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In 2008 when the market crashed I was 16-years old and visiting London for the very first time. At that age I was already obsessed with the markets. Feeling confident that I could understand the crash after having read the classic investment books such as Security Analysis, The Intelligent Investor, and Common Stocks and Uncommon Profits, I bought a copy of the Financial Times and started reading. I didn't understand any of it. Some of the questions on my mind were: What are quants? What is securitization? What are credit derivatives? What does insurance have to do with the stock market? And how does a derivatives crash cause the market to crash?

This experience opened my eyes to the reality of the market - it is a complex adaptive system run on models and computer algorithms that almost nobody understands [1]. In pursuit of understanding I read books, studied Computer Science, and secured a job as a quant. This article explains how I now see the financial crisis and whilst it is almost-surely not 100% correct, it is based on the many books and articles I have read including The Big Short, The Greatest Trade Ever Made, The Crisis of Crowding, Models Behaving Badly, The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It, and A Colossal Failure of Common Sense.

[1] A Gordon Gekko quote from Wall Street II, Money Never Sleeps sums this up quite nicely:

"They've got all these fancy names for trillions of dollars of credit: CMO's, CDO's, SIV's, MBS's. You know, I honestly think there's maybe only 75 people in the world who know what they are."

But to be fair, the financial crisis was not just caused by credit derivatives. The financial crisis was caused by a combination of many intertwined factors and events including, but not limited to, moral hazard, economic policy, deregulation, an over-reliance on quantitative models, insurance, excessive leverage and the availability of cheap credit, and dangerous assumptions regarding market dynamics. These factors, which I will explain in the following sections, created a self-reinforcing pattern that resulted in a massive credit derivatives bubble. When the bubble burst, indirect linkages between markets caused by excessive leverage took the stock market down with it.

This article is broken up into the following sections each of which details a cause of the crisis. Please feel free to jump around - moral hazard, model hazard, insurance, leverage, a timeline of events, and the conclusion. Additionally, all of the data used to construct the graphs in this post can be found on Quandl.com. In particular, the US Interest Rates and the US Housing collections were used. For information about the issuance of credit derivatives including credit default swaps and collateralized debt obligations I used Sifma data-sets.

Moral Hazard

Moral hazard may exist in any situation wherein one party gets involved in a risky event knowing that it is protected against the risk and that some other party would incur the cost.

In my opinion, the biggest contributor to the financial crisis was the moral hazard created in the mortgage lending industry as a result of the transfer of risk from lenders to investors through the financial process of securitization.

Mortgage lending companies lend home-buyers lump-sums of money and in exchange the home-buyer agrees to pay back the mortgage lender over a fixed period of time, typically 15 to 30 years, with interest. If the interest is fixed up-front this is called a fixed-rate mortgage and if the interest is allowed to fluctuate over time this is called a variable-rate mortgage. The mortgage lender assumes the risk that the home-buyer will not earn enough money to pay them back and that they might default on the loan. The higher the risk of default (i.e. the higher the default probability), the higher the interest rate on the mortgage to compensate the lender.

From the mortgage lenders perspective the risk of credit default sits on their balance sheet so their incentive is to try and issue mortgages to home-buyers who are likely to be to pay them back in the future. From the home-buyers perspective, they don't mind paying an interest rate because in the long run the appreciation in the value of their home will exceed the cost of buying it. If it doesn't then the home-buyer is incentivized to default on their loan. This is called strategic default. Oliver Wyman did a study in 2009 which showed that 20% of all the defaults in 2008 were strategic in nature many of which were attributed to businesses.

A mortgage behaves similarly to a bond when the home-buyer pays off his or her mortgage every month and does not default. The main difference between a bond and a mortgage is that the interest earned on a mortgage by the mortgage lender is usually higher than on bonds. Because home prices were rising driven by higher demand than supply of houses, and because mortgage lending companies only extended credit to individuals with high credit ratings, home-buyers didn't often default and mortgage lenders made good money.

The profits earned by mortgage lenders attracted the eye of savvy investors who wanted in and the process of securitization was invented. Securitization allows financiers to create securities whose pay-off was linked to the mortgage payments made by home-buyers month after month. At first the system worked quite well. Put simply the mortgage-lender issued mortgages, sold those at a premium to the bank, who would would package them into securities and sell them at a premium to investors, who would be happy to receive a coupon every month linked to the mortgage payments. This approach also freed up capital so home lenders could lend more.

Many names were given to these securities including mortgage backed securities (MBS's), collateralized mortgage obligations (CMO's), and collateralized debt obligations (CDO's). Some of these securities even included different sources of debt including commercial mortgages, auto-loans, credit-card debt, and more. There are many technicalities associated with the securitization process which are, unfortunately, beyond the scope of this article. For more information I highly recommend reading this Wikipedia entry.

At first securitization was great, it resulted in higher turnaround times for mortgage lending companies (meaning that more people could buy homes), banks were making money from charging securitization fees, and investors got access to credit derivatives whose pay-off was often higher than bonds of equivalent risk. The problem with securitization is that it worked so well the demand for credit derivatives sky-rocketed and moral hazard entered the process as mortgage lenders dropped standards and decreased their risk aversion.

Figure One

To meet the demand for mortgages existing mortgage lenders lowered their standards and issued loans to higher-risk individuals, and new mortgage lenders entered the game. In particular, mortgage lenders were selling variable-rate sub-prime mortgages to individuals with low credit scores, few assets, and low incomes. This worked while interest rates were artificially low and housing prices kept going up, but when these two things changed the house of cards came down. People who could no longer afford their monthly mortgage payments defaulted, and others strategically defaulted because the value of there homes had dropped below the cost of the mortgage.

Figure Two

The above graph shows the average sale price of houses sold quarterly in the United States. As can be seen, housing prices peaked towards the end of 2006 and then started falling causing the amount of defaults began to spike.

Figure Three

The above graph shows that the demand for new homes (and most probably existing homes as well) dropped started dropping off by 2006 which is what probably the reason behind decline in house prices.

As mentioned a contributor to the financial crisis were the artificially low interest rates set by the federal reserve. After the dot com bubble the federal reserve dropped rates to stimulate the economy and they kept them low for a very long time. During this period many home-buyers secured adjustable-rate mortgage. Many people assumed that rates would remain low but they also secured mortgages because they were easier than ever to get. Lending to somebody when you believe that they have no means to pay back the loan is called predatory lending.

Figure Four

Interest rates represent the 'cost of debt'; when interest rates are low debt is cheap and when interest rates are high debt is expensive. The interest rate on adjustable rate mortgages often moved with the federal reserve rate. So between 2004 and 2006 when the federal reserve increased rates this resulted in higher adjustable mortgage rates. Many home-owners found that after the rate hike they could no longer afford their monthly mortgage payments and started to default on their mortgages. This was unprecedented.

Figure Five

Delinquency, as shown in the graph above, are mortgages for which the home-buyer has failed to make payments as required in the mortgage contract. If the borrower can't bring the payments on a delinquent mortgage current within a certain time period, the lender may begin foreclosure proceedings. Foreclosure rates are shown below,

Figure Six

The above foreclosure rates information was obtained from the Zillow real-estate research database on Quandl.

So why did home-buyers start defaulting?

This was a combination of two factors; firstly, the average price of home was dropping because demand was shrinking meaning that it made sense to strategically default on mortgages whose cost exceeded the future value of the home; and secondly, an increase in adjustable mortgage rates increased financial distress, especially for riskier loans at higher interest rates, meaning that people could not afford the loans and thus defaulted.

However, credit defaults by themselves were not enough to cause the financial crisis. The remaining sections will discuss some of the other contributors to the crisis including deregulation, model hazard, insurance, and leverage.

Model Hazard

Essentially, all models are wrong, but some are useful - George E.P. Box

The use of quantitative models in finance has become almost ubiquitous, yet it seems to me that very few people who use those models know the assumptions upon which the models were built. Model hazard, a term I made up for this article, is when people apply models to problems without understanding the models's assumptions and limitations. In this section I will first discuss the misuse of the Gaussian copula model for estimating the correlation of credit defaults and then I will digress from the topic and discuss how machine learning models are being mis-used today. For a related article on some sources of Model Risk click here.

The Gaussian Copula

Before we get into the details of the Gaussian copula, it is worth mentioning two fundamental tenets of modern portfolio theory; firstly, the unsystematic risk of a portfolio is less than or equal to the weighted sum of the unsystematic risk of the constituent assets in the portfolio; and secondly, the degree to which the portfolio's unsystematic risk is reduced depends on the correlation between the constituent assets of the portfolio. In other words, by combining assets with low correlations we can produce a portfolio that is less risky than the assets by themselves. This is more commonly known as diversification.

Given a universe of credit derivatives, each of which is exposed to credit default risk, we can combine them to create portfolios with lower credit default risk than any of the individual credit derivatives by themselves. In other words, we can reduce the risk of credit default through diversification. At the turn of the new millennium a big unanswered question was, how much is the risk reduced. To answer this question a quantitative method was required to measure the correlations of defaults between independent credit derivatives.

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In his 2000 paper, On Default Correlation: A Copula Function Approach, David X. Li pioneered the use of the Gaussian copula for modelling the correlation of defaults between the credit derivatives in a credit derivative portfolio. His approach was inspired by how life insurance companies measure the risk of mortality or survivorship. In summary, Li proposed that if given a credit curve which measures the probability, at any point in time from now until maturity, that any specified credit derivative will experience a credit default, then the probability that a portfolio of credit derivatives will experience a credit default is defined by the joint distribution of those curves. Copula's are used to calculate joint distributions in actuarial science. The Gaussian copula is the most popular.

where denotes the inverse of the cumulative distribution function of the normal distribution (quantile) of the cumulative distribution that credit derivative will default in the next one year, , and is the joint cumulative probability distribution that credit derivatives and will default in the next one year, and is the Gaussian copula. The Gaussian copula basically asserts that the behaviour of default for and (correlation of defaults) are normally distributed. This is an assumption which was probably made using historical data which actually fitted, the problem with markets is that they change.

There were two flaws with the use of the Gaussian copula which caused the model to underestimate the riskiness of credit derivatives portfolios. This underestimation resulting in mis-priced derivatives which ultimately contributed significantly to the financial crisis. The first flaw was in the calibration of the model and the second flaw was in assuming independence between credit default events. Ironically, both of these flaws (as well as some others) were acknowledged by David X. Li in his original paper.

Calibration and Stationarity

In his paper Li proposed three possible methods of calibration,

Obtaining historical default information from rating agencies, Taking the Merton option theoretical approach ( simulation methods ), or Taking the implied approach using market prices of default-able bonds or asset swap spreads

In his paper, Li proposed that the third method be followed. One of the reasons he gave was, "The information available from a rating agency is usually the one year default probability for each rating group and the rating migration matrix. Neither the transition matrices, nor the default probabilities are necessarily stable [stationary] over long periods of time. In addition, many credit derivative products have maturities well beyond one year, which requires the use of long term marginal default probability". And this is exactly what we have seen in the information presented previously, the probabilities of default as observed by the historical delinquency and foreclosure rates were not stationary.

Because the model was either calibrated to historical data, or ratings (which are also based on historical data), or uninformed market prices, the model underestimated the risk of credit derivatives portfolios. This was because the historical probability distribution of credit defaults was not representative of the future probability distribution of credit defaults. In other words, the distribution was non-stationary. It was (and still is) non-stationary because changes externalities, such as excessively low interest rates and moral hazard, fundamentally changed the behaviour of home-buyers thereby changing the probability of future credit defaults occurring for the worse.

Independence Assumption

Another problem with the model is that it assumed independence between the probability of credit default events in the underlying credit derivatives. Li knew that this is a dangerous assumption and write in his own paper that, "the independence assumption of the credit risks is obviously not realistic; in reality, the default rate for a group of credits tends to be higher in a recession and lower when the economy is booming. This implies that each credit is subject to the same set of macroeconomic environment, and that there exists some form of positive dependence among the credits." So when the housing market dipped and the number of defaults surged.

Despite the problems mentioned above it is hard to lay the blame with David X. Li and his Gaussian copula because the Gaussian copula is just a tool and like any other tool it has its limitations. In the quant world, those limitations are now referred to as model risk. Model risk is the risk of loss resulting from using models to make decisions. After the 2008 financial crisis a much larger emphasis has been placed on quantifying the risk of using models in an uncertain world. No good comes from placing blind faith in models because the market doesn't follow rules.

Machine Learning

Unfortunately the same blind faith placed in quantitative models is now being placed in machine learning models. New funds are relying on neural networks to make investment decisions without taking the time to understand the assumptions upon which most neural network models are built. As an example, as with the Gaussian copula, neural networks assume that the distribution of input patterns is stationary and outlier free. If the financial crisis has taught us anything it should be that in the markets nothing stays the same and nothing is normal. I advocate the proper use of machine learning and quantitative models in finance.

Insurance

In addition to credit derivatives whose value was linked to the underlying mortgages banks and insurance companies created derivatives whose value was linked to the rate of credit default on those underlying mortgages. These derivatives are called credit default swaps (CDS's) and basically insure (pay-out) if the number of credit defaults on the underlying mortgages cause the CDO's to lose value. If you owned them in 2007 and 2008 you are probably retired right now; some funds returned more than 1000% in 2008.

Before I get into the problems with CDS's it is worth elaborating on the business of insurance. Imagine you own a short-term insurance company which insures cars against damages. Your best estimate (prudent) estimate of the number of cars which could be damaged in one year is 50% and the average cost to repair a car is $1000. You could then charge 1000 people $500 each for car insurance. Your income would be $500,000 ($500 * 1000) and your claims during the year would also be $500,000 ($1000 * 1000 * 50%). To make operating profits your insurance company would add a profit margin to the cost of insurance e.g. $50. Now your income is $550,000; and your claims are $500,000 so your profit is $50,000.

But what happens when your estimate of 50% is wrong? Assume that a hail-storm hits the city where your customers are and your claims rate reaches 80%. You now need to pay out $800,000 so you make a loss of $250,000. In insurance you need to be very confident about the number of people who will "claim" during the year in order to make money. This seemingly silly example illustrates what happened in 2008. Insurance companies and banks sold CDS's which assumed that the number of credit defaults would be significantly less than they actually were, so when they were not they had to pay out vast sums of money. This problem was only compounded by the massive number of CDS's which were issued and sold by the banks and large insurance companies,

Figure Seven

If you are wondering why banks would be selling CDS's when they are not insurance companies, you would be right. Most banks simply re-insured their CDS's with an insurance giant called AIG. In order for AIG to have expected to make a profit they must have assumed than an even lower rate of credit defaults would happen. Having made this poor assumption AIG was happy to re-insure almost all of the banking industries credit default exposure. Eventually when AIG was bailed out, all of the $60 billion bail-out package for AIG actually went to paying out the banks who had taken out re-insurance from AIG.

Leverage

Another key contributor to the financial crisis was the excessive leverage in banks and hedge funds caused by the deregulation of the financial services industry in the United States (and the rest of the world) from the early 1970's up to the financial crisis of 2008. For a more detailed overview of the deregulation which occurred during this time-period I highly recommend reading the paper, A Short History of Financial Deregulation in the United States.

There are two types of banks, investment banks and commercial banks and after the financial crisis of 1929 the Glass-Steagall Act prevented financial institutions from operating as both investment and commercial banks or insurance providers. Unfortunately during the late 1990's this act was repealed which resulted in previously risk-averse commercial banks partaking in riskier core-business activities including investment banking, proprietary trading, and securitization. Additionally, in 2000 the commodity futures modernization act essentially prevented the commodity futures trading commission from regulating over-the-counter derivative contracts, including credit derivatives such as collateralized debt obligations (CDO's) and credit default swaps (CDS's). Last, but definitely not least, in 2004 the SEC proposed a voluntary-regulation system for banking which allowed banks to hold less capital in reserves and increase their financial leverage.

These acts of deregulation resulted in a less robust and more exposed banking system. One popular metric for measuring the financial condition of the United States is the Chicago fed national financial conditions index (NFCI). Positive values of the NFCI indicate financial conditions that are tighter than on average, while negative values indicate financial conditions that are looser than on average. The graphs below show that the period leading up to the financial crisis experienced loose financial conditions (probably as a result of low interest rates) and easy access to leverage. Another metric is margin debt, although this articles mentioned some of it's nuances.

Figure(s) Eight

Leverage refers to the borrowing of additional funds for investment purposes. Banks and hedge funds use leverage to increase their returns. Trading using leverage is also called trading 'on margin' because the institution borrowing the funds does so through a margin account. Most margin accounts come with limits which stipulate that if the value of your investments fall below a certain ratio you are required to top-up the margin account until the ratio is met. This is called a margin call. If the required top-up is large then funds need to raise capital.

How do hedge funds and proprietary trading desks, which keep thin capital buffers, raise capital? For proprietary trading desks, sometimes the funds can come from other parts of the bank, but for hedge funds the capital is probably going to be met by liquidating positions in liquid securities such as stocks and bonds. In other words when the credit derivatives bubble started to pop funds were hit with margin calls and in order to 'bail out' their leveraged loss-making positions in credit derivatives those funds sold off stocks and bonds (de-leveraging).

Because the credit derivatives market was crowded and full of copy cats, there was a very large sales pressure on the stock and bond markets which caused the markets to start dropping at which point fear took over the market. From August 2008 till the first of January 2009 the S&P 500 index fell by more than 30% experiencing multiple one-day losses greater than 8%.

Figure Nine

Unfortunately the proceeds generated from the sale of liquid assets could not cover the banks nor AIG's liabilities and because all of the banks were suffering the liquidity in the inter-bank network dried up. Lehman Brothers was the worst affected and after unsuccessfully trying to raise funds from the Federal Reserve, The Bank of South Korea, and even Warren Buffet, Lehman Brothers was forced to file for bankruptcy which only worsened the situation at the time. Eventually the Federal Reserve realized the severity of the situation and arranged the controversial bail-out programme we all probably remember. In my opinion, the bail out was necessary.

Whilst almost everybody believes that Lehman Brothers "got what it deserved", I believe that letting Lehman Brothers file for bankruptcy only worsened the situation for every other bank and exacerbated the liquidity crisis in the inter-bank network. The reason why Lehman Brothers was allowed to fail is because the economic models we use to make decisions do not capture the interconnectedness and complexity of markets. I am not alone in this thinking; I belong to a small group of people who subscribe to the belief that the economy can and, more importantly, should be understood and modeled as a complex adaptive system. Only through this framework should policies be set and decisions be made.

When the crisis came, the serious limitations of existing economic and financial models became apparent - J.C. Trichet (Governor of the ECB 2010) There is also a strong belief, which I sahre, that bad or over-simplistic and over-confident economic models helped create the crisis - Lord Turner (Chairman of the UK FSA, 2012)

For a really interesting talk about this philosophy I recommend the TED talk by James B. Glattfelder

Timeline of Events

Given everything I have discussed in this article we can now construct a time-line of events leading up to the financial crisis. As I mentioned in the beginning of this article, this breakdown is almost surely not 100% correct, so if you know of any causes or events I am missing, please let me know in the comment section below.

The financial crisis was felt all across the world and affected many people, including myself, in a deeply personal way. I originally sent this email to my friends and family to express my personal belief that as quantitative analysts and financial professionals it is our duty to understand and remember how easily things can go wrong and that the road to hell is paved with good intentions. I actually kept the front page of that Financial Times, I keep it hanging above my desk as a reminder.

Conclusion

The more things change the more they stay the same. While many things have changed since the financial crisis - the Volcker rule prohibits banks from having proprietary trading desks, Basel III and Solvency II require banks, insurance companies, and large hedge funds to reserve more capital and undergo stress tests, and the Dodd Frank act was instituted to improve accountability and transparency in the financial system and end bail-outs; many things remain the same - governments still make important economic decisions using antiquated economic models, we are becoming ever more over-reliant on quantitative models without understanding their assumptions, and while leverage still couples seemingly distinct markets by the firms which trade in them we cling to the notion of correlation in risk management.

Another financial crisis will eventually happen and it will take on a different form. That said, I believe that some of the causes discussed in this article will come to play their part. Additionally, new operational risks are forming - the rise of similar algorithmic trading systems, loosely coupled electronic exchanges, and poorly engineered software have shown their dark side historically in 1987 and more recently during the Flash Crash of 2010. In my humble opinion, operational risks will continue to play a more dominant and more dangerous role in the financial system in the future. For more information on the 2008 financial crisis check out Salman Khan's videos on the crisis.

Disclaimer

This is a personal blog. The opinions expressed here are my own and do not represent those of my employer. Furthermore, all information on this blog is for educational purposes and should not be interpreted as financial advice.