Eurodollar Future

<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="table8"> <tr> <td width="740"> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" height="37" id="table9"> <tr> <td height="35" width="100%"> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" cellpadding="0" id="table10"> <tr> <td width="100%" align="left" valign="top"> <p class="header_gold">Eurodollar Future</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="table11"> <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="#bundles">bundle</a><p class="word_list"> <a href="#Eurocurrency_futures">Eurocurrency future</a><p class="word_list"> <a href="#Eurodollar_futures">Eurodollar future</a><p class="word_list"> <a href="#Eurodollar_futures_strip,">Eurodollar futures strip</a><p class="word_list"> <a href="#Eurodollar_strip">Eurodollar strip</a><p class="word_list"> <a href="#Euroeuro_futures">Euroeuro future</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="#Eurosterling_futures">Eurosterling future</a><p class="word_list"> <a href="#Euroswiss_futures">Euroswiss future</a><p class="word_list"> <a href="#Euroyen_futures">Euroyen future</a><p class="word_list"> <a href="#Libor-swap_curve">Libor-swap curve</a><p class="word_list"> <a href="#packs">pack</a><br> <img border="0" src="../images/blank_1x160.gif" width="160" height="1"></td> </tr> </table> </td> </tr> </table> <p class="body"><b><a name="Eurodollar_futures">Eurodollar futures</a></b> are the most widely traded <a href="../articles/future.htm">futures</a> in the world. They were launched in 1982 by the Chicago Mercantile Exchange (CME). Today, contracts trade there as well on the Singapore Futures Exchange (SGX) and Euronext. Most of the volume is in Chicago, followed by Singapore and then Europe. The Chicago and Singapore contracts are identical, and there is a mutual offset program between the two exchanges that makes their contracts fungible. The Chicago and Singapore contracts are <a href="../articles/physical%20settlement.htm">cash settled</a>. So is the European contract, but for historical regulatory reasons, it also offers a <a href="../articles/physical%20settlement.htm">physical settlement</a> option, which the others do not. This is rarely used. Despite its minor differences, and the fact that it cannot be offset against the Chicago or Singapore contracts, prices of the European contracts closely track those of the other two.</p> <p class="body">A Eurodollar future is a future on a three-month <a href="../articles/eurodollar_deposit.htm">Eurodollar deposit</a> of one million US dollars. Final <a href="../articles/settlement.htm">settlement</a> at expiration is based on the value of 3-month <a href="../articles/libor.htm">BBA Libor</a>. Eurodollar futures are the exchange-traded equivalent of <a href="../articles/exchange_traded.htm">over-the-counter</a> <a href="../articles/forward_rate_agreement.htm">forward rate agreements</a> (FRAs). FRAs have the advantage of being customizable. Eurodollar futures offer greater <a href="../articles/liquidity.htm">liquidity</a> and lower <a href="../articles/transaction_costs.htm">transaction costs</a>. Also, like all futures, Eurodollar futures eliminate <a href="../articles/credit_risk.htm">credit risk</a> through a <a href="../articles/future.htm">margining</a> process. FRAs do not.</p> <p class="body">If Eurodollar futures were being introduced today, they would probably be quoted with <a href="../articles/fixed_income_term_structure.htm">forward interest rates</a> on the <a href="../articles/derivative_instrument.htm">underlying</a> deposits. Back in 1982, though, cash settled financial futures were a novelty. Trading was performed face-to-face in "trading pits" by traders who were more familiar with trading cattle or pork bellies. They thought in terms of prices instead of interest rates, so the exchange specified a formula for the "price" of a Eurodollar future in terms of its interest rate. This is the same formula the exchange had introduced for its t-bill future. If a trader wants to quote a Eurodollar future for some interest rate <i>r</i>, she converts <i>r</i> to a price for quoting purposes with</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"> price = 100 (1 – <i>r</i>)</td> <td width="5%" align="right">[1]</td> </tr> </table> <p class="body">For example, if a Eurodollar future is quoted at 94.25, this corresponds to an interest rate of 5.75%.</p> <p class="body">Each .01 unit of price corresponds to a <a href="../articles/basis_point.htm">basis point</a>, but it is called a tick. Prices are quoted to within a half tick (.005) for all contracts except the one closest to expiration, which is quoted to within a quarter tick. Daily margining is set equal to $25 per tick. For example, if a contract's <a href="../articles/future.htm">settlement price</a> changes from 94.25 to 94.22 from one day to the next, traders who are <a href="../articles/short_sale.htm">long</a> must pay 3 <font face="Arial">x</font> ($25) = $75 per contract in margin.</p> <p class="body">There are contracts that expire every March, June, September and December out to ten years. Additionally, there are contracts expiring in the upcoming four months not covered by the quarterly expirations. In total, 44 contracts trade at any given time. Exhibit 1 shows available contracts and their settlement prices for June 25, 2007.</p> <div align="center"> <table border="0" style="border-collapse: collapse" bordercolor="#111111" width="320" cellpadding="0" id="table13"> <tr> <td width="320"> <p class="exhibit_header"><span class="exhibit_header">Eurodollar Futures Contracts:<br> June 25, 2006</span><br> <span class="exhibit_subheader">Exhibit 1</span></td> </tr> <tr> <td bgcolor="#CC9966" height="2" width="320"> <img border="0" src="../images/blank_2x2.gif" width="2" height="2"></td> </tr> <tr> <td width="320"> <div align="center"> <table id="table14" cellSpacing="1" cellPadding="3" border="0" width="100%"> <tr style="FONT-WEIGHT: bold" vAlign="top" align="middle" bgColor="#ccccff" border="##d4d0c8"> <td width="80" bgcolor="#FFFFCC" class="explanatory_text" style="border-bottom: 1px solid #CC9966"> <p style="margin-bottom: 4px">Contract month</td> <td width="80" bgcolor="#FFFFCC" class="explanatory_text" style="border-right: 1px solid #CC9966; border-bottom: 1px solid #CC9966"> <p style="margin-bottom: 4px">Settlement price</td> <td width="80" bgcolor="#FFFFCC" class="explanatory_text" style="border-bottom: 1px solid #CC9966"> <p style="margin-bottom: 4px">Contract month</td> <td width="80" bgcolor="#FFFFCC" class="explanatory_text" style="border-bottom: 1px solid #CC9966"> <p style="margin-bottom: 4px">Settlement price</td> </tr> <tr> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> JUL 2007</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text" style="border-right: 1px solid #CC9966"> 94.6500</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> MAR 2012</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> 94.2700</td> </tr> <tr> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> AUG 2007</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text" style="border-right: 1px solid #CC9966"> 94.6650</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> JUN 2012</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> 94.2400</td> </tr> <tr> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> SEP 2007</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text" style="border-right: 1px solid #CC9966"> 94.6800</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> SEP 2012</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> 94.2100</td> </tr> <tr> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> OCT 2007</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text" style="border-right: 1px solid #CC9966"> 94.7050</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> DEC 2012</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> 94.1700</td> </tr> <tr> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> NOV 2007</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text" style="border-right: 1px solid #CC9966"> 94.7400</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> MAR 2013</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> 94.1500</td> </tr> <tr> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> DEC 2007</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text" style="border-right: 1px solid #CC9966"> 94.7400</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> JUN 2013</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> 94.1200</td> </tr> <tr> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> MAR 2008</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text" style="border-right: 1px solid #CC9966"> 94.8000</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> SEP 2013</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> 94.0850</td> </tr> <tr> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> JUN 2008</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text" style="border-right: 1px solid #CC9966"> 94.8300</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> DEC 2013</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> 94.0450</td> </tr> <tr> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> SEP 2008</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text" style="border-right: 1px solid #CC9966"> 94.8150</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> MAR 2014</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> 94.0250</td> </tr> <tr> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> DEC 2008</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text" style="border-right: 1px solid #CC9966"> 94.7750</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> JUN 2014</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> 94.0000</td> </tr> <tr> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> MAR 2009</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text" style="border-right: 1px solid #CC9966"> 94.7350</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> SEP 2014</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> 93.9800</td> </tr> <tr> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> JUN 2009</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text" style="border-right: 1px solid #CC9966"> 94.6850</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> DEC 2014</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> 93.9450</td> </tr> <tr> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> SEP 2009</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text" style="border-right: 1px solid #CC9966"> 94.6350</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> MAR 2015</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> 93.9300</td> </tr> <tr> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> DEC 2009</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text" style="border-right: 1px solid #CC9966"> 94.5850</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> JUN 2015</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> 93.9150</td> </tr> <tr> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> MAR 2010</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text" style="border-right: 1px solid #CC9966"> 94.5500</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> SEP 2015</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> 93.8950</td> </tr> <tr> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> JUN 2010</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text" style="border-right: 1px solid #CC9966"> 94.5050</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> DEC 2015</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> 93.8650</td> </tr> <tr> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> SEP 2010</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text" style="border-right: 1px solid #CC9966"> 94.4700</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> MAR 2016</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> 93.8450</td> </tr> <tr> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> DEC 2010</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text" style="border-right: 1px solid #CC9966"> 94.4200</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> JUN 2016</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> 93.8250</td> </tr> <tr> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> MAR 2011</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text" style="border-right: 1px solid #CC9966"> 94.3950</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> SEP 2016</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> 93.8050</td> </tr> <tr> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> JUN 2011</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text" style="border-right: 1px solid #CC9966"> 94.3600</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> DEC 2016</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> 93.7700</td> </tr> <tr> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> SEP 2011</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text" style="border-right: 1px solid #CC9966"> 94.3300</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> MAR 2017</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text"> 93.7550</td> </tr> <tr> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text" style="border-bottom: 2px solid #CC9966"> DEC 2011</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text" style="border-right: 1px solid #CC9966; border-bottom: 2px solid #CC9966"> 94.2900</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text" style="border-bottom: 2px solid #CC9966"> JUN 2017</td> <td align="middle" bgColor="#ffffff" border="d4d0c8" width="80" class="explanatory_text" style="border-bottom: 2px solid #CC9966"> 93.7400</td> </tr> </table> </div> </td> </tr> <tr> <td width="320"> <p class="exhibit_legend">Source: CME</td> </tr> </table> </div> <p class="body">Although the contracts are cash settled, the underlying deposits are thought of as <a href="../articles/settlement.htm">spot</a> deposits commencing on the third Wednesday of a contract's expiration month. Since a spot deposit has two days' settlement, trading ceases two London business days before that date.</p> <p class="body">Eurodollar futures are widely used for <a href="../articles/hedging_and_diversification.htm">hedging</a> fixed income obligations and especially fixed income <a href="../articles/derivative_instrument.htm">derivatives</a>. A simple example can be informative. Suppose today is June 25, 2007, so the contracts of Exhibit 1 are available. A trader is to make a cash payment of $3 million on December 15, 2008, and she wants to hedge the <a href="../articles/interest_rate_risk.htm">interest rate risk</a>. She goes long three each of the Sep 2007, Dec 2007, Mar 2008, Jun 2008 and Sep 2008 contracts. If you think of each future as a 3-month <a href="../articles/fixed_income_term_structure.htm">forward loan</a>, she has strung together a series of five 3-month forward loans to make a 15-month forward loan, commencing in September 2007 and maturing in December 2008. That forward loan would, if futures were physically settled, have her pay a sum equal to the present value of $3 million in September 2007 and return $3 million to her in December 2008, offsetting her $3 million cash outflow scheduled for that month. The hedge has the effect of replacing an eighteen-month <a href="../articles/duration_and_convexity.htm">duration</a> portfolio with a three-month duration portfolio, substantially reducing the interest rate risk. The Eurodollar futures hedge and its interpretation as a forward loan are illustrated in Exhibit 2.</p> <div align="center"> <table border="0" style="border-collapse: collapse" bordercolor="#111111" width="460" cellpadding="0" id="table15"> <tr> <td> <p class="exhibit_header"><span class="exhibit_header">Example: <br> Hedging with a Eurodollar Futures Strip</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 width="450"> <img border="0" src="../images/ex2_eurodollar_future_a.gif" width="450" height="279"><img border="0" src="../images/ex2_eurodollar_future_b.gif" width="450" height="279"></td> </tr> <tr> <td> <p class="exhibit_legend">The top chart illustrates how it takes fifteen Eurodollar futures contracts, with five different expirations, to hedge a single cash flow in the example. This is typical in hedging with Eurodollar futures. Such a laddered hedge is called a Eurodollar futures strip. The bottom chart illustrates how, in the example, the strip behaves like an eighteen month loan. Combined with the cash flow to be hedged, it has the effect of replacing the eighteen month cash outflow with one at three months. Note that cash flows don't actually occur as in the bottom chart. The Eurodollar futures are cash settled through the daily margining process, so no forward loans actually take place. However, the hedged position's market value will respond to changes in interest rates as if it had the cash flows depicted in the bottom chart.</td> </tr> </table> </div> <p class="body">In the example, we see that it took fifteen futures contracts, of five different expirations, to hedge a single cash flow. Such laddered positions arise frequently in hedging with Eurodollar futures, and they have a name. A <a name="Eurodollar_futures_strip,"> <b> Eurodollar futures strip</b>,</a> or simply a <a name="Eurodollar_strip"> <b>Eurodollar strip</b></a>, is a position consisting of an equal number of each of several consecutive quarterly Eurodollar futures.</p> <p class="body">To facilitate hedging, the CME allows trading in entire strips, which the exchange calls <b><a name="bundles">bundles</a></b>. A bundle is a strip of consecutive quarterly contracts—one future for each expiration. Bundles generally start with the front quarterly contract, so a one-year bundle consists of the first four quarterly contracts; a two-year bundle consists of the first eight quarterly contracts, etc. There is also a <b><a name="forward_bundle">forward bundle</a></b>, which comprises 20 contracts, covering years five through ten. Another form of strip that can be directly traded on the CME is <b> <a name="packs">packs</a></b>. These are strips of one each of four consecutive quarterly contracts. There is a pack for the first four quarterly contracts, the second four quarterly contracts, and so on.</p> <p class="body">There are several shortcomings of the hedge in our example. One is that it hedges interest rate risk but leaves <a href="../articles/liquidity_risk.htm">liquidity risk</a> unaddressed. This is typical of any hedge using cash-settled futures. More importantly, the hedge only partially addresses the interest rate risk. Consider three issues:</p> <p class="body"><img border="0" src="../images/bullet.gif" width="20" height="10">The hedge has the effect of replacing an eighteen-month duration portfolio with a three-month duration portfolio, but a better hedge would replace it with a cash (zero duration) portfolio. There simply isn't a short-dated Eurodollar future that she can add to her hedge to accomplish this.</p> <p class="body"><img border="0" src="../images/bullet.gif" width="20" height="10">There is another timing issue at eighteen months. The cash flow to be hedged occurs on December 15, but the hypothetical forward loan she has constructed with the Eurodollar strip matures on December 19.</p> <p class="body"><img border="0" src="../images/bullet.gif" width="20" height="10">When a forward loan is constructed from a series of shorter forward loans, the maturity value of each loan in the series should equal the loan amount of the subsequent loan. This doesn't happen in our example, where the underlying deposits of the Eurodollar futures are all for $1 million.</p> <p class="body">As a practical matter, Eurodollar hedges are far from perfect. If our trader wanted a more perfect hedge, she would go out and negotiate an actual deposit commencing immediately and maturing on December 15. Arranging such a customized deal would take time, and she would have to pay a <a href="../articles/spreads.htm">bid-ask spread</a>. </p> <p class="body">As exchange-traded instruments, Eurodollar futures offer only standardized expirations and a fixed $1 million <a href="../articles/notional_amount.htm">notional amount</a>. A trader has to construct the best hedge she can with what is available. What she gains with Eurodollar futures is savings in time and money. The Eurodollar futures market is extremely liquid, so she can hedge even large exposures quickly and for almost no cost.</p> <p class="body">If she wanted to, a trader could tweak the hedge in our example to better address the interest rate risk. The example was useful for illustrating how Eurodollar strips arise naturally when hedging with Eurodollar futures. As a practical matter, traders don't think of their Eurodollar futures hedges as forming hypothetical forward loans. They construct hedges using sensitivity analysis as follows:</p> <p class="body"><img border="0" src="../images/bullet.gif" width="20" height="10">Represent the portfolio to be hedged with a series of spot and forward 3-month loans.</p> <p class="body"><img border="0" src="../images/bullet.gif" width="20" height="10">Calculate the present value of a basis point (PV01) for each of the loans. That is, determine by how much the present value of each loan would change if the applicable interest rate for the loan were to rise by a basis point.</p> <p class="body"><img border="0" src="../images/bullet.gif" width="20" height="10">Divide each PV01 by $25 to determine how many Eurodollar futures of the corresponding expiration to hedge with.</p> <p class="body">During the early 1990s, awareness spread that the margining process for Eurodollar futures introduced a slight bias in how they are priced. Called <a href="../articles/convexity_bias.htm">convexity bias</a>, this should cause Eurodollar futures rates to slightly exceed corresponding forward rates, especially at longer maturities. Until the 1990s, traders would construct a <a href="../articles/fixed_income_term_structure.htm"> forward curve</a> directly from Eurodollar rates and use this for pricing other instruments, such as swaps and FRAs. Recognizing that there is a convexity bias in Eurodollar rates, traders no longer do that. Instead, they construct a <a href="../articles/fixed_income_term_structure.htm">spot curve</a> from Libor rates and <a href="../articles/interest_rate_swap.htm">swap rates</a>. Called the <b><a name="Libor-swap_curve">Libor-swap curve</a></b>, this has emerged as the benchmark for pricing many dollar-denominated fixed income obligations.</p> <p class="body">Modeled after Eurodollar futures, there are other cash-settled futures traded on exchanges around the world for 3-month deposits in different currencies. These include <b> <a name="Eurosterling_futures">Eurosterling futures</a></b>, <b> <a name="Euroyen_futures">Euroyen futures</a></b>, <b> <a name="Euroswiss_futures">Euroswiss futures</a></b> and <b> <a name="Euroeuro_futures">Euroeuro futures</a></b>. 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