Feature-Selection Risk

Companies have overlapping exposures to many different features that might plausibly affect their returns, like whether they're involved in a crowded trade, whether they're mentioned in an M&A rumor, or whether their supplier recently missed an earnings forecast. Yet, at any point in time, only a handful of these features actually matter. As a result, traders have to simultaneously infer both the identity and the value of the few relevant features. I show theoretically that, when traders face this sort of joint inference problem, the risk of selecting the wrong features can spill over and distort how they value assets — that is, the high-dimensional nature of modern financial markets can act like a cognitive constraint even if traders themselves are fully rational. Moreover, I show how modeling feature-selection risk leads to additional predictions that are outside the scope of noise-trader risk. For instance, to discover pricing errors as quickly as possible, a model with feature-selection risk suggests that traders should simultaneously trade a random assortment of complex, heterogeneous assets rather than Arrow securities. Empirically, I find that using an estimation strategy that explicitly accounts for traders' joint inference problem increases out-of-sample return predictability at the monthly horizon by 144.3%, from R2 = 3.65% to R2 = 9.35%, suggesting that this feature-selection problem is important to real-world traders