Course Content:

1. Introduction of basic concepts (Chapters 1-3 in the textbook):
   1. Demand for Assets, Rate of Return, Short Sales, Arbitrage
   2. Stochastic Processes: Martingales, Random Walk: Basic Definitions and Examples
   3. Distribution of Returns: We analyze the return distribution of stocks using financial data. We will see that there are more extreme returns in the data than a log-normal distribution would predict. This matters for derivative pricing, since the pricing models rely on log-normality of returns.
2. Choice under Uncertainty (Chapter 4): Brief review of decision theory from Econ302, and additional material (e.g., CRRA utility).
3. Review of Constrained Optimization (Lagrange): Starting from optimization problems that you have been introduced to in Econ302, will discuss how to solve to solve optimization problems with multiple constraints using the Lagrangean technique. We apply this to determine the fundamental valuation relationship (FVR) which relates returns to marginal utilities of investors.
4. The Mean-Variance Model of Portfolio Choice (Chapter 5) and the Capital Asset Pricing Model (CAPM) (Chapter 6)
   1. Efficient Frontier, definition of the Sharpe ratio and estimation: Portfolios on the efficient frontier must have that maximum Sharpe ratio. We review concepts from Econ 202 and 203 in order to determine whether one portfolio has (statistically) a higher sharper ratio than another portfolio.
   2. The Capital Market Line, Risk adjusted discounting, risk premium.
5. Empirical Evaluation of the CAPM (Chapter 9): We show how to determine alpha and beta for stocks or portfolios of stocks, and their confidence intervals.
6. Arbitrage (Chapter 7) and addition material (e.g., form Chapters 14, 15, 16 about Futures Markets and Chapters 18,19,20 about Option Markets, and selected material from Hull's book): This chapter develops the models used to price derivative securities. We introduce the binomial pricing model and then show how the binomial model converges to a continuous time model when the interval between trading periods converges to zero. When we take the limit, the return process converges to a geometric Brownian motion, which also yields the distribution that allows risk-neutral valuation.
   1. State Prices, Risk Neutral Valuation, Equivalent Martingale Measure
   2. No Arbitrage Pricing of Forward and Future Contracts
   3. The Binomial Price Process and the Geometric Brownian Motion
   4. Option Pricing: European Put and Call options
   5. Pricing of American Put Options
   6. Pricing of Mortgage Backed Securities
   7. Dynamic Hedging Strategies and Portfolio Insurance
7. Present Value and Price Variability (Chapter 10)
   1. Volatility of Stock Prices
   2. Bubbles
   3. PE ratios
8. Bond Markets and Fixed Interest Securities (Chapter 12) and Term Structure of Interest Rates (Chapter 13)
   1. Treasury Bills and Bonds
   2. Yield to Maturity
   3. Bond Pricing (no default risk): If there is no default risk, then we can compute state prices from bonds with different maturities, which allows us to price bonds and determine the yield curve.
   4. Yield Curve and Models of the Term Structure of Interest Rates: What determines the shape of the yield curve? We will again use the asset pricing model introduced in chapter 3.
   5. Clean and Dirty Prices: We determine the yield curve empirically using data on bond prices.
   6. Pricing of bonds with default risk: We will use the methods from chapter 6 to determine the yield of such bonds.
9. Swap Contracts and Swap Markets (Chapter 17)
10. Justification for Government/Regulatory intervention: In this section of the course we will consider a brief overview of justification of political authority.

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