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This video discusses how financial crises can be caused by a number of small events that lead to a larger, final event. It explains how companies use Value at Risk (VaR) calculations to assess the risk of their activities, and how the law of large numbers can sometimes not apply.

**00:00:00**This video discusses the probability of financial crises, and how these can be caused by a number of small events that lead to a larger, final event. Financial theorists focus on understanding the underlying probabilities of these events in order to better predict future crises.**00:05:00**Systematic risk is a concept in finance that refers to the possibility that small events can have large impacts. In this lecture, Professor Shiller explicates two breakdowns in probability theory that contributed to the 2008 financial crisis - the failure of independence and the tendency for fat-tailed distributions. He stresses that these concepts are not new, and that they are revisited in the review session Elan Fuld will be conducting.**00:10:00**In this video, Professor Shiller discusses risk and financial crises. He explains that when investing, you need to consider the time interval involved - monthly, yearly, or even longer. The return (p t plus 1 minus p t ) is the increase in price, plus the dividend, which is a check you receive from the company you are investing in. The return can be positive or negative, but it can never be more than 100% of the initial investment. Gross return is always positive, between zero and infinity. Shiller then discusses some basic statistical concepts - expected value and the mean. He explains that the mean is the average of a discrete or a continuous random variable and that it is a measure of the central tendency. He also explains that the expected value of a random variable is the weighted sum of all possible values, weighted by their probabilities. Finally, he explains that the mean is used to estimate the expected value of a random variable.**00:15:00**This video explains how to calculate the average or mean of a sample, as well as the variance and standard deviation. These are all measures of variability, and can be used to evaluate risk.**00:20:00**The concepts of variance and covariance are explained in simple terms. Covariance is a measure of how two random variables move together, while correlation is a scaled covariance. When two variables have a positive correlation, they move together perfectly in unison, while when two variables have a negative correlation, they move in opposite directions. This explains how risk can be thought of in terms of unrelatedness.**00:25:00**This lecture discusses the concept of independence and how it can break down in financial crises. The author explains that there are three types of independence: positive, negative, and zero. If two variables are independent, their covariance is zero. However, this is not always the case, as we'll see in the stock market example. The author goes on to discuss how probability models can be used to understand how shocks to a company's stock can accumulate and lead to a financial crisis.**00:30:00**The video discusses the concept of risk, with a focus on how companies use Value at Risk (VaR) calculations to assess the risk of their activities. The law of large numbers states that, averaged over many independent events, the uncertainty in an individual event will diminish. This is important for finance and insurance, as it allows for the calculation of probability models. However, in the wake of the 2008 financial crisis, many companies were using very small numbers in their VaR calculations, which led to overestimates of the risk they were taking.**00:35:00**This video discusses how financial crises can happen, and how the law of large numbers can sometimes not apply. It explains how VaR and CoVaR can be used to analyze risk.**00:40:00**The video discusses the financial crisis of 2007-2008 and how it differed from the stock market crash of 2000. The video discusses how Apple's stock price went up and down, and how it was a complex story.**00:45:00**In this video, Provost Peter Salovey tells a story about a class of Yale students who invested $375,000 in a risky portfolio in order to give it to Yale on their 50th anniversary. The story highlights the roller coaster ride that such investments can often have, and discusses the risks and financial crises that can occur.**00:50:00**This YouTube video discusses how financial crises can be complex, with different factors affecting stock prices at different times. It shows how the return on Apple stock changes depending on the return on the S&P 500, and how the two returns are related.**00:55:00**In this video, Elan discusses the concept of beta, which is a measure of how a particular investment responds to changes in the stock market. The beta for Apple, for example, is 1.45, which is greater than 1 but less than 2. This suggests that Apple responds more than one for one to the stock market due to the company's high level of idiosyncratic risk. The Lehman Brothers collapse in 2008 was a significant event that affected the stock market, and for Apple, the stock market response was negative 16%. However, for the average investor, the stock market response was only negative 5%.

This video discusses the stock market crash of 1929, which had two consecutive days of declines. The probability of this event is estimated to be 10 to the minus 71 power, which is an awfully small number. The crash didn't rebound, and this suggests that something was wrong with independence.

**01:00:00**The curve plotted in this video is thought by statisticians to recur in nature many different ways. The normal distribution, shown as the black line, is the most common, with a probability law that results in an area under the curve of 1. The fat-tailed distribution, shown as the pink line, has a different probability law that results in an area between any two points, like between minus 5 and minus 10, that is, the area under the curve is much larger. Occasionally, we will have a 2% day, an event that is rare but can happen 2,000 times. After those events, the stock market seems to return to its more typical fluctuations of between +/- 1%.**01:05:00**This video discusses the stock market crash of 1929, which had two consecutive days of declines. The probability of this event is estimated to be 10 to the minus 71 power, which is an awfully small number. The crash didn't rebound, and this suggests that something was wrong with independence.

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