A curriculum built around recursive preference theory
I came here because the models that actually explain equity premiums — Epstein-Zin utility, long-run risk, recursive competitive equilibria — were nowhere to be found in one coherent place. This curriculum follows the logic from first principles all the way through to equilibrium asset prices, without skipping the mathematics that makes it meaningful.
Fully structured
6 modules
Curriculum depth
Theory coverage
Research grade
How the learning pathway unfolds
From intertemporal utility foundations through recursive equilibrium and empirical applications, each stage builds precisely on the one before it.
01
Foundations of Utility Theory
The pathway opens with the intertemporal consumption problem — budget constraints, preference representation, and the limitations of time-separable expected utility. Before Epstein-Zin preferences can be understood, the learner needs a precise account of what standard models can and cannot do. This stage builds that account carefully, working through dynamic programming and Bellman equations until the scaffolding is solid enough to support what follows. No step is assumed; every derivation is shown.
02
Recursive Preferences and Epstein-Zin Utility
With foundations in place, the curriculum turns to the central object:
recursive utility as formulated by Epstein and Zin. The critical
separation of risk aversion from the elasticity of intertemporal
substitution is developed in full, with attention to why that separation
matters for asset pricing and what it implies for the stochastic
discount factor. The learner works through the preference aggregator,
the value function, and the first-order conditions that connect
preferences to prices in a general equilibrium setting.
03
Stochastic Discount Factors and Risk Premiums
Equilibrium asset prices are functions of the stochastic discount factor, and understanding that object — its construction, its properties, and its relationship to marginal utility — is the work of this stage. The curriculum examines the Hansen-Jagannathan bounds, the relationship between discount factor volatility and the equity premium, and how recursive preferences alter the discount factor relative to the standard power-utility benchmark. Each result is connected back to observable implications.
04
Long-Run Risk and the Equity Premium
The Bansal-Yaron long-run risk model is developed in detail — its
assumptions, its calibration strategy, and its resolution of the equity
premium and risk-free rate puzzles that motivated it. The learner
examines how small, persistent components in consumption growth generate
large risk premiums when preferences are recursive. The empirical
evidence for and against the long-run risk mechanism is assessed
honestly, including the debates that remain unresolved in the current
literature.
05
Empirical Asset Pricing Applications
The final stage connects theory to data. Methods for estimating stochastic discount factors, testing asset pricing models, and calibrating preference parameters are examined alongside the models themselves. The curriculum covers the generalised method of moments, cross-sectional tests of risk premiums, and the challenges of identifying long-run risk in finite samples. Learners leave this stage able to read and critically evaluate empirical asset pricing papers that use recursive preference frameworks.
Curriculum modules
Five modules that build recursive asset pricing from the ground up
01
Core preference structures
Foundations of Recursive Utility Theory
This opening module establishes the conceptual and mathematical ground on which the entire curriculum rests. The learner works through time-separable expected utility, its axiomatic foundations, and the well-documented anomalies — the equity premium puzzle, the risk-free rate puzzle — that motivated the development of recursive alternatives. Dynamic programming is introduced not as a technical aside but as the central tool for representing intertemporal choice. By the end of this module, the learner understands precisely what standard models leave unexplained and why recursive preferences were developed to address those gaps. The Bellman equation, the value function, and the envelope condition are all derived and interpreted in the context of asset pricing.
- Time-separable utility and its limits
- Dynamic programming and Bellman equations
- Equity premium and risk-free rate puzzles
02
Separating risk and time
Epstein-Zin Preferences and Preference Aggregation
The module develops the Epstein-Zin-Weil preference specification in full
mathematical detail, beginning with the aggregator function and working through
to the optimality conditions that connect preferences to equilibrium prices. The
separation of the coefficient of relative risk aversion from the elasticity of
intertemporal substitution — the defining feature of recursive utility — is
derived carefully, with attention to the economic interpretation of each
parameter. The learner examines how different parameter configurations alter the
model's predictions for the equity premium, the risk-free rate, and the term
structure of interest rates. Special attention is given to the knife-edge case
of expected utility and what departures from it imply for asset prices.
- Preference aggregator and recursive structure
- Risk aversion versus intertemporal substitution
- Parameter interpretation and model predictions
03
Connecting preferences to prices
Stochastic Discount Factors in Recursive Economies
Asset prices in any frictionless economy are determined by the stochastic discount factor, and this module builds a precise account of how recursive preferences shape that object. The learner derives the discount factor under Epstein-Zin utility, compares it with the power-utility benchmark, and examines what the recursive formulation implies for the Hansen-Jagannathan volatility bound. The module also covers the relationship between discount factor dynamics and the cross-section of expected returns, developing the intuition for why assets that pay off poorly in bad states of the world carry higher risk premiums. The co-movement between the stochastic discount factor and asset payoffs is examined in both theoretical and calibrated settings.
- Deriving the recursive stochastic discount factor
- Hansen-Jagannathan bounds and volatility
- Cross-sectional implications for risk premiums
04
Persistent growth and equity premiums
Long-Run Risk Models and Equilibrium Prices
This module develops the long-run risk framework of Bansal and Yaron in careful detail, explaining how small but persistent components in expected consumption growth generate large equilibrium risk premiums when the representative agent has recursive preferences. The learner works through the log-linearisation of the equilibrium conditions, the solution for the price-dividend ratio, and the calibration of preference and endowment parameters to match key asset pricing moments. The module examines what the model implies for the term structure of equity risk, the behaviour of the risk-free rate, and the predictability of excess returns. Competing explanations — habit formation, rare disasters — are assessed alongside long-run risk in a structured comparison.
- Persistent consumption growth and risk premiums
- Equilibrium price-dividend ratio solution
- Comparison with habit and disaster models
05
Theory tested against data
Empirical Asset Pricing and Model Assessment
The closing module bridges the theoretical framework developed throughout the
curriculum and the empirical methods used to assess it. The generalised method
of moments is introduced as the primary tool for estimating and testing
stochastic discount factor models, with worked examples drawn from the recursive
utility literature. Cross-sectional regression methods for testing factor models
are covered alongside their limitations in small samples. The module examines
the identification challenges that arise when testing long-run risk — the
persistence of the predictive component in consumption growth is difficult to
measure precisely in historical data — and surveys the range of evidence that
researchers have brought to bear. Learners leave equipped to read and evaluate
the current empirical literature with genuine critical understanding.
- Generalised method of moments for SDF models
- Cross-sectional tests of risk premiums
- Identification challenges in long-run risk
Research-grade depth versus standard finance programmes
Where conventional MBA and CFA-level content stops, this curriculum continues — into the
recursive structure of preferences, the mathematics of equilibrium, and the open debates at
the frontier of asset pricing research.
Cuenyzuaslaim
Standard programmes
Equity Premium Treatment
Module coverage
Cuenyzuaslaim
Derives equity premium from recursive preferences, separating risk aversion and intertemporal substitution parameters with full mathematical rigour and equilibrium derivation.
Research grade
•
Full derivation
Прогресс
92%
Standard programmes
Introduces equity premium as an observed historical fact, typically without deriving its source from preference fundamentals or equilibrium conditions.
Introductory
•
Descriptive only
Прогресс
38%
Stochastic Discount Factor
Technical depth
Cuenyzuaslaim
Builds the stochastic discount factor from Epstein-Zin optimality conditions, examines Hansen-Jagannathan bounds, and connects discount factor volatility to cross-sectional risk premiums.
Full derivation
•
Equilibrium level
Прогресс
89%
Standard programmes
Mentions the stochastic discount factor as a pricing tool without deriving its structure under recursive preferences or examining its volatility properties.
Surface level
•
Conceptual only
Прогресс
32%
Long-Run Risk Models
Model coverage
Cuenyzuaslaim
Develops the Bansal-Yaron framework in full, including log-linearisation, equilibrium solution, calibration strategy, and assessment of empirical evidence for and against the model.
Complete coverage
•
Full framework
Прогресс
95%
Standard programmes
Rarely covers long-run risk models at all; when mentioned, they appear as brief references without derivation, calibration, or empirical assessment.
Not covered
•
Rarely included
Прогресс
12%
Cuenyzuaslaim
92%
Standard programmes
27%
Standard finance programmes build sufficient grounding for many professional contexts, but they do not reach the recursive preference models that dominate current asset pricing research. This curriculum begins where those programmes end, working through the mathematics and equilibrium logic that connects recursive utility to observed risk premiums.
Curriculum questions answered
What background knowledge is expected before starting?
- Familiarity with calculus and basic probability is assumed
- Prior exposure to microeconomic theory is helpful
- Graduate-level finance background is beneficial but not required
- The foundations module is designed to build necessary scaffolding
How much time does working through the full curriculum require?
- Each module is designed for careful, unhurried engagement
- Most learners progress at their own pace across several weeks
- The empirical module benefits from repeated reading
- Depth of engagement matters more than speed of completion
Is a certificate or formal credential issued upon completion?
- The platform focuses on substantive understanding rather than credentials
- No formal certificate is currently issued
- The curriculum is designed for genuine comprehension, not assessment performance
How does this content apply to real-world investment analysis?
- Recursive preference models underpin much of modern asset pricing research
- Understanding them sharpens how one reads and evaluates empirical findings
- The stochastic discount factor framework applies across many asset classes
- Model limitations are discussed honestly alongside their applications
How long does access to the curriculum content remain available?
- All published content remains accessible on an ongoing basis
- Modules are updated when the relevant research literature develops
- Learners may return to earlier sections at any point
- No access expiry is applied to existing content
Begin working through recursive utility asset pricing
The curriculum is here for learners who are ready to engage seriously with the mathematics and
equilibrium logic of recursive preferences. There is no simplified version — only the careful,
step-by-step path through Epstein-Zin utility, stochastic discount factors, and long-run risk
that the subject actually requires. If that is the kind of understanding you are looking for,
the place to start is the research section, where the foundational material is laid out in full.
