RAROC and Economic Capital

<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">RAROC and Economic Capital</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="1%" 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="99%" align="left" valign="top"><p class="word_list"> <a href="#economic capital">economic capital</a><p class="word_list"> <a href="#RAPMs">RAPM</a><p class="word_list"> <a href="#RAROC">RAROC</a><p class="word_list"> <a href="#RARORAC">RARORAC</a><p class="word_list"> <a href="#return on assets">return on assets</a><p class="word_list"> <a href="#return on capital">return on capital</a><p class="word_list"> <a href="#return on equity">return on equity</a><p class="word_list"> <a href="#risk-adjusted performance metrics">risk-adjusted performance metric</a><p class="word_list"> <a href="#RORAC">RORAC</a><br> <img border="0" src="../images/blank_1x160.gif" width="160" height="1"></td> </tr> </table> </td> </tr> </table> <p class="body">While the term <b> <a name="economic capital">economic capital</a></b> is a more recent development, the concept it represents dates to the 1980s. Regulators have always been interested in the <a href="../articles/capital_allocation.htm">capital ratios</a> of the financial institutions they oversee, but is was during the 1970s and 1980s that they started to implement explicit <a href="../articles/capital_allocation.htm">capital</a> adequacy regulations. To do so, they had to specify formulas for a firm's capital and required capital. Intended for regulatory purposes, these were not always suitable for corporate internal purposes—so <a href="../articles/regulatory_capital.htm">regulatory capital</a> and economic capital diverged.</p> <table border="0" cellpadding="0" style="border-collapse: collapse" bordercolor="#111111" width="310" align="right" id="table5"> <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">The purpose of regulatory capital is to enforce minimum capital requirements. Tools such as capital ratios or <a href="../articles/capital_allocation.htm">risk-based capital</a> are used for this purpose. Economic capital is primarily used by financial institutions to support decisions about what business lines or transactions to pursue. A firm defines its economic capital as comprising, among other things, owners equity, retained earnings, and subordinated debt. Formulas are specified for assigning economic <a href="../articles/capital_allocation.htm">capital charges</a> to specific business lines or transactions. The focus is on identifying those business lines or transactions that offer, in some sense, the best use of the firm's limited economic capital. To make such assessments, firms employ <b> <a name="risk-adjusted performance metrics">risk-adjusted performance metrics</a></b> (<b><a name="RAPMs">RAPMs</a></b>). A RAPM is a performance metric that is based on a standard accounting performance metric but with some adjustment to reflect "true" or "economic" risk.</p> <p class="body">RAPMs have their origins in the accounting notion of <b><a name="return on assets">return on assets</a></b> (ROA), which was long used as a bank-wide performance metric:</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/economc_capital_ROA.gif" alt="return on assets equals (revenues minus expenses) divided by assets." width="185" height="41"></td> <td width="5%" align="right">[1]</td> </tr> </table> <p class="body">Widespread use of <a href="../articles/exchange_traded.htm">OTC</a> <a href="../articles/derivative_instrument.htm">derivatives</a> and other off-balance-sheet items have largely rendered the accounting notion of assets a meaningless indicator of a bank's risk or the financial resources it has deployed. For assessing bank-wide performance, <b> <a name="return on equity">return on equity</a></b> (ROE) has largely replaced <a name="[2]">it</a>:</p> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" cellpadding="0" height="36" id="table7"> <tr> <td width="100%" align="center"> <img border="0" src="../formulas/economic_capital_ROE.gif" alt="return on assets equals (revenues minus expenses) divided by equity." width="182" height="44"></td> <td width="5%" align="right">[2]</td> </tr> </table> <p class="body">While widely used by <a href="../articles/common_stock.htm">equity</a> analysts and investors, ROE has two shortcomings that limit its use for internal purposes:</p> <p class="bullet_line_space"><img border="0" src="../images/bullet.gif" width="20" height="10">The accounting notion of equity can be a poor indicator of a bank's risk.</p> <p class="bullet_line_space"><img border="0" src="../images/bullet.gif" width="20" height="10">While ROE is defined bank-wide, it is not defined for individual business lines or transactions.</p> <p class="body">By replacing equity with capital in formula [<a href="#[2]">2</a>], we obtain <b><a name="return on capital">return on capital</a></b> (ROC):</p> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" cellpadding="0" height="36" id="table8"> <tr> <td width="100%" align="center"> <img border="0" src="../formulas/economic_capital_ROC.gif" alt="return on assets equals (revenues minus expenses) divided by capital." width="183" height="44"></td> <td width="5%" align="right">[3]</td> </tr> </table> <p class="body">Because economic capital reflects "true" or "economic" risk, this is our first example of a RAPM. When applied to individual business lines or transactions, the formula may be modified <a name="[4]"> slightly</a>:</p> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" cellpadding="0" height="36" id="table9"> <tr> <td width="100%" align="center"> <img border="0" src="../formulas/economic_capital_ROC_2.gif" alt="return on assets equals (revenues minus expenses plus income from capital) divided by capital." width="325" height="44"></td> <td width="5%" align="right">[4]</td> </tr> </table> <p class="body">Here, capital is the capital charge for the business line or transaction, and </p> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" cellpadding="0" height="36" id="table10"> <tr> <td width="100%" align="center"> income from capital = capital (risk-free rate)</td> <td width="5%" align="right">[5]</td> </tr> </table> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="165" align="left" id="table11"> <tr> <td width="160">  </td> <td width="11"> </td> </tr> <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">In formula [<a href="#[4]">4</a>], the "income from capital" term is included because allocating capital to a business line is different from investing the capital in the business line or transaction. Typically, capital is held in addition to any assets invested in the business line or transaction. The capital is presumably invested somewhere, and ROC should reflect the extra income from that investment. Since the capital is supporting a risky business line or transaction, it (hypothetically) should be invested in something risk free. Accordingly, it is ascribed income at the risk-free rate. Occasionally, a bank will actually invest in a business line or transaction the capital allocated to that business line or transaction. In this case, formula [<a href="#[4]">4</a>] will still be correct so long as the expenses term in the numerator includes a transfer pricing charge for the financing cost of the capital. </p> <p class="body">When ROA, ROE or ROC are used to assess a bank's (actual or projected) performance, they are generally applied to one year's (actual or projected) results. This may not be appropriate when ROC is applied to assess a business line's or transaction's performance. If the purpose is to select desirable business lines or transactions to invest in, one-year's projected ROC may be misleading. A business line or transaction might be expected to lose money in its first year only to turn profitable in subsequent years. Accordingly, when ROC is used for internal decision making, the ROC of a business line or transaction is typically calculated as an average ROC over several years or the life of the transaction. The same consideration applies to other RAPMs described below.</p> <p class="body">During the 1980s, Bankers Trust developed a firm wide RAPM that they called risk-adjusted return on capital (<b><a name="RAROC">RAROC</a></b>). Bankers Trust was a <a href="../articles/united_states_financial_regulation.htm">commercial bank</a> that had adopted a business model much like that of an <a href="../articles/united_states_financial_regulation.htm">investment bank</a>. It had divested its retail deposit and lending businesses. It actively dealt in <a href="../articles/united_states_financial_regulation.htm">exempt securities</a> and had an emerging derivatives business. Such wholesale activities are easier to model than the retail businesses Bankers Trust had divested, and this certainly facilitated the development of the system. RAROC was well publicized, and during the 1990s, a number of other banks developed their own firm wide systems. Those firms and their consultants came up with various names for these, including return on risk-adjusted capital <b><a name="RORAC">RORAC</a></b> and risk-adjuster return on risk-adjusted capital (<b><a name="RARORAC">RARORAC</a></b>). The names were more buzzwords than anything else. Today, most any RAPM derived from ROC is simply called RAROC. Perhaps the most common definition of RAROC is simply ROC with an adjustment for expected loss:</p> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" cellpadding="0" height="36" id="table12"> <tr> <td width="100%" align="center"> <img border="0" src="../formulas/economic_capital_RAROC.gif" width="450" height="44"></td> <td width="5%" align="right">[6]</td> </tr> </table> <p class="body">where expected loss is the <a href="../articles/mean.htm">mean</a> of the loss distribution associated with some activity—most typically it represents expected loss from defaulting loans or from <a href="../articles/operational_risk.htm">operational risk</a>. The original Bankers Trust RAROC system provided results on an after-tax basis. Today, systems typically perform calculations before tax.</p> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table13"> <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="table14"> <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/asset_liability_management.htm">asset-liability management</a></strong></span><strong style="font-weight: 400"> Techniques for protecting a firm's solvency in the context of accrual accounting.</strong><p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/basle_committee.htm">Basel Committee</a> A committee of representatives from central banks and regulatory authorities that has played a leading role in standardizing bank regulations across jurisdictions.<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/capital_allocation.htm">capital</a> A firm's value—assets minus liabilities.</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/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/economic_profit.htm">economic profit</a> Profit in excess of the opportunity cost of capital.</p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/risk_management.htm">financial risk management</a> Practices by which a firm optimizes the manner in which it takes financial risk.<p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/market_risk.htm">market risk</a> 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"><strong style="font-weight: 400"><a href="../articles/operational_risk.htm">operational risk</a> Risk </strong>of loss resulting from inadequate or failed internal processes, people and systems, or from external events.<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/regulatory_capital.htm">regulatory capital</a> Capital held in accordance with statutory or regulatory requirements.</strong></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="table15"> <tr> <td width="100%"> <p class="explanatory_text">Matten (<a target="_blank" href="http://www.riskbook.com/link/matten_c_(2000).htm">2000</a>) discusses bank capital generally from a practitioner's perspective. Belmont (<a target="_blank" href="http://www.riskbook.com/link/belmont_david_(2004).htm">2004</a>) takes a more focused look at economic capital, RAROC and related topics. For researchers or theoretically inclined practitioners, Schroeck (<a target="_blank" href="http://www.riskbook.com/link/schroeck_g_(2002).htm">2002</a>) is excellent.</p> <table border="0" cellpadding="4" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table16"> <tr> <td width="100" align="left" valign="top"> <map name="FPMap478"> <area target="_blank" href="http://www.riskbook.com/link/matten_c_(2000).htm" shape="rect" coords="0, 0, 82, 124"> </map> <img border="0" src="../images/book_matten_chris_(2000)_125.jpg" usemap="#FPMap478" 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="table17"> <tr> <td width="90%" colspan="3"> <p class="title"> <a target="_blank" href="http://www.riskbook.com/link/matten_c_(2000).htm"> Managing Bank Capital</a></td> </tr> <tr> <td colspan="3"> <p class="author"><b>Chris Matten</b></td> </tr> <tr> <td width="10%"> <map name="FPMap482"> <area target="_blank" href="http://www.riskbook.com/main/ratings.htm" shape="rect" coords="0, 1, 89, 16"> </map> <img border="0" src="../images/star_5.gif" usemap="#FPMap482" 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="FPMap483"> <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="#FPMap483" width="90" height="16"></td> <td width="10%" class="author">technical</td> <td width="70%">  </td> </tr> <tr> <td width="10%"> <p class="author">2000</td> <td width="10%"> </td> <td width="70%"> <p align="center"><map name="FPMap477"> <area target="_blank" coords="0, 0, 145, 19" shape="rect" href="http://www.riskbook.com/link/matten_c_(2000).htm"> </map> <img border="0" src="../images/pointer_review.gif" usemap="#FPMap477" 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="table18"> <tr> <td width="100" align="left" valign="top"> <map name="FPMap480"> <area target="_blank" coords="0, 0, 84, 124" shape="rect" href="http://www.riskbook.com/link/belmont_david_(2004).htm"> </map> <img border="0" src="../images/book_belmont_david_(2004)_125.jpg" usemap="#FPMap480" width="85" height="125"></td> <td align="left" valign="top"> <table border="0" cellpadding="1" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table19"> <tr> <td width="90%" colspan="3"> <p class="title"> <a target="_blank" href="http://www.riskbook.com/link/belmont_david_(2004).htm"> Value Added Risk Management</a></td> </tr> <tr> <td colspan="3"> <p class="author"><b>David Belmont</b></td> </tr> <tr> <td width="10%"> <map name="FPMap474"> <area target="_blank" href="http://www.riskbook.com/main/ratings.htm" shape="rect" coords="0, 1, 89, 16"> </map> <img border="0" src="../images/star_5.gif" usemap="#FPMap482" 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="FPMap427"> <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="#FPMap483" 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="FPMap366"> <area target="_blank" coords="0, 0, 145, 19" shape="rect" href="http://www.riskbook.com/link/belmont_david_(2004).htm"> </map> <img border="0" src="../images/pointer_review.gif" usemap="#FPMap366" 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="table20"> <tr> <td width="100" align="left" valign="top"> <map name="FPMap481"> <area target="_blank" href="http://www.riskbook.com/link/schroeck_g_(2002).htm" shape="rect" coords="0, 0, 83, 124"> </map> <img border="0" src="../images/book_schroeck_g_(2002)_125.jpg" usemap="#FPMap481" 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="table21"> <tr> <td width="90%" colspan="3"> <p class="title"> <a target="_blank" href="http://www.riskbook.com/link/schroeck_g_(2002).htm"> Risk Management and Value Creation in Financial Institutions</a></td> </tr> <tr> <td colspan="3"> <p class="author"><b>Gerhard Schroeck </b></td> </tr> <tr> <td width="10%"> <map name="FPMap420"> <area target="_blank" href="http://www.riskbook.com/main/ratings.htm" shape="rect" coords="1, 2, 89, 15"> </map> <img border="0" src="../images/star_4.gif" usemap="#FPMap420" 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="FPMap421"> <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_3.gif" usemap="#FPMap421" 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="FPMap479"> <area target="_blank" coords="0, 0, 145, 19" shape="rect" href="http://www.riskbook.com/link/schroeck_g_(2002).htm"> </map> <img border="0" src="../images/pointer_review.gif" usemap="#FPMap479" 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_2.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 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="table22"> <tr> <td width="100%"> <p class="explanatory_text"> <img border="0" src="../images/bullet_paper_glossary.gif" width="21" height="15">Holton, Glyn A. (2004). <a target="_blank" href="http://www.riskexpertise.com/papers/Capital.PDF">Capital calculations: Has the CCRO missed the point?</a>, <i>Energy Risk</i>, 1 (3), 41–42.</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="table23"> <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/01-2/00000c46.htm">RAROC</a> <i>20 Mar 2001<br> </i>RAROC: time horizon and trades with negative marginal risk.<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/00-3/00000910.htm">Realistic scaling of VaRs to annual horizons ...</a> <i>08 Jun 2000 </i> <br> Challenges of scaling value-at-risk to long horizons.<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/00-1/0000076d.htm">RAROC</a> <i>18 Jan 2000</i><br> References on risk-adjusted return on capital (RAROC).<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/00-1/00000734.htm">RAROC</a> <i>21 Dec 1999</i><br> What banks were using RAROC in 1999?</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="table24"> <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>