Risk and Financial Crises: Lecture 2: Financial Markets (2011), Robert Shiller

Shiller discusses the basics of finance and how it can help us understand risks affecting financial markets and big crises such as the 2007-8 meltdown. His big take home message is that there are two major breakdowns in the assumptions of finance that lead to crises: failures of independence and a tendency for too many outliers (values that fall very far from the mean) or fat-tailed distributions.

To provide context Shiller starts with an historical narrative of the 2007-8 crisis: it began with bubbles (enthusiam driving up prices to unsustainable highs that inevitably crash) in the stock, housing, and the commodities markets which led to major institutional failures (bankruptcies). Disaster was averted by governments around the world bailing out their institutions and we are now enjoying a nice rebound.

There is another important point of view that helps us better understand risks and crises in financial markets: probability theory. The probability model of a crisis sees big events as the aggregate result of lots of little events. He suggests that the stories may not be so helpful in understanding the underlying risks that affect financial markets.

Probability in its present meaning wasn't coined until the 1600s. It was a major advance in human understanding and plays a central role in financial markets. The idea is that the world is extraordinarily complex with many tiny events that lead to outcomes. Understanding how the laws of probability accumulate is the key idea in weather forcasting and in finance.

Shiller provides an elementary introduction to the basic concepts of finance and their definitions in terms of probability. He defines return (the most basic concept in finance: a measure of gain or loss), gross return, expected value, average, mean, the general concept of measures of central tendancy, variance and standard deviation (measures of variability), covariance (a measure of how two random variables move together), correlation (covariance scaled to between -1 and 1), and systematic and idiosyncratic risk (risks coming from correlation with movements in the broader market and risks coming from particulars of a given institution, respectively). He gives a wonderful explanation for why the geometric mean rather than the arithmetic mean (the one we all think of when we say the "average") is better in finance.

The basic idea of the "Law of Large Numbers" is implicit in Aristotle's observation that uncertainty tends to vanish with a large number of observations. The idea underlies insurance which was practiced in ancient times before the mathematization of probability starting in the 1500s. Critically important is the realization that the law of large numbers assumes the independence of the variables! The law states the outcome of a large number of results will approximate the expected value (a sort of generalized average).

The law of large numbers with its basic assumption of independence is at the core of risk management in finance. When independence breaks down, we get financial crises.

Another important assumption in finance is normality meaning the random variables fit a normal distribution which is sometimes called the Bell curve. Extreme outliers should not appear in a normal distribution. Shiller presents compelling graphs showing that stock market returns include extreme outliers. Therefore stocks are probably not normally distributed. Benoit Mandelbrot discussed the Cauchy distribution and other non-normal distributions as probably being a better fit for stock prices than the normal distribution. These are sometimes referred to as long tail distributions.

Independence across time or stocks is supposed to make you safe, but independence is just an assumption! The assumption of normality can often be unjustified even though it is a basic premise of much financial theory.

This lecture leads me to ask two big questions: If the assumptions of finance are so shaky, why do we trust our money to banks and stock markets and insurance firms? If the basis of finance is probability theory, why don't we study it with more depth and vigor?

2. Risk and Financial Crises
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