This tutorial is the first in two parts covering fixed income.  The objective of these sessions is to build on the foundation created in Level 1 in order to establish a competency of valuing more complex fixed income securities beyond basic coupon paying and zero coupon bonds.

Given the complexity of some of the material plus the need to recall certain concepts from Level 1, candidates are advised to keep Level 1 materials available as reference when preparing for the Level 2 fixed income questions.

A reasonable expectation for students is to expect two item sets (twelve questions) on the exam covering material from parts 1 and 2 of fixed income.

This module aligns with Study Session 14 material in the Level II CFA Program Curriculum ©.

NOTES:

The Fixed Income topics of the Level 2 exam draw heavily upon the foundation created in Level 1.  Candidates are strongly encouraged to review the following from Level 1:
<ul>
	<li>How to value annual pay bonds with a <a href="https://financetrain.com/cfa-calculator-financial-calculator-for-cfa-exam/">CFA approved calculator</a>.</li>
	<li>How to value zero coupon bonds with a CFA approved calculator.</li>
	<li>The relationship between par, spot, and forward interest rates.</li>
	<li>The concept and formula to calculate a bond’s effective duration.</li>
</ul>
<div class="formula1">Effective Duration = (Bond Price <sub>lower rate</sub> – Bond Price <sub>higher rate</sub>) / (2 * Bond Price <sub>current</sub> * change in interest rate)</div>
<ul>
	<li>The concept and formula to <a href="https://financetrain.com/bond-duration-and-convexity-simplified-part-1-of-2/">calculate a bond’s convexity</a>.</li>
</ul>
<div class="formula1">Effective Convexity = (Bond Price <sub>lower rate</sub> + Bond Price <sub>higher rate</sub> - (2 * Bond Price <sub>current</sub>)) / (2 * Bond Price <sub>current</sub> * change in interest rate<sup>2</sup>)</div>
<ul>
	<li>Negative convexity of callable bonds on the price-yield graph.</li>
	<li>Price floor of a putable bond on the pried-yield graph.</li>
</ul>
Never, ever, ever, ever forget that the value of a bond moves inversely with interest rate changes!  If interest rates go up, then the value of the bond will drop.

<strong>Material:</strong>

The following material will be covered in this tutorial:

I.          <a href="https://financetrain.com/principles-of-credit-analysis/">Credit Analysis</a>

II.        The Term Structure and Volatility of Interest Rates

III.       Bonds with Embedded Options

<strong> <br clear="all" /> </strong>

CFA Level 2: Fixed Income Part 1 – Introduction

<p>Credit Risk to Investors: Three Types</p>



<ul><li><strong>Default Risk:</strong> The risk that a borrower fails to make an interest or principal payment on schedule.</li><li><strong>Credit Spread Risk:</strong> The risk that market conditions change in a manner that causes the yield spread of a fixed income security to widen against its benchmark yield.</li><li><strong>Downgrade Risk:</strong> This is the risk that the value of a fixed income security will decrease because the borrower’s credit worthiness has been downgraded by a credit rating agency, such as Moody’s.</li></ul>



<h2>Corporate Credit Analysis and the “Four C’s of Credit”</h2>



<p>The “four C’s of credit” provide an analytical framework evaluating the credit quality of a company.</p>



<ul><li><strong>Character:</strong> This is an interpretation of managerial ability.  Does the company have a sound strategy?  Is the company financially conservative?  Does leadership respond effectively to a changing business environment?  Etc.</li><li><strong>Capacity:</strong>This is an evaluation of the company’s ability to generate sufficient cash flows to service debt on time. <ul><li>In analyzing “capacity”, an analyst will look at <a href="https://financetrain.com/common-ratios-in-financial-analysis/" class="rank-math-link">profitability ratios, liquidity ratios and solvency ratios</a> (including interest coverage ratios).</li><li><strong>Discretionary Cash Flow = Cash Flow from Ops – CapEx – Cash Dividend</strong></li><li>Analysts will also want to look for off-balance sheet financing techniques, such as the use of operating leases, and also understand the frequency and application of short term debt financing. </li></ul></li></ul>



<ul><li><strong>Collateral:</strong> This is an evaluation of the quality of a company’s assets.&nbsp; Are the assets sufficiently valuable and liquid enough to serve as borrowing collateral?&nbsp; Can the assets be sold in order to return funds in the event of default?</li><li><strong>Covenants:</strong>The analyst will need to ensure that the bond indenture contains terms that will facilitate debt payment.
<ul>
<li><strong>Affirmative covenants:</strong> Borrower promises to lenders.</li>
<li><strong>Negative covenants:</strong> Constrain borrow activities.</li>
<li>Common tests included in bond covenants include:
<ul>
<li>Maintenance test: Specifies minimum interest coverage ratios.</li>
<li>Working capital requirements: Specify minimum levels of working capital.</li>
<li>Cash flow test: Specify minimum cash flow levels.</li>
<li>Debt incurrence test: Restricts a company from issuing new debt unless interest coverage exceeds a specified level.</li>
<li>Restricted subsidiaries are subsidiaries must be consolidated with the parent for the above covenant tests.</li>
</ul>
</li>
</ul>
</li></ul>

Principles of Credit Analysis

“Junk” bonds are a special segment of the corporate debt universe. High yield bonds, also called non-investment grade, speculative grade, or junk bonds, are the bonds rated below investment grade. As the rating suggests, these bonds carry a higher risk of default, and pay a higher yield to compensate for the higher risk.

When evaluating high yield debt, the analyst must pay close attention to:
<ul>
	<li>Debt structure</li>
	<li>Corporate Structure</li>
	<li>Covenants</li>
</ul>
<strong>Debt Structure</strong>

High yield borrowers may utilize the following debt types:
<ul>
	<li>Bank loans are commonly short term and have priority over other corporate debt if liquidation occurs.</li>
	<li>Broker loans are commonly intermediate in term.</li>
	<li>Reset notes will have coupons that are periodically adjusted to maintain the bond’s price at par.</li>
	<li>Senior debt is not senior to bank loans in liquidation; if the senior debt is zero-coupon, then analysts must ensure that the company can make the cash payment at maturity.</li>
	<li>Senior subordinated debt is only prioritized over subordinated debt.</li>
	<li>Subordinated debt can include payment in kind (PIK) bonds which allow the borrower to pay interest in the form of more bonds.</li>
</ul>
<strong>Corporate Structure </strong>

High yield borrowers may be structured as holding companies.  Therefore, the analyst may need to evaluate every subsidiary to comprehensively assess risk.

<strong>Covenants</strong>

Analysts should review the covenants of high yield issuers, but should also keep an eye out for loopholes.
<h2>Equity Approach to Junk Bonds</h2>
The returns from high yield debt more closely correlate with stocks than with investment grade bonds.  This implies that analysts may want to employ the same type of equity valuation cash flow forecasting when valuing high yield debt.

High Yield Corporate Debt (aka Junk bonds)

An asset-backed security is a security whose price and income is derived from a specific pool of underlying assets (or collateral).

These securities are debt obligations that represent claims to the payments or cash flows from pools of different asset classes (loans). Some examples of these assets are credit card loans, auto loans, bank loans, etc. If the underlying collateral is mortgages, then the securities are called <a href="https://financetrain.com/introduction-to-mortgage-backed-securities/">mortgage-backed securities</a>. These loans from banks, mortgage companies, and other originators are assembled into pools. The entity then issues securities based on these pools that represent claims on the principal and interest payments/cash flows made by borrowers on the loans in the pool.

Common considerations for analyzing asset-backed securities include:
<ul>
	<li><strong>Credit quality of the underlying collateral.</strong> This is the most important factor, as the quality of the collateral will define the success of an ABS deal, the timely payments of cash flows, etc. We also need to look for the concentration risk, that is, the scenario where an asset pool holds loans from only a small group of borrowers, or is concentrated in a particular demographic.</li>
</ul>
<ul>
	<li><strong>Servicer quality:</strong> Given the servicer’s key role in administering and managing the loan pool, it is imperative to understand the servicer’s ability to effectively perform its functions.</li>
</ul>
<ul>
	<li><strong>Payment structure and cash flow capability</strong> of the asset pool. The analyst must carefully analyze the payment structure and the cash flows of the asset pool. The availability of liquidity / credit enhancement / insurance are also important. In case of a fully supported ABS transaction, the repayment is supported by a financial guarantee, such as a surety, letter of credit, third-party guarantee, or liquidity facility. In case of a partially-supported ABS deal, the repayments are supported by cash flows from the pool, and liquidity and credit enhancement.</li>
	<li><strong>Legal structure</strong> of the asset backed security.</li>
</ul>
<strong> </strong>

Analyzing Credit of Asset Backed Securities

Two general types of municipal <a href="https://financetrain.com/c/49">bonds</a> (or “munis” as they are commonly called):
<ul>
	<li>Tax-backed or general obligation bonds.</li>
	<li>Revenue bonds.</li>
</ul>
These bond types require their own distinct approaches when performing <a href="https://financetrain.com/principles-of-credit-analysis/">credit analysis</a>.

<strong>Tax backed bonds: factors to consider</strong>
<ul>
	<li>The debt burden of the community.  This is commonly examined in terms of debt per capita, debt as a percent of real estate values, and/or debt as a percent of community personal income.</li>
</ul>
<ul>
	<li>The community’s budget history (i.e. does the community have a history of budget deficits?).</li>
</ul>
<ul>
	<li>Calculate the community’s tax base and its access to other sources of revenue.</li>
</ul>
<ul>
	<li>Evaluate the community’s socioeconomic landscape.</li>
</ul>
<strong>Revenue bonds: factors to consider</strong>
<ul>
	<li>Four C’s Analysis: With respect to cash flow analysis, revenue bonds are more similar to corporate bonds, than tax backed bonds are, so a four C’s approach is relevant when assessing the credit quality of a revenue bond issue.</li>
</ul>
<ul>
	<li>Understand the revenue source backing the bond.</li>
</ul>
<ul>
	<li>Understand the flow of funds for the bond. Bondholders commonly receive a net revenue pledge, which means that debt service payments come after operational expenses of the municipality’s project are covered.</li>
</ul>
<ul>
	<li>Understand the charge rates, which is the manner in which the customers of the bond financed project are charged for using the service provided by the project.</li>
</ul>
<ul>
	<li>Understand the legal priority of revenue claims.</li>
</ul>
<ul>
	<li>Understand the conditions under which additional bonds can be issued.</li>
</ul>
 

Analyzing Credit of Municipal Bonds

Sovereign debt is debt issued by foreign governments.

Sovereign debt is unique because analysts and investors will need to evaluate not only the government’s ability to repay (economic risk), but also its willingness to repay (political risk).

Because default rates on sovereign debt issued in foreign currency have been higher than sovereign debt issued in local currency (after all, a government can print its own currency, but not the currency of another country), two separate ratings (a foreign currency rating and a local currency rating) are typically issued for sovereign debt.

While the four C’s approach is relevant to sovereign debt, the principles must be considered in a macroeconomic and political context.

Sovereign debt analysis takes on a more qualitative nature than that of corporate date, which can be more numbers driven.  Additionally, audited corporations may report more accurate data to the public than foreign governments.

Sovereign Debt

<ul>
	<li><strong>Term Structure of Interest Rates:</strong> The <a href="https://financetrain.com/the-term-structure-of-interest-rates/">term structure of interest rates</a> is the relationship between the spot rate of U.S. Treasury securities and their time until maturing.</li>
	<li><strong><a href="https://financetrain.com/understanding-yield-curve/">Yield Curve</a>:</strong> The relationship between U.S. Treasury yields and time to maturity.</li>
</ul>
<h2>Three Shapes of the Yield Curve</h2>
<ul class="list2">
<ul class="list2">
	<li><strong>Positive Slope:</strong> Short term bonds have lower yields than long term bonds. Because a longer borrowing time frame entails greater uncertainly, a positively sloped yield curve is considered "normal."</li>
</ul>
</ul>
<ul class="list2">
<ul class="list2">
	<li><strong>Flat:</strong> Yields across the spectrum, primarily from two year to thirty year are all about the same.</li>
	<li><strong>Inverted (negative slope):</strong> Longer term bonds have lower yields than short term bonds. This scenario is associated with anticipation of dropping interest rates in expectation of a recession.</li>
</ul>
</ul>
<img src="/wp-content/uploads/positiveyc.png" alt="" width="200px" /><img src="/wp-content/uploads/flatyc.png" alt="" width="200px" /><img src="/wp-content/uploads/negativeyc.png" alt="" width="200px" />

Three Shapes of the Yield Curve

<h2>Parallel Shift</h2>

Rates across the maturity spectrum change by a constant amount and the slope of the <a href="https://financetrain.com/understanding-yield-curve/">yield curve</a> remains consistent.

<img src="https://financetrain.com/wp-content/uploads/parallel-shift.png" alt="" />

<h2>Non-Parallel Shifts</h2>
<ul class="list2">
	<li><strong>Twist:</strong> The slope of the yield curve becomes flatter (the spread between short and long term yields narrows) or steeper (the spread between short and long term yields widens).</li>

<img src="https://financetrain.com/wp-content/uploads/twist.png" alt="" />

	<li><strong>Butterfly:</strong> Change to the curvature of the yield curve.<br><br>



<strong>Positive butterfly:</strong> The yield curve goes loses some of its "hump" and becomes straighter.



<strong>Negative butterfly:</strong> The yield curve takes on more of a hump and ceases to look similar to a straight line.</li>
<img src="https://financetrain.com/wp-content/uploads/butterfly.png" alt="" />
</ul>

Parallel and Non-parallel Shifts in Yield Curve

Zero coupon U.S. Treasuries have historically seen their returns driven by the following:
<ul>
	<li><strong>Interest Rate Level Changes:</strong> This is measured by <a href="https://financetrain.com/what-is-macaulay-duration/">duration</a> and has shown to account for 90% of historical investor returns.This is the inverse of the P/E ratio.</li>
	<li><strong>Yield Curve Slope Changes:</strong> This is measured by key rate duration and accounts for 8 - 9% of returns. These are changes in which the <a href="https://financetrain.com/understanding-yield-curve/">yield curve</a> becomes more or less steep.</li>
	<li><strong><a href="https://financetrain.com/parallel-and-non-parallel-shifts-in-yield-curve/" title="Parallel and Non-parallel Shifts in Yield Curve">Yield Curve Curvature Changes</a>:</strong> These changes are illustrated by the positive and negative butterfly shifts and account the small remainder of returns.</li>
</ul>

<h2>Bond Price Risk: Duration and Yield Volatility Influences</h2>

As interest rates change, a bond's price sensitivity is a function of:
<ul>
	<li><b>Maturity:</b> Bonds with shorter maturities have less price volatility in the face of changing interest rates.</li>
	<li><b>Coupon:</b> Low coupon bonds show more price volatility than high coupon bonds.</li>
	<li><b>Interest Rate Level:</b> When interest rates are higher, bond price volatility tends to be lower.  In other words, when rates tend to be exceptionally low, bond prices are more sensitive to an increase in interest rates.</li>
</ul>




Factors Driving Treasury Investment Returns and Bond Price Risk

The Treasury bond <a href="https://financetrain.com/understanding-yield-curve/">yield curve</a> can be built from several different sources:
<div class="formula1">
<ul class="list2">
 	<li><strong>On the Run Treasuries:</strong> This entails plotting the observed yields from the most recently issued Treasuries.</li>
 	<li><strong>On the Run + Selected Off the Run Treasuries:</strong> On the run issues may not cover the all time periods needed, particularly for longer maturities, so off the run issues may be incorporated into yield curve construction.</li>
 	<li><strong>All Treasuries:</strong> This is a complete picture of the yield curve, but some issues, such as those which are <a href="https://financetrain.com/price-of-a-callable-bond/">callable</a>, would need to be excluded.</li>
 	<li><strong><a href="https://financetrain.com/treasury-strips/">Treasury Coupon STRIPS</a></strong> (separate trading of registered interest and principal securities): interest coupon STRIPS can be used to construct the yield curve, but this approach has the following deficiencies:</li>
 	<li><strong>Liquidity:</strong> Lower than liquidity of coupon paying <a href="https://financetrain.com/general-characteristics-of-bonds/">bonds</a>.</li>
 	<li><strong>U.S. Taxes:</strong> Tax treatment may be different for STRIPS.</li>
 	<li><strong>Foreign Taxes:</strong> Principal strips and coupon strips may be treated differently for taxation purposes in foreign countries.</li>
</ul>
</div>

Yield Curve Construction with Treasuries

<ul>
 	<li>The London Inter-bank Offered Rate (LIBOR) is the U.S. dollar borrowing rate for high quality banks among one another, outside the U.S.</li>
 	<li><strong>Swap Rates:</strong> The fixed interest rate in a <a href="https://financetrain.com/details-of-an-interest-rate-swap-contract/">swap contract</a> where two parties have agreed to exchange fixed rate and floating rate payments based on a notional principal.</li>
 	<li>LIBOR is commonly used as the floating rate in swap agreements.</li>
 	<li><strong>LIBOR Swap Rate Curve:</strong> Rates at future time periods to convert fixed rates to floating rates and floating rates to fixed rates.</li>
 	<li>The swap rate curve may be a better basis for the market<a href="https://financetrain.com/understanding-yield-curve/"> yield curve</a> than the government bond yields because:
<ul>
 	<li>The swap market is not regulated by governments, so swap rates are more comparable across different countries where foreign and domestic investors may receive different tax treatment.</li>
 	<li>The swap market may be unaffected by changes in demand for government bonds in the repurchase (or "repo") market.</li>
 	<li>Theoretically, the swap curve reflects bank <a href="https://financetrain.com/overview-of-credit-risk/">credit risk</a>.</li>
 	<li>The swap market has more maturities with which to construct a yield curve than the government bond market.</li>
</ul>
</li>
</ul>

LIBOR Swap Rate Curve

The shape of the yield curve has two major theories, one of which has three variations.
<ul>
	<li><b>Market Segmentation Theory:</b> Assumes that borrowers and lenders live in specific sections of the yield curve based on their need to match assets and liabilities.  The theory goes further to assume that these participants do not leave their preferred maturity section.  Thus, the <a href="https://financetrain.com/three-shapes-of-the-yield-curve/" title="Three Shapes of the Yield Curve">yield curve shape</a> is determined by supply and demand at different maturities.

The Market Segmentation Theory could be used to explain any of the three yield curve shapes.
	</li>
	<li><b>Expectations Theories (3):</b>  There are three variations of the Expectations Theory, one being "pure" and the other two "biased".  All three variations share a common assumption that short term forward interest rates reflect market expectations of short term rates will be in the future.</li>
	<ol>
		<li><b>Pure Expectations Theory ("pure"):</b> Only market expectations for future rates will consistently impact the yield curve shape. A positively shaped curve indicates that rates will increase in the future, a flat curve signals that rates are not expected to change, and an inverted yield curve points to interest rates falling in the future.</li>
		
		<li><b>Liquidity Preference Theory ("biased"):</b> Assumes that investors prefer short term bonds to long term bonds because of the increased uncertainty associated with a longer time horizon.  Therefore investors demand a liquidity premium for longer dated bonds. This theory has a natural bias toward a positively sloped yield curve.</li>

		<li><b>Preferred Habitat Theory ("biased"):</b> Postulates that the shape of the yield curve reflects investor expectations of future interest rates, but rejects the notion of a liquidity preference because some investors prefer longer holding periods.  The Preferred Habitat Theory relies heavily on the notion that investors will match assets and liabilities.</li>
	</ol>


Theories of the Term Structure of Interest Rates

Effective <a href="https://financetrain.com/bond-duration-and-convexity-simplified-part-1-of-2/">duration</a> calculates the approximate change in a bond’s price given a 100 basis point (1%) move in interest rates as part of a <a href="https://financetrain.com/parallel-and-non-parallel-shifts-in-yield-curve/" title="Parallel and Non-parallel Shifts in Yield Curve">parallel shift in the yield curve</a>.

When the <a href="https://financetrain.com/parallel-and-non-parallel-shifts-in-yield-curve/" title="Parallel and Non-parallel Shifts in Yield Curve">yield curve shifts in a non-parallel manner</a>, the portfolio’s effective duration cannot be used to estimate the change in portfolio value.

Key rate duration is the duration at specific maturity point on the <a href="https://financetrain.com/understanding-yield-curve/">yield curve</a>. Keeping all other maturities constant, key rate duration is a measure of the sensitivity of a bond’s price to a 100 basis point change in yield for a given maturity.

When the yield curve changes in a non-parallel manner, key rate durations (and not the portfolio’s effective duration) must be used to estimate the change in portfolio value.

Key rate duration is calculated using the following formula:
<div class="formula1">

[latex size="3" background="F0F0F0"]Key Rate Duration = \frac{P_{-} - P_{+}}{2 \times 1 \% \times P_{0}} [/latex]
<br><br>
<p style="margin-top:10px;">Where:

P<sub>- </sub>= Price with a 1% decrease in yield

P<sub>+ </sub>= Price with a 1% increase in yield

P<sub>0 </sub>= Original price</p>
</div>
On the Treasury spot curve, there are 11 maturities. So, key rate duration can be calculated for each maturity. The sum of all key rate durations on the yield curve will be equal to the effective duration.

In order to estimate a portfolio’s change in value in the event of a non-parallel yield curve shirt, an analyst will need to perform a weighted average calculation utilizing the key rate durations to the portfolio’s weights at different maturities (i.e., the percent invested at two year, five year, ten year, and twenty year bonds).

Key Rate Duration

<ul class="list2">
<li><b>Step 1:</b> Calculate yield change ratios as follows: YCR <sub>t</sub> = r <sub>t</sub> / r <sub>t-1</sub> 
<p style="margin-top:10px;">The yield change ratios are typically daily ratios (i.e., today's yield or interest rate divided by yesterday's) that are annualized later at a later step in the process.</p>
</li>

<li><b>Step 2:</b> Convert yield change ratios into a continuously compounded return (X<sub>t</sub>) as follows: </li>
	<div class="formula1">X <sub>t</sub> = ln YCR<sub>t</sub> </div>
<li><b>Step 3:</b> Calculate the average of continuously compounded returns (X <sub>t</sub>) for the time period.</li>
<li><b>Step 4:</b> Sum the squared the differences between the individual continuously compounded rates of return and the average calculated in step 3.</li>
	<div class="formula1">= &Sigma;(X <sub>t</sub> - X <sub>average</sub>)<sup>2</sup></div>
<li><b>Step 5:</b> Divide the sum of squared differences by the number of time periods minus 1.</li>
	<div class="formula1">
	= step 4 value / (n-1)
	<br><br>In the context of statistics, this value represents the yield variance

	</div>
<li><b>Step 6:</b> Take the square root of step 5 to arrive at a periodic (commonly daily) standard deviation (&sigma; <sub>daily</sub>) for the bond's yield.
<br><br>This value represents the percentage of the yield's daily standard deviation and not the actual basis point standard deviation.
</li>
<li><b>Step 7:</b> Annualize daily percentage standard deviation.</li>
	<ul class="list2">
		<div class="formula1">&sigma; <sub>annual</sub> = &sigma; <sub>daily</sub> &times; &#8730;num. of trading days per year </div>
		<li>The annual standard deviation of a bond's yield is equal to the daily standard deviation multiplied by the square root of the number of trading days in a year.</li>
		<li>The convention is 250 trading days per year.</li>
		<li>This value reflects the percentage standard deviation of the yield, not the basis points standard deviation.</li>

	</ul>
<li><b>Step 8:</b> Compute the basis points the standard deviation of the <a href="https://financetrain.com/price-yield-relationship/">bond's yield</a>.</li>

	<div class="formula1">&sigma; <sub>yield</sub> = Yield * &sigma; <sub>annual</sub>
	<br><br>This value will reflect the standard deviation in terms of basis points around the current yield of the bond.
	</div>
	<li>A bond's yield can be analyzed in conjunction with the standard deviation of the yield in basis point terms from step 8 and z-score distribution to create a confidence interval for the bond's yield.</li>
	<li>Candidates are advised to apply this approach to practice questions in order to completely understand the analysis of yield volatility and be appropriately prepared for the exam.</li>
</ul>


How to Calculate Interest Rate Volatility?

<ul class="list2">
	<li>Whereas stocks have their ratio comparables with similar companies and certain indexes, bonds have <a href="https://financetrain.com/understanding-yield-curve/">yield</a> spreads.</li>
	<li>A bond may be considered under-valued or over-priced based on its yield spread above a relevant benchmark yield.</li>
	<li><b>Nominal Spread:</b> This is the difference in yield between the yield to maturity of a bond and the yield to maturity of a comparable benchmark.</li>
	<div class="special-area">
	Example, a fixed income analyst might compare the yield to maturity of a 10 year bond for a U.S. company with a high credit rating to the yield to maturity of 10 year U.S. Treasury bonds.
<br><br>
If the spread has widened in recent months, this could indicate that the company is showing signs of weakness, that the economy is showing signs of weakness, or that the bond is now under-valued by the market and a buying opportunity is at hand.
<br><br>
Nominal spread is best applied to traditional bullet bonds (i.e., bonds that pay a periodic fixed coupon payment and return the loaned principal at maturity).
<br><br>
For corporate bonds, the nominal spread reflects: credit risk, liquidity risk, and option risk.
<br><br>
When both bonds compared in the nominal spread are option free, there is no option risk reflected in the nominal spread.
	</div><br>
	
	<li><b>Z-Spread:</b> This is the zero volatility or static spread.</li>
	<div class="special-area">The Z-Spread reflects credit, option, and liquidity risk.</div><br>
	<li><b>Option Adjusted Spread (OAS):</b> This spread removes the effect of embedded options on future returns, to reflect non-option risks when comparing a bond to a benchmark.</li>
		<div class="special-area">
			<ul class="list2">
				<li>OAS reflects only credit and liquidity risk.</li>
				<li>The OAS is based on the Treasury spot curve and is considered the best tool for comparing the yields of bonds with embedded options to Treasury yields.</li>
				<li>When the OAS for a bond is higher than the OAS of comparable bonds relative to the same benchmark, the bond is considered undervalued.</li>
				<li>Alternatively, when the OAS for a bond is lower than the OAS of comparable bonds against their relevant benchmark, the bond is considered overvalued.</li>
				
			</ul>
		</div>
</ul>


Benchmark Yield Spreads

<h2>The Binomial Interest Rate Tree</h2>



<p>An issuer's bonds can be valued with a binomial interest rate tree. In order to do this, the analyst will need to:</p>



<ul><li>Calculate the spot rate curve for the borrower based on that company's most recently issued debt.</li><li>Use the spot rate curve to calculate forward rates for the issuer.
<ul>
<li>Applying forward rates when discounting cash flows is arbitrage free valuation.</li>
</ul>
</li><li>Develop a higher and lower interest rate scenario around each projected forward rate on the tree, based on an estimation of interest rate volatility.</li><li>If necessary, adjust the tree so it properly values the currently issued bonds.
<ul class="list2">
<li>If the tree leads to a bond value that is above the market price, then interest rates will need to be increased; if the tree leads to a bond value that is below the market price, then interest rates will need to be lowered.</li>
</ul>
</li><li>For bonds with <a href="https://financetrain.com/common-options-embedded-in-a-bond-issue/">embedded options</a>, cash flows will need to be forecasted along all of the interest rate paths; these cash flows will need to be discounted to the present value to create a value for the bond.</li></ul>



<h2>Valuing an Option Embedded Bonds</h2>



<h3>Valuing a Callable Bond from a Binomial Interest Rate Tree</h3>



<ul><li>When valuing a <a href="https://financetrain.com/price-of-a-callable-bond/" class="rank-math-link">callable bond</a> with a binomial interest rate tree, the analyst must assume that the bond will be called back by the issuer when the strike price is exceeded.</li><li>At any nodes where the calculated bond price exceeds the call price, the calculated price is replaced with the call price.</li></ul>



<h3>Valuing a Putable Bond from an Binomial Interest Rate Tree</h3>



<ul><li>When valuing a putable bond with a binomial interest rate tree, the analyst must assume that the bond will be put back to the issuer when the price falls below the put floor.</li><li>At any nodes where the calculated bond price is below the put price, the calculated price is replaced with the put price.</li></ul>



<h2>The Value of an Embedded Option</h2>



<div class="formula1"><b>Price <sub>callable bond</sub> = Price <sub>ncb</sub> - Call <sub>option value</sub> </b>
<p>&nbsp;</p>
<p>The price of a callable bond is lower than that of a comparable bond that does not contain an embedded option.</p>
</div>



<div class="formula1"><b>Price <sub>putable bond</sub> = Price <sub>npb</sub> + Put <sub>option value </sub></b>
<p>&nbsp;</p>
<p>The price of a putable bond is higher than that of a comparable bond that does not contain an embedded option.</p>
</div>



<ul class="list2"><li>Put options increase the cost of the bond to the investor as they serve as an "insurance policy" that the value of the bond cannot drop below the floor established by the put.</li><li>Call options reduce the cost of the bond to the investor as the call serves creates a ceiling for the borrower. By embedding a call option in its bond issuance, the borrower is preserving the ability to refinance its debt on more favorable terms, should interest rates drop significantly.</li><li>The Effect of Interest Rate Volatility on the Value of Embedded Options
<ul class="list2">
<li>As interest rate volatility increases, so do the value of embedded options.</li>
<li>For example, in the case of a putable bond, the value of the embedded put goes up when interest rate volatility increases. This increases the purchase price of the putable bond to the investor.</li>
</ul>
</li></ul>

Valuing an Option Embedded Bond using Binomial Interest Rate Tree

Some common momentum indicators include:

<ul>
	<li><strong>Convertible Security:</strong> Debt security that can be converted into a specified number of shares of the issuer's common stock at the option of the security owner.</li>
	<li><strong>Exchangeable Security:</strong> Debt security that can be converted into a specified number of common stock shares for a company other than the exchangeable security issuer.</li>

</ul>
<div class="formula1">
<h3>Convertible Bond Analysis Process</h3>
<ul>
	<li>Calculate Conversion Value: which is the current market value of the shares that the bond can be converted into.</li>
<ul>
	<li>Conversion Value = Market Price per Common Share * Conversion Ratio</li>
	<li>Straight Value: price where the bond would trade if it were not convertible to stock.</li>
	<li>Minimum Value of a Convertible Bond: a convertible bond should, at the lowest, trade at the higher of either the conversion value or straight value.</li>
</ul>
	<li>Calculate Market Conversion Price: which is the price per share paid when buying the convertible bond and turning it into stock.</li>
<ul>
	<li>Market Conversion Price = Convertible's Market Price / Conversion Ratio</li>
</ul>
	<li>Calculate Market Conversion Premium per Share: which is the excess paid per share when the convertible is bought and converted rather than simply buying the common stock.</li>
	<li>Market Conversion Premium per Share =Market Conversion Price - Current Market Price per Share of Stock</li>
	<li>Calculate Market Conversion Premium Ratio: which is the share price mark-up percentage when the convertible is bought and converted rather than simply buying the common stock.</li>
<ul>
	<li>Market Conversion Premium Ratio = Market Conversion Premium per Share / Current Market Price per Share of Stock</li>
</ul>
	<li>Calculate the Premium Payback Period: which is the length of years it takes an investor to earn back the conversion premium, given the higher income yield on the bond than the income yield on the stock.</li>
<ul>
	<li>Premium Payback Period = Market Conversion Premium per Share / Extra Income per Share</li>
	<li>Extra Income per Share = (Bond Coupon Interest - (Conversion Ratio * per Share Dividend)) / Conversion Ratio</li>
</ul>
	<li>Calculate Premium over Straight Value: this value helps investors interpret downside risk of a convertible bond because the convertible will not trade below its straight bond value.</li>
<ul>
	<li>Premium over Straight Value = (Market Price of Convertible / Straight Value) - 1</li>
</ul>
</ul>
</div>
<ul>
	<li>When thinking in a realistic manner about convertible bonds, the convertible bond for a company will trade more like a straight bond when the stock price is low because the convertible option has almost no value. Alternatively, the convertible bond will trade more like a stock when the company's share price is high because the conversion option has value.</li>
</ul>
<h2>Option Based Valuation for Convertible Bonds</h2>
As an alternative to the approach outlined in the prior segment, an analyst can take apply option prices to value a convertible bond.
<div class="formula1">Price <sub>convertible bond</sub> = Price <sub>straight bond</sub> + Price <sub>stock call option</sub> - Price <sub>bond call option</sub> + Price <sub>bond put option</sub>
<ul class="list2">
	<li>The bond call is applicable if the issuer's convertible bond is callable.</li>
	<li>The bond put is applicable if the issuer's convertible bond is putable.</li>
</ul>
Note that this formula is an identity, so any one variable can be solved for if the other variables are known.

</div>
<h2>Risk/return Profile of a Convertible Bond</h2>
When thinking about the risk/return profile of a convertible bond, consider:
<ul>
	<li>The convertible bond will outperform the company's stock, when the stock does not change in value because the interest income from the bond is usually higher than the dividend of the stock.</li>
	<li>The convertible bond will outperform the company's stock, when the stock declines in value because the convertible has a "price floor" equal to the straight bond value.</li>
	<li>The convertible bond will underperform the company's stock, when the stock appreciates significantly because the investor paid a conversion premium on the convertible bond.</li>

</ul>


 

How to Price Convertible Bonds?

Fixed Income Part 1

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COURSE

Fixed Income Part 1

LESSONS