Risk Limits

<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">Risk Limits</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="#Exposure limits">exposure limit</a><p class="word_list"> <a href="#limits">limit</a><p class="word_list"> <a href="#limit violation">limit violation</a><p class="word_list"> <a href="#notional limits">notional limit</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"> <a href="#Risk limits">risk limit</a><p class="word_list"> <a href="#stop-loss limit">stop-loss limit</a><p class="word_list"> <a href="#utilization">utilization</a><p class="word_list"> <a href="#VaR limits">VaR limit</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"><b><a name="Risk limits">Risk limits</a></b> (or simply <b> <a name="limits">limits</a></b>) are a device for authorizing specific forms of <a href="../articles/risk.htm">risk</a> taking. A pension fund hires an outside investment manager to invest some of its assets in <a href="../articles/corporate_bond.htm">corporate bonds</a>. The fund wants the manager to take risk on its behalf, but it has a specific form of risk in mind. It doesn’t want the manager investing in equities, precious metals, or pork belly <a href="../articles/future.htm">futures</a>. It communicates its intentions with investment guidelines. These specify acceptable investments. They also specify risk limits, such as requirements that: </p> <p class="body"><img border="0" src="../images/bullet.gif" width="20" height="10">the portfolio’s <a href="../articles/duration_and_convexity.htm"> duration</a> always be less than 7 years; </p> <p class="body"><img border="0" src="../images/bullet.gif" width="20" height="10">all <a href="../articles/coupon_bond.htm">bonds</a> have a credit rating of triple-B or better. </p> <p class="body">The first is an example of a <a href="../articles/market_risk.htm">market risk</a> limit; the second of a <a href="../articles/credit_risk.htm">credit risk</a> limit. </p> <p class="body">When an organization authorizes a risk limit for risk-taking activities, it must specify three things: </p> <ol> <li> <p class="body">a <a href="../articles/risk_metric_and_risk_measure.htm">risk metric</a>, </li> <li> <p class="body">a <a href="../articles/risk_metric_and_risk_measure.htm">risk measure</a> for calculating the value of the risk metric on an ongoing basis, and </li> <li> <p class="body">a value for the risk metric that is not to be exceeded. </li> </ol> <p class="body">At any point in time, a limit’s <b><a name="utilization">utilization</a></b> is the actual amount of risk being taken, as quantified by the risk measure. Any instance where utilization exceeds the risk limit is called a <b><a name="limit violation">limit violation</a></b>. </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"> <p class="body"> </td> </tr> </table> <p class="body">Suppose a bank’s corporate lending department is authorized to lend to a specific counterparty subject to a <a href="../articles/credit_risk.htm">credit exposure</a> limit of <a href="../articles/currency_codes.htm">GBP</a> 10<a href="../articles/mm.htm">MM</a>. For this purpose, the bank measures credit exposure as the sum amount of outstanding loans and loan commitments to the counterparty. The lending department lends the counterparty GBP 8MM, causing its utilization of the limit to be GBP 8MM. Since the limit is GBP 10MM, the lending department has remaining authority to lend up to GBP 2MM to the counterparty. </p> <p class="body">A metals trading firm authorizes a trader to take gold price risk subject to a 2000 troy ounce <a href="../articles/delta_and_gamma.htm"> delta</a> limit. Using a specified measure of delta, his portfolio’s delta is calculated at 4:30 PM each trading day. Utilization is calculated as the absolute value of the portfolio’s delta. </p> <p class="body">For managing credit risk, a firm will generally set an exposure credit limit for each counterparty to which it has credit exposure. This is standard procedure in many contexts. It could be a bank making corporate loans, a derivative dealer transacting with counterparties, a company extending trade credit to customers or a credit card company providing credit to cardholders. All entail credit risk. All are contexts where credit exposure limits are used.</p> <p class="body">A firm may also use aggregate credit exposure limits. A bank might set credit exposure limits by industry. It might also set a total exposure credit limit for all its corporate lending activities.</p> <p class="body">For monitoring market risk, many organizations segment portfolios in some manner. They may do so by trader and trading desk. Commodities trading firms may do so by delivery point and geographic region. A hierarchy of market risk limits is typically specified to parallel such segmentation with each segment of the portfolio having its own limits. Limits generally increase in size as you move up the hierarchy—from traders to desks to the overall portfolio or from individual delivery points to geographic regions to the overall portfolio. </p> <p class="body">Exhibit 1 illustrates how a hierarchy of market risk limits might be implemented for a trading unit. A risk metric is selected, and risk limits are specified based upon this. Each limit is depicted with a cylinder. The height of the cylinder corresponds to the size of the limit. The trading unit has three trading desks, each with its own limit. There are also limits for individual traders, but only those for trading desk A are shown. The extent to which each cylinder is shaded green corresponds to the utilization of that limit. Trader A3 is utilizing much of his limit. Trader A4 is utilizing little of hers. </p> <div align="center"> <center> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="400" cellpadding="0" id="table7"> <tr> <td> <p class="exhibit_header"><span class="exhibit_header">Example: A hierarchy of Market Risk Limits</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_risk_limits.gif" width="400" height="360"></td> </tr> <tr> <td> <p class="exhibit_legend">A typical system of market risk limits is depicted. Each limit is indicated with a cylinder. The height of the cylinder corresponds to the size of the limit. The trading unit has three trading desks, each with its own limit. There are also limits for individual traders, but only those for trading desk A are shown. The extent to which each cylinder is shaded green corresponds to the utilization of that limit.</td> </tr> </table> </center> </div> <p class="body">For such a hierarchy of risk limits to work, an organization must have a suitable risk measure to calculate utilization of each risk limit on an ongoing basis. Below, we describe three types of market risk limits, culminating with VaR limits. </p> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="345" align="right" id="table8"> <tr> <td align="right" width="9"> </td> <td width="336">  <p style="margin-top: 0; margin-bottom: 2" class="ad_legend"> <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=82402;type=iframe" style="margin: 0px; padding: 0px; border-width: 0px" width="336" height="265" frameborder="0" marginwidth="0" marginheight="0" scrolling="no" name="I1" target="_top"> <![if lt IE 4]> <script src="http://servedbyadbutler.com/adserve/;ID=147917;size=336x265;setID=82402;type=js" type="text/javascript"> </script> <noscript> <a href="http://servedbyadbutler.com/go2/;ID=147917;size=336x265;setID=82402"> <img src="http://servedbyadbutler.com/adserve.ibs/;ID=147917;size=336x265;setID=82402;type=img" border="0" height="265" width="336" alt=""></a> </noscript><![endif]></iframe>   </td> </tr> </table> <p class="body">A <b><a name="stop-loss limit">stop-loss limit </a></b>indicates an amount of money that a portfolio’s single-period market loss should not exceed. Various periods may be used, and sometimes multiple stop-loss limits are specified for different periods. A trader might be given the following stop-loss limits: </p> <p class="body"><img border="0" src="../images/bullet.gif" width="20" height="10">1-day EUR 0.5MM, </p> <p class="body"><img border="0" src="../images/bullet.gif" width="20" height="10">1-week EUR 1.0MM, </p> <p class="body"><img border="0" src="../images/bullet.gif" width="20" height="10">1-month EUR 3.0MM. </p> <p class="body">A limit violation occurs whenever a portfolio’s single-period market loss exceeds a stop-loss limit. In such an event, a trader is usually required to unwind or otherwise <a href="../articles/hedging_and_diversification.htm">hedge</a> material exposures—hence the name stop-loss limit. </p> <p class="body">Stop-loss limits have shortcomings. Single-period market loss is a retrospective risk metric. It only indicates risk after the financial consequences of that risk have been realized. Also, it provides an inconsistent indication of risk. If a portfolio suffers a large loss over a given period, this is a clear indication of risk. If the portfolio does not suffer a large loss, this does not indicate an absence of risk! Another problem is that traders cannot control the specific losses they incur, so it is difficult to hold traders accountable for isolated stop-loss limit violations. However, the existence of stop-loss limits does motivate traders to manage portfolios in such a manner as to avoid limit violations. </p> <p class="body">Despite their shortcomings, stop-loss limits are simple and convenient to use. Non-specialists easily understand stop-loss limits. A single risk metric can be applied consistently across an entire hierarchy of limits. Calculating utilization is as simple as marking a portfolio to market. Finally, because portfolio loss encompasses all sources of market risk, just one or a handful of limits is required for each portfolio or sub-portfolio. For these reasons, stop-loss limits are widely implemented by trading organizations. </p> <p class="body"><b><a name="Exposure limits">Exposure limits</a></b> are limits based upon an exposure risk metric. For limiting market risk, common metrics include: duration, convexity, delta, <a href="../articles/delta_and_gamma.htm">gamma</a>, and <a href="../articles/vega.htm">vega</a>. Crude exposure limits may also be based upon <a href="../articles/notional_amount.htm">notional amounts</a>. These are called <b><a name="notional limits">notional limits</a></b>. Many exposure metrics can take on positive or negative values, so utilization may be defined as the absolute value of exposure. </p> <p class="body">Exposure limits address many of the shortcomings of stop-loss limits. They are prospective. Exposure limits indicate risk before its financial consequences are realized. Also, exposure metrics provide a reasonably consistent indication of risk. For the most part, traders can be held accountable for exposure limit violations because they largely control their portfolio’s exposures. There are rare exceptions. A sudden market rise may cause a positive-gamma portfolio’s delta to increase, resulting in an unintended delta limit violation. </p> <p class="body">For the most part, utilization of exposure limits is easy to calculate. There may be analytic formulas for certain exposure metrics. At worst, a portfolio must be evaluated under multiple market scenarios with some form of <a href="../articles/interpolation.htm">interpolation</a> applied to assess exposure. </p> <p class="body">Exposure limits pose a number of problems. A hierarchy of exposure limits will depend upon numerous risk metrics. Not only is delta different from gamma, but crude oil delta is different from natural gas delta. Because a portfolio or sub-portfolio can have multiple exposures, it will require multiple exposure limits. An <a href="../articles/common_stock.htm">equity</a> derivatives trader might have delta, gamma, and vega limits for each of 1000 equities—for a total of 3000 exposure limits. </p> <p class="body">Exposure limits are ineffective in contexts where <a href="../articles/futures_spread.htm">spread trading</a>, cross-hedging, or similar strategies minimize risk by taking offsetting positions in <a href="../articles/correlation.htm">correlated</a> assets. Large exposure limits are required in order to accommodate each of the offsetting positions. Because they cannot ensure reasonable hedging, the exposure limits allow for net risk far in excess of that required by the intended hedging strategy. </p> <p class="body">With the exception of notional limits, non-specialists do not easily understand exposure limits. It is difficult to know what might be a reasonable delta limit for an electricity trading desk if you don’t have both: </p> <p class="body"><img border="0" src="../images/bullet.gif" width="20" height="10">a technical understanding of what delta means, and </p> <p class="body"><img border="0" src="../images/bullet.gif" width="20" height="10">practical familiarity with the typical size of market fluctuations in the electricity market. </p> <p class="body">This, and the sheer number of exposure limits that are often required, makes it difficult for managers to establish effective hierarchies of exposure limits. </p> <p class="body"><b><a name="VaR limits">Value-at-risk (VaR) limits</a></b> combine many of the advantages of exposure limits and stop-loss limits. </p> <p class="body">Like exposure metrics, <a href="../articles/risk_metric_and_risk_measure.htm">VaR metrics</a> are prospective. They indicate risk before its economic consequences are realized. Also like exposure metrics, VaR metrics provide a reasonably consistent indication of risk. Finally, as long as utilization is calculated for traders in a timely and ongoing manner, it is reasonable to hold them accountable for limit violations. As with exposure limits, there are rare exceptions. Consider a trader with a negative gamma position. While she is responsible for hedging the position on an ongoing basis, it is possible that a sudden move in the underlier will cause an unanticipated spike in VaR. </p> <p class="body">As with stop-loss limits, non-specialists intuitively understand VaR metrics. If a portfolio has 1-day 90% USD VaR of 7.5MM, a non-specialist understands that such a portfolio will lose less than USD 7.5MM an average of 9 days out of 10. </p> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="345" align="right" id="table9"> <tr> <td align="right" width="9"> <p class="body"> </td> <td width="336"> <script type="text/javascript"></script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script> <p class="body"> </td> </tr> </table> <p class="body">With VaR limits, a single metric, such as 1-day 99% USD VaR, can be applied consistently across an entire hierarchy of limits. In theory, VaR encompasses all sources of market risk. Just one limit is required for each portfolio or sub-portfolio. </p> <p class="body">VaR aggregates across assets. Depending upon the sophistication of a <a href="../articles/var_measure.htm">VaR measure</a>, it can reflect even the most complex hedging or <a href="../articles/hedging_and_diversification.htm"> diversification</a> effects. Accordingly, VaR limits are perfect for limiting risk with spread trading, cross-hedging, or similar trading strategies. </p> <p class="body">VaR limits have one significant drawback: utilization may be computationally expensive to calculate. For many portfolios, VaR is easy to calculate. It can often be done in real time on a single processor. For other portfolios, it may take minutes or hours to calculate, even with parallel processors. </p> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table10"> <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="table11"> <tr> <td width="100%"> <p class="explanatory_text" align="left"> <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 exposure</a> Potential for loss due to credit risk.</strong><p class="explanatory_text" align="left"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><strong style="font-weight: 400"><a href="../articles/duration_and_convexity.htm">duration and convexity</a> Factor sensitivities employed in fixed income markets.</strong><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" align="left"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/greeks.htm"><strong style="font-weight: 400">Greeks</strong></a><strong style="font-weight: 400"> A set of factor sensitivities used to measure risk exposures related to options or other derivatives.</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/risk.htm">risk</a> Comprises two components: uncertainty and exposure.</strong><p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/value_at_risk.htm">value-at-risk</a> A category of market risk measures.</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%">  <p class="ad_legend" style="margin-left: 0; 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