Option-Adjusted Spread

<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">Option-Adjusted Spread</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="99%" align="left" valign="top"><p class="word_list"> <a href="#Option-adjusted spread">option-adjusted spread</a><p class="word_list"> <a href="#option-adjusted yield">option-adjusted yield</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">Fixed income instruments are often described as trading at a <a href="../articles/spreads.htm">spread</a> over some benchmark <a href="../articles/yield.htm">yield</a>. For example, a 10-year <a href="../articles/callable_bond.htm">callable</a> <a href="../articles/corporate_bond.htm">corporate bond</a> might have a <a href="../articles/yield.htm">yield to maturity</a> (YTM) of 6.7%. If the <a href="../articles/treasury_securities.htm">on-the-run</a> 10-year <a href="../articles/treasury_note_and_bond.htm">Treasury note's</a> YTM is 5.5%, the bond would be described as trading at a spread of 1.2%, or 120 <a href="../articles/basis_point.htm">basis points</a>, over the Treasury. Such spreads can be attributed to a number of factors, including <a href="../articles/credit_risk.htm">credit quality</a>, <a href="../articles/liquidity.htm"> liquidity</a> and embedded <a href="../articles/option.htm">options</a>. </p> <p class="body">If a <a href="../articles/coupon_bond.htm">bond</a> has embedded options, its <b><a name="Option-adjusted spread">Option-adjusted spread</a></b> (OAS) is the spread at which it presumably would be trading over a benchmark if it had no embedded optionality. More precisely, it is the instrument's current spread over the benchmark minus that component of the spread that is attributable to the cost of the embedded options:</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/option_adjusted_spread_[2].gif" width="273" height="36"></td> <td width="5%" align="right">[1]</td> </tr> </table> <p class="body">or, rearranging:</p> <table border="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" cellpadding="0" height="36" id="table7"> <tr> <td width="100%" align="center"> <img border="0" src="../formulas/option_adjusted_spread_[1].gif" width="434" height="67"></td> <td width="5%" align="right" valign="top"> <p style="margin-top: 2; margin-bottom: 12">[2]</p> <p style="margin-top: 16">[3]</td> </tr> </table> <p class="body">OAS can be calculated with respect to various benchmarks: Treasuries, <a href="../articles/interest_rate_swap.htm">swap rates</a>, a short-term "risk-free" rate, etc. Most often, the benchmark is Treasuries. To avoid dependency on a particular benchmark, <b><a name="option-adjusted yield">option-adjusted yield</a></b> may be quoted instead of OAS:</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/option_adjusted_spread_[4].gif" width="348" height="35"></td> <td width="5%" align="right">[4]</td> </tr> </table> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="345" align="left" id="table9"> <tr> <td width="336" height="10"><font size="2"> </font></td> <td width="9" height="10"></td> </tr> <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">Prior to the 1970s, investors made only rudimentary efforts to adjust their analysis of fixed income instruments to recognize the effects of embedded options. There were several reasons for this. Back then, the bond market was less diverse than it is today. Instruments like <a href="../articles/mortgage_backed_security.htm">mortgage-backed securities</a> (MBS) didn't exist. I oversimplify only slightly if I describe the US market as offering two types of bonds: callable <a href="../articles/corporate_bond.htm">corporates</a> and non-callable Treasuries. Call features differed little from one bond to the next, so investors could reasonably compare corporates based on their <a href="../articles/yield.htm">yield to first call</a> or <a href="../articles/yield.htm">yield to worst</a>. Corporates offered yields in excess of Treasuries, and some of the excess yield could presumably be attributed to embedded call features, but there was no particular need to put a number on this. No one was shorting corporates against Treasuries as a volatility play! Another issue was the fact that analytics for assessing option values didn't exist. The <a href="../articles/black_scholes_1973.htm">Black-Scholes model</a> for pricing options had not yet been published. Computer technology was cumbersome and expensive. Finally, interest rates tended to be stable prior to 1970, so embedded call options weren't worth much to begin with.</p> <p class="body">All this started to change in the 1970s. New forms of fixed income instruments were brought to market. Interest rates became increasingly volatile. A robust theory of <a href="../articles/option_pricing_theory.htm">option pricing</a> emerged, and the processing power needed to implement the new theory became easier to use and less costly.</p> <p class="body">Option-adjusted spreads were first widely employed in the mortgage-backed securities market in the late 1980s. Investors were offered instruments with extraordinary current yields—500 or 600 basis points over Treasuries. To analyze these, they needed to somehow subtract out the yield component that was attributable to the embedded options. They wanted to know what the yield over Treasuries would be if the exact same instruments did not have embedded options. </p> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="345" align="left" id="table10"> <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">The value of option-adjusted spread analysis is that it enables investors to separate out optionality and judge the degree to which an instrument's yield compensates them for <a href="../articles/credit_risk.htm">credit risk</a>, <a href="../articles/liquidity_risk.htm">liquidity risk</a> or other such factors. Suppose an investor is comparing two similar bonds. Both have comparable maturities, credit qualities and liquidity, but they have different embedded options. The investor might purchase whichever bond has the higher option-adjusted spread—that bond would offer higher compensation for the risks being taken.</p> <p class="body">This is how OAS is used in theory. Practice is not so simple. OAS is more a philosophy that can be implemented in different ways than it is a well defined metric of yield. Models abound. Proprietary models used by bond dealers tend to be sophisticated. Those that are available to investors can be crude. Routinely, an investor will survey a number of dealers on the option-adjusted spread those dealers calculate for a particular MBS and be troubled by the broad range of replies. 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