Dalton Malmin | January 3rd, 2025
Between 2007 and 2008, the global financial crisis categorically reshaped today’s economic landscape, impacting jobs, housing, and debt in ways that still affect us daily. It is likely the most relevant economic event in young people’s lives thus far. To make sense of what happened, economists have primarily used mathematical models, which have helped shed light on the cause of the financial crisis.
Forecasting volatility
One of the earliest agreed-upon signs of trouble in 2008 was extreme volatility in asset prices — sharp and unpredictable swings in market value — especially for mortgage-backed securities (investments backed by bundles of home loans). Volatility models, like GARCH (Generalized Autoregressive Conditional Heteroskedasticity), capture these sudden fluctuations by identifying “volatility clustering,” a phenomenon where high-volatility periods follow each other. Typically, clustering can indicate that markets are becoming unstable.
The GARCH model allows economists to forecast volatility patterns based on historical data, providing a lens through which analysts can spot potential risks. During the lead-up to the 2008 crisis, these early volatility patterns in mortgage-backed securities went largely unnoticed, as advanced mathematical models like GARCH had yet to be widely applied in real-time risk assessment. Today, GARCH continues to be an essential tool for identifying periods of market stress and helps forecast economic turbulence.
Amplifying market instability through feedback loops
A critical driver of the 2008 financial crisis was the role of leverage and the feedback loops it created within financial markets. Leverage — borrowing to amplify potential returns — can intensify market trends, as rising asset prices allow for increased borrowing and investment. This creates a self-reinforcing cycle: as prices rise, leverage grows, driving prices even higher. However, this cycle also works in reverse, amplifying losses when prices fall.
Leverage-based feedback loops play a central role in creating market instability. Their research shows how leveraged investors are forced to liquidate positions when asset prices drop, further driving prices down and triggering a cascade of selling. This mechanism explains the clustering of extreme events (fat tails) and volatility observed in financial markets during crises.
During the 2008 crisis, these dynamics were particularly evident in the market for mortgage-backed securities. As housing prices rose, financial institutions increased their exposure to these assets, fueled by borrowed funds. When housing prices began to fall, leveraged positions became unsustainable, forcing widespread asset sales. This feedback loop intensified the market collapse, spreading losses across the financial system.
These insights highlight how leverage-driven feedback loops exacerbate financial fragility. Models that incorporate these dynamics remain critical tools for identifying vulnerabilities in financial systems and understanding how speculative behavior can amplify risks.
Post-crisis hedge fund performance: Vanderbilt’s contribution
A significant research contribution to the discussion of economic modeling comes from Nicolas Bollen, a professor at the Owen Graduate School of Management at Vanderbilt University. Professor Bollen’s work on hedge funds (private funds that pool capital to pursue diverse investment strategies) performance aids in demonstrating how the 2008 crisis ultimately redefined the financial economy. Professor Bollen’s research examined hedge fund returns from 1997 to 2016, identifying a notable decline in risk-adjusted returns following the crisis.
Professor Bollen’s research suggests that post-crisis regulations and central bank interventions fundamentally altered hedge fund performance. The increased oversight and reduced volatility in the market limited hedge funds’ capacity to deliver high returns, especially compared to pre-crisis levels. This work underscores how the regulatory response to the crisis has had lasting effects on the behavior and profitability of hedge funds.
Building economic stability with mathematics
The 2007 to 2008 crisis defined the importance of using mathematical models to understand and anticipate economic risks. Models like GARCH and feedback loop analysis allow analysts to detect early warning signs and assess potential bubbles, offering a clearer picture of market vulnerabilities. Ongoing research at Vanderbilt, such as Professor Bollen’s work on hedge funds, highlights the role of academia in developing a more robust economic system.
Mathematics plays a critical role in modern economics, providing economists with tools to analyze and interpret market changes and support policies that prevent future crises. As research advances, these models will not only help us characterize past events but also help us steer future policy decisions.
References
Bollen, N. P. B., Joenväärä, J., & Kauppila, M. (2021). Hedge Fund Performance: End of an Era? Financial Analysts Journal, 77(3), 109–132. https://doi.org/10.1080/0015198X.2021.1921564
Engle, R. (2001). GARCH 101: The use of Arch/GARCH models in applied econometrics. Journal of Economic Perspectives, 15(4), 157–168. https://doi.org/10.1257/jep.15.4.157
Thurner, S., Farmer, J. D., & Geanakoplos, J. (2012). Leverage causes fat tails and clustered volatility. Quantitative Finance, 12(5), 695–707. https://doi.org/10.1080/14697688.2012.674301
