Abnormal return

Stock market

In stock market trading, abnormal returns are the differences between a single stock or portfolio's performance and the expected return over a set period of time. Usually a broad index, such as the S&P 500 or a national index like the Nikkei 225, is used as a benchmark to determine the expected return. For example, if a stock increased by 5% because of some news that affected the stock price, but the average market only increased by 3% and the stock has a beta of 1, then the abnormal return was 2% (5% - 3% = 2%). If the market average performs better (after adjusting for beta) than the individual stock, then the abnormal return will be negative.

:\textrm{Abnormal}\ \textrm{Return} = \textrm{Actual}\ \textrm{Return} - \textrm{Expected} \ \textrm{Return}

Calculation

The calculation formula for the abnormal returns is as follows:

AR_{it}=R_{it}-E(R_{it})

where:

ARit - abnormal return for firm i on day t

Rit - actual return for firm i on day t

E(Rit) – expected return for firm i on day t

A common practice is to standardise the abnormal returns with the use of the following formula:

SAR_{it}=AR_{it}/SD_{it}

where:

SARit - standardised abnormal returns

SDit – standard deviation of the abnormal returns

The SDit is calculated with the use of the following formula:

SD_{it}=[S_i^2*(1+\frac{1}{T}*\frac{(R_{mt}-R_m)^2}{\textstyle \sum_{t=1}^T \displaystyle(R_{mt}-R_m)^2})]^{0,5}

where:

Si2 – the residual variance for firm i,

Rmt – the return on the stock market index on day t,

Rm – the average return from the market portfolio in the estimation period,

T – the numbers of days in the estimation period.

Cumulative abnormal return

Cumulative abnormal return, or CAR, is the sum of all abnormal returns. Cumulative Abnormal Returns are usually calculated over small windows, often only days. This is because evidence has shown that compounding daily abnormal returns can create bias in the results.

References

References

1. "Definition of Abnormal Returns". About.com - Economics.
2. Szutowski, Dawid. (2016). "Innovation and Market Value. The Case of Tourism Enterprises". Difin.
3. McWilliams, A., Siegel, D.. (1997). "Event Studies in Management Research: Theoretical and Empirical Issues". Academy of Management Journal.
4. Trading-Glossary {{usurped
5. (1985). "Using daily stock returns: the case of event studies". Journal of Financial Economics.