Conference Agenda

Measurement error in features affects the out-of-sample performance of portfolios and of return predictions. In a high-dimensional feature space, increasing model complexity under proper regularization can enhance the predictability of asset returns; however, the Sharpe ratio of a portfolio of assets and the R-squared of the prediction of the asset returns decrease monotonically and are convex as the noise level in features increases. Furthermore, when only a subset of features is observed, there is an optimal level of complexity beyond which incorporating additional features can degrade portfolio performance due to the effect of noise in the features. Thus, the marginal benefits of increasing model complexity will, at some point, start to diminish as the number of observed features increases. Our findings underscore a limited virtue of complexity in financial forecasting, where the performance of portfolios depends on the noise level in features, and where more complex models do not necessarily lead to better performance when features are not perfectly observed.

This paper proposes a tractable model of “complexity aversion”. The key ingredient is “first order complexity aversion”: when people know they're making a mistake (because the situation is complex) they experience dread, which is a utility loss proportional to the expected size of their error. This adds a new complexity aversion term to the traditional utility function. This simple enrichment has a host of consequences, which I illustrate in five examples. (i) If complexity aversion is high enough, the price of a good will be constant over time, even though the marginal cost might be variable, to avoid annoying the consumer with a complex price system. (ii) The optimal tax system recommended by traditional economics should be considerably more complex than the (admittedly complex) system that we observe; With complexity aversion, the optimal tax system is “simpler” than the extremely complex tax system recommended by traditional economics (which is considerably more complex than what we observe in practice), e.g. it yields uniform tax. (iii) Whereas the traditional model predicts that contracts should be indexed aggregate factors (e.g. on inflation, GDP, or the stock market), with enough complexity aversion, contracts are non-indexed, “simple”. (iv) As higher inflation leads to a more complex planning process, complexity aversion leads first order cost of inflation, which much larger than the second order costs of the traditional model. (v) This in turn changes optimal monetary policy, which de facto should ensure zero inflation (more generally, zero deviation from the inflation target), to the exclusion of other goals, except in rare circumstances such as an extreme recession. I finally discuss how using this model of complexity aversion will lead to a useful “behavioral mechanism design” theory, and more realistic—simpler—mechanisms.

We offer a novel resolution to several asset pricing puzzles by investigating how complexity affects pricing errors when rational, risk-averse agents have imperfect knowledge of the data-generating process. Our theoretical framework yields three key implications as complexity increases: (1) equilibrium pricing errors grow systematically larger, (2) the optimal portfolio increasingly exploits estimation error components rather than fundamental risk, and (3) multiple strategies achieve higher Sharpe ratios while maintaining low cross-correlations. Our model explains the limited pricing power of parsimonious factor models, the weak relationship between betas and average returns, and the proliferation of anomalies. Empirically, we document substantial complexity in return predictability and covariance structures. Analyzing sophisticated quantitative strategies, we find remarkably low correlations, with an average $R^2$ below 1\% among systematic hedge funds' active positions, consistent with our model's prediction that different strategies exploit distinct dimensions of estimation error in complex markets.