Yield

<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">Yield</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="#current yield">current yield</a><p class="word_list"> <a href="#current yield (stock)">current yield (equity)</a><p class="word_list"> <a href="#dividend yield">dividend yield</a><p class="word_list"> <a href="#nominal yield">nominal yield</a><p class="word_list"> <a href="#Yield">yield</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="#yield to call">yield to call</a><p class="word_list"> <a href="#yield to first call">yield to first call</a><p class="word_list"> <a href="#Yield to first par call">yield to first par call</a><p class="word_list"> <a href="#yield to maturity">yield to maturity</a><p class="word_list"> <a href="#Yield to worst">yield to worst</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="Yield">Yield</a></b> is a financial concept with archaic origins. Prior to the 20th century, there wasn't the active secondary market for fixed income securities of today. There also weren't the great institutional investors—mutual funds and pension plans. <a href="../articles/coupon_bond.htm">Bonds</a> were mostly owned by wealthy families or fledgling insurance companies like the Metropolitan Life Insurance Company or the New York Life Insurance Company. These investors would buy bonds <a href="../articles/par_value.htm">at par</a> when they issued, clip the <a href="../articles/coupon_bond.htm">coupons</a> every six months, and hold the bonds to maturity. When the issuer returned their <a href="../articles/par_value.htm">par value</a>—thirty or so years later—they would reinvest it in new bonds. The goal was preservation of wealth—preservation for the benefit of heirs or policyholders. Investors looked for two things in a bond:</p> <p class="bullet"><cop yrigh t( c)c ont i ngen cy anal y sis, 2 00 5> <img border="0" src="../images/bullet.gif" width="20" height="10">impeccable <a href="../articles/credit_risk.htm">credit quality</a>, and</p> <p class="bullet"> <img border="0" src="../images/bullet.gif" width="20" height="10">high coupons.</p> <p class="body">Coupons were quoted as yield, which was simply the sum of a bond's coupons payable in a year divided by the bond's par value. Today, different metrics of yield have emerged, so we call this original metric <a name="nominal yield"><b>nominal yield</b></a>:</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/yield_[1].gif" width="323" height="39"></td> <td width="5%" align="right">[1]</td> </tr> </table> <p class="body">For example, if a bond has a par value of <a href="../articles/currency_codes.htm">USD</a> 1,000 and pays a USD 32.50 coupon every six months, its yield would is 6.5%. </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">During the late nineteenth century, but especially during the twentieth century, an active secondary market emerged for bonds. Brokers and dealers—whose profits are proportional to the trading activity of their clients—promoted the idea that bonds should be actively traded for the purpose of achieving capital gains. Investors who embraced this paradigm came to care less about the credit quality of a bond—buying a bond was no longer a thirty year commitment. Theirs was a trading attitude, and they were looking for three things in a bond:</p> <p class="bullet"> <img border="0" src="../images/bullet.gif" width="20" height="10">acceptable credit quality,</p> <p class="bullet"> <img border="0" src="../images/bullet.gif" width="20" height="10">high coupons, and</p> <p class="bullet"> <img border="0" src="../images/bullet.gif" width="20" height="10">potential for capital gains.</p> <p class="body">In this context, nominal yield isn't particularly informative. Suppose two bonds are trading in the secondary market. They have the same maturity date and similar credit quality, but one has a nominal yield of 4% while the other has one of 8%. All this really tells us is that the two bonds must have been issued at different times. One was issued when interest rates were around 4%, while the other was issued when interest rates were around 8%. Which is more attractive: an 8% bond trading <a href="../articles/par_value.htm">above par</a> or a 4% bond trading <a href="../articles/par_value.htm">below par</a>? The former has higher coupons, but the later will realize a nice capital gain when it matures at its par value. To distinguish between such bonds, investors might calculate their internal rates of return. </p> <p class="body">A bond's <b><a name="yield to maturity">yield to maturity</a></b> (YTM) is the internal rate of return an investor would achieve if she purchased that bond at its current <a href="../articles/bond_accrued_interest.htm">dirty price</a> and held it to maturity, assuming all coupon and principal payments are received as scheduled.</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/yield_[2].gif" width="419" height="62"></td> <td width="5%" align="right">[2]</td> </tr> </table> <p class="body">Prior to the age of computers, YTM was difficult to calculate. An easier <a href="../articles/risk_metric_and_risk_measure.htm">metric</a> to calculate was <b><a name="current yield"> current yield</a></b>, which is the sum of a bond's coupons payable in a year divided by the bond's <a href="../articles/bond_accrued_interest.htm"> clean price</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/yield_[3].gif" width="323" height="39"></td> <td width="5%" align="right">[3]</td> </tr> </table> <p class="body">This is a sort of compromise between nominal yield and YTM. Like nominal yield, it is easy to calculate. It also ignores anticipated capital gains or losses that will be realized at maturity. Obviously, if a bond is trading at par, nominal yield, current yield and YTM are equal. If the bond is trading above par, nominal yield exceeds current yield, which exceeds YTM. If the bond is trading below par, those inequalities reverse.</p> <p class="body">Today, computers have resolved the computational issues with yield to maturity, but there is another problem that affects all yield metrics. This is embedded <a href="../articles/option.htm">options</a>. Many <a href="../articles/corporate_bond.htm">corporate bonds</a> and <a href="../articles/municipal_securities.htm">municipal bonds</a> are <a href="../articles/callable_security.htm">callable</a>. If one is trading near its <a href="../articles/callable_security.htm">call price</a>, yield to maturity will be misleading because the bond is likely to be called long before it matures. To address this, investors may calculate <b><a name="yield to call">yield to call</a></b>:</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"> <img border="0" src="../formulas/yield_[4].gif" width="401" height="62"></td> <td width="5%" align="right">[4]</td> </tr> </table> <p class="body"><a href="../articles/callable_bond.htm">Callable bonds</a> may be callable on multiple dates or, in other cases, on any date following the <a href="../articles/callable_security.htm">first call date</a>, so yield to call can be calculated for different assumed call dates. Usually, it is calculated for the first date on which the bond may be called. This metric is called <b><a name="yield to first call">yield to first call</a></b>. However, a bond may be callable at different prices on different dates. <b> <a name="Yield to first par call">Yield to first par call</a></b> is calculated assuming the bond is called on the first date on which it is callable at its par value. <a name="Yield to worst"><b>Yield to worst</b></a> is the minimum yield obtainable based on all possible call dates as well as the possibility that the bond is never called. Accordingly, yield to worst is always less than or equal to YTM.</p> <p class="body">Yield to worst would seem the solution for calculating a meaningful metric of yield for callable bonds, but it is not. The problem is that it is static. It ignores the likelihood that interest rates will fluctuate over the life of the bond. A bond's call feature is a <a href="../articles/option.htm">call option</a> in every sense of the word. It has both an <a href="../articles/time_value_and_intrinsic_value.htm">intrinsic value</a> and a <a href="../articles/time_value_and_intrinsic_value.htm">time value</a>. Seen in this light, yield to worst is the (discounted) intrinsic value of the call feature. It ignores the time value. </p> <p class="body">The theoretically most meaningful metric of yield for bonds with embedded options is <a href="../articles/option_adjusted_spread.htm">option-adjusted yield</a>. This is widely used for <a href="../articles/mortgage_backed_security.htm"> mortgage-backed securities</a> (MBSs). It is not as widely used for callable corporate bonds. The problem is not theoretical so much as practical. The metric must be calculated with a fixed income option pricing model. Different institutions use different models, and these may not be easy to calibrate to the market. If inputs, including assumed <a href="../articles/volatility.htm">implied volatilities</a>, are somewhat arbitrary, then so is the output. An institutional investor who queries several dealers about the option-adjusted spread on a particular MBS is likely to receive a broad range of opinions.</p> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="345" align="left" id="table11"> <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">Mathematically, yields are like interest rates. This means they may be expressed according to different <a href="../articles/compounding.htm">compounding</a> conventions—<a href="../articles/compounding.htm">annual compounding</a>, <a href="../articles/compounding.htm">semiannual compounding</a>, <a href="../articles/compounding.htm">continuous compounding</a>, etc. This is not much of an issue for nominal yield or current yield. Based on how they are calculated, they necessarily reflect the compounding convention of the bond for which they are calculated. For example, if a bond pays quarterly coupons, the quarterly coupon could be extracted from the nominal yield by dividing by four and multiplying by the par value—math that is consistent with quarterly compounding. Since YTM or yield to call is an internal rate of return, they could be quoted according to any compounding convention. In practice, they are quoted based on the frequency with which a bond pays coupons—semi-annual compounding for most bonds.</p> <p class="body">Short-term <a href="../articles/discount_instrument.htm">discount instruments</a>, such as <a href="../articles/treasury_bill.htm">T-bills</a>, are generally quoted as <a href="../articles/discount_yield.htm">discount yields</a>. These may be converted to <a href="../articles/bond_equivalent_yield.htm">bond equivalent yields</a> for comparison with yields quoted on coupon-bearing instruments.</p> <p class="body">Yields are also calculated for <a href="../articles/common_stock.htm">stocks</a>. The formula is analogous to that for the current yield of a bond. Not surprisingly, it is also called <b><a name="current yield (stock)">current yield</a></b>, although the name <b><a name="dividend yield">dividend yield</a></b> is also used. The formula is </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/yield_[5].gif" width="324" height="41"></td> <td width="5%" align="right">[5]</td> </tr> </table> <p class="body">The numerator is calculated as the value of the most recently declared <a href="../articles/common_stock.htm">dividend</a> multiplied by the number of times a dividend is payable a year. The denominator is simply the stock's current market price. For example, if a stock currently pays a <a href="../articles/currency_codes.htm">USD</a> 1.05 dividend four times a year, and it last traded at a price of USD 132.00, its current yield is 3.18%.</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 align="left" class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/coupon_bond.htm">bond</a> Securitized debt.</p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/bond_accrued_interest.htm">bond accrued interest</a> Interest that is earned but not yet paid on a bond.<p align="left" class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/bond_equivalent_yield.htm">bond-equivalent yield</a> A convention for converting discount yields to a form more comparable to bond yields.</p> <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/callable_security.htm">callable security</a> </strong>A security that can be retired ("called" or redeemed") early.<p align="left" class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/common_stock.htm">common stock</a> Non-preferred stock.</p> <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/compounding.htm">compound interest</a> Any of several methods of crediting interest in which interest is earned on interest.</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/corporate_bond.htm">corporate bond</a> A bond issued by a corporation.</strong></p> <p align="left" class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/discount_yield.htm">discount yield</a> A convention for calculating yield on a discount instrument.</p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/duration_and_convexity.htm">duration and convexity</a> Risk metrics employed in fixed income markets.<p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/fixed_income_term_structure.htm">fixed income term structures</a> Overview article.</p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/interest_rate_risk.htm">interest rate risk</a> Risk due to uncertain future interest rates.</p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/interest_rate_spreads.htm">interest rate spreads</a> Discusses credit spreads, liquidity spreads, optionality spreads, etc. in the fixed income markets.<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/junk_bond.htm">junk bond</a> A bond whose credit rating is below BBB-.</strong><p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/option_adjusted_spread.htm">option-adjusted spread</a> Yield spread not attributable to embedded options.</p> <p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/par_value.htm">par value</a> A stated value for a security.</p> <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/preferred_stock.htm">preferred stock</a> Stock that is senior to common stock and pays a fixed dividend.</strong><p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/return.htm">return</a> Any of a number of metrics for the change in an asset's or portfolio's accumulated value.<p class="explanatory_text"> <img border="0" src="../images/bullet_link_glossary.gif" width="26" height="15"><a href="../articles/security.htm">security</a> A financial instrument such as a stock or bond.</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 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="table15"> <tr> <td width="100%"> <p class="explanatory_text"> <img border="0" src="../images/bullet_bullhorn_narrow.gif" align="left" width="27" height="22"><b><a target="_top" href="http://www.riskarchive.com/link_thread/01-3/000002d5.htm">Dividend Yield of S&P 500</a></b> <i>29 Aug 2001</i><br> Challenges of calculating a dividend yield for the S&P 500.</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="table16"> <tr> <td width="100%" bgcolor="#FFFFFF"> <p align="center" style="margin-top: 18"><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, 2005<p align="center"><map name="FPMap1"> <area target="_top" href="http://www.contingencyanalysis.com" shape="rect" coords="0, 0, 240, 88"> </map><img border="0" src="../images/logo_glossary_white.gif" usemap="#FPMap1" width="241" height="89"></td> </tr> </table> </td> </tr> </table> </td> <td>  </td> </tr> </table> </div> </body>