Asset Pricing

A chart with the mean of the stochastic discount factor on the horizontal axis, from 0.45 to 1.25, and its standard deviation on a logarithmic vertical axis, from 0.01 to 30. Two V-shaped bounds with their lowest points near a mean of 1 mark the admissible region above them: a dashed one for the market and the Treasury bill, with its bottom near 0.5, and a higher solid one for 25 size and value portfolios, with its bottom near 1.2. A red curve for power utility starts near a mean of 0.96 and a small standard deviation and moves up and to the left as risk aversion rises, through gamma equal to 2, 10 and 25, reaching its leftmost point near a mean of 0.54 just past gamma equal to 50. It then turns back to the right, passing gamma equal to 100 at a mean of 0.75, and crosses both bounds near a mean of 1, with gamma equal to 120 inside the admissible region, before leaving it to the right. — Hansen-Jagannathan bounds on the stochastic discount factor from annual real U.S. returns, 1948 to 2025. SDFs that price these returns must lie above the bound: the dashed curve uses the market and the Treasury bill, and the solid curve the 25 size and value portfolios and the bill, whose in-sample maximum Sharpe ratio overstates the attainable one. The red curve is the power-utility SDF \beta(C_{t+1}/C_t)^{-\gamma} with \beta = 0.98 and growth in annual average real personal consumption expenditures per capita. As \gamma rises its mean first falls, to about 0.54 near \gamma = 57, a real interest rate above 80%, and then turns back, so the curve reaches the admissible region only for \gamma between about 113 and 123 with the market.

Welcome to my Asset Pricing content site. Here you will find a collection of notebooks related to the asset pricing courses I teach.

The notebooks cover equilibrium pricing, stochastic discount factors, and continuous time finance. They are organized by topic and available in both HTML and PDF formats. I typically use a subset of these in my Topics in Quantitative Finance (FIN 5018) class at WashU, and some of this material was developed when I taught the PhD-level Asset Pricing course at ESSEC Business School.

The material is split into three parts. Part I: Portfolios and No-Arbitrage covers portfolio theory and no-arbitrage pricing. Part II: Preferences and Equilibrium brings in preferences, the CAPM, and multiperiod economies in discrete time. Part III: Continuous Time reformulates these ideas with Itô calculus and applies them to consumption-portfolio choice, derivatives, and bond pricing.

I will continue adding and refining content so this site remains a reliable companion for all my asset pricing-related classes.