# Quantifying Uncertainty and Risk

Until now, the models we've used in this course have focused on the case where everyone can perfectly forecast future economic conditions. Clearly, to understand financial markets, we have to incorporate uncertainty into these models. The first half of this lecture continues reviewing the key statistical concepts that we'll need to be able to think seriously about uncertainty, including expectation, variance, and covariance. We apply these concepts to show how diversification can reduce risk exposure. Next we show how expectations can be iterated through time to rapidly compute conditional expectations: if you think the Yankees have a 60% chance of winning any game against the Dodgers, what are the odds the Yankees will win a seven game series once they are up 2 games to 1? Finally we allow the interest rate, the most important variable in the economy according to Irving Fisher, to be uncertain. We ask whether interest rate uncertainty tends to make a dollar in the distant future more valuable or less valuable.

*Source: Open Yale Courses*

- Why Finance?
- Utilities, Endowments, and Equilibrium
- Computing Equilibrium
- Efficiency, Assets, and Time
- Present Value Prices and the Real Rate of Interest
- Irving Fisher's Impatience Theory of Interest
- Shakespeare's Merchant of Venice and Collateral, Present Value and the Vocabulary of Finance
- How a Long-Lived Institution Figures an Annual Budget Yield
- Yield Curve Arbitrage
- Dynamic Present Value
- Financial Implications of US Social Security System
- Overlapping Generations Models of the Economy
- Will the Stock Market Decline when the Baby Boomers Retire?
- Quantifying Uncertainty and Risk
- Uncertainty and the Rational Expectations Hypothesis
- Backward Induction and Optimal Stopping Times
- Callable Bonds and the Mortgage Prepayment Option
- Modeling Mortgage Prepayments and Valuing Mortgages
- Dynamic Hedging
- Dynamic Hedging and Average Life
- Risk Aversion and CAPM
- The Mutual Fund Theorem and Covariance Pricing Theorems
- Risk, Return, and Social Security
- Leverage Cycle and the Subprime Mortgage Crisis
- Shadow Banking: Parallel and Growing?

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