The Hidden Cost of Volatility Drag

The stock market has always been a volatile beast, with its ups and downs affecting investors' fortunes in unpredictable ways. One aspect of the market that is particularly challenging for investors is understanding how volatility affects their portfolios. This is where self-conforming equilibria come into play.

That said, the concept of self-conforming equilibria is not new to economists. A self-conforming equilibrium is a stable state in which agents' beliefs become correct about events that are observed sufficiently often. It's like rational expectations equilibria, but not vice versa. The idea was first proposed by Christopher Sims in the 1970s as a sensible equilibrium concept.

On the one hand, Sims' argument has been widely accepted and applied to competitive or infinitesimal agents. By using naive adaptive learning schemes (various versions of recursive least squares), agents can learn every conditional distribution they need to play best responses within an equilibrium. This is particularly useful for macroeconomic models that require agents to be highly adaptable.

On the other hand, large agents like governments in macro models are a different story altogether. They have significant influence over market outcomes and cannot expect to learn everything they need to know to make good decisions. In a self-conforming equilibrium, large agents may base their decisions on conjectures about equilibrium path behaviors that turn out to be incorrect.

What's interesting is that a rational expectations equilibrium is a self-conforming equilibrium, but not vice versa. While agents' beliefs can be incorrect about the equilibrium path, the self-conforming equilibria path still restricts them in interesting ways. For macroeconomic applications, the government's model must be such that its equilibrium path beliefs rationalize the decisions revealed to them along the equilibrium path.

The restrictions on government beliefs required to sustain self-conforming equilibria have only begun to be explored in macroeconomics. Mainly, in examples like those by [16]. Analogous restrictions have been more thoroughly analyzed in the context of games [10].

A widely used idea for renning self-conforming equilibrium is to embed the decision-making problem within a learning process in which decision makers estimate unknown parameters through repeated interactions, and then to identify a stable stationary point of the learning dynamics (e.g., [8, 7, 6]). The gap between a self-conforming equilibrium and a rational expectations equilibrium can be vital for governments designing Ramsey plans, as their calculations necessarily involve projecting outcomes of counterfactual experiments.

For macro-economists, an especially interesting feature of self-conforming equilibria is that because a government can have a model that is wrong about the equilibrium path, policy that it thinks is optimal can very well be far from optimal. Even if a policy model tracks historical data correctly and is unimprovable, one cannot conclude that the policy is optimal.

What does this mean for portfolios? Be specific. Discuss risks and opportunities separately. An important aspect of self-conforming equilibria is that they do not require investors to have perfect knowledge about market conditions. However, the implications are still significant.