Is mathematics a force for accountability? Or is it a shield against accountability?
Our lives are increasingly governed by algorithms that influence what to buy, where to go, who to date, and sometimes even how we vote. Corporations and governments collect data about us and use it to analyze our personalities, our social ties, and our beliefs. Are the decisions made by these analyses fair? How much control do we have over the assumptions that algorithms make about us? Who creates and controls these algorithms, and how accountable are they to those of us on the receiving end?
I recently gave a talk to the Undergraduate Math Union at the University of Toronto to explore one instance of a mathematical algorithm used in Wall Street that enabled the 2008 Financial Crisis. It was manipulated by the "auditors of the financial system" to make over-optimistic predictions about the economy, helping large investment banks sell toxic investment products all over the world. The implosion of those toxic products sparked the Financial Crisis.
Blurb for the talk
The pandemic has shaken the core of the economy, prompting fears of an economic catastrophe like the 2008 Financial Crisis. How resilient is our financial system to waves of financial losses on a national scale, which could arise from lockdown restrictions on businesses? An important cause of the 2008 crisis was the spread of "package deals" that bundled together smaller investments. The investments in each package deal were assumed to be more or less independent from each other so that the risks of different investments could cancel each other out. Unfortunately, the investments were more correlated (interdependent) than expected, and enough of them failed at the same time to cripple the banks all over the world that had bought the package deals.
The correlation was underestimated by Credit Rating Agencies (the "auditors" of the financial system), misleading banks into buying those package deals. We will explore some weaknesses in the mathematical models of these agencies that led them to underestimate the correlation. We will also touch on conflicts of interest that drove the agencies to manipulate their analyses, in order to underestimate correlation even further. How is math used or abused by these "auditors" who wield so much power over the financial system - a power that affects even our savings and retirement funds?
No background knowledge is necessary, beyond a familiarity with plotting functions as graphs and calculating the area under them (which you might get from a Calculus course).
Where to learn more?
Thank you to ComSciConCAN-GTA for giving me the opportunity to practice explaining this complex topic in an accessible way through their Write-a-Thon!