Feature Selection Risk (2014) [Paper]: Real world traders face a sparse, high-dimensional, inference problem. This paper argues that uncertainty about the underlying cause of a market swing—i.e., feature selection risk—can serve as an important limit to arbitrage for rational traders. The key insight is that there is a theoretical minimum number of observations that a trader needs to see in order to identify a set of sparse shocks regardless of the inference strategy he uses. I employ tools from the compressed sensing literature to characterize this minimum number of observations, , which I call the feature selection bound. I then embed this bound in a Kyle (1985)-type information-based asset pricing model to show how it delays arbitrage. This limit to arbitrage stems from an information-theoretic bound on how helpful market signals can be rather than a cognitive constraint or trading friction. The model makes a pair of novel predictions: i) informed trader profits are increasing in the number of payout-relevant features each asset has, and ii) arbitrageurs can identify sparse shocks using fewer assets if they study complex derivatives rather than Arrow securities.
No Coincidence, No Story (2014) [Paper, R&R]: Even if you are absolutely certain that some group of stocks is mispriced somewhere in the market, you still have to start with some idea about where to look. The problem of choosing ahead of time which groups of stocks are worth analyzing is a cognitive control problem, and this paper proposes that it has first order asset pricing implications. I proceed in steps. First, to fix ideas I write down an asset pricing model where arbitrageurs face a cognitive control problem. Asset values are the sum of many attribute-specific shocks. As the market grows large the number of attribute groupings grows exponentially faster than the number of stocks, so pricing errors might persist because arbitrageurs can’t exhaustively search through every single attribute. Next, I show that only analyzing attributes which display a coincidence—i.e., attributes with or more stocks in the top or bottom past returns—is a good heuristic solution to this cognitive control problem. Moreover, it is a strategy that is only useful in this context, so trading on coincidences is a tell-tale sign of a cognitive control problem. Finally, I give empirical evidence of trading on coincidences. I find that stocks from an industry that realized a positive coincidence over the previous quarter have higher abnormal returns in the subsequent month than stocks from an industry that realized a negative coincidence. Industries where stock has returns in the top and another stock has returns ranked somewhere between th and th display no such pattern. This effect is not explained by momentum effects, market frictions, or large to small stock cross-autocorrelation.
Misinformed Speculators and Mispricing in the Housing Market (2014, w/ Chris Mayer) [Paper, Slides, NBER Digest]: We examine the contribution of out-of-town second house buyers to mispricing in the housing market. These buyers behave like misinformed speculators, earning lower capital gains and consuming smaller dividends. Increases in out-of-town second house buyer demand predict increases in house price and implied-to-actual rent ratio appreciation rates. Although an increase in the value of owning a second house in a particular city is a common shock to the investment opportunity set of all potential second house buyers, buyers from across the country do not adjust their city-specific demand for second houses in unison suggesting reverse causality isn’t driving our results.
Work in Progress
Emergent Aggregate Risk (2014)
The Positive Externality of Accurate Prices (2014)
Investor Horizon and Idiosyncratic Volatility (2014, w/ Mao Ye)