Financial Theory

This course attempts to explain the role and the importance of the financial system in the global economy.

Rather than separating off the financial world from the rest of the economy, financial equilibrium is studied as an extension of economic equilibrium. The course also gives a picture of the kind of thinking and analysis done by hedge funds.

Course Content

Lecture 1 – Why Finance?
Lecture 2 – Utilities, Endowments, and Equilibrium
Lecture 3 – Computing Equilibrium
Lecture 4 – Efficiency, Assets, and Time
Lecture 5 – Present Value Prices and the Real Rate of Interest
Lecture 6 – Irving Fisher’s Impatience Theory of Interest
Lecture 7 – Shakespeare’s Merchant of Venice and Collateral, Present Value and the Vocabulary of Finance
Lecture 8 – How a Long-Lived Institution Figures an Annual Budget; Yield
Lecture 9 – Yield Curve Arbitrage
Lecture 10 – Dynamic Present Value
Lecture 11 – Social Security
Lecture 12 – Overlapping Generations Models of the Economy
Lecture 13 – Demography and Asset Pricing: Will the Stock Market Decline when the Baby Boomers Retire?
Lecture 14 – Quantifying Uncertainty and Risk
Lecture 15 – Uncertainty and the Rational Expectations Hypothesis: Applications to Predicting Stock Prices, Default Probabilities, and Hyperbolic Discounting
Lecture 16 – Backward Induction and Optimal Stopping Times
Lecture 17 – Callable Bonds and the Mortgage Prepayment Option
Lecture 18 – Modeling Mortgage Prepayments and Valuing Mortgages
Lecture 19 – History of the Mortgage Market: A Personal Narrative
Lecture 20 – Dynamic Hedging
Lecture 21 – Dynamic Hedging and Average Life
Lecture 22 – Risk Aversion and the Capital Asset Pricing Theorem
Lecture 23 – The Mutual Fund Theorem and Covariance Pricing Theorems
Lecture 24 – Risk, Return, and Social Security
Lecture 25 – The Leverage Cycle and the Subprime Mortgage Crisis
Lecture 26 – The Leverage Cycle and Crashes

Requirements

Math in the course
Finance is a quantitative subject that can only be understood by solving concrete problems. But it uses mostly elementary mathematics. You need to be good at arithmetic (the distributive law is the basis for double entry bookkeeping), and be able to solve two or three simultaneous linear equations (x + y =10; x – y = 4. Solve for x and y). You must also be able to differentiate three elementary functions: dxn/dx =nxn-1; d ln x/dx = 1/x; deax/dx= aeax. The functions “log” and its inverse “exponential base e” are so important to finance because of continuous compounding of interest. Though they may be the most important functions in all of mathematics, they were discovered by bankers. You will also be taught how to use Excel.

Course reading
The textbook readings are meant to clarify or elaborate material presented in class, or to give you an idea of alternative presentations of the same material. For example, we might discuss bonds, how they pay, and how to value them. The readings might cover the specifics of particular bond markets (local, state, different countries), how they are taxed etc.

There is no official textbook. In the past I have used Corporate Finance, by former Yale professor Steve Ross and two co-authors, and two others, by Sharpe and Merton, both Nobel Prize winners in economics (for contributions to financial economics). Their books were regarded as insufficiently quantitative, but might be useful to browse in.

Another very good book is by Luenberger, but it is a little too advanced for this course. I have listed a dozen or so good alternatives and supplements, to give you an idea of where you could read more if you become interested.

None of these is required. You should be able to follow the course simply by attending the lectures, reading the web notes, and doing the problem sets.