Editing Abnormal return

In [[finance]], an '''abnormal return''' is the difference between the actual [[Rate of return|return]] of a [[Security (finance)|security]] and the [[expected return]]. Abnormal returns are sometimes triggered by "events." Events can include [[Mergers and acquisitions|merger]]s, [[dividend]] announcements, company earning announcements, interest rate increases, [[lawsuit]]s, etc. all of which can contribute to an abnormal return. Events in finance can typically be classified as information or occurrences that have not already been priced by the [[Financial market|market]].

==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.<ref>{{Cite web |url=http://economics.about.com/cs/economicsglossary/g/abnormal_return.htm |title=Definition of Abnormal Returns |access-date=2008-08-07 |publisher=About.com - Economics |archive-url=https://web.archive.org/web/20080917160612/http://economics.about.com/cs/economicsglossary/g/abnormal_return.htm |archive-date=17 September 2008 |url-status=dead |df=dmy-all }}</ref> 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 (finance)|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.

:<math>\textrm{Abnormal}\ \textrm{Return} = \textrm{Actual}\ \textrm{Return} - \textrm{Expected} \ \textrm{Return}</math>

== Calculation ==
The calculation formula for the abnormal returns is as follows:<ref name=":0">{{Cite book|url=https://books.google.com/books?id=cqJoDgAAQBAJ|title=Innovation and Market Value. The Case of Tourism Enterprises|last=Szutowski|first=Dawid|date=2016|publisher=Difin|isbn=9788380852471|pages=153|language=en}}</ref>

<math>AR_{it}=R_{it}-E(R_{it})</math>

where:

AR<sub>it</sub> - abnormal return for firm i on day t

R<sub>it</sub> - actual return for firm i on day t

E(R<sub>it</sub>) – expected return for firm i on day t

A common practice is to standardise the abnormal returns with the use of the following formula:<ref>{{Cite journal|last=McWilliams, A.|first=Siegel, D.|date=1997|title=Event Studies in Management Research: Theoretical and Empirical Issues|journal=Academy of Management Journal|volume=40|issue=3|pages=626–657|doi=10.2307/257056|jstor=257056}}</ref>

<math>SAR_{it}=AR_{it}/SD_{it}</math>

where:

SAR<sub>it</sub> - standardised abnormal returns

SD<sub>it</sub> – standard deviation of the abnormal returns

The SD<sub>it</sub> is calculated with the use of the following formula:<ref name=":0" />

<math>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}</math>

where:

S<sub>i</sub><sup>2</sup> – the residual variance for firm i,

R<sub>mt</sub> – the return on the stock market index on day t,

R<sub>m</sub> – 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.<ref>Trading-Glossary {{usurped|1=[https://web.archive.org/web/20030506064739/http://trading-glossary.com/c0580.asp Cumulative abnormal return (CAR)]}} Retrieved on July 18, 2007</ref> 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.<ref>{{cite journal | last1 = Brown | first1 = Stephen | last2 = Warner | first2 = Jerold | year = 1985 | title = Using daily stock returns: the case of event studies | journal = Journal of Financial Economics | volume = 14 | pages = 3–31 | doi=10.1016/0304-405x(85)90042-x}}</ref>

==See also==
* [[Market value]]
* [[Rate of return]]

==References==
{{Reflist}}

{{DEFAULTSORT:Abnormal Return}}
[[Category:Equity securities]]
[[Category:Stock market]]