# Trading Volume Event Study

Besides return event studies, there are also event studies investigating whether the trading volumes of assets display statistically significant anomalies. These volume event studies apply the general principles of the event study methodology to time series of trading volumes. One major application of volume event studies is the investigation of insider trading preceding M&A announcements. In the US, volume event studies are increasingly used in security fraud litigation cases.

**Measures of Abnormal Trading Volume**

The main difference between volume and return event studies is that instead of returns, the log-transformed relative volume per firm is used (Campell and Wasley, 1996), namely

$$V_{it} = \log{\left(\frac{n_{it} \cdot 100}{S_{it}} + 0.000255\right)},\label{eq:log}$$

where $n_{it}$ is the number of shares traded for firm $i$ on day $t$ and $S_{it}$ is the outstanding share of firm $i$ on the trading day. The constant $.000255$ in the above equation is added to avoid a log transformation of zero in the case of zero trading volume on a given day.

The **mean-adjusted abnormal trading volume** then is:

$$v_{it} = V_{it} - \overline{V_{i}}$$

with $$\overline{V_{i}}=\frac{1}{T}\sum\limits_{t=f}^{l}V_{it}$$

T represents the number of days in the estimation period, f is the first day of the estimation period, and l is the last.

Another expected volume model used is the market model. Since it comes with more challenging data requirements, we set the mean-adjusted model as default in AVC. The **market model abnormal trading volume** is:

$$v_{it} = V_{it} - (\alpha_{i} + \beta_{i}V_{mt})$$

with

$$V_{mt}=\frac{1}{N}\sum\limits_{i=1}^{N}V_{it}$$

Of this OLS estimated market model, an EGLS (estimated generalized least squares) variant exists.

**Bibliography**

Campbell, CJ. and Wasley, CE. 'Measuring abnormal daily trading volume for samples of NYSE/ASE and NASDAQ securities using parametric and nonparametric test statistics'. Review of Quantitative Finance and Accounting, 6.3 (1996): 309-326