Part I: Discrete Time

These notebooks develop asset pricing in discrete time, from one-period portfolio theory to dynamic economies. They are available in HTML and PDF formats, and the sections build on each other progressively.

The course begins with the mathematics of portfolio selection. Before introducing any economic assumptions, these notebooks develop the geometry of the mean-variance frontier and show how expected returns must relate to risk through beta pricing. The arrival of a risk-free asset simplifies the picture considerably, and the section ends with the CAPM as an economic theory that gives content to what had been a purely mathematical relationship.

With the portfolio theory in place, the next section approaches pricing from a different angle: through the absence of arbitrage rather than through optimization. The key insight is that any linear pricing functional can be represented by a single random variable, the stochastic discount factor, that prices all traded payoffs simultaneously. The geometric structure of the payoff space makes this result intuitive and general.

The following section asks where the SDF comes from. The answer lies in the first-order conditions of an investor who is optimally choosing consumption and portfolio holdings over time. Starting from simple two-period preferences 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 numerical section works through the Critical Line Algorithm, which computes the exact mean-variance frontier when short sales are prohibited.

The story continues in Part II: Continuous Time.