Which Daily Price is Less Noisy?

Abstract

The daily efficient price is the price that wouldprevail if the market were frictionless. I show that volume-weighted average price (VWAP) provides a less noisy estimate for the unobservable efficient price as compared to the closing price. The variance of daily returns computed with VWAPs is smaller than that computed with closing prices. The difference between these two realized variances is economically significant. The volatility of log closing price change tends to understate the beta risk and Sharpe ratio. A higher noise level in the closing price leads to derivative prices that favor option and volatility-related swap writers. The daily closing price is often used as the end-of-day market value of a stock but despite its popularity, traders' transaction performance is not measured against it. Instead, practitioners use the volume-weighted average price (VWAP) as the benchmark. This price is the ratio of the dollar volume to the number of shares exchanged over a trading period. For a trader who buys a stock at several different prices and share volumes, the VWAP is the break-even price before transaction costs. To calculate the profit and loss in dollars before costs, investors use the VWAP rather than the closing price. Moreover, broker-dealers provide services to fund managers by implementing VWAP strategies to rebalance their clients' portfolios. At times, broker-dealers may buy directly from fund managers at an ex ante VWAP. The acquired shares are then disposed of by selling in the open markets with VWAP strategies (Madhavan, 2002). Since both the closing price and the VWAP are popular reference prices, in this article, I present a method for ascertaining which of them is relatively closer to the efficient price. The method is based on the intuition that if the random variable of a stochastic process is generally smaller than the random variable of another stochastic process with which it shares a common component, then the variance of the change in the smaller random variable will also tend to be smaller. The two random variables are the closing price and the VWAP, both of which are noisy estimates of the daily efficient price. If the noise level in the VWAP is lower (higher) than that of the closing price, then the realized variance of the log VWAP change will be smaller (larger) than the realized variance of the log closing price change. I provide strong evidence that the VWAP gives rise to a smaller realized variance. I show that its noise level is lower, which implies that the deviation from the efficient price is smaller. Thus, the VWAP is relatively closer to the efficient price than is the closing price. An important by-product of the method is that I can infer the realized variance of the log efficient price change under reasonable assumptions. Using a large sample ofNYSE common stocks, I find that the inferred realized volatility of the log efficient price change is smaller than that computed with I thank Aurobindo Ghosh, Jun Yu, and especially an anonymous referee for many insightful suggestions and comments to improve the paper I am also grateful to William G Christie (the Editor) for his suggestions in the review process, and Sandra Sizer for editorial assistance.