Beta

<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">Beta</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 target="_self" href="#Beta">Beta</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> <table border="0" cellpadding="0" style="border-collapse: collapse" bordercolor="#111111" width="310" align="right" id="table5"> <tr> <td align="right" width="9" height="14"></td> <td width="300" height="14"> <font size="2"> </font><font size="4"> </font></td> </tr> <tr> <td align="right" width="9"> </td> <td width="300"> <script type="text/javascript"></script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script>  </td> </tr> </table> <p><b><a name="Beta">Beta</a></b> is a <a href="../articles/risk_metric_and_risk_measure.htm">risk metric</a> employed primarily in the <a href="../articles/common_stock.htm">equity</a> markets. It measures the <a href="../articles/capital_asset_pricing_model.htm">systematic risk</a> of a single instrument or an entire portfolio. William Sharpe (<a target="_self" href="#Sharpe">1964</a>) first used the notion in his landmark paper introducing the <a href="../articles/capital_asset_pricing_model.htm">capital asset pricing model</a> (CAPM). The name "beta" was applied later.</p> <p>Beta describes the sensitivity of an instrument or portfolio to broad market movements. The stock market (represented by an index such as the S&P 500 or FT-100) is assigned a beta of 1.0. By comparison, a portfolio (or instrument) which has a beta of 0.5 will tend to participate in broad market moves, but only half as much as the market overall. A portfolio (or instrument) with a beta of 2.0 will tend to benefit or suffer from broad market moves twice as much as the market overall. </p> <p>The formula for beta is.</p> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" cellpadding="0" height="36" id="table6"> <tr> <td width="100%" align="center"> <img border="0" src="../formulas/beta_definition.gif" width="84" height="47"></td> <td width="5%" align="right">[1]</td> </tr> </table> <p>where</p> <p class="bullet"> <img border="0" src="../images/bullet.gif" width="20" height="10"><img border="0" src="../formulas/beta_covariance.gif" align="absbottom" width="75" height="15"> is the <a href="../articles/correlation.htm">covariance</a> between the portfolio (or instrument) <a href="../articles/return.htm">return</a> and the market return, and<p class="bullet"> <img border="0" src="../images/bullet.gif" width="20" height="10"><img border="0" src="../formulas/beta_variance.gif" align="absbottom" width="18" height="20"> is the <a href="../articles/standard_deviation.htm">variance</a> of the market's return (<a href="../articles/volatility.htm">volatility</a> squared).<table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="345" align="left" id="table7"> <tr> <td width="336" height="10"><font size="2"> </font></td> <td width="9" height="10"></td> </tr> <tr> <td width="336"> <script type="text/javascript"></script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script>  </td> <td width="9"> </td> </tr> </table> <p>Both quantities are calculated using <a href="../articles/return.htm">simple returns</a>. Beta is generally estimated from historical price <a href="../articles/time_series_stochastic_process.htm">time series</a>. For example, 60 trading days of simple returns might be used with sample estimators for <a href="../articles/correlation.htm">covariance</a> and <a href="../articles/standard_deviation.htm">variance</a>.</p> <p>It is possible to construct negative beta portfolios. Approaches include  </p> <p class="bullet"><img border="0" src="../images/bullet.gif" width="20" height="10">holding <a href="../articles/common_stock.htm">stocks</a> (such as gold mining stocks) that tend to move against the market, </p> <p class="bullet"><img border="0" src="../images/bullet.gif" width="20" height="10">shorting stocks, or </p> <p class="bullet"><img border="0" src="../images/bullet.gif" width="20" height="10">putting on suitable <a href="../articles/options_spread.htm">options spreads</a>. </p> <p>Beta is sometimes used as a metric of a portfolio's <a href="../articles/market_risk.htm">market risk</a>. This can be misleading because beta does not capture <a href="../articles/capital_asset_pricing_model.htm">specific risk</a>. Because of specific risk, a portfolio can have a low beta but still be highly volatile. Its price fluctuations will simply have a low <a href="../articles/correlation.htm">correlation</a> with those of the overall market. </p> <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%"> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/capital_asset_pricing_model.htm">capital asset pricing model</a>—a model for asset pricing and portfolio construction.<p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/capital_market_line.htm">capital market line</a>—a set of portfolios obtainable by leveraging or de-leveraging positions in a "super-efficient" portfolio.<p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/efficient_frontier.htm">efficient frontier</a>—a set of portfolios that each maximize expected return for a given level of risk.<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/market_risk.htm">market risk</a> </strong>Exposure to the uncertain market value of a portfolio.<p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/portfolio_theory.htm">portfolio theory</a>—a body of theory for how risk averse investors construct portfolios.</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_3.jpg" width="103" height="285"></td> <td bgcolor="#FFFFCC" width="99%">  <p class="ad_legend" style="margin-left: 0; margin-bottom:2"> <a target="_top" href="http://www.riskexpertise.com/link/advertising.htm"> <font color="#000000">Ads by Contingency Analysis</font></a></p> <p style="margin-top: 0; margin-bottom: 0"> <iframe src="http://servedbyadbutler.com/adserve/;ID=147917;size=336x265;setID=82436;type=iframe" style="margin: 0px; padding: 0px; border-width: 0px" width="336" height="265" frameborder="0" marginwidth="0" marginheight="0" scrolling="no" name="I1"> <![if lt IE 4]> <script src="http://servedbyadbutler.com/adserve/;ID=147917;size=336x265;setID=82436;type=js" type="text/javascript"> </script> <noscript> <a href="http://servedbyadbutler.com/go2/;ID=147917;size=336x265;setID=82436"> <img src="http://servedbyadbutler.com/adserve.ibs/;ID=147917;size=336x265;setID=82436;type=img" border="0" height="265" width="336" alt=""></a> </noscript><![endif]></iframe>   </td> </tr> <tr> <td height="30" valign="bottom" colspan="2"> <p class="header2_black">Related Books</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="table10"> <tr> <td width="100%"> <p class="explanatory_text">The following books discuss beta from different perspectives. Bernstein (<a target="_blank" href="http://www.riskbook.com/link/bernstein_p_(1993).htm">1993</a>) is a must-read history of finance during the 20th century. Body, Kane and Marcus (<a target="_blank" href="http://www.riskbook.com/link/bodie_kane_marcus_(2002).htm">2004</a>) is the standard university text on finance. For the practitioner's perspective, see either Grinold and Kahn (<a target="_blank" href="http://www.riskbook.com/link/grinold_and_kahn_(1999).htm">1999</a>) or Fabozzi and Markowitz (<a target="_blank" href="http://www.riskbook.com/link/fabozzi_and_markowitz.htm">2002</a>). All four books discuss beta. All are exceptional. </p> <table border="0" cellpadding="4" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table11"> <tr> <td width="100" align="left" valign="top"> <map name="FPMap492"> <area target="_blank" href="http://www.riskbook.com/link/bernstein_p_(1993).htm" shape="rect" coords="0, 0, 81, 124"> </map> <img border="0" src="../images/book_bernstein_peter_(1993)_125.jpg" usemap="#FPMap492" width="82" height="125"></td> <td align="left" valign="top"> <table border="0" cellpadding="1" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table12"> <tr> <td width="90%" colspan="3"> <p class="title"> <a target="_blank" href="http://www.riskbook.com/link/bernstein_p_(1993).htm"> Capital Ideas</a></td> </tr> <tr> <td colspan="3"> <p class="author"><b>Peter L. Bernstein</b></td> </tr> <tr> <td width="10%"> <map name="FPMap458"> <area target="_blank" coords="2, 1, 89, 15" shape="rect" href="http://www.riskbook.com/main/ratings.htm"> </map> <img border="0" src="../images/star_6.gif" usemap="#FPMap458" width="90" height="16"></td> <td width="10%" class="author">quality</td> <td width="70%"> <p class="author"> </td> </tr> <tr> <td width="10%"> <map name="FPMap491"> <area target="_blank" href="http://www.riskbook.com/main/ratings.htm" shape="rect" coords="0, 0, 89, 15"> </map> <img border="0" src="../images/tech_0.gif" usemap="#FPMap491" width="90" height="16"></td> <td width="10%" class="author">technical</td> <td width="70%">  </td> </tr> <tr> <td width="10%"> <p class="author">1993</td> <td width="10%"> </td> <td width="70%"> <p align="center"><map name="FPMap368"> <area target="_blank" coords="0, 0, 145, 19" shape="rect" href="http://www.riskbook.com/link/bernstein_p_(1993).htm"> </map> <img border="0" src="../images/pointer_review.gif" usemap="#FPMap368" width="146" height="20"></td> </tr> </table> </td> </tr> </table> <table border="0" cellpadding="4" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table13"> <tr> <td width="100" align="left" valign="top"> <map name="FPMap493"> <area target="_blank" href="http://www.riskbook.com/link/bodie_kane_marcus_(2002).htm" shape="rect" coords="0, 0, 98, 124"> </map> <img border="0" src="../images/book_bodie_kane_marcus_(2004)_125.jpg" usemap="#FPMap493" width="99" height="125"></td> <td align="left" valign="top"> <table border="0" cellpadding="1" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table14"> <tr> <td width="90%" colspan="3"> <p class="title"> <a target="_blank" href="http://www.riskbook.com/link/bodie_kane_marcus_(2002).htm"> Investments</a></td> </tr> <tr> <td colspan="3"> <p class="author"><b>Zvi Bodie, Alex Kane, Alan J. Marcus</b></td> </tr> <tr> <td width="10%"> <map name="FPMap288"> <area target="_blank" coords="2, 1, 89, 15" shape="rect" href="http://www.riskbook.com/main/ratings.htm"> </map> <img border="0" src="../images/star_6.gif" usemap="#FPMap288" width="90" height="16"></td> <td width="10%" class="author">quality</td> <td width="70%"> <p class="author"> </td> </tr> <tr> <td width="10%"><map name="FPMap457"> <area target="_blank" href="http://www.riskbook.com/main/ratings.htm" shape="rect" coords="0, 0, 89, 15"> </map> <img border="0" src="../images/tech_2.gif" usemap="#FPMap457" width="90" height="16"></td> <td width="10%" class="author">technical</td> <td width="70%">  </td> </tr> <tr> <td width="10%"> <p class="author">2004</td> <td width="10%"> </td> <td width="70%"> <p align="center"><map name="FPMap367"> <area target="_blank" coords="0, 0, 145, 19" shape="rect" href="http://www.riskbook.com/link/bodie_kane_marcus_(2002).htm"> </map> <img border="0" src="../images/pointer_review.gif" usemap="#FPMap367" width="146" height="20"></td> </tr> </table> </td> </tr> </table> <table border="0" cellpadding="4" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table15"> <tr> <td width="100" align="left" valign="top"> <map name="FPMap494"> <area target="_blank" href="http://www.riskbook.com/link/grinold_and_kahn_(1999).htm" shape="rect" coords="0, 0, 82, 124"> </map> <img border="0" src="../images/book_grinold_and_kahn_(1999).gif" usemap="#FPMap494" width="83" height="125"></td> <td align="left" valign="top"> <table border="0" cellpadding="1" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table16"> <tr> <td width="90%" colspan="3"> <p class="title"> <a target="_blank" href="http://www.riskbook.com/link/grinold_and_kahn_(1999).htm"> Active Portfolio Management</a></td> </tr> <tr> <td colspan="3"> <p class="author"><b>Richard C. Grinold, Ronald N. Kahn</b></td> </tr> <tr> <td width="10%"><map name="FPMap373"> <area target="_blank" href="http://www.riskbook.com/main/ratings.htm" shape="rect" coords="0, 0, 89, 15"> </map> <img border="0" src="../images/star_6.gif" usemap="#FPMap373" width="90" height="16"></td> <td width="10%" class="author">quality</td> <td width="70%"> <p class="author"> </td> </tr> <tr> <td width="10%"> <span style="font-family: Times New Roman; letter-spacing: -0.2pt"> <map name="FPMap410"> <area target="_blank" href="http://www.riskbook.com/main/ratings.htm" shape="rect" coords="1, 2, 89, 15"> </map> <img border="0" src="../images/tech_3.gif" usemap="#FPMap410" width="90" height="16"></span></td> <td width="10%" class="author">technical</td> <td width="70%">  </td> </tr> <tr> <td width="10%"> <p class="author">1999</td> <td width="10%"> </td> <td width="70%"> <p align="center"><map name="FPMap366"> <area target="_blank" coords="0, 0, 145, 19" shape="rect" href="http://www.riskbook.com/link/grinold_and_kahn_(1999).htm"> </map> <img border="0" src="../images/pointer_review.gif" usemap="#FPMap366" width="146" height="20"></td> </tr> </table> </td> </tr> </table> <span style="font-family: Times New Roman; letter-spacing: -0.2pt"> <table border="0" cellpadding="4" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table17"> <tr> <td width="100" align="left" valign="top"> <map name="FPMap571"> <area target="_blank" href="http://www.riskbook.com/link/fabozzi_and_markowitz.htm" shape="rect" coords="0, 0, 82, 124"> </map> <img border="0" src="../images/book_fabozzi_markowitz_(2002)_125.gif" usemap="#FPMap571" width="83" height="125"></td> <td align="left" valign="top"> <table border="0" cellpadding="1" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table18"> <tr> <td width="90%" colspan="3"> <p class="title"> <a target="_blank" href="http://www.riskbook.com/link/fabozzi_and_markowitz.htm">Theory and Practice of Investment Management</a></td> </tr> </span> <tr> <td colspan="3"> <p class="author"><b>Frank J. Fabozzi and Harry M. Markowitz</b></td> </tr> <span style="font-family: Times New Roman; letter-spacing: -0.2pt"> <tr> <td width="10%"> <map name="FPMap564"> <area target="_blank" coords="2, 1, 89, 15" shape="rect" href="http://www.riskbook.com/main/ratings.htm"> </map> <img border="0" src="../images/star_6.gif" usemap="#FPMap564" width="90" height="16"></td> <td width="10%" class="author">quality</td> <td width="70%"> <p class="author"> </td> </tr> <tr> <td width="10%"><map name="FPMap565"> <area target="_blank" href="http://www.riskbook.com/main/ratings.htm" shape="rect" coords="0, 0, 89, 15"> </map> <img border="0" src="../images/tech_2.gif" usemap="#FPMap565" width="90" height="16"></td> <td width="10%" class="author">technical</td> <td width="70%">  </td> </tr> <tr> <td width="10%"> <p class="author">2002</td> <td width="10%"> </td> <td width="70%"> <p align="center"><map name="FPMap572"> <area target="_blank" coords="0, 0, 145, 19" shape="rect" href="http://www.riskbook.com/link/fabozzi_and_markowitz.htm"> </map> <img border="0" src="../images/pointer_review.gif" usemap="#FPMap572" width="146" height="20"></td> </tr> </table> </td> </tr> </table> </span> </td> </tr> </table> </td> </tr> <tr> <td height="30" valign="bottom" colspan="2"> <p class="header2_black">Cited Papers</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="table19"> <tr> <td width="100%"> <p class="explanatory_text"> <img border="0" src="../images/bullet_paper_glossary.gif" width="21" height="15"><a name="Sharpe">Sharpe</a>, William F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk, <i>Journal of Finance</i>, 19 (3), 425-442.</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 height="30" valign="bottom" colspan="2"> <p class="header2_black">Related Forum Discussions</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="table20"> <tr> <td width="100%"> <p class="explanatory_text"> <img border="0" src="../images/bullet_bullhorn_narrow.gif" align="left" width="27" height="22"><a target="_top" href="http://www.contingencyanalysis.com/archive/link_thread/99-3/000000df.htm">Measuring Beta</a> <i>03 Jun 1999</i><br> References to the scholarly literature on beta.<p class="explanatory_text"> <img border="0" src="../images/bullet_bullhorn_narrow.gif" align="left" width="27" height="22"><a target="_top" href="http://www.contingencyanalysis.com/archive/link_thread/99-2/00000036.htm">Does Beta work for bonds?</a> <i>19 Apr 1999</i><br> Applicability of beta to bonds.</td> </tr> </table> </td> </tr> <tr> <td bgcolor="#FFFFCC" colspan="2"> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" cellpadding="6" id="table21"> <tr> <td width="100%" bgcolor="#FFFFFF">  <p align="center"><map name="FPMap0_I1"> <area target="_top" href="http://www.riskglossary.com" shape="rect" coords="0, 0, 164, 102"> </map><img border="0" src="../images/logo.jpg" usemap="#FPMap0_I1" width="165" height="103"></p> <p align="center"><span class="verdana10"> <a href="http://www.riskglossary.com/main/disclaimer.htm">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, 1996 - current</p> <p align="center"><map name="FPMap1_I1"> <area target="_top" href="http://www.contingencyanalysis.com" shape="rect" coords="0, 0, 240, 88"> </map><img border="0" src="../images/logo_glossary_white.gif" usemap="#FPMap1_I1" width="241" height="89"></p> </td> </tr> </table> </td> </tr> </table> </td> <td>  </td> </tr> </table> </div>   </body>