Mean Reversion

<body onLoad="MM_checkPlugin('Shockwave Flash','','http://www.riskglossary.com/default_nofl.htm',false);return document.MM_returnValue" stylesrc="../_private/template.htm" bgcolor="#FFFFFF" link="#669933" vlink="#000000" alink="#000000"> <div align="left"> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table1"> <tr> <td width="740"> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" height="37" id="table2"> <tr> <td height="35" width="100%"> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" cellpadding="0" id="table3"> <tr> <td width="100%" align="left" valign="top"> <p class="header_gold">Mean Reversion</td> <td width="45" align="right" valign="bottom"> <map name="FPMap6"> <area href="http://www.contingencyanalysis.com" shape="rect" coords="1, 0, 44, 11" target="_top"> </map> <img border="0" src="../images/home.gif" usemap="#FPMap6" width="45" height="12"></td> </tr> </table> </td> </tr> <tr> <td width="100%" bgcolor="#CC9966" height="2"> <img border="0" src="../images/blank_2x2.gif" width="2" height="2"></td> </tr> <tr> <td width="0%" valign="top" bgcolor="#FFFFCC"> <table border="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" cellpadding="0" cellspacing="1" id="table4"> <tr> <td width="0%" align="left" valign="top"> <p class="header2_black">Explained:<br> <img border="0" src="../images/blank_1x100.gif" width="100" height="1"></td> <td width="0%" align="left" valign="top"><p class="word_list"> <a href="#Mean reversion">mean reversion</a><br> <img border="0" src="../images/blank_1x160.gif" width="160" height="1"></td> <td width="100%" align="left" valign="top"><p class="word_list"> <br> <img border="0" src="../images/blank_1x160.gif" width="160" height="1"></td> </tr> </table> </td> </tr> </table> <p><b><a name="Mean reversion">Mean reversion</a></b> is a tendency for a <a href="../articles/time_series_stochastic_process.htm">stochastic process</a> to remain near, or tend to return over time to a long-run <a href="../articles/mean.htm">average</a> value. For example, interest rates and <a href="../articles/volatility.htm">implied volatilities</a> tend to exhibit mean reversion. Exchange rates and <a href="../articles/common_stock.htm">stock</a> prices tend not to. Stock market <a href="../articles/return.htm">returns</a>, however, do tend to exhibit mean reversion. Exhibit 1 provides an intuitive illustration of the difference between mean reverting and non-mean reverting behavior. </p> <div align="center"> <center> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="300" cellpadding="0" id="table5"> <tr> <td> <p class="exhibit_header"><span class="exhibit_header">Mean Reversion</span><br> <span class="exhibit_subheader">Exhibit 1</span></td> </tr> <tr> <td bgcolor="#CC9966" height="2"> <img border="0" src="../images/blank_2x2.gif" width="2" height="2"></td> </tr> <tr> <td> <img border="0" src="../images/ex1_mean_reversion.gif" width="256" height="210"></td> </tr> <tr> <td> <p class="exhibit_legend">Mean reversion is a tendency for a stochastic process to remain near, or return over time to a long-run average.</td> </tr> </table> </center> </div> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table6"> <tr> <td width="50%" height="12"> </td> <td width="345" height="12"></td> </tr> <tr> <td width="50%" valign="top">Mean reversion is a model. We choose either to, or not to, model any given quantity with a mean reverting stochastic process. In some cases, the decision is obvious, as in the examples cited above. Other cases are more subtle. Looking at a <a href="../articles/time_series_stochastic_process.htm">time series</a> over a few weeks—or even a few years—may be misleading. Mean reversion may only reveal itself over very long horizons. Usually, a decision to model a quantity with a mean reverting stochastic process is based both on empirical observation of that quantity over time, as well as some theoretical argument as to why it should be mean reverting.<p>Can you think of a theoretical argument why interest rates or implied volatilities should be mean reverting but exchange rates or stock prices should not be?</p> </td> <td width="345" valign="top"> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="345" align="right" id="table7"> <tr> <td align="right" width="9"> </td> <td width="336"> <script type="text/javascript"></script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script>  </td> </tr> </table> </td> </tr> </table> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table8"> <tr> <td height="30" valign="bottom" colspan="2"> <p class="header2_black">Related Internal Links</td> </tr> <tr> <td colspan="2" bgcolor="#CC9966" height="2"> <img border="0" src="../images/blank_2x2.gif" width="2" height="2"></td> </tr> <tr> <td bgcolor="#FFFFCC" colspan="2"> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" cellpadding="6" id="table9"> <tr> <td width="100%"> <span style="font-family: Times New Roman; letter-spacing: -0.2pt"> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/heteroskedasticity.htm">heteroskedasticity</a> A condition where a stochastic process has non-constant second moments.</p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/martingale.htm">martingale</a> A type of stochastic process that has zero drift.<p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><strong style="font-weight: 400"><a href="../articles/time_series_stochastic_process.htm">time series and stochastic processes</a> <i>An introductory article.</i></strong></p> </span> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><strong style="font-weight: 400"><a href="../articles/volatility.htm">volatility</a> A metric of  variability in a stochastic process.</strong></p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/volatility_skew.htm">volatility skew</a> A dependence of implied volatilities upon options' strikes</td> </tr> </table> </td> </tr> <tr> <td height="30" valign="bottom" colspan="2"> <p class="header2_black">Sponsored Links</td> </tr> <tr> <td colspan="2" bgcolor="#CC9966" height="2"> <img border="0" src="../images/blank_2x2.gif" width="2" height="2"></td> </tr> <tr> <td bgcolor="#FFFFCC" width="75"> <img border="0" src="../images/ad_side_banner_1.jpg" width="103" height="285"></td> <td bgcolor="#FFFFCC" width="99%"> <script type="text/javascript"></script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script>  </td> </tr> <tr> <td bgcolor="#FFFFCC" colspan="2"> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" cellpadding="6" id="table10"> <tr> <td width="100%" bgcolor="#FFFFFF"> <p align="center"><map name="FPMap365"> <area target="_top" href="http://www.riskglossary.com" shape="rect" coords="0, 0, 164, 102"> </map><img border="0" src="../images/logo.jpg" usemap="#FPMap365" width="165" height="103"></p> <p align="center"><span class="verdana10"> <a href="http://www.riskglossary.com/main/disclaimer.htm" target="_self"> Disclaimer</a></span></p> <p align="center">website: <span class="verdana10"> <a target="_top" href="http://www.contingencyanalysis.com"> http://www.contingencyanalysis.com</a></span><br> glossary direct link: <span class="verdana10"> <a target="_top" href="http://www.riskglossary.com"> http://www.riskglossary.com</a></span><br> copyright © Contingency Analysis, 2004</td> </tr> </table> </td> </tr> </table> </td> <td>  </td> </tr> </table> </div> </body>