid by Wall Street investment banks and hedge funds, since the 1980s, a large number of senior talents with mathematical background have entered Wall Street to engage in the creation, pricing and arbitrage of financial derivatives.
At this time, by coincidence, Xianglin Li, who works in JPMorgan Chase, published a paper entitled "On Default Correlation: Dependency Function Method" in the magazine of Fixed Income. This paper adopts a relatively simple mathematical method (relative to the level of Wall Street elites, of course), without referring to historical default data, but uses the market price data of a financial derivative product-Credit Default Swap (CDS) as the basis for judging the correlation of default.
If you are an investor, you can choose to lend the money directly to the borrower or sell the CDS products to the lender. An insurance equivalent to a loan in case the borrower defaults. Both methods can charge a fixed income-interest or premium. The income of the two companies is close, but the supply of CDS products is not limited by the number of bonds issued, so the CDS market in its initial stage is growing at an extraordinary speed, and its scale greatly exceeds that of the bond market as its basic asset.
When the price of CDS rises, it indicates that the possibility of default of its underlying assets increases. Xianglin Li's breakthrough is that he didn't waste time waiting to collect enough data on actual breach of contract, because there are few actual breaches in reality. Instead, the historical data of the CDS market is used as the basis for judgment. Suppose there are two borrowers, it is difficult to calculate their default correlation through their past actual defaults, because maybe they didn't default in the past. However, we can observe the historical price changes of CDS of these two borrowers, and if the trends are more consistent, we can prove that they are highly correlated. Xianglin Li regards the correlation of this price trend as a "shortcut" and assumes that the financial market, especially the CDS market, can correctly deal with the possibility of default.
This is a clever simplification of a complex problem. In addition, Xianglin Li not only simplified the calculation of correlation, but also decided not to consider the complex relationship changes between loans in the asset pool at all. For example, what happens if the number of loans in the asset pool increases? If the negatively related loan portfolio and the positively related loan portfolio are put together, how will the risk of the entire asset pool change? He said, don't worry. We only need to manage a final related data, and a simple and clear data represents everything we need to consider.
This invention made the market develop rapidly.
The invention of this formula has a lightning effect on the asset securitization market. With this risk pricing formula, the elites on Wall Street see new infinite possibilities. They immediately set out to create a large number of new 3A securities. Rating agencies like Moody's no longer need to worry about the asset risks behind these securities. They just need to consider this simple correlation data, and then come up with a rating that tells people how risky these assets are.
Therefore, almost any asset can be tied together into 3A securities-corporate bonds, bank loans, mortgage-backed securities and so on. The asset pool thus formed is usually called debt-backed securities (CDOs). By classifying asset pools, you can create 3A-level securities, even if none of the constituent assets of the securities are 3A-level. What about the lower-level securities in the asset pool? They also came up with a good idea: bundling the low-level securities in various CDO asset pools to form an asset pool and rating it again. This investment tool is called CDO2. So far, no one really knows what basic assets this product contains. But they don't care, all they need is Xianglin Li's connection function.
Over the years, CDS and CDO markets have been interdependent and growing together. The data shows that at the end of 200 1, the total amount of CDS circulating abroad was as high as $920 billion. By the end of 2007, this figure had soared to $62 trillion. Similarly, the total size of CDO market was only $275 billion in 2000, but it expanded to $4.7 trillion in 2006.
The development of these markets is based on the Xianglin Li formula. If you ask some market participants, they will use the words "excellent, concise and easy to handle" to describe this formula. This formula is almost universally applicable, so everyone will use this formula whether banks package new bonds or traders and hedge funds conduct complex transactions on these bonds.
The hidden trouble behind the formula
Darrell, who once served on Moody's Academic Advisory Research Committee and is now a professor of finance at Stanford University in the United States? Darrell Duffie pointed out that the CDO market depends almost entirely on this correlation model, and the word Gaussian copula has become a widely accepted vocabulary in the global financial community, and even brokers quote bonds of a certain level according to this formula. Like Jenny, the derivative master? As Janet Tavakoli described, correlation-based trading has spread throughout the financial market like a highly contagious ideological virus.
In fact, as early as 1998, before Xianglin Li invented this function, Paul Wilmott, a consultant and lecturer in quantitative finance, pointed out that the correlation between financial quantities is notoriously unstable, and no theory can be based on such unpredictable parameters. There is more than one such voice. During the boom years of American financial industry, you can cite many reasons to prove that this function formula is not perfect and can't cope with unpredictable situations: it assumes that correlation is a constant rather than a variable. Investment banks often call Professor Duffy of Stanford University and invite him to explain this formula. Every time, he warned investment banks that this formula does not apply to risk management and valuation.
Now it seems foolish to turn a deaf ear to these warnings. But at that time, it was really a very simple thing. Investment banks ignore these warnings, on the one hand, because the managers in control do not understand the arguments of various factions of financial engineering elites and cannot understand the true meaning of various mathematical models; On the other hand, they earn so much money that greed can't stop them.
In the financial market, risks can never be eliminated. We can only try to establish a market, so that people who don't want to take risks can pass on the risks to those who love to take risks. In the CDO market, people use this formula to convince themselves that they are risk-free, but in fact, they are risk-free only 99% of the time. Once the possibility of 1% appears, they will give up all their efforts and have no bones.
Xianglin Li's formula is used to price the CDO asset pool composed of hundreds of millions of housing loans. Because his formula is based on the historical price trend of related CDS, the calculation of correlation can only be limited to the year after the emergence of CDS. In the past less than ten years, house prices have been rising, so the correlation of mortgage default is relatively small. Once the housing boom is over, house prices will fall all over the country, and the correlation of mortgage default will suddenly soar.
In fact, banks that securitize mortgage assets also understand that this formula is very sensitive to the rise of house prices. Once the house price falls, all the risk-free bonds rated as 3A will collapse instantly, and there is no way out. However, they are unwilling to stop making CDOs. No one can resist the temptation of profiteering. All they have to do is enjoy huge profits and pray that house prices will continue to rise.
Who is to blame?
In the autumn of 2005, Li Xianglin told the Wall Street Journal that few people really understood the core of this formula. In the financial field, most people think that Xianglin Li should not be blamed. After all, he just invented this mathematical model. We should blame those financial institutions that abuse the model. Their greed leads to blind profit-seeking in the whole financial field, ignoring the limitations of this model and turning a deaf ear to the warnings from the outside world.
At present, Dr. Li has faded out of the current discussion on the causes of the financial crisis and left the United States for China last year.
In the real financial world, too many financial analysts only see the lifeless figures in front of them and forget the tangible and real reality they represent. In their opinion, it is possible to simulate and calculate only by data with only a few years' value, and then determine the probability that those events may occur only once every 10000 years. Since then, people have invested with such a probability, without thinking about whether these data have practical significance. As Dr. Li himself said to his model, the most dangerous thing is that people blindly believe that this model can bring them the desired results.