Sharpe Ratio, Treynor Ratio

<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="table7"> <tr> <td width="740"> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" height="37" id="table8"> <tr> <td height="35" width="100%"> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" cellpadding="0" id="table9"> <tr> <td width="100%" align="left" valign="top"> <p class="header_gold">Sharpe Ratio, Treynor Ratio</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="table10"> <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="#Sharpe_ratio">Sharpe ratio</a><p class="word_list"> <a href="#Treynor">Treynor ratio</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="table11"> <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">During the 1960s, <a href="../articles/efficient_market_hypothesis.htm">Eugene Fama</a> developed his <a href="../articles/efficient_market_hypothesis.htm">efficient market hypothesis</a> and <a href="../articles/capital_asset_pricing_model.htm">William Sharpe</a> published his <a href="../articles/capital_asset_pricing_model.htm">capital asset pricing model</a> (CAPM). The latter proved important for empirically confirming the former. </p> <p class="body">CAPM states that assets' <a href="../articles/mean.htm">expected</a> <a href="../articles/return.htm">returns</a> depend on their <a href="../articles/capital_asset_pricing_model.htm">systematic risk</a>. Those with greater systematic risk have higher expected returns than those with lower systematic risk. This means an investment manager can boost his returns by merely increasing the systematic risk (<a href="../articles/beta.htm">beta</a>) of his portfolio—which has nothing to do with his ability to time the market or pick stocks. Early studies of investment manager performance—including Cowles (<a href="#Cowles">1933</a>), Friend et al (<a href="#Friend">1962</a>) and Horowitz (<a href="#Horowitz">1963</a>)—were flawed because they assessed managers' returns without any adjustment for <a href="../articles/risk.htm">risk</a>.</p> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="165" align="left" id="table12"> <tr> <td width="160"> <script type="text/javascript"></script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script> </td> <td width="11"> </td> </tr> </table> <p class="body">Not only did CAPM highlight this problem, it provided a framework for assessing—and hence adjusting returns for—a portfolio's risk. Between 1965 and 1970, a number of papers were published on investment managers' performance, and these suggested various <a href="../articles/RAPM.htm">risk-adjusted performance metrics</a> (RAPM) based on CAPM. Jack Treynor (<a href="#Treynor">1965</a>) proposed that managers' risk-adjusted performance be measured as</p> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" cellpadding="0" height="36" id="table13"> <tr> <td width="100%" align="center"> <p style="margin-top: 10px; margin-bottom: 10px"> <img border="0" src="../formulas/sharpe_ratio_[1].gif" width="208" height="45"></td> <td width="5%" align="right">[1]</td> </tr> </table> <p class="body">Sharpe (<a href="#Sharpe">1966</a>) proposed a <a href="../articles/risk_metric_and_risk_measure.htm">metric</a> with the same numerator but a different denominator. He felt it appropriate to penalize a portfolio manager for not fully <a href="../articles/hedging_and_diversification.htm">diversifying</a>, so his metric was</p> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" cellpadding="0" height="36" id="table14"> <tr> <td width="100%" align="center"> <p style="margin-top: 10px; margin-bottom: 10px"> <img border="0" src="../formulas/sharpe_ratio_[2].gif" width="207" height="44"></td> <td width="5%" align="right">[2]</td> </tr> </table> <p class="body">where the denominator is generally calculated as the <a href="../articles/standard_deviation.htm">standard deviation</a> of <a href="../articles/return.htm">simple return</a>.</p> <p class="body">Formulas [1] and [2] have come to be known, respectively, as the <b><a name="Treynor_ratio">Treynor ratio</a></b> and the <b><a name="Sharpe_ratio">Sharpe ratio</a></b>. Both have been widely adopted by practitioners for performance assessments. The Sharpe ratio is the more popular of the two. </p> <p class="body" style="margin-bottom: 32px">In 1968, Michael Jensen published a RAPM that proved even more popular than the Sharpe ratio. Today, it is more than a RAPM. For proponents of active portfolio management, it symbolizes their belief in the ability of active managers to outperform the overall market. Its name is Jensen's alpha.</p> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table15"> <tr> <td height="30" valign="bottom" colspan="2"> <p class="header2_black"><a name="Exercises">Exercises</a></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="table16"> <tr> <td width="100%"> <p class="body" style="margin-left: 10; margin-top: 8; margin-bottom: 8"> <img border="0" src="../images/bullet_exercise.gif" align="absbottom" width="19" height="17">Is it possible for the Treynor ratio to ever take on a negative value? If so, how might we interpret such a result?. [<a href="../solutions/sharpe_ratio_1.htm">solution</a>]<p class="body" style="margin-left: 10; margin-top: 8; margin-bottom: 8"> <img border="0" src="../images/bullet_exercise.gif" align="absbottom" width="19" height="17">Is it possible for the Sharpe ratio to ever take on a negative value? If so, how might we interpret such a result?. [<a href="../solutions/sharpe_ratio_2.htm">solution</a>]</td> </tr> </table> </td> </tr> <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="table19"> <tr> <td width="100%"> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><span class="verdana10"><strong style="font-weight: 400"><a href="../articles/capital_asset_pricing_model.htm">c</a></strong><a href="../articles/capital_asset_pricing_model.htm"><strong style="font-weight: 400">apital asset pricing model</strong></a></span><strong style="font-weight: 400"> A model for valuing financial assets based upon their systematic risk.</strong><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/portfolio_theory.htm">portfolio theory</a> A body of theory relating to how investors optimize portfolio selections.</strong><p align="left" class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><strong style="font-weight: 400"><a href="../articles/RAPM.htm">risk-adjusted performance metric</a> Any metric of performance that balances reward against risk.</strong></p></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%"> <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">References</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_paper_glossary.gif" width="21" height="15"><a name="Cowles">Cowles</a>, Alfred 3rd (1933). Can stock market forecasters forecast? <i> Econometrica</i>, 1 (3), 309-324.<p class="explanatory_text"> <img border="0" src="../images/bullet_paper_glossary.gif" width="21" height="15"><a name="Friend">Friend</a>, Irwin, F. E. Brown, Edward S. Herman, and Douglas Vickers (1962). <i>A Study of Mutual Funds: Investment Policy and Investment Company Performance</i>, Report to the Committee on Interstate and Foreign Commerce, House Report no. 2274, 87th Congress, Second Session.<p class="explanatory_text"> <img border="0" src="../images/bullet_paper_glossary.gif" width="21" height="15"><a name="Horowitz">Horowitz</a>, Ira (1963). The varying (?) quality of investment trust management, <i>Journal of the American Statistical Association</i>, 58 (304), 1011-1032.<p class="explanatory_text"> <img border="0" src="../images/bullet_paper_glossary.gif" width="21" height="15"><a name="Sharpe">Sharpe</a>, William F. (1966). Mutual fund performance, <i>Journal of Business</i>, 39 (1) Part 2, Supplement, 119-138.<p class="explanatory_text"> <img border="0" src="../images/bullet_paper_glossary.gif" width="21" height="15"><a name="Treynor">Treynor</a>, Jack (1965). How to rate management of investment funds, <i> Harvard Business Review</i>, 43 (1), 63-75.</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" style="margin-top: 18"><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, 2006<p align="center"><map name="FPMap1"> <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" width="241" height="89"></td> </tr> </table> </td> </tr> </table> </td> <td>  </td> </tr> </table> </div> </body>