Capital Market Line

<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">Capital Market Line</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="#capital market line">capital market line</a><p class="word_list"> <a href="#separation theorem">separation theorem</a><p class="word_list"> <a href="#super efficient portfolio">super-efficient portfolio</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 class="body">James Tobin (<a href="#Tobin">1958</a>) added the notion of <a href="../articles/leverage.htm">leverage</a> to <a href="../articles/portfolio_theory.htm">portfolio theory</a> by incorporating into the analysis an asset which pays a <a href="../articles_old/glossaryriskfreerate.htm"> risk-free rate</a>. By combining a risk-free asset with a portfolio on the <a href="../articles/efficient_frontier.htm">efficient frontier</a>, it is possible to construct portfolios whose <a href="../articles/risk.htm">risk</a>-<a href="../articles/return.htm">return</a> profiles are superior to those of portfolios on the efficient frontier. Consider Exhibit 1:</p> <div align="center"> <center> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="350" cellpadding="0" id="table5"> <tr> <td> <p class="exhibit_header"><span class="exhibit_header">Capital Market Line</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_capital_market_line.gif" width="270" height="170"></td> </tr> <tr> <td> <p class="exhibit_legend">The capital market line is the tangent line to the efficient frontier that passes through the risk-free rate on the expected return axis.</td> </tr> </table> </center> </div> <table border="0" cellpadding="0" style="border-collapse: collapse" bordercolor="#111111" width="310" align="right" id="table6"> <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 class="body">In Exhibit 1, the risk-free rate is assumed to be 5%, and a tangent line—called the <b><a name="capital market line">capital market line</a></b>—has been drawn to the efficient frontier passing through the risk-free rate. The point of tangency corresponds to a portfolio on the efficient frontier. That portfolio is called the <b> <a name="super efficient portfolio">super-efficient portfolio</a></b>.</p> <p class="body">Using the risk-free asset, investors who hold the super-efficient portfolio may: </p> <p class="bullet_line_space"><img border="0" src="../images/bullet.gif" width="20" height="10">leverage their position by <a href="../articles/short_sale.htm">shorting</a> the risk-free asset and investing the proceeds in additional holdings in the super-efficient portfolio, or <p class="bullet_line_space"><img border="0" src="../images/bullet.gif" width="20" height="10">de-leverage their position by selling some of their holdings in the super-efficient portfolio and investing the proceeds in the risk-free asset. <p class="body">The resulting portfolios have risk-reward profiles which all fall on the capital market line. Accordingly, portfolios which combine the risk free asset with the super-efficient portfolio are superior from a risk-reward standpoint to the portfolios on the efficient frontier. </p> <p class="body">Tobin concluded that portfolio construction should be a two-step process. First, investors should determine the super-efficient portfolio. This should comprise the risky portion of their portfolio. Next, they should leverage or de-leverage the super-efficient portfolio to achieve whatever level of risk they desire. Significantly, the composition of the super-efficient portfolio is independent of the investor's appetite for risk. The two decisions:</p> <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> <p class="body"><img border="0" src="../images/bullet.gif" width="20" height="10">the composition of the risky portion of the investor's portfolio, and<p class="body"> <img border="0" src="../images/bullet.gif" width="20" height="10">the amount of leverage to use,<p class="body">are entirely independent of one another. One decision has no effect on the other. This is called Tobin's <b> <a name="separation theorem">separation theorem</a></b>.</p> <p class="body">William Sharpe's (<a href="#Sharpe">1964</a>) <a href="../articles/capital_asset_pricing_model.htm">capital asset pricing model</a> (CAPM) demonstrates that, given strong simplifying assumptions, the super-efficient portfolio must be the <a href="../articles/market_portfolio.htm">market portfolio</a>. From this standpoint, all investors should hold the market portfolio leveraged or de-leveraged to achieve whatever level of risk they desire.</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/beta.htm">beta</a>—a measure of the systematic risk of a portfolio.<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/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"><a href="../articles/leverage.htm">leverage</a> Debt financing or anything that can similarly magnify the risk and reward of an investment.<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_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 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 offer different perspectives on portfolio theory and the capital market line. 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 Fabozzi and Markowitz (<a target="_blank" href="http://www.riskbook.com/link/fabozzi_and_markowitz.htm">2002</a>). All three books 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="FPMap559"> <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="#FPMap559" 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="FPMap560"> <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="#FPMap560" 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="FPMap561"> <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="#FPMap561" 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="FPMap562"> <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="#FPMap562" 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="FPMap563"> <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="#FPMap563" 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="FPMap572"> <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="#FPMap572" 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="FPMap573"> <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="#FPMap573" 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="FPMap566"> <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="#FPMap566" 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="table15"> <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="table16"> <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%"> <img border="0" src="../images/star_6.gif" usemap="#FPMap572" width="90" height="16"></td> <td width="10%" class="author">quality</td> <td width="70%"> <p class="author"> </td> </tr> <tr> <td width="10%"> <img border="0" src="../images/tech_2.gif" usemap="#FPMap573" 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="FPMap366"> <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="#FPMap366" 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="table17"> <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.<p class="explanatory_text"> <img border="0" src="../images/bullet_paper_glossary.gif" width="21" height="15"><a name="Tobin">Tobin</a>, James (1958). Liquidity preference as behavior towards risk, <i> The Review of Economic Studies</i>, 25, 65-86.</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 bgcolor="#FFFFCC" colspan="2"> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" cellpadding="6" id="table18"> <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>