Futures

<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">Futures</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="#delivery month">delivery month</a><p class="word_list"> <a href="#Exchange for physicals">exchange for physicals</a><p class="word_list"> <a href="#first notice date">first notice date</a><p class="word_list"> <a href="#future">future</a><p class="word_list"> <a href="#initial margin">initial margin</a><p class="word_list"> <a href="#Maintenance margin">maintenance margin</a><p class="word_list"> <a href="#margin">margin</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="#margin account">margin account</a><p class="word_list"> <a href="#notice date">notice date</a><p class="word_list"> <a href="#notice of delivery">notice of delivery</a><p class="word_list"> <a href="#Offset">offset</a><p class="word_list"> <a href="#Settlement prices">settlement price</a><p class="word_list"> <a href="#variational margin">variation margin</a><br>  </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">A <b><a name="future">future</a></b> is an <a href="../articles/exchange_traded.htm">exchange-traded</a> <a href="../articles/derivative_instrument.htm">derivative</a> which is similar to a <a href="../articles/forward.htm">forward</a>. Both futures and forwards represent agreements to buy/sell some <a href="../articles/derivative_instrument.htm">underlying</a> asset in the future for a specified price. Both can be for <a href="../articles/physical%20settlement.htm">physical settlement</a> or <a href="../articles/physical%20settlement.htm">cash settlement</a>. Both offer a convenient tool for hedging or speculation. For little or no initial cash outlay, both instruments provide price exposure without a need to immediately pay for, hold or warehouse the underlying asset. In this sense, both instruments are leveraged. Futures and forwards trade on a variety of underliers: wheat, oil, live beef, Eurodollar deposits, gold, foreign exchange, the S&P 500 stock index, etc.</p> <p class="body">The fundamental difference between futures and forwards is the fact that futures are traded on exchanges. Forwards trade <a href="../articles/exchange_traded.htm">over the counter</a>. This has three practical implications.</p> <ol> <li> <p class="bullet_line_space">Futures are standardized instruments. You can only trade the specific contracts supported by the exchange. Forwards are entirely flexible. Because they are privately negotiated between parties, they can be for any conceivable underlier and for any settlement date. Parties to the contract decide on the <a href="../articles/notional_amount.htm">notional amount</a> and whether physical or cash settlement will be used. If the underlier is for a physically settled commodity or energy, parties agree on issues such as delivery point and quality.</p> </li> <li> <p class="bullet_line_space">Forwards entail both <a href="../articles/market_risk.htm">market risk</a> and <a href="../articles/credit_risk.htm">credit risk</a>. A counterparty may fail to perform on a forward. With futures, there is only market risk. This is because exchanges employ a system whereby counterparties exchange daily payments of profits or losses on the days they occur. Through these <b><a name="margin">margin</a></b> payments, a futures contract's market value is effectively reset to zero at the end of each trading day. This all but eliminates credit risk.</p> </li> <li> <p class="bullet_line_space">The daily cash flows associated with margining can skew futures prices, causing them to diverge from corresponding <a href="../articles/forward.htm">forward prices</a>. </p> </li> </ol> <p class="body">A future is transacted through a brokerage firms that hold a "seat" on the exchange that trades that particular contract. Working through their respective brokers, two parties will transact a trade. <i> Legally</i>, that trade is structured as two trades, both with a clearinghouse owned by or closely affiliated with the exchange. For example, suppose Party A and Party B trade five May natural gas futures at <a href="../articles/currency_codes.htm">USD</a> 3.24. Party A is long and Party B is short. This would be legally structured as</p> <p class="bullet_line_space"><img border="0" src="../images/bullet.gif" width="20" height="10">Party A being long five May natural gas futures at USD 3.24 with the exchange's clearinghouse being the counterparty; and</p> <p class="bullet_line_space"><img border="0" src="../images/bullet.gif" width="20" height="10">The exchange's clearinghouse being long five May natural gas futures at USD 3.24 with Party B being the counterparty.</p> <p class="body">Party A and B then have no legal obligation to each other. Their respective legal obligations are to the exchange's clearinghouse. The clearinghouse never takes market risk because it always has offsetting positions with different counterparties. This is illustrated in Exhibit 1.</p> <div align="center"> <center> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="400" cellpadding="0" id="table6"> <tr> <td> <p class="exhibit_header"><span class="exhibit_header">The Clearinghouse Stands Between Parties</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 class="exhibit_header" align="center"><br> <span class="verdana10">Two parties negotiate a futures transaction</span></p> <p class="exhibit_header" align="center"> <img border="0" src="../images/ex1_futures_top.gif" width="350" height="95"></p> <p align="center"><b><span class="verdana10">Legally, it is structured as two transactions.</span></b></p> <p align="center"> <img border="0" src="../images/ex1_futures_bottom.gif" width="350" height="95"><br>  </td> </tr> <tr> <td> <p class="exhibit_legend">Two parties negotiate (through their respective brokers) a futures transaction. They agree on the price and the number of contracts. Legally, the transaction is structured as two contracts, each between one of the parties and the exchange's clearinghouse. In this way, the parties are not exposed to each others' credit risk. There is credit risk between the respective parties and the clearinghouse, but that is all but eliminated through a margining process. Because the clearinghouse always takes offsetting positions, it never takes market risk.</td> </tr> </table> </center> </div> <p class="body">Before you can trade a futures contract, the broker collects a deposit from you called <b><a name="initial margin">initial margin</a></b>. This may be in the form of cash or acceptable <a href="../articles/security.htm">securities</a>. The broker holds this deposit for you in a <a name="margin account"> <b>margin account</b></a> and, in the case of a cash deposit, credits interest on the balance. The amount of initial margin is determined according to a formula set by the exchange. For a single futures contract, it will be a small fraction of the <a href="../articles/valuation.htm">market value</a> of the futures' underlier. For <a href="../articles/futures_spread.htm">futures spreads</a>, or if you are using futures to hedge a physical position in the underlier, initial margin may be even lower. Generally, initial margin is intended to represent the maximum one-day net loss you could reasonably be expected to incur on a position.</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="body">Every day, the profit or loss is calculated on your futures position. If a loss, your broker transfers that amount from your margin account to the clearinghouse. If a profit, the clearinghouse transfers that amount to your broker who then deposits it into your margin account. This is the daily margining process. The clearinghouse's margin cash flows net to zero. For every margin payment it receives from one party, it makes an offsetting margin payment to another party. </p> <p class="body">Through the margining process, futures <a href="../articles/settlement.htm">settle</a> every day. Unlike a forward, where all contract obligations are satisfied at maturity, obligations under the futures contract are satisfied every day on an ongoing basis as mark-to-market profits or losses are realized. This essentially eliminates credit risk for futures.</p> <p class="body">The calculation of the daily profit or loss for margin purposes is straightforward. On the day a futures position is first entered into, the formula for each contract is</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"> (notional) (today's settlement price – transaction price)</td> <td width="5%" align="right">[1]</td> </tr> </table> <p class="body">On all subsequent days, the formula becomes</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"> (notional) (today's settlement price – yesterday's settlement price)</td> <td width="5%" align="right">[2]</td> </tr> </table> <p class="body"><b><a name="Settlement prices">Settlement prices</a></b> are official prices calculated by the exchange at the close of trading for the purpose of making margin calculations. Formulas vary and may depend upon how active trading was at the close. Generally, settlement prices are calculated as some average of transaction prices immediately before the close of trading or as some average of indicative quotes obtained from traders at the close. </p> <p class="body"><b><a name="Maintenance margin">Maintenance margin</a></b> is some fraction—perhaps 75%—of initial margin for a position. Should the balance in your margin account fall below the maintenance margin, your broker will require that you deposit funds or securities sufficient to restore the balance to the initial margin level. Such a demand is called a <a href="../articles/collateral.htm">margin call</a>. The additional deposit is called <b><a name="variational margin">variation margin</a></b>. Should you fail to make a variation margin payment, your broker will immediately liquidate some or all of your positions.</p> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="165" align="left" id="table10"> <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 the margin payments made in daily settlement of a future are not <a href="../articles/collateral.htm">collateral</a> in a legal sense. When a party posts collateral to, say, secure an OTC derivative obligation, that party legally still owns the collateral. With futures contracts, money transferred from a margin account to an exchange as a margin payment legally changes hands. A deposit in a margin account at a broker is collateral. It legally still belongs to the client, but the broker can take possession of it any time to satisfy obligations arising from the client's futures positions.</p> <p class="body">There are four ways to close out a futures contract:</p> <p class="bullet_line_space"><img border="0" src="../images/bullet.gif" width="20" height="10"><b><a name="Offset">Offset</a></b> is the transaction of a reversing trade on the exchange. If you are short 20 March soybean futures traded on the Chicago Board of Trade, you can close the position by taking an offsetting long position in 20 March soybean contracts on the same exchange. There will be a final margining at the end of the day, and then the position will be closed.</p> <p class="bullet_line_space"><img border="0" src="../images/bullet.gif" width="20" height="10">Cash settlement is simply the holding of a cash settled future until expiration. At that time, there is a final margin payment, and the contract expires.</p> <p class="bullet_line_space"><img border="0" src="../images/bullet.gif" width="20" height="10">Delivery is the holding of a physically settled future until it physically settles according to exchange rules.</p> <p class="bullet_line_space"><img border="0" src="../images/bullet.gif" width="20" height="10"><b><a name="Exchange for physicals">Exchange for physicals</a></b> (EFP) is a form of privately negotiated physical settlement of long and short futures positions held by two parties.</p> <p class="body">Every futures contract has a last trade date and a delivery period specified by the exchange. In the case of a cash settled future, the delivery period is the last trade date. On that date, the settlement price is set equal to the cash price of the underlier. There is a final margining based on that settlement price, and then the contract expires.</p> <p class="body">For physically settled futures, exchange rules depend upon the specific underlier. Usually, there is an entire month—called the <b> <a name="delivery month">delivery month</a></b>—during which delivery may occur. The last trading day for the future falls towards the end of that month. A party that is short a future may elect to deliver the underlier on any business day in the delivery month. Typically, <b> <a name="notice of delivery">notice of delivery</a></b> must be made to the exchange two business days prior to delivery. The date on which notice is given is called the <b><a name="notice date">notice date</a></b>. The first possible date for notice comes towards the end of the month preceding the delivery month. It is called the <b> <a name="first notice date">first notice date</a></b>. Upon receiving notice of delivery, the exchange selects a party that is long the future to take the delivery. This may be the party with the largest long position in the future. Alternatively, the party to take delivery may be selected by lot. </p> <p class="body">The vast majority of futures contracts are traded by hedgers or speculators with no interest in taking or delivering the underlier. Such parties holding long futures will offset them prior to the first notice date. Those with short positions will offset them by the last trade date. Most futures are closed out by offset.</p> <p class="body">Exchanges specify conditions of delivery. These include acceptable locations for delivery, in the case of commodities or energies. It includes specifics about the quality, grade or nature of the underlier to be delivered. For example, only certain <a href="../articles/treasury_note_and_bond.htm">Treasury bonds</a> may be delivered under the Chicago Board of Trade's Treasury bond future. Only certain growths of coffee may be delivered under the Coffee, Sugar and Cocoa Exchange's coffee future.</p> <p class="body">In many commodity or energy markets, parties want to settle futures by delivery, but exchange rules are too restrictive for their needs. For example, the New York Mercantile Exchange requires that natural gas be delivered at the Henry Hub in Louisiana. Suppose two parties need to buy/sell gas at some other hub and have transacted futures to hedge against price movements prior to the transaction. What should they do?</p> <p class="body">One answer is that they could privately negotiate the trade and then reverse their futures positions by offset. This requires that they take price risk during the period between closing the physical trade and offsetting their respective futures positions. Many exchanges offer an alternative called exchange for physicals (EFP). The mechanics of EFP vary by exchange. Generally, the parties privately negotiate their physical trade. Then, instead of offsetting their futures hedges with trades on the exchange, they inform the exchange that they want to transfer the futures from one party to the other, closing out their respective positions. Essentially, EFP is customizable physical delivery.</p> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table11"> <tr> <td height="30" valign="bottom"> <p class="header2_black">Related Internal Links</td> <td align="right" valign="bottom"> </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="table12"> <tr> <td width="100%"> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><span class="verdana10"><a href="../articles/collateral.htm"><strong style="font-weight: 400">collateral</strong></a></span><strong style="font-weight: 400"> Assets held to secure an obligation.</strong><p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/derivative_instrument.htm">derivative instrument</a> An instrument which derives value from the value of some commodity, energy, or other financial instrument.<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/forward.htm">forward contract</a> A </strong>trade that is agreed to at one point in time but will take place at some later time.<p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/futures_spread.htm">futures spread</a> A long-short futures position.<p align="left" class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/managed_futures.htm">managed futures</a> Portfolios of forwards or futures managed as an "alternative asset category."</p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/option.htm">option</a> A type of derivative instrument.<p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/settlement.htm">settlement</a> In finance, performance on a contractual obligation.</p> </td> </tr> </table> </td> </tr> <tr> <td height="30" valign="bottom"> <p class="header2_black">Related Books</td> <td align="right" valign="bottom"> </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="table13"> <tr> <td width="100%"> <p class="explanatory_text" style="margin-bottom: 14">Kolb (<a target="_blank" href="http://www.riskbook.com/link/kolb_r_(1998).htm">1998</a>) is the standard introductory text on futures. 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Both provide extensive information on futures.</p> <table border="0" cellpadding="4" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table14"> <tr> <td width="100" align="left" valign="top"> <map name="FPMap426"> <area target="_blank" href="http://www.riskbook.com/link/kolb_r_(1998).htm" shape="rect" coords="0, 0, 95, 124"> </map> <img border="0" src="../images/book_kolb_125.jpg" usemap="#FPMap426" width="96" height="125"></td> <td align="left" valign="top"> <table border="0" cellpadding="1" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table15"> <tr> <td width="90%" colspan="3"> <p class="title"> <a target="_blank" href="http://www.riskbook.com/link/kolb_r_(1998).htm"> Understanding Futures Markets</a> </td> </tr> <tr> <td colspan="3"> <p class="author"><b>Robert Kolb</b></td> </tr> <tr> <td width="10%"><map name="FPMap40"> <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="#FPMap40" 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="FPMap430"> <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_1.gif" usemap="#FPMap430" width="90" height="16"></td> <td width="10%" class="author">technical</td> <td width="70%">  </td> </tr> <tr> <td width="10%"> <p class="author">1998</td> <td width="10%"> </td> <td width="70%"> <p align="center"><map name="FPMap37"> <area target="_blank" coords="0, 0, 145, 19" shape="rect" href="http://www.riskbook.com/link/kolb_r_(1998).htm"> </map> <img border="0" src="../images/pointer_review.gif" usemap="#FPMap37" width="146" height="20"></td> </tr> </table> </td> </tr> </table> <span style="font-family: Times New Roman; letter-spacing: -0.2pt"> <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="FPMap591"> <area target="_blank" href="http://www.riskbook.com/link/das_satyajit_(2003).htm" shape="rect" coords="0, 0, 84, 124"> </map> <img border="0" src="../images/book_das_satyajit_(2003)_125.gif" usemap="#FPMap591" 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="table17"> <tr> <td width="90%" colspan="3"> <p class="title"> <a target="_blank" href="http://www.riskbook.com/link/das_satyajit_(2003).htm"> Swaps/Financial Derivatives</a></td> </tr> <tr> <td colspan="3"> <p class="author"><b>Satyajit Das</b></td> </tr> <tr> <td width="10%"> <p class="author"> <map name="FPMap592"> <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="#FPMap592" width="90" height="16"></td> <td width="10%" class="author">quality</td> <td width="70%"> <p class="author"> </td> </tr> <tr> <td width="10%"> <p class="author"> <map name="FPMap593"> <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="#FPMap593" width="90" height="16"></td> <td width="10%" class="author">technical</td> <td width="70%">  </td> </tr> <tr> <td width="10%"> <p class="author">2003</td> <td width="10%"> </td> <td width="70%"> <p align="center"><map name="FPMap594"> <area target="_blank" coords="0, 0, 145, 19" shape="rect" href="http://www.riskbook.com/link/das_satyajit_(2003).htm"> </map> <img border="0" src="../images/pointer_review.gif" usemap="#FPMap594" width="146" height="20"></td> </tr> </table> </td> </tr> </table> </span> </td> </tr> </table> </td> </tr> <tr> <td height="30" valign="bottom"> <p class="header2_black">Related Forum Discussions</td> <td align="right" valign="bottom"> </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="table18"> <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.riskarchive.com/link_thread/05-1/00000575.htm"> VaR for futures - based on notional or P/L (market value)?</a> <i> 19 Jan 2005<br> </i>Calculating value-at-risk for a futures portfolio.<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/00-4/00000ab7.htm">convexity of the futures strip</a> <i>10 Nov 2000</i><br> Convexity bias of futures.</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="table19"> <tr> <td width="100%" bgcolor="#FFFFFF"> <p align="center"><map name="FPMap0"> <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" 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"><span class="verdana10">website:</span> <span class="verdana10"> <a target="_top" href="http://www.contingencyanalysis.com"> http://www.contingencyanalysis.com</a><br> glossary direct link: <a target="_top" href="http://www.riskglossary.com"> http://www.riskglossary.com</a><br> <font size="3" face="Times New Roman">copyright © Contingency Analysis, 2004</font></span></td> </tr> </table> </td> </tr> </table> </td> <td>  </td> </tr> </table> </div> </body>