Part II: Preferences and Equilibrium

These notebooks bring investors’ preferences into the pricing results of Part I: Portfolios and No-Arbitrage, first in one period and then over many periods, all in discrete time. They are available in HTML and PDF formats, and the sections build on each other progressively.

The first section opens with the CAPM, the first equilibrium model of the course: mean-variance investors with common beliefs, together with market clearing, identify the tangency portfolio of Part I with the market portfolio. It then asks where the stochastic discount factor comes from. The answer lies in the first-order conditions of an investor who is optimally choosing consumption and portfolio holdings. Starting from one-period portfolio choice and building up to recursive Epstein-Zin utility, these notebooks show how the SDF emerges from the trade-off between consuming today and investing for tomorrow, and why separating risk aversion from the willingness to substitute consumption over time turns out to matter.

The multiperiod section then puts all of this together in dynamic economies. The Euler equation extends naturally to many periods, and the notebooks work through how time-varying investment opportunities create hedging demand, how the Epstein-Zin SDF takes a two-factor form in general equilibrium, and how lognormality delivers tractable closed-form expressions for risk premia. The section closes by applying the same SDF machinery to the term structure of interest rates.

The story continues in Part III: Continuous Time.