Gap Analysis

<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" height="25"> <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">Gap Analysis</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="#cash flow matching">cash flow matching</a><p class="word_list"> <a href="#cash matching">cash matching</a><p class="word_list"> <a href="#Gap analysis">gap analysis</a><p class="word_list"> <a href="#interest rate gap">interest rate gap</a><p class="word_list"> <a href="#liquidity gaps">liquidity gap</a><p class="word_list"> <a href="#repricing gaps">repricing gap</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="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="Gap analysis">Gap analysis</a></b> is a technique of <a href="../articles/asset_liability_management.htm">asset-liability management</a> that can be used to assess <a href="../articles/interest_rate_risk.htm">interest rate risk</a> or <a href="../articles/liquidity_risk.htm">liquidity risk</a>. Implementations for those two applications differ in minor ways, so people distinguish between interest rate gaps and liquidity gaps. This article discusses both.</p> <p class="body">Gap analysis was widely adopted by financial institutions during the 1980s. When used to manage interest rate risk, it was used in tandem with <a href="../articles/duration_and_convexity.htm">duration</a> analysis. Both techniques have their own strengths and weaknesses. </p> <p class="body">Duration is appealing because it summarizes, with a single number, exposure to parallel shifts in the <a href="../articles/fixed_income_term_structure.htm">term structure</a> of interest rates. It does not address exposure to other term structure movements, such as tilts or bends. Gap analysis is more cumbersome and less widely applicable, but it assesses exposure to a greater variety of term structure movements.</p> <div align="center"> <center> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="275" cellpadding="0" id="table6"> <tr> <td> <p class="exhibit_header"><span class="exhibit_header">Changes in the Term Structure of Interest Rates</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> <p style="margin-left: 5; margin-top: 6"> <img border="0" src="../images/ex1_gap_analysis.gif" width="250" height="470"></td> </tr> <tr> <td> <p class="exhibit_legend">The term structure of interest rates can move in many ways. Duration analysis addresses exposure to parallel shifts only. Gap analysis can warn of exposure to more complex movements, including tilts and bends.</td> </tr> </table> </center> </div> <p class="body">Let's start our discussion with <b> <a name="cash flow matching">cash flow matching</a></b> (or simply <b> <a name="cash matching">cash matching</a></b>). This is an effective, but largely impractical means of eliminating interest rate risk. If a portfolio has a positive fixed cash flow at some time <i>t</i>, its <a href="../articles/valuation.htm">market value</a> will increase or decrease inversely with changes in the <a href="../articles/fixed_income_term_structure.htm">spot interest rate</a> for maturity <i>t</i>. If the portfolio has a negative fixed cash flow at time <i>t</i>, it's market value will increase or decrease in tandem with changes in that spot rate. Stated simply, interest rate risk arises from either positive or negative net future cash flows. The concept of cash matching is to eliminate interest rate risk by eliminating all net future cash flows. A portfolio is cash matched if </p> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="345" align="left" id="table7"> <tr> <td width="336"> <script type="text/javascript"></script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script>  </td> <td width="9"> </td> </tr> </table> <p class="bullet_line_space"><img border="0" src="../images/bullet.gif" width="20" height="10">every future cash inflow is balanced with an offsetting cash outflow on the same date, and</p> <p class="bullet_line_space"><img border="0" src="../images/bullet.gif" width="20" height="10">every future cash outflow is balanced with an offsetting cash inflow on the same date.</p> <p class="body">The net cash flow for every date in the future is then 0. Obviously, this is an ideal that we usually don't want to achieve, but it is a theoretically useful concept. In its most basic form, gap analysis assesses how close a portfolio is to being cash matched. Here is how it works. </p> <p class="body">Start by considering a portfolio with only fixed cash flows—that is, the timing and amount of all cash flows is known. The portfolio contains no <a href="../articles/floater.htm">floaters</a>, no <a href="../articles/option.htm">options</a> and no <a href="../articles/coupon_bond.htm">bonds</a> with embedded options. Soon we will loosen the restriction against floaters, but let's keep it for now. Gap analysis doesn't consider <a href="../articles/credit_risk.htm">credit risk</a>, so assume all cash flows will occur.</p> <! c o p y r i g h t ( c ) C o n t i n g e n c y A n a l y s i s , 2005 > <p class="body">Gap analysis comprises aggregating cash flows into maturity buckets and checking if cash flows in each bucket net to 0. Different bucketing schemes might be used. As a simple example, consider a portfolio whose cash flows all mature in less than three years. We aggregate maturities into five buckets:</p> <p class="bullet"><img border="0" src="../images/bullet.gif" width="20" height="10">0 - 3 months</p> <p class="bullet"><img border="0" src="../images/bullet.gif" width="20" height="10">3 - 6 months</p> <p class="bullet"><img border="0" src="../images/bullet.gif" width="20" height="10">6 - 12 months</p> <p class="bullet"><img border="0" src="../images/bullet.gif" width="20" height="10">12 - 24 months</p> <p class="bullet"><img border="0" src="../images/bullet.gif" width="20" height="10">24 - 36 months</p> <p class="body">An <b><a name="interest rate gap">interest rate gap</a></b> is simply a positive or negative net cash flow for one of the buckets. Exhibit 2 illustrates a gap analysis using our buckets and some hypothetical cash flows.</p> <div align="center"> <center> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="510" cellpadding="0" id="table8"> <tr> <td> <p class="exhibit_header"><span class="exhibit_header">Example: Gap Analysis</span><br> <span class="exhibit_subheader">Exhibit 2</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/ex2_gap_analysis.gif" width="510" height="120"></td> </tr> <tr> <td> <p class="exhibit_legend">Bucketed cash flows in <a href="../articles/currency_codes.htm">USD</a> millions. A gap is any net cash flow for a bucket, so there is a USD 100<a href="../articles/mm.htm">MM</a> gap for the 3 - 6 month bucket. There is a negative gap of USD 30MM for the 12 - 24 month bucket. </td> </tr> </table> </center> </div> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="165" align="left" id="table9"> <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">Note that this portfolio is exposed to tilts in the term structure of interest rates. If rates for the 3 - 6 month bucket rise and rates for the 12 - 24 month bucket decline, the portfolio will incur a <a href="../articles/valuation.htm">mark-to-market</a> loss on both gaps. This exposure would not be identified by duration. If you calculate the <a href="../articles/duration_and_convexity.htm">Macaulay duration</a> of the portfolio, it is about 0.</p> <p class="body">Now let's add floating rate instruments to the portfolio. These generally are not bucketed according to their maturity but according to their next <a href="../articles/floater.htm">reset date</a>. Consider a <a href="../articles/currency_codes.htm">USD</a> 100<a href="../articles/mm.htm">MM</a> <a href="../articles/floater.htm">floating rate note</a> (FRN) that pays 3-month <a href="../articles/libor.htm">Libor</a> flat. Its last reset was a month ago at 2.8%. It will pay USD 0.7MM in two months, and then the rate will be reset again. </p> <p class="body">From a market value standpoint, the FRN is equivalent to a fixed cash payment of USD 100.7MM to be received in two months (see the discussion of pricing in the <a href="../articles/floater.htm">article on floaters</a>). Accordingly, that is how we bucket it—we bucket the entire FRN as a single USD 100.7MM cash flow in the 0 - 3 month bucket.</p> <p class="body">Because of how floaters are treated, buckets are often called repricing buckets as opposed to maturity buckets—instruments are bucketed according to their next repricing date as opposed to their maturity date. We are moving away from cash matching and towards repricing date matching. From this standpoint, interest rate gaps are sometimes called <b> <a name="repricing gaps">repricing gaps</a></b>.</p> <p class="body">So far, we have discussed the use of gap analysis for assessing interest rate risk. It can also be used to assess liquidity risk. Cash flows are bucketed as above. The only difference is that cash flows from floaters are bucketed according to their maturity. The actual values of floating rate cash flows will not be known, but estimated values may be used. The idea of liquidity gap analysis is to anticipate periods when a portfolio will have large cash out-flows. Such buckets are called <b><a name="liquidity gaps">liquidity gaps</a></b>.</p> <p class="body">A shortcoming of gap analysis—both interest rate and liquidity gap analysis—is the fact that it does not identify mismatches within buckets. An even more significant shortcoming is the fact that it cannot handle options in a meaningful way. In today's markets, options proliferate. Fixed income portfolios routinely hold <a href="../articles/cap.htm">caps</a>, <a href="../articles/floor.htm">floors</a>, <a href="../articles/swaption.htm">swaptions</a>, <a href="../articles/mortgage_backed_security.htm">mortgage-backed securities</a>, <a href="../articles/callable_bond.htm">callable bonds</a>, etc. Options have cash flows whose magnitudes—and sometimes timing—is highly uncertain. Those uncertain cash flows cannot be bucketed. For this reason, gap analysis has largely fallen out of use. 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