Measuring stock returns in the presence of transaction uncertainty

Abstract

The asset pricing literature models uncertainty in assets' payoffs, but typically assumes that any quantity of an asset can be traded at observed prices. For an investor observing a price quote, there is uncertainty about the effective transaction price for an order of a given size. This transaction uncertainty encompasses uncertainty about depth at quoted prices and uncertainty about the slope of the price schedule for transactions executing at prices inferior to the quotes. For an order in excess of quoted depth, the difference between a transaction price and that quoted is referred to as price impact. In the presence of transaction uncertainty, realized investment return has a random component, due to price impact, that is distinct from the effects of uncertainty about firm performance. CRSP closing-price returns do not account for the transaction uncertainty component of returns. CRSP returns are shown to be an inadequate proxy for monthly returns with realistic transaction uncertainty. On a monthly horizon, transaction uncertainty significantly affects measurement of mean returns, the variance/covariance matrix of returns, and the covariance of returns with risk factors. A more appropriate way to measure returns is proposed, along with a practical means for correcting historical data sets. Evidence is presented that transaction uncertainty risk is systematic and examples of the impact on asset pricing tests are given. In particular, two studies of Amihud and Mendelson (AM: JFE 1986 and JF 1989) are revisited. AM model returns that correctly reflect expected liquidity costs. They predict cross-sectional differences in returns, induced by differences in liquidity cost and in investor holding period. Data limitations forced AM to use CRSP returns and average annual bid/ask spread in their tests. CRSP returns are shown to induce a spurious positive return/spread relation that mimics the investment horizon clientele effect predicted by AM. Better proxies for liquidity costs and for AM's returns can now be constructed using fitted values of spread and price impact. Tests using these alternate proxies obtain strikingly different results.