ABSTRACT In statistics, samples are drawn from a population in a data‐generating process (DGP). Standard errors measure the uncertainty in estimates of population parameters. In science, evidence is generated to test hypotheses in an evidence‐generating process (EGP). We claim that EGP variation across researchers adds uncertainty—nonstandard errors (NSEs). We study NSEs by letting 164 teams test the same hypotheses on the same data. NSEs turn out to be sizable, but smaller for more reproducible or higher rated research. Adding peer‐review stages reduces NSEs. We further find that this type of uncertainty is underestimated by participants.

We reexamine the asset pricing performance of systematic skewness ("coskewness"), a risk factor in the three-moment CAPM model of Kraus and Litzenberger (1976). In an influential paper, Harvey and Siddique (2000) test a coskewness factor constructed by sorting stocks on past coskewness. We replicate and extend their paper. Overall, coskewness appears to be priced in the cross section of stocks, especially when using an alternative coskewness proxy like (i) the predicted systematic skewness (PSS) of Langlois (2020), where coskewness is predicted by various firm characteristics, or (ii) a modified PSS factor (mPSS) that uses only return-based characteristics.

This document includes supplementary material to the paper. Section 1 provides a variable description and the significance levels for skewness and coskewness used in Table 1 in the paper and Tables IA.3 to IA.9 in this Internet Appendix. Section 2 describes the test assets used in this Internet Appendix and shows (i) replications of Table 1 in the paper for other test assets, including those used in Table 1 in Harvey and Siddique (2000), (ii) replications of Table 4 Panel C in the paper when the NASDAQ stocks are removed from the sample, and (iii) replications of Table 5 in the paper for other sample periods. Section 3 shows summary statistics and the results of asset pricing tests of several coskewness proxies for different sample periods. Section 4 shows robustness checks for asset pricing tests of coskewness proxies.

We study both theoretically and empirically option prices on firms undergoing a cash merger offer. To estimate the merger's success probability, we use a Markov Chain Monte Carlo (MCMC) method using a state space representation of our model. Our estimated probability measure has significant predictive power for the merger outcome even after controlling for variables used in the merger literature. As predicted by the model, a graph of the target firm's implied volatility against the strike price has a kink at the offer price, and the kink's magnitude is proportional to the merger's success probability.

How does informed trading affect liquidity in limit order markets, where traders can choose between market orders (demanding liquidity) and limit orders (providing liquidity)? In a dynamic model, informed trading overall helps liquidity: A higher share of informed traders i) improves liquidity as proxied by the bid–ask spread and market resiliency, and ii) has no effect on the price impact of orders. The model generates other testable implications, and suggests new measures of informed trading.

Do the rich always get richer by investing in a cryptocurrency for which new coins are issued according to a proof-of-stake (PoS) protocol? We answer this question in the negative: Without trading, the investor shares in the cryptocurrency are martingales that converge to a well-defined limiting distribution and, hence, are stable in the long run. This result is robust to allowing trading when investors are risk neutral. Then, investors have no incentive to accumulate coins and gamble on the PoS protocol but weakly prefer not to trade. This paper was accepted by Kay Giesecke, finance.

I develop a model in which traders receive a stream of private signals, and differ in their information processing speed. In equilibrium, the fast traders (FTs) quickly reveal a large fraction of their information. If a FT is averse to holding inventory, his optimal strategy changes considerably as his aversion crosses a threshold. He no longer takes long-term bets on the asset value, gets most of his profits in cash, and generates a “hot potato” effect: after trading on information, the FT quickly unloads part of his inventory to slower traders. The results match evidence about high-frequency traders.

Does a larger fraction of informed trading generate more illiquidity, as measured by the bid--ask spread? We answer this question in the negative in the context of a dynamic dealer market where the fundamental value follows a random walk, provided we consider the long run (stationary) equilibrium. More informed traders tend to generate more adverse selection and hence larger spreads, but at the same time cause faster learning by the market makers and hence smaller spreads. This latter effect offsets the adverse selection effect when the trading frequency is equal to one, and dominates at larger frequencies.

This paper studies the quote-to-trade (QT) ratio, and its relation with liquidity, price discovery and expected returns. Empirically, we find larger QT ratios in small or illiquid firms, yet large QT ratios are associated with low expected returns. The results are driven by quotes, not by trades. We propose a model of the QT ratio consistent with these facts. In equilibrium, market makers monitor the market faster (and thus increase the QT ratio) in difficult-to-understand stocks. They also monitor faster when their clients are less risk averse, which reduces mispricing and lowers expected returns.

In an empirical study of cash mergers since 1996, we find that the equity options on target firms display a pronounced smile pattern in their implied volatilities which gets more pronounced when the merger success probability gets higher. We propose an arbitrage-free model to analyze option prices for firms undergoing a cash merger attempt. Our formula matches well the observed merger volatility smile. Furthermore, as predicted by the model, we show empirically that the merger volatility smile has a kink at the offer price, and that the magnitude of the kink is proportional to the merger success probability.

We compare the optimal trading strategy of an informed speculator when he can trade ahead of incoming news (is fast), versus when he cannot (is slow). We find that speed matters: the fast speculator's trades account for a larger fraction of trading volume, and are more correlated with short-run price changes. Nevertheless, he realizes a large fraction of his profits from trading on long-term price changes. The fast speculator's behavior matches evidence about high-frequency traders. We predict that stocks with more informative news are more liquid even though they attract more activity from informed high-frequency traders.

We define news as a sequence of private signals received by a set of traders about an asset value that is moving over time. Usually, in continuous time market microstructure models of asymmetric information, informed traders only contribute to the drift of price changes, while the volatility component is generated entirely by the noise traders. In contrast, we show that in the presence of news, competition among informed traders adds a stochastic component to their trading, and hence contribute to an informed component of volatility.

This paper presents a model of an order-driven market where fully strategic, symmetrically informed liquidity traders dynamically choose between limit and market orders, trading off execution price and waiting costs. In equilibrium the bid and ask prices depend only on the numbers of buy and sell orders in the book. The model has a number of empirical predictions: (i) higher trading activity and higher trading competition cause smaller spreads and lower price impact; (ii) market orders lead to a temporary price impact larger than the permanent price impact, therefore to price overshooting; (iii) buy and sell orders can cluster away from the bid-ask spread, generating a hump-shaped order book; (iv) bid and ask prices display a comovement effect: after e.g. a sell market order moves the bid price down, the ask price also falls, by a smaller amount, so the bid-ask spread widens; (v) when the order book is full, traders may submit quick, or fleeting, limit orders.

When a cash merger is announced but not completed, there are two main sources of uncertainty related to the target company: the probability of success and the price conditional on the deal failing. We propose an arbitrage-free option pricing formula that focuses on these sources of uncertainty. We test our formula in a study of all cash mergers between 1996 and 2008 which have suciently liquid options traded on the target company. The estimated success probability is a good predictor of the deal outcome. Our option formula for cash mergers does significantly better than the Black‐ Scholes formula and produces a volatility smile close to the one observed in practice. In particular, we provide an explanation for the kink in the volatility smile and show that the kink increases with the probability of deal success.

When liquidity is measured by the bid-ask spread or price impact, markets with more trading activity are typically more liquid than markets with less trading activity. But showing a causal connection from trading activity to spreads is difficult because these variables are endogenous. In the case of Finland's fully electronic limit order market, we use deseasonalized sunshine as an instrument for trading activity, and find that indeed higher trading activity causes lower spreads in the time series. We introduce another instrument for spreads and show that causality runs the other way as well: lower bid-ask spreads invite more trading activity. By using the lagged CBOE Volatility Index as an instrument, we also find that an exogenous increase in intra-day volatility causes larger spreads.

When liquidity is measured by bid-ask spreads or price impact, markets with more trading activity (such as foreign exchange markets) are typically more liquid than markets with less trading activity (such as municipal bond markets). But showing a causal connection from trading activity to spreads is difficult, due to the endogenous nature of these variables. In the case of Finland’s fully electronic limit order market, we show that the weather (measured by sunshine, cloudiness and precipitation) is a valid instrument for trading activity, and that indeed higher trading activity causes lower spreads, both in the time-series and in the crosssection. We further show that weather affects only individual traders, and not institutions. JEL Classification: C7, etc.

For T an abelian compact Lie group, we give a description of T-equivariant K-theory with complex coefficients in terms of equivariant cohomology. In the appendix we give applications of this by extending results of Chang-Skjelbred and Goresky-Kottwitz-MacPherson from equivariant cohomology to equivariant K-theory.