Stochastic Processes and Financial Mathematics
(part two)
Chapter 18 The financial crisis of 2007/8 \(\offsyl \)
In Section 17.3 we mentioned briefly that the cause of the Black Monday stock market crash, the single biggest fall in the S&P 500, has never been fully understood. The second, third, and fourth biggest one day falls in the S&P 500 all occurred towards the end of 2008, and form part of what is often referred to as the ‘sub-prime mortgage crisis’. They present a very different picture. The U.S. Financial Crisis Enquiry Commission reported in 2011 that
“the crisis was avoidable and was caused by: widespread failures in financial regulation, including the Federal Reserve’s failure to stem the tide of toxic mortgages; dramatic breakdowns in corporate governance including too many financial firms acting recklessly and taking on too much risk; an explosive mix of excessive borrowing and risk by households and Wall Street that put the financial system on a collision course with crisis; key policy makers ill prepared for the crisis, lacking a full understanding of the financial system they oversaw; and systemic breaches in accountability and ethics at all levels.”
Let us take some time to unpick the chain of events that occurred.
Availability of credit during 2000-07
During 2000-07 it was easy to obtain credit (i.e. borrow money) in Europe and the United States. Unrelated events in Russia and Asia during the late 1990s resulted in investors moving their money away, in many cases meaning they moved it into the U.S. and Europe. Part of this investment financed a boom in construction (i.e. house building) and also financed a boom in mortgages (i.e. loans with which people buy houses).
Loans have value: they are a contract which says that, at some point in the future, the money will be paid back, with interest. As a result loans are, essentially, a commodity. A ‘share in a loan’ is a share of the right to be re-paid when the time limit on the loan expires. These rights can be bought and sold.
As a consequence of these two factors, there was an increase in the number of financial derivatives for which the underlying ‘stock’ was mortgages. There was also a rise in house prices, because the easy availability of mortgages led to higher demand. We’ll come back to this.
Deregulation of lending
In all economies, business that wish to grow require the ability to borrow money, in order to fund their growth. Investors (private investors, banks, governments, pension funds, etc.) provide this money, typically as a loan or by purchasing newly created stock. These investors take a risk: the value of their investment depends on the future success of the businesses in which they invest. Investment banks are one of the vehicles through which this process takes place. They act as middlemen, connecting multiple investors and business together.
Since the 1970s, governments in both the U.S. and Europe tended towards policies of deregulation. They aimed to offer more freedom to financial institutions, and (consequently) increase investment and activity within the wider economy.
Deregulation meant that financial institutions had to share less data about their own activities with regulators and policy makers. As a result, regulators did not immediately recognize the growth and increasing importance of investment banks and hedge funds to the wider economy. These institutions became major providers of credit, but were subject to less regulation than commercial banks. In part this lack of regulation was due to their use of complex financial derivatives, which were not well understood by regulators or subject to much regulation.
The housing boom
From around 2000 onwards, relaxed regulations allowed large numbers of lenders in U.S. to issue ‘sub-prime’ mortgages. These are mortgages issued to individuals who are at higher than normal risk of defaulting on their mortgage payments. When a homeowner is unable to keep up their mortgage payments, the bank takes ownership of their house (and its occupants must leave).
Of course, financial institutions are in a much better position than ‘ordinary’ people to predict, in the long run, whether or not someone is capable of paying back their mortgage – but (at least, initially) selling the mortgages was profitable, including selling the mortgages that were at high risk of eventually defaulting. As a result many financial institutions were keen to sell sub-prime mortgages. Moreover, deregulation allowed financial institutions to attract customers into ‘variable rate’ mortgages, that required lower repayments in their initial years, followed soon after by higher repayments.
At this point, you may hear alarm bells ringing and guess what happens next. Of course, you have the benefit of hindsight; in 2006/07 the prevalent view was that financial innovations were supporting a stable, high-growth housing market, with the (politically popular, and widely enjoyed) consequence of increased home-ownership.
The end of the housing boom
A house building boom, accompanied by a fast rise in house prices, does not continue forever. In around 2006, a point was reached where the supply of new houses outstripped demand for them, and house prices began to fall. Those who had taken out mortgages became less wealthy, since they owned a house whilst it decreased in value, but still owed the same mortgage repayments. In addition, the variable rate mortgages began to require higher repayments, with the result that many individuals (particularly in the U.S.) defaulted and lost their homes. This, in turn, increased the supply of empty houses, and further lowered house prices.
The mortgages (and the houses that became owned by banks when defaults occurred) were now worth much less. Some investment banks and other financial institutions simply ran out of money and collapsed. At this point, another unfortunate (and not foreseen) part of financial system came to light. Major investment banks had sold and re-sold large volumes of financial derivatives to each other, but there was no global register of who owed what to whom. Consequently, no-one knew which institution was most at risk of collapsing next, and no institution knew exactly which of its own investments were at risk of not being repaid. Worse, perhaps the collapse of a single large institution would result in enough unpaid debts that a chain of other institutions would be bought down with it.
The result was a situation where banks were very reluctant to lend, to anyone, including each other. This resulted in less investment in businesses, which as we have already commented, hurts the wider economy. Moreover, since lending is the major source of income for banks, a lack of lending results in all banks becoming weaker – and the cycle continues. Worse still, the divide between investment banks and commercial banks had gradually eroded: some of the institutions at risk of collapse were (also) high street banks, who hold the savings of the general public and operate ATMs. This situation, which occurred during 2008, seems good reason for the term ‘the financial crisis’.
Outcomes
The possibility of the general public losing savings, along with wider effects on the economy, resulted in governments and central banks stepping in. Broadly speaking, they choose to provide loans and investment (using public money), to support financial institutions that were at risk of collapse and were also important to the public and the wider economy. Not all institutions were offered protection. We won’t discuss the details of how these arrangements worked. In many countries, the amount of cash that was used to prop up failing financial institutions led to a very substantial deterioration in the state of public finances.
The impacts on the U.S. economy were huge. In the U.S. the S&P 500 lost around 45% of its value during 2008. The total value of houses within the U.S. dropped from \(\$ 13\) trillion1 in 2006 to less than \(\$9\) trillion at the end of 2008. Total savings and investments owned by the general public, including retirement savings, dropped by around \(\$8.3\) trillion (approximately \(\$27,000\) per person, around \(25\%\) of an average persons savings).
Although the effects of the housing boom, and the housing boom itself, were greatest in the U.S., similar situations had occurred to varying extents in European countries. Coupled with the globally linked nature of the economy, and the fact that most major financial institutions now operate internationally, the financial crisis quickly spread to affect most of the developed world. A decrease in the amount of global trade resulted, along with a prolonged reduction in economic growth (which is still present today).
The process of changing the regulatory environment, in response to the financial crisis, is still ongoing. Broadly speaking, there is a move to involve macroprudential measures, which means considering the state of the financial system as a whole, instead of focusing in isolation only on the health of individual institutions. Mathematicians involved in this effort often argue that greater volumes of data on market activity should be collected and made public.
The role of financial derivatives
As we can see from this story, many different parties are involved and most of them can reasonably be attributed with a share of the blame. From our point of view, perhaps the most interesting aspect is that (with hindsight) it is clear that financial derivatives that were built on sub-prime mortgages were, prior to 2008, being priced incorrectly. These prices were typically computed by traders using variants and extensions of the Black-Scholes model.
The over-use of collateralized debt obligations (CDOs) is often cited as a practice that contributed greatly the financial crisis. CDOs are financial derivatives in which many different loans of varying quality are packaged together, and the holders of the CDO receive the repayments on the loans. Typically, not all loans are repaid and the CDO contract specifies that some of its holders are paid in preference to others.
Participation in a CDO is worth something and is therefore a tradeable asset. However, the underlying loans became packaged, bought, sold, divided, renamed, and repackaged, to such an extent that CDOs became highly complicated products in which the level of risk could not be known accurately. Moreover, packaging assets together in multi-party contracts increased the extent to which financial institutions became dependent on each other. Both these factors were not adequately captured by pricing models.
Another factor was credit default swaps (CDSs) in which an investor (typically an insurance company) would be paid an up-front sum, in cash, in return for promising to pay off the value of a loan in the case of a default. There was little regulation of this practice. Some institutions took on large volumes of mortgage CDSs and, in the short term, earned cash from doing so. Later, when mortgages defaulted, most were unable to cover their costs.
At the heart of the problem with CDSs was a widespread belief (before 2007) that the price of CDSs were correlated with the price of the underlying mortgages. This belief was realized through a pricing model known as the Gaussian copula formula, which became widely (and successfully) used during 2000-07. The intention of the model was to capture and predict correlations within the movements of prices of different assets. However, the shortcomings of the model were poorly understood and, in particular, it turned out to fail in the market conditions that emerged during 2007 when house prices dropped sharply.
Further reading
I recommend The End of Alchemy: Money, Banking, and the Future of the Global Economy, published in 2017 and written by Mervyn King, who was governor of the Bank of England from 2003 to 2013.