Brown, Stephen J., and Jerold B. Warner, 1985, “Using Daily Stock Returns: The Case of Event Studies,” *Journal of Financial Economics 14 (1995)*, 3-31.

**Purpose:** To observe the statistical properties of daily stock data, and to explain what effect these properties can have on firm-specific event studies.

**Motivation:** Event studies are commonly undertaken using daily data. This paper examines issues with daily data and whether anything ought to be done to address them.

**Findings:** There are several potential issues with using daily data:

- The central limit theorem suggests the cross section of returns should be normally distributed, but the evidence shows a fat-tailed distribution
- A security’s return and the return on a market index are not always measured over identical intervals
- This non-synchronous trading makes the OLS estimate of β biased and inconsistent.
- This means observations can be serially dependent, complicating estimates of variance
- This can also affect the calculation of the mean excess return

- Estimating variance is further complicated by cross-sectional dependence between observations, and by evidence that variance increases in the days surrounding certain events like earnings announcements
- Autocorrelation between returns is small but statistically significant

**Data/Methods:** Samples of varying sample size are randomly selected from a pool of securities, and “event” dates are randomly assigned to the securities. Expected returns for each security are estimated using the security returns over the period (-244,-6), and excess returns are calculated on day 0 (the event date). All data and event dates are for the period 1962-1979. Parameter distributions for different sample sizes are examined.

Abnormal returns are “imposed” by adding a constant (e.g. 0.02 for 2%) to actual security returns on their event dates. The frequency that the null hypothesis of no abnormal return is rejected varies depending on sample size and on whether and how large an abnormal return has been imposed. This technique analyzes the power of various estimation methods.

**Conclusions:**

- Methods using the OLS market model are good enough in most cases
- The potential issues with daily data, though, are sometimes worth confronting
- When the variance increases around an event date
- When autocorrelation is especially high

- Daily excess returns are non-normal, but mean excess returns converge to normality as sample size increases
- Non-OLS methods do not improve the frequency of detecting abnormal returns under non-synchronous trading
- Tests that assume cross-sectional dependence are less powerful and no better specified