Portfolio-choice models have households choosing both savings, and the division of savings between safe and risky assets. Next period assets depend on these two decisions, as well as on a stochastic return to the risky asset. Version 2.1 of VFI Toolkit introduces riskyasset specifically for these problems in which aprime(d,u), that is, the next period endogenous state, aprime, depends on decision variable(s), d, and an i.i.d. shock that occurs between this period and next period, u.

There are four examples in the Intro To Life-Cycle Models, and an implementation of the baseline model of Cocco, Gomes & Maenhout (2005) – Consumption and Portfolio Choice over the Life Cycle. The four life-cycle models build various aspects of Portfolio-Choice models. Life-Cycle Model 31 introduces Portfolio-Choice in an otherwise standard life-cycle model, showing how to set up a riskyasset to solve these. Life-Cycle Model 32 adds Epstein-Zin preferences, Life-Cycle Model 33 shows how to do Warm-Glow of Bequests which are more complicated with Epstein-Zin preferences, and Life-Cycle Model 34 adds endogenous labor.

Epstein-Zin preferences are important in the Portfolio-Choice literature as they allow separating risk aversion (which is important to the division of savings between safe and risky assets) from the elasticity of intertemporal substitution (which is important to how much to save for retirement); both of these are controlled by the same parameter in standard (vonNeumann-Morgenstern) preferences. As part of Version 2.1 Epstein-Zin preferences have undergone a (breaking) overhaul. This added two additional aspects to Epstein-Zin: (i) there is an option to choose between Epstein-Zin preferences in utility-units, or to use the more traditional consumption-units, (ii) handling of survival probabilities (a.k.a. mortality risk) and warm-glow of bequests. For more about Epstein-Zin preferences and how to use them see the Appendix of the Intro to Life-Cycle Models.

There is code implementing an example of the baseline model of Cocco, Gomes & Maenhout (2005) – Consumption and Portfolio Choice over the Life Cycle. This example uses portfolio-choice, Epstein-Zin preferences, and permanent types all together and shows how these models can be handled.


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Cocco, Gomes & Maenhout (2005) have permanent shocks in their model. The correct way to handle permanent shocks is a renormalization of the model that makes them disappear from the state-space. Instead the example codes keep them as a state, this means that computationally the example code is actually solving a much more difficult problem. It also means that you can easily switch to a more modern earnings process (my reading of Gomes (2020) is that he views the recent evidence as clearly against using permanent shocks).