Craig W. Holden

Risk aversion, imperfect competition, and long-lived information

Abstract This paper presents a methodology for characterizing the optimal dynamic behavior of risk-averse, strategic agents with private information, by building on Kyle (Econometrica, 1985, 53, 1315–1335). It is shown that both monopolistic and competing informed traders choose to exploit rents rapidly, causing market depth to be low in the initial periods and high in later periods, and causing information to be revealed rapidly, unlike in the case of a risk-neutral monopolist considered by Kyle.

What Are the Best Liquidity Proxies for Global Research

Liquidity plays an important role in global research. We identify high-quality liquidity proxies based on low-frequency (daily) data, which provide 1,000× to 10,000× computational savings compared to computing high-frequency (intraday) liquidity measures. We find that: (i) Closing Percent Quoted Spread is the best monthly percent-cost proxy when available, (ii) Amihud, Closing Percent Quoted Spread Impact, LOT Mixed Impact, High–Low Impact, and FHT Impact are tied as the best monthly cost-per-dollar-volume proxy, (iii) the daily version of Closing Percent Quoted Spread is the best daily percent-cost proxy, and (iv) the daily version of Amihud is the best daily cost-per-dollar-volume proxy.

News Events, Information Acquisition, and Serial Correlation

Prior research finds that momentum strategies (buying past losers and selling past winners) generate abnormal returns over medium-term (3- to 12-month) horizons. The Fama and French factors are unable to account for this effect, though they account for long-term reversals in asset returns. We develop a model which accounts for the medium-term continuation (momentum) by analyzing information acquisition about news events (such as earnings announcements) in a multiperiod setting. As more and more agents become informed about news events, temporal uncertainty is resolved endogenously through market prices over time, which leads to positive autocorrelations in asset returns. We empirically estimate serial correlations over medium-term horizons for portfolios sorted by firm size and past stock performance, and find that calibration of serial correlations in our model spans the range of empirically estimated correlations.

A simple model of payment for order flow, internalization, and total trading cost

Abstract We show that externally-verifiable characteristics (inexpensive for a third-party to verify) of traders or orders allow profitable purchasing of order flow and internalization. We introduce total trading cost , defined as the effective half spread plus the brokers per share commission, as a measure of execution quality. We use this measure to reinterpret prior empirical studies of: (1) execution quality across trading venues and (2) cream-skimming by purchasers of order flow. Finally, we show brokers can use their direct relationships with customers to assess internally-verifiable characteristics (inexpensive for direct verification) in order to increase profits extracted from customer orders.

The Empirical Analysis of Liquidity

We provide a synthesis of the empirical evidence on market liquidity. The liquidity measurement literature has established standard measures of liquidity that apply to broad categories of market microstructure data. Specialized measures of liquidity have been developed to deal with data limitations in specific markets, to provide proxies from daily data, and to assess institutional trading programs. The general liquidity literature has established local cross-sectional patterns, global cross-sectional patterns, and time-series patterns. Commonality in liquidity is prevalent. Certain exchange designs enhance market liquidity: a limit order book for high volume markets, a hybrid exchange for low volume markets, and multiple competing exchanges. Automatic execution increases speed, but increases spreads. A tick size reduction yields a large improvement in liquidity. Providing ex-post transparency to an otherwise opaque market dramatically improves liquidity. Opening up the limit order book improves liquidity. Regulatory reforms that increase the number of competitive alternatives, move toward linking them up, and level the playing field between exchanges improves liquidity. High-frequency traders trade in both a passive, liquidity-supplying manner and an aggressive, liquidity-demanding manner. Their overall impact improves both liquidity and price efficiency, but concerns remain regarding occasional trading glitches, order anticipation strategies, and latency arbitrage at the expense of slow traders. The liquidity and corporate finance literature provides abundant evidence that liquidity is beneficial in many corporate settings: liquidity increases the power of governance via exit, reduces the cost of governance via intervention, facilitates the entrance of informed traders who produce valuable information about the firm, enhances the effectiveness of equity-based compensation to managers, reduces the cost of equity financing, mitigates trading frictions investors encounter when trading in the market to recreate a preferred payout policy, and lowers the immediate transaction costs and subsequent liquidity costs for firms conducting large share repurchases. Further, the influence goes both ways. There is evidence that firms influence their own liquidity through a broad range of corporate decisions including internal governance standards, equity issuance form and pricing, share repurchases, acquisition targets, and disclosure timeliness and quality. The literature on liquidity and asset pricing demonstrates that both average liquidity cost and liquidity risk are priced, liquidity enhances market efficiency, and liquidity strengthens the arbitrage linkage between related markets. We conclude with directions for future research.

On the Existence of Linear Equilibria in Models of Market Making

We derive necessary and sufficient conditions for a linear equilibriumin three types of competitive market making models: Kyle type models (when market makers only observe aggregate net order flow), Glosten–Milgrom and Easley–O’Hara type models (when market makers observe and trade one order at a time), and call markets models (individual order models when market makers observe a number of orders before pricing and executing any of them). We study two cases: when privately informed (strategic) traders are symmetrically informed and when they have differential information. We derive necessary and sufficient conditions on the distributions of the randomvariables for a linear equilibrium. We also explore those features of the equilibrium that depend on linearity as opposed to the particular distributional assumptions and we provide a large number of examples of linear equilibria for each of the models.

Performance Share Plans: Valuation and Empirical Tests

Performance share plans are an increasingly important component of executive compensation. They are equity-based, long-term incentive plans where the number of shares to be awarded is a quasi-linear function of a performance result over a fixed time period. We derive closed-form formulas for the value of a performance share plan when the performance measure is: (1) a non-traded measure following an Arithmetic Brownian Motion (e.g., earnings per share), (2) a non-traded measure following a Geometric Brownian Motion (e.g., revenue), or (3) a rank-order tournament of traded asset returns that are following Arithmetic Brownian Motions (e.g., percentile of ranked stock returns). Then we empirically test our valuation formulas. We find that our valuation formulas are more accurate for performance share plans based on earnings per share when forecasting using analyst consensus prior to the grant date. We also find that the efficiency of our valuation model greatly depends on the method used to forecast future firm performance. The policy implication is that FASB should consider requiring that grant date fair value be estimated using valuation formulas such as ours.

Price Discovery in the Stock, OTC Corporate Bond, and NYSE Corporate Bond Markets

This paper examines intraday price discovery in three closely-related U.S. markets: stocks, Over-The-Counter (OTC) corporate bonds, and New York Stock Exchange (NYSE) electronically-traded corporate bonds. We calculate the Hasbrouck (1995) information shares of these three markets over five years. We find that OTC corporate bond trades have a 5.7% information share, despite zero pre-trade transparency in the OTC market. Further, NYSE corporate bonds have a 45.8% information share, despite having a tiny market share, because of publicly-displayed, frequently-updated bid-ask quotes that can be traded at any time. OTC corporate bond information shares are inversely related to credit quality and are relatively constant over time. This is consistent with multi-security informed trading theory and the Merton (1974) corporate bond model. NYSE corporate bond information shares are positively related to their update frequency. Thus, the subset of NYSE bonds that are updated more frequently are more informative.

Are Volatility Over Volume Liquidity Proxies Useful For Global Or US Research

We examine a general class of volatility over volume liquidity proxies as computed from low frequency (daily) data. We start from the Kyle and Obizhaeva (2016) hypothesis of transaction cost invariance to identify a new volatility over volume liquidity proxy “VoV(%Spread)” for percent spread cost and a new volatility over volume liquidity proxy “VoV(λ)” for the slope of the transaction cost function “λ”. We test the monthly and daily versions of these new and existing liquidity proxies against liquidity benchmarks as estimated from high frequency (intraday) data on both a global and US basis. We find that both the monthly and daily versions of VoV(λ) dominate the equivalent versions of Amihud and other cost-per-dollar-volume proxies on both a global and US basis. We also find that both the monthly and daily versions of VoV(%Spread) dominate the equivalent versions of other percent-cost proxies for US studies that cover pre-1993 years. In a case study, we find that our new VoV liquidity proxies yield different research inferences than the best previous liquidity proxies from the prior literature. The success of our invariance-based liquidity proxies across exchanges and over time supports the prediction of Kyle and Obizhaeva of a specific functional form for transaction costs across exchanges and over time.

Testing the LCAPM vs. Generalized Liquidity-Adjusted Asset Pricing: New Evidence and New Perspectives

The Liquidity-adjusted Capital Asset Pricing Model (LCAPM) includes two specific testable predictions: (1) the coefficient on expected liquidity cost equals average turnover and (2) the coefficient on market beta equals the coefficient on net liquidity risk beta. By contrast, generalized liquidity-adjusted asset pricing models allow liquidity characteristics and/or liquidity risk factors without such parameter restrictions. We empirically test these alternative theories. In doing so, we expand the range of evidence in multiple ways. First, we extend forward and backwards in time to cover 80 years. Second, we analyze NASDAQ-listed stocks as well as NYSE/AMEX-listed stocks. Third, we analyze four alternative liquidity measures: (1) the Corwin and Schultz proxy, (2) closing percent quoted spread, (3) the Amihud proxy, and (4) zeros. Fourth, we analyze the impact of adding Fama and French/Carhart risk factors to the model. Our main finding is that both of these specific predictions of LCAPM are robustly rejected. This outcome supports generalized liquidity-adjusted asset pricing. Finally, we ask can the original LCAPM results be replicated? We qualitatively replicate most tables, but obtain mixed results for two tables. We make publicly available our SAS code and the resulting data files for both our new empirical tests and our replication.First, we replicate the Liquidity-adjusted Capital Asset Pricing Model (LCAPM) tests of Acharya and Pedersen (2005) using their original methodology and covering both their original time period and a more recent period. We successfully qualitatively replicate the descriptive and the first-stage tables and figures, but are not successful in replicating the second-stage tables that perform cross-sectional tests. In the large majority of cases, our replication evidence fails to support that the main LCAPM predictions all hold simultaneously. Next, we extend tests of the LCAPM following the Lee (2011) methodology and expanding to: (1) three different time periods spanning 90 years, (2) add NASDAQ stocks, (3) use four alternative liquidity measures, and (4) add risk or characteristic factors. Our extension evidence always fails to support that the main predictions of the Lee two-beta LCAPM and of the four-beta LCAPM hold at the same time. Overall, we fail to support that liquidity risk matters in the specific functional form predicted by the LCAPM. However, we are silent on the more general question of whether liquidity risk matters in some different functional form. We make publicly available our SAS code.