Portfolio Credit Risk

<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"> <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">Portfolio Credit Risk</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="95%" align="left" valign="top"><p class="word_list"> <a href="#default mode">default mode</a><p class="word_list"> <a href="#expected loss:">expected loss</a><p class="word_list"> <a href="#mark-to-market mode">mark-to-market mode</a><p class="word_list"> <a href="#portfolio credit risk">portfolio credit risk</a><p class="word_list"> <a href="#Portfolio credit risk models">portfolio credit risk model</a><p class="word_list"> <a href="#unexpected loss:">unexpected loss</a><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 class="body">During the 1950s, <a href="../articles/portfolio_theory.htm">Harry Markowitz</a> championed the notion that <a href="../articles/market_risk.htm">market risk</a> should be managed at the portfolio level. It took almost 50 years for researchers to develop effective models for doing the same thing with corporate <a href="../articles/credit_risk.htm">credit risk</a>. Certainly, retail credit risk—auto loans, mortgages, credit card debt—has been managed at a portfolio level for decades. This has been possible due to the relative homogeneity of retail obligors. Corporate obligations—loans, <a href="../articles/coupon_bond.htm">bonds</a>, <a href="../articles/derivative_instrument.htm">derivatives</a>, etc.—are far less homogenous. Also, they represent greater concentrations of risk. We are more comfortable modeling 50,000 consumer loans of <a href="../articles/currency_codes.htm">USD</a> 10,000 each as homogenous than we are doing so with 10 corporate obligations of USD 50<a href="../articles/mm.htm">MM</a> each!</p> <p class="body">Investors and counterparties have generally managed the portfolio-level implications of credit risk by <a href="../articles/hedging_and_diversification.htm">diversifying</a> their <a href="../articles/credit_risk.htm">exposures</a> and avoiding concentrations.</p> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="165" align="left" id="table6"> <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">Several factors have contributed to the new interest in more systematically measuring and managing the sum credit risk of an entire portfolio of obligations—what is called <b> <a name="portfolio credit risk">portfolio credit risk</a></b>. These include:</p> <p class="bullet_line_space"><img border="0" src="../images/bullet.gif" width="20" height="10">bank industry interest in having the <a href="../articles/basle_committee.htm">Basel II</a> accordpermit the use of internal models for calculating credit risk <a href="../articles/capital_allocation.htm">capital charges</a>;</p> <p class="bullet_line_space"><img border="0" src="../images/bullet.gif" width="20" height="10">efforts to improve the application of <a href="../articles/risk_limits.htm">risk limits</a> and <a href="../articles/capital_allocation.htm">capital allocation</a> for portfolio credit risk;</p> <p class="bullet_line_space"><img border="0" src="../images/bullet.gif" width="20" height="10">efforts to price <a href="../articles/credit_derivative.htm">credit derivatives</a> linked to baskets of defaultable obligations;</p> <p class="bullet_line_space"><img border="0" src="../images/bullet.gif" width="20" height="10">the emergence of collateralized debt obligations, which represent customized interests in portfolios of defaultable bonds.</p> <p class="body"><b><a name="Portfolio credit risk models">Portfolio credit risk models</a></b> are financial models that assess portfolio credit risk. Output takes various forms. Many models can be run in either of two modes. In a <b><a name="mark-to-market mode">mark-to-market mode</a></b> fluctuations in a portfolio's <a href="../articles/valuation.htm">market value</a> resulting from defaults or changes in credit ratings are modeled. Output might be the standard deviation or some quantile of market value. This form of analysis differs from that of <a href="../articles/value_at_risk.htm">value-at-risk</a> measures of market risk in that they consider changes in market value due only to obligor-specific credit events. It does not consider, for example, changes in credit spreads due to general market sentiment or changes in liquidity. In a <b><a name="default mode">default mode</a></b>, portfolio losses due to actual defaults are modeled. Output generally includes what are known as:</p> <p class="bullet_line_space"><img border="0" src="../images/bullet.gif" width="20" height="10"><b><a name="expected loss:">expected loss:</a></b> the <a href="../articles/mean.htm">expected value</a> over some specified horizon of portfolio losses due to default;</p> <p class="bullet_line_space"><img border="0" src="../images/bullet.gif" width="20" height="10"><b><a name="unexpected loss:">unexpected loss:</a></b> some metric related to the second moment of portfolio losses due to default over the same horizon. Metrics may be the <a href="../articles/standard_deviation.htm">standard deviation</a> or some <a href="../articles/quantile.htm">quantile</a> of portfolio loss.</p> <p class="body">Both CreditMetrics and KMV offer mark-to-market and default modes.</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">Portfolio credit risk models are constructed by associating some sort of <a href="../articles/correlation.htm">correlation</a> model with a <a href="../articles/default_model.htm">default model</a>. The default model specifies unconditional probabilities of default for individual obligations. The correlation model assigns default correlations to pairs of obligations. A simple correlation model might assign all pairs of obligations the same correlation. This may be reasonable if obligations are fairly homogenous—perhaps all bank loans. More sophisticated are factor models (also called sector models). These split each obligation's default probability into two components. One is a function of some factor, such as the performance of the stock market. The other is obligor specific. For example, if the the factor is the stock market's performance and all obligors are publicly traded firms, the allocation might be made based upon the <a href="../articles/beta.htm">betas</a> of the obligors' <a href="../articles/common_stock.htm">stocks</a>. Having a common factor impact all of their default probabilities to a greater or lesser extent imposes a correlation on the obligations' defaults. Generalizations allow for multiple factors.</p> <p class="body">The literature on portfolio credit risk models is extensive. Crouhy et al. (<a href="#Crouhy, Michel, Dan Galai and Robert Mark (2000)">2000</a>) and Gordy (<a href="#Gordy, Michael B. (2000)">2000</a>) survey the literature and compare standard models.</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 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/asset_value_model.htm">asset value model</a> A type of default model.</strong></p> <p class="explanatory_text" align="left"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/collateralized_debt_obligation.htm">collateralized debt obligation</a> A securitized interest in debt.</p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/credit_derivative.htm">credit derivative</a> A derivative instrument designed to transfer credit risk from one party to another.<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/credit_risk.htm">credit risk</a> Risk</strong> due to uncertainty in a counterparty's ability to meet its obligations.</p> <p align="left" class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/default_model.htm">default model</a> A type of model that assess the likelihood of default by an obligor.</p> <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/intensity_model.htm">intensity model</a> A type of default model.</strong></p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/netting.htm">netting</a> The offsetting of cash flows or other obligations against each other.<p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/presettlement_risk.htm">pre-settlement risk</a> Credit risk of default on a derivative instrument prior to final settlement.</td> </tr> </table> </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">Crouhy et al. (<a target="_blank" href="http://riskbook.com/link/crouhy_galai_and_mark_(2001).htm">2001</a>) and Saunders and Allen (<a target="_blank" href="http://www.riskbook.com/link/saunders_and_allen_(2002).htm">2002</a>) both offer accessible introductions to and comparisons of standard portfolio credit risk models. Bluhm et al. (<a target="_blank" href="http://www.riskbook.com/link/bluhm_overbeck_wagner_(2003).htm">2002</a>) is the essential text. See also Arvanitis and Gregory (<a target="_blank" href="http://www.riskbook.com/link/arvanitis_and_gregory_(2001).htm">2001</a>), especially for implementation issues. </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="FPMap455"> <area target="_blank" href="http://riskbook.com/link/crouhy_galai_and_mark_(2001).htm" shape="rect" coords="0, 0, 83, 124"> </map> <img border="0" src="../images/book_crouhy_125.gif" usemap="#FPMap455" width="84" 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://riskbook.com/link/crouhy_galai_and_mark_(2001).htm">Risk Measurement</a></td> </tr> <tr> <td colspan="3"> <p class="author"><b>M. Crouhy, et al.</b></td> </tr> <tr> <td width="10%"><map name="FPMap456"> <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_4.gif" usemap="#FPMap456" 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="FPMap453"> <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="#FPMap453" width="90" height="16"></td> <td width="10%" class="author">technical</td> <td width="70%">  </td> </tr> <tr> <td width="10%"> <p class="author">2001</td> <td width="10%"> </td> <td width="70%"> <p align="center"><map name="FPMap454"> <area target="_blank" coords="0, 0, 145, 19" shape="rect" href="http://riskbook.com/link/crouhy_galai_and_mark_(2001).htm"> </map> <img border="0" src="../images/pointer_review.gif" usemap="#FPMap454" 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="FPMap20"> <area target="_blank" href="http://www.riskbook.com/link/saunders_and_allen_(2002).htm" shape="rect" coords="0, 0, 81, 124"> </map> <img border="0" src="../images/book_saunders_and_allen_(2002)_125.gif" usemap="#FPMap20" 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="table14"> <tr> <td width="90%" colspan="3"> <p class="title"> <a target="_blank" href="http://www.riskbook.com/link/saunders_and_allen_(2002).htm">Credit Risk Measurement</a></td> </tr> <tr> <td colspan="3"> <p class="author"><b>Anthony Saunders and Linda Allen</b></td> </tr> <tr> <td width="10%"><map name="FPMap18"> <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_4.gif" usemap="#FPMap18" 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="FPMap19"> <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="#FPMap19" 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="FPMap24"> <area target="_blank" coords="0, 0, 145, 19" shape="rect" href="http://www.riskbook.com/link/saunders_and_allen_(2002).htm"> </map> <img border="0" src="../images/pointer_review.gif" usemap="#FPMap24" 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="FPMap660"> <area target="_blank" href="http://www.riskbook.com/link/bluhm_overbeck_wagner_(2003).htm" shape="rect" coords="0, 0, 81, 124"> </map> <img border="0" src="../images/book_bluhm_et_al_(2002)_125.gif" usemap="#FPMap660" 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="table16"> <tr> <td width="90%" colspan="3"> <p class="title"> <a target="_blank" href="http://www.riskbook.com/link/bluhm_overbeck_wagner_(2003).htm"> <font size="2">An Introduction to</font><br> Credit Risk Modeling</a></td> </tr> <tr> <td colspan="3"> <p class="author"><b>C. Bluhm, L. Overbeck and C. Wagner</b></td> </tr> <tr> <td width="10%"><map name="FPMap661"> <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_5.gif" usemap="#FPMap661" 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="FPMap662"> <area target="_top" href="http://www.riskbook.com/main/ratings.htm" shape="rect" coords="0, 0, 89, 15"> </map> <img border="0" src="../images/tech_4.gif" usemap="#FPMap662" 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="FPMap663"> <area target="_blank" coords="0, 0, 145, 19" shape="rect" href="http://www.riskbook.com/link/bluhm_overbeck_wagner_(2003).htm"> </map> <img border="0" src="../images/pointer_review.gif" usemap="#FPMap663" 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="table17"> <tr> <td width="100" align="left" valign="top"> <map name="FPMap664"> <area target="_blank" href="http://www.riskbook.com/link/arvanitis_and_gregory_(2001).htm" shape="rect" coords="1, 0, 86, 124"> </map> <img border="0" src="../images/book_arvanitis_and_gregory_(2001)_125.jpg" usemap="#FPMap664" width="86" 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/arvanitis_and_gregory_(2001).htm">Credit<br> <font size="2">The Complete Guide to Pricing, Hedging and Risk Management</font></a></td> </tr> <tr> <td colspan="3"> <p class="author"><b>Angelo Arvanitis and Jon Gregory</b></td> </tr> <tr> <td width="10%"><map name="FPMap665"> <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="#FPMap665" 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="FPMap666"> <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_4.gif" usemap="#FPMap666" width="90" height="16"></td> <td width="10%" class="author">technical</td> <td width="70%">  </td> </tr> <tr> <td width="10%"> <p class="author">2001</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/arvanitis_and_gregory_(2001).htm"> </map> <img border="0" src="../images/pointer_review.gif" usemap="#FPMap366" width="146" height="20"></td> </tr> </table> </td> </tr> </table> </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 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="Crouhy, Michel, Dan Galai and Robert Mark (2000)">Crouhy, Michel, Dan Galai and Robert Mark (2000)</a>. A comparative analysis of current<br> credit risk models, <i>Journal of Banking and Finance</i>, 24 (1-2), 59-117.<p class="explanatory_text"> <img border="0" src="../images/bullet_paper_glossary.gif" width="21" height="15"><a name="Gordy, Michael B. (2000)">Gordy, Michael B. (2000)</a>. A comparative anatomy of credit risk models, <i>Journal of Banking and Finance</i>, 24 (1-2), 119-149.</td> </tr> </table> </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/04-3/000000f1.htm">Validating Credit Model</a><i> 07 Jul 2004</i> <br> Is it even possible to validate today's credit risk models?<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/99-4/00000289.htm">Backtesting Credit Risk Models</a> <i>19 Oct 1999</i><br> Brief exchange about how or if portfolio credit risk models can be backtested.</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> </body>