By Robert J. Shiller from Yale

VaR - Value at Risk, invented after 1987. 1% one-year VaR of $10 million means a 1% chance that a portfolio will lose $10 million in a year.

Stress Test - Test by the government to see how well firms are able to withstand an economic crisis.

The difference in growth between Apple and S&P 500 is significant since 2000. However, if you look at the monthly returns, apple is very noisy with a lot of variabilities. It also correlates with S&P 500.

Beta is the regression slope coefficient when the return on the ith asset is regressed on the return on the market. If it's 1 the returns are equal; if greater then the ith asset has a better return. Gold is negative beta to market.

Market Risk - Risk with the market.

Idiosyncratic Risk - Risk with the specific asset. (Like death of Steve of jobs for Apple)

When investing, keep in mind covariance between stocks since they can be both independent or dependent.

$$ B_i = \frac{COV(R_1, R_{market})}{VAR(R_{market})} $$

Insurance

Risk pooling - Source of value in insurance

The standard deviation of the fraction of policies that result in a claim is

$$ \sqrt{p(1-p)/n} $$

Law of large numbers: as n gets large, std approaches zero.

However, this is not always easy since

1. Moral Hazard - Take more risk because of being insured
2. Selection Bias - Insurance companies do not always see the risk

Capital Asset Pricing Model (CAPM) - a model of an optimized portfolio. Asserts that every investor will hold that portfolio.

Credit Default Swap - a financial derivative or contract that allows an investor to "swap" or offset his or her credit risk with that of another investor.

Short Sales - Borrowing stocks and buying them later. Betting stock prices will go down.