CFA® Level I – Fixed Income Revision and Formulae for CFA® Level I Exam December 2011

CFA® Level I: Fixed Income Revision, SS 15, for the CFA® Level I December 2011.

Bond Indentures:

The bond indenture is the agreement in which all the rights of the bondholder as well as all the obligations related to the debt, on the part of the issuer, are documented in detail.

Affirmative Covenants:

These provide  details of activities that the issuer (borrower) must perform; such as paying taxes, maintaining property as collateral, paying interest and principal on a
timely basis and periodically reporting compliance to the Trustee.

Negative Covenants:

These provide details of restrictions on the issuer (borrower). Negative Covenants may include; restrictions on further borrowings, limits on dividend payments, restrictions on sale of assets and on purchase of own stock (Treasury Stock).

Basic Features of a Bond:

The Maturity of a bond is the term after which the bond is retired or paid back.

Par Value is the sum of money that will be repaid by the borrower at the end of the maturity term of the bond. The Par Value of the bond is fixed at the start. At any given time, the bond may be trading at, above or below its par value. However, at retirement of the bond, it is the Par Value that will be repaid to extinguish the debt.

The Coupon rate stated for the bond is the percentage rate of interest that will be paid by the issuer (borrower), to the bondholder (lender), on a periodic basis. In the U.S., the coupon payments are made semi-annually.

Bonds without Coupons:

Zero Coupon Bonds are bonds that do not have stated coupon rate. These are issued at a deep discount to their par value.

Accrual Bonds are another kind of bonds that do not have a coupon payment during the period these remain outstanding. However, all interest that
is due to the lender (bondholder) is accrued and paid along with the principal, at Maturity.

Bonds with Coupons:

Step-Up Notes have a low initial coupon, which increases once or more as a ‘Step-Up’ function.

Deferred-Coupon Bonds the interest payments are deferred for an initial period, called a ‘Deferred Period’. At the end of this time, the bond
begins to make regular, periodic payments to the bondholder.

Floating-Rate Bonds are also called variable rate securities; these bonds have coupon rates that are re-set periodically in relation to the changes in an
agreed reference rate. For example; Coupon Rate = LIBOR + Quoted Margin.

Mechanics of a Floating Rate Bond:

Once the coupon rate on a floater has been Re-Set, the new rate is paid at the end of the subsequent coupon period. Floating rate bonds may have a ‘Cap’ or a ‘Floor’ which determine the maximum or minimum values that the coupon rate can take on at any given time, in order to restrict the maximum and minimum limits for the coupon rate. Floating rate bonds may have a fixed or a variable quoted margin, which is added on top of the Reference Rate.

Accrued Interest on Bonds:

In order to separately account for the accrued interest on the bond, the price of the bond is expressed in two different ways; firstly with the accrued interest included in it, which is called ‘Full Price’ or ‘Dirty Price’. Alternatively the bond’s price without the accrued interest is referred to as the ‘Clean Price’ or simply ‘Price’.

Methods through which Bonds are paid off by the Issuer:

There are several methods according to which a bond is retired. The issuer can make the final principal repayment in a single lump sum, or the principal may be paid in partial repayments periodically.

Embedded Options:

Certain embedded options in bonds extend rights to the bondholders. These rights could include; a ‘Put Option’ or a ‘Conversion Option’. The presence of embedded options can create challenges in the valuation of bonds since the cash flows related to the bond cannot be forecasted with accuracy due to the possibility of exercise of an embedded option.

Margin Buying:

Investors can borrow funds via the brokers through who they trade in the securities markets. The investor puts a certain deposit percentage and the broker provides the rest as a loan. The broker in turn borrows these funds from the banks at a special rate called the ‘Call Money’ rate and adds a service charge.

Repurchase Agreements – REPO:

A REPO involves the sale of a security with a promise to repurchase at an agreed, higher price on a specified date. This period could be a single day ‘Overnight REPO’ or for a longer period ‘Term REPO’, the party that originally makes the sale is the borrower of capital. This party pays a higher price upon repurchase, the difference representing the cost of borrowing.

Risk Categories in Bond Investing

Interest rate risk *

Call Risk & Prepayment Risk       Reinvestment risk       Credit Risk         Liquidity risk         Exchange rate risk        Volatility risk       Inflation risk      The Yield curve risk       Event risk       Sovereign Risk

Changes in Market Interest Rates:

The interest rates prevailing in the market are constantly subject to change. For a fixed coupon bond, the attractiveness of the bond will be determined through a comparison between the bond’s coupon rate and the prevailing market interest rates at the time of issuance.

Bond’s Coupon < Market Interest Rate => Bond is Issued at Discount

Bond’s Coupon > Market Interest Rate => Bond is Issued at Premium

Bond’s Coupon = Market Interest Rate => Bond is Issued at Par

Defining Interest Rate Risk:

The fluctuation in the price of a bond in response to changes in the market’s interest rate environment is referred to as ‘Interest Rate Risk’. The Price of a bond is inversely related to the market interest rate.

Bond Features Affecting Interest Rate Risk:

Certain features of a bond instrument have an impact on the level of interest rate risk that the bond instrument will be exposed to. A longer maturity bond will have greater price sensitivity to interest rate fluctuations.  A lower coupon rate bond will have greater price sensitivity to interest rate. Accordingly, the greatest interest rate risk is involved with zero coupon bonds.  An embedded call option is valuable to the issuer. The issuer may call the bond in a falling interest rate environment. From a
bondholder’s perspective, a callable bond should be less valuable and hence should be cheaper than a regular bond.

Value of a Callable bond = Value of Regular bond – Value of Call Option

Interest Rate Risk of Floating Rate Security:

The price of a fixed income bond changes due to the fact that the market rate of interest keeps on changing whereas the bond’s own coupon rate is fixed. For a variable coupon bond, the interest rate is periodically re-set according to a coupon formula that is often linked to a market based interest rate reference. Thus the divergence between the coupon rate and the prevailing market interest rate is frequently eliminated, with every re-set of the coupon rate for an overall lower interest rate risk compared to fixed coupon bonds.

Interest Rate Risk:

The interest rate risk of a bond can be quantified and measured through the calculation of the bond’s ‘Duration’. Duration measures the price sensitivity of a bond in response to a change in the market interest rates. More specifically, Duration measures the ‘Approximate percentage change in the price of a bond in response to a 100 bps change in the market rate of interest’.

Duration =        Price of Bond when Yield Falls – Price of Bond when Yield Rises

                        2 x (Initial Price before Rates Changes) x (Change in yield in decimals)

 

Dollar Duration:

Dollar Duration relates closely to the Duration calculation seen earlier. Dollar Duration simply measures the ‘Approximate Dollar change in bond price in response to a 100 basis points change in yield’.

     Dollar Duration = (Duration x Dollar Value of Bond) / 100

Yield Curve:

The Yield Curve is a plot of interest rates of similar credit-quality bonds against various maturities, where the interest rates are those prevailing at a particular point in time. The interest rates are plotted on the ‘y’ axis and the maturities are plotted on the ‘x’ axis. The yield curve can be of any shape.

Duration of a Portfolio of Bond:

The Duration of a single bond provides us an interest rate risk measure. The Duration of a bond portfolio will be the weighted average duration of the individual bonds comprising the portfolio. Furthermore, a bond portfolio will contain several bonds of different maturities.The Duration measure assumes that the underlying change in interest rates will be a parallel shift of the yield curve, which implies that the interest rate should have changed equally for all maturities. This is a simplifying assumption, where in reality; the yield curve may shift in any manner, including non-parallel type moves.

Yield Curve Risk:

Based on the component weightings of different maturity bonds held in a portfolio, each portfolio will have a unique exposure to changes in the yield curve, which cannot be accounted for simply through using Duration. This risk related to yield curve changes and its impact on the overall value of the bond portfolio comprising of various maturities, is referred to as ‘Yield Curve Risk’.

Callable Bond:

A callable bond has a call option embedded in it. The call option allows the issuer (borrower) to redeem or call back the bond prior to maturity. The issuer is likely to call the bond back early in the event that market interest rates decline to a level that is significantly lower than the stated coupon rate of the bond.

Disadvantages of a Callable Bond, for the Investor (Bondholder)

• Reinvestment Risk in a Falling Interest Rate Scenario:
  From the perspective of the bondholder, the exercise of the call option by the issuer, in a falling interest rate environment implies that the bondholder (investor) will ave to reinvest the returned principal at lower prevailing rates.
• Cash-Flow Uncertainty: The pattern of cash flows will not be known with certainty by the bondholder, for a callable bond.
• Reduced Price Appreciation: When interest rates fall, the price of a regular bond increases. For a callable bond, falling interest rates also increase the prospect of the bond being recalled; therefore the price of the callable bond will not increase as much that of a regular bond (Called Price Compression).

Pre-Payable Bond e.g. Mortgage Backed Security:

A mortgage backed security is a bond that is based on a pool of home mortgages. As an investor, the holder of the mortgage backed security is the lender of the capital, whereas the homeowners belonging to the mortgage pool are the borrowers.

Disadvantages of a Pre-payable Security for the Investor (Bondholder)

The same disadvantages apply to pre-payable securities as applied to the callable securities.

Reinvestment Risk in Amortizing Security:

In the case of an amortizing security, in which coupon and principal are paid monthly, the cash flows received have to be reinvested at the prevailing market rates. Therefore reinvestment risk is significant for amortizing securities such as Mortgage Securities, since investment decisions will have to be successfully executed each time a payment is received. This is more frequent for an amortizing security compared to a regular bond; hence reinvestment risk is higher for amortizing securities. On the other hand, a zero coupon bond carries no reinvestment risk.

Credit Risk:

Credit Risk exists due to the risk of default, the risk of the credit spread changing, and the risk that the security may be downgraded.

Liquidity Risk:

Dealer interest in a security changes over time, as other, more attractive issues come to market. This results in a widening of bid-ask spreads and changes in liquidity risk.

Exchange Rate and Inflation Risk:

When investors purchase bonds that are denominated in another currency, the investors face exchange rate risk. This is the risk that the foreign currency, in which the bond is denominated, and in which it makes coupon payments may depreciate relative to the investor’s domestic currency. A depreciation of the foreign currency implies that the coupon proceeds and the ultimate principal repayment will translated into a fewer units of the investor’s domestic currency. When investors purchase bonds in their local currency, they face inflation risk. This implies that the investor could suffer a loss of purchasing power due to Inflation, when he receives the coupon proceeds and the principal repayment.

Yield Volatility and Bonds with Embedded Options:

Price of a Callable Bond = Price of a Regular Bond – Price of Call Option

Price of a Put-able Bond = Price of Regular Bond + Price of Put Option

Callable Bonds:

When expected yield volatility increases, the value of the call option will increase and the Price of the callable bond will decrease (since the price of the call option is subtracted).

Put-able Bonds:

An increase in the expected yield volatility will increase the price of the put option, which will cause an increase in the price of the put-able bond (since the price of the put option is added).

Event Risk:

Event Risk is the result of natural disasters, regulatory changes and corporate takeover and merger activity that may impair the issuer’s ability to make regular payments on their bonds. Alternatively, these events may increase the inherent risk in the issuer’s operations which may increase the yield required by investors from these instruments.

Sovereign Risk:

Sovereign Risk is the risk faced by an investor when he purchases the government bonds of a foreign government. The foreign government may default on its debt or it may take actions or suffer economic outcomes due to which the credit quality of its sovereign debt may increase. This would cause the sovereign risk spread to increase significantly and the government bonds would suffer an adverse price impact.

Credit Risk of Government Securities:

The debt issued by national governments is referred to as Sovereign Debt, which is often the largest sector of the bond market in any country. Bonds that are issued by the US government are considered by the market to contain no credit risk. The debt of national governments may be denominated in their own domestic currency or it may be denominated in a foreign currency. For any national government, the likelihood that the national government will default on its local currency bond obligations, will be virtually nil, since any government has the mechanisms for raising local currency tax revenue and even the ability to print more of the local currency. Different countries will have different sovereign ratings, which will are affected by the country’s economic prospects.

Four Methods for Auctioning Sovereign Bonds:

Regular Cycle – Single Price: Regularly bringing new sovereign bonds issues to the market. The government will select the lowest yield bid that has come forward (which corresponds to the highest price for the bond issue), and sell the entire issue at that single price to all bidders. Used in the U.S.

Regular Cycle – Multiple Price: This auction is a regularly held auction for new bond issues; however the bonds are issued at the various price levels to the different bidders corresponding to the prices they have bid.

Ad-Hoc Auction Cycle: This auction mechanism is used by a government for any new ad-hoc issues it may plan to bring to the market at opportune economic times, or based on its need for funds. Used by the Bank of England.

Tap Method: For issuing new bonds of an existing issue. The government issues the new bonds identical in characteristics to an existing issue, as and when the need arises. Used in the UK, the US and the Netherlands.

Securities Issued by the U.S. Treasury:

Fixed Principal U.S. Treasury Securities:

T-Bills are a treasury security with maturities less than 12 months. The three maturities for T-Bills are 1 month, 3 months and 6 months. T-Bills are
pure discount instruments. Treasury Notes are coupon paying securities with maturities of 2, 3, 5 and 10 years. Treasury Notes pay semi-annual coupon, and are initially issued at a price that is close to their Par Value. Treasury Bonds have original maturities exceeding 10 years, and are usually of 20 or 30 year maturity. Coupon is paid semi-annually. T-Bond and T-Note trading prices are quoted as a percentage of Par Values, along with a fraction of 32.

TIPS:

Treasury Inflation Protected Securities are a ‘Variable Principal’ instrument issued by the U.S Treasury. The coupon rate for the TIPS is set at a fixed level determined through the auction process. Subsequently, the Par Value, or the principal amount to be repaid at maturity, is adjusted semi-annually in relation to the inflation rate, as measured by the Consumer Price Index, particularly, the CPI-U, which is the CPI for all Urban Consumers. TIPS pay semi-annual coupon.

Demand for Longer Maturity Zero Coupon Bonds:

The U.S Treasury only issues Zero Coupon Treasury-Bills, T-Bills, which have a maturity less than 1 year. However, the Treasury does not issue zero coupon Treasury Notes or Treasury Bonds. There is however a demand for zero coupon instruments with maturities longer than one year. The private sector thus created such securities by decomposing the coupon payments and the principal payments of Coupon-Paying Treasury Notes and Coupon-Paying Treasury Bonds, which are then sold as zero coupon securities. A 3 year 6% coupon, semi-annual, $1000 par value Treasury instrument can be decomposed into 6 coupon strips of $30 each and 1 principal strip of $1000.

On-the-Run and Off-the-Run Treasury Securities:

On-the-Run securities are Treasury issues that have been brought to the market most recently. Generally, the level of interest and liquidity of on-the-run issues is higher. Because of higher liquidity, on the run issues are slightly more expensive in trading. On the run treasury yields are used in developing the par yield curve, which will be explained later. Off-the-Run Treasury Securities are treasury securities previously issued, and for similar maturities as these issues, a new bond issue has also been brought to market. Trading volume and interest is generally lower in off-the-run issues.

Federal Agency Securities:

The national government has the authority to establish subordinate agencies for the purpose of issuing bonds. The bonds issued by these agencies may carry the direct guarantee, or the implied guarantee of the government. Bonds issued by these agencies are referred to as ‘Federal Agency Securities’.

Federally Related Institutions:

These institutions are considered to be semi-government organizations which function as an arm of the federal government, e.g. Government National Mortgage Association ‘Ginnie-Mae’. The securities issued by Federally Related Institutions are considered to be free of Credit Risk since these are backed by the full faith and credit of the federal
government itself.

Government Sponsored Enterprises – GSEs:

These are privately owned entities that operate under a Public Charter. The GSEs include most prominently; Federal National Mortgage Association ‘Fannie-Mae’ and Federal Home Loan Mortgage Corporation ‘Freddie-Mac’. The bond issues of GSEs are not backed by the full faith and credit of the government and are subject to credit risk and default.

Mortgage Backed Securities ‘MBS’:

Mortgage Backed Securities are bonds for which the underlying collateral for the loan is a pool of home mortgage loans. The cash flows from a home mortgage loan are different from the cash flows of a regular coupon paying bond as these include scheduled and un-scheduled principal pre-payments. There are three main types of mortgage backed securities: Mortgage Pass-through Securities, Collateralized Mortgage Obligations and Stripped Mortgage Backed Securities.

Mortgage Pass-through Securities:

Different lenders have lent money to the home owners as mortgage loans. These loans are purchased and pooled by government agencies to create a pool of such mortgage loans. Every month, as home owners make payments of interest along with principal payments, including early principal pay-downs, the cash-flows are routed to the investors in proportion to the ownership share of the pool that their securities represents. When interest rates fall, home-owners tend to re-finance their mortgages (paying off the old mortgage which was in the pool), which implies that pre-payment risk increases in a falling interest rate scenario. All holders of a mortgage pass-through security
are equally exposed to pre-payment risk.

Collateralized Mortgage Obligation ‘CMO’:

In a CMO security, different tranches of cash flows are created from the underlying pool such that holders of any tranche of the CMO will receive the regular interest payments pro-rata to their investment, however all principal payments (scheduled and unscheduled) are allocated sequentially to the various tranches. Only after the principal due to the first trance has been fully paid from the principal amounts received in the pool, the next lower tranches begins to receive the principal payments. The highest tranche is thus exposed to the greatest pre-payment risk whereas the pre-payment risk is lower as we move down the various tranches. Thus pre-payment risk partitioning and redistribution is the primary motivation for the creation of Collateralized Mortgage Obligations.

Stripped Mortgage Backed Securities:

These securities are created by separating the interest payments and principal payments (including early principal pay-downs) of a pool of mortgages. The securities created from the interest cash-flows of the property owner’s mortgage payments are called ‘Interest Only Strips’. Securities created from the principal payment component of the home owner’s mortgage payments are called ‘Principal Only Strips’.  Only the principal payments are subject to Pre-Payment Risk.

Municipal Securities:

Within the U.S, state and local governments issue Municipal Securities, including the various counties, school districts, water boards etc. Municipal Securities expose investors to Credit Risk. Municipal Securities are often referred to as Tax-Exempt securities. This refers the fact that Interest income from Municipal Securities is tax exempt at the federal level; however, individual state taxes may apply on the interest income according to the legislation prevalent in a particular state. Capital Gains from Municipal Securities are taxable.

Municipal Tax Backed Debt:

Such bonds are issued by school districts, counties, towns, and states. The bonds are backed by the full faith and taxing power of the issuer. Tax-Backed debt includes General Obligation bonds, Moral Obligation bonds, and obligations supported through Public Credit Enhancement programs, which are supported through binding and legally enforceable credit quality enhancement guarantees provided either by a state or a federal agency. These bonds are frequently used for funding school districts.

Municipal Revenue Bonds:

These bonds are backed by the Revenues generated from specific projects. These bond issues are used for funding of revenue-generating or public infrastructure projects such as transportation, housing, healthcare, ports, and sports facilities. The issuance of these bonds does not require the specific approval of the voters, as they fall outside the General Obligation ‘GO’ debt limits. Some bonds may be backed through a pledge of funds from the General Fund as well.

Corporate Funding:

Corporations may raise debt capital either through banks and financial institutions or through the issuance of debt securities. The market for corporate debt securities in most countries is fairly small and undeveloped. Large Corporations however have the ability to raise capital through issuance of debt securities in their domestic market as well as from international markets. Bondholders of a corporation have a superior claim over equity shareholders of the corporation, in the event of bankruptcy.

Credit-Rating Agencies:

Credit Rating Agencies assign ratings to corporate bond issued based on an assessment of default. Credit ratings can be assigned to the Corporate Entity or to a particular bond obligation, and the two ratings may not be the same, as it is entirely possible that a particular bond issue possesses a different risk profile relative to the entity bringing forth the issue. Broadly, the agencies consider the following elements in assigning a credit rating, which have commonly come to be known as the 4 C’s of Credit: Character, Capacity, Collateral and Covenants.

Corporate Debt – Corporate Bonds:

These are fixed coupon bonds that pay regular coupon periodically and principal is repaid at maturity. Corporate bonds may be secured or unsecured. Secured bonds have an underlying pledge of collateral of physical assets or through a pledge of financial assets such as share certificates. Bonds that are secured through financial assets held by the company are referred to as Collateral Trust Bonds. Unsecured bonds have no such underlying collateral, and are referred to as Debentures. Holders of debentures however do have a claim against the general pool of the company’s assets. Some corporate bonds are issued with a Credit Enhancements, as part of which an additional third party guarantee is made available for the enhancement of the credit quality of the issue.

Corporate Debt – Medium Term Notes ‘MTNs’:

MTNs are a fairly unique and extremely flexible mechanism for enabling corporations, agencies and national governments, to raise debt capital. By registering an MTN issue with the Securities and Exchange Commission ‘SEC’ under ‘Shelf Registration’ Rule 145, a Corporate entity may continuously bring to market; bonds issues of various maturities. In a Structured MTNs an issuer of an MTN may enters a transaction in the derivatives market and utilize the cash flows from the derivative instrument to create the cash flow pattern of the MTN issue. This way, an issuer may structure the MTN to possess the characteristics of some other derivative instrument rather than remaining a pure and simple debt instrument.

Corporate Debt – Commercial Paper:

These are short term promissory notes issued by Corporations that have high credit ratings. There is no stated coupon on promissory notes and maturities are typically shorter than 270 days. Holders of commercial paper are generally paid off from the issuance of new commercial paper by the issuer. Commercial paper can be directly placed in the market or it can be placed through dealers, Dealer-placed paper. In Directly-placed paper there is no intermediary between the issuer and the investors.

Funding Requirements of Banks:

Banks are themselves large corporations that have funding requirements of their own. Banks will use the various debt instruments that are available to all corporations for raising debt capital. Additionally, banks raise funds through; 1) Negotiable Certificates of Deposit and through 2) Bankers Acceptances.

Negotiable Certificates of Deposit:

A certificate of deposit ‘CD’ is issued by a bank against a deposit made by an investor into the bank. A certificate of deposit is issued for a fixed denomination, carries a fixed interest rate as well as bears a maturity date. A CD may be non-negotiable or negotiable. For the Non-Negotiable CDs, the investor cannot transact the CD in the open market as financial instrument and must wait till the maturity of the CD. A Negotiable CD on the other hand can be traded in the open market with a usual denomination of $1 million.

Bankers Acceptances:

This instrument serves the purpose of international trade settlement between exporters and importers. At both ends, a financial institution is involved; the exporter’s bank and the importer’s bank.

Asset Backed Securities:

Securitization is a process under which a group of credit card loans, customer receivables or auto loans may be packaged to create an interest-bearing security backed by the
cash flows of the loans. An ABS issue is backed by the collateral of the underlying cash flows of the loan portfolio. The motivations from the lender’s perspective are to turn an illiquid loan portfolio into a liquid investment.

SPV for an ABS:

Since the ABS issue is interest bearing, the issuer is concerned with obtaining the funds at the lowest possible interest rate. This requires that the ABS issue should be assigned a high credit rating. To achieve a high credit rating for an ABS issue, the mechanism of a Special Purpose Vehicle ‘SPV’ is used. An SPV is a separate legal entity that can be created specifically for this purpose. The loan portfolio is sold to this SPV and since the SPV is a separate legal entity, the existing creditors of the car company will not be able to claim the cash-flows from the car loans in the event of a bankruptcy. The SPV is thus a bankruptcy remote entity, and the ABS issue can achieve a higher credit rating compared to the corporate credit rating, at lower interest rates. The company can further achieve external or internal credit enhancements.

Collateralized Debt Obligation:

A CDO is a special category of asset backed securities where the CDO is backed by a diversified asset pool. The asset types include domestic and international bonds, bank loans, residential and commercial mortgages, bonds of various yield grades, as well as other CDOs. A CDO backed by a pool of various bond obligations is referred to as a ‘CBO’ i.e. A Collateralized Bond Obligation. When a CDO is backed by a pool of various bank loans, it is referred to as a ‘CLO’, i.e. A Collateralized
Loan Obligation.

Primary Market for Sale of New Bonds Issues:

New bond issues are placed with public investors through the primary markets. Most commonly, bond issues are underwritten by an investment bank on the basis of either a firm commitment, or a best effort basis. Bonds are also underwritten via a ‘Bought Deal’ or an ‘Auction Process’. Bonds can also be privately placed with a small group of
institutional investors under rule 144A in the U.S., when an investment bank is involved and under non-Rule 144A for traditional private placement.

Secondary Market for Subsequent Trading:

Subsequent to the issuance of bonds, trading between investors takes place primarily in the OTC, Over the Counter market. In the OTC market, dealers quoted bid ask spreads. Dealers own capital is tied up in this market-making process as dealers buy and sell from their own inventory. Increasing capital requirements, lower margins and higher risk in bond trading due to volatility in bond prices, the trend in trading mechanism is shifting towards the Electronic Trading Platforms. Electronic trading can be through a Single-Dealer System, which is simply an electronic version of the conventional OTC trading, or through a Multi-Dealer System.

Interest Rate Policy Tools:

The Federal Reserve implements Monetary Policy through the following interest rate policy tools. Most frequently, the Fed employs Open Market Operations and Discount Rate determination to implement its monetary policy. Open market operations are used to affect the Federal Funds Rate. This is the rate for interbank borrowing and lending. When the Fed sells Treasury securities, the effect is that funds are withdrawn from the market and the resultant scarcity of capital raises interest rates. The purchase of Treasury Securities in the open market increases the supply of funds in the market which lowers interest rates. The Discount Rate refers to the interest rate at which banks can borrow funds from the Fed’s discount window. Increasing the discount rate raises the cost of funding for the banks thereby raising interest rates. Further, banks are required to maintain a mandatory level of funds as reserve that the banks cannot lend out. Increasing the reserve requirement creates scarcity of funds in the market and raises interest rates. Federal Reserve can also use Verbal Persuasion to convince banks to lend more or less.

Various Shapes of the Yield Curve:

As stated earlier, the normal shape of the yield curve is upward sloping, indicating higher interest rates for longer maturities compared to shorter maturities. The yield curve could also be downward sloping, flat or humped.

Theories of Term Structure:

According to the Pure Expectations Theory, long term rates are a function of the short term rates that are likely to be prevailing at a future point in time. Any shape of the yield curve can be explained through this theory based on expectations. According to the Liquidity Preference Theory, since longer term bonds have lower
liquidity than shorter term bonds, investors require an additional risk premium to compensate them for the lower liquidity and the yield curve is likely to be
upward sloping. If however expectations are that short term rates will fall significantly in the future, it is possible that the yield curve may still be downwards sloping. Any shape of the yield curve may be explained by this theory. The Market Segmentations Theory states that different investor groups have different maturity sector preferences. All yield curve shapes are consistent with this theory as well. A modification of the market segmentation theory, the Preferred Habitat theory states that investors move slightly out of their maturity preference ranges, induced by preferential yields in a segment adjacent to their own preferred maturity habitat.

Conventional Valuation Method for a Bond:

A bond’s intrinsic value is determined by computing the present value of its future cash flow. A single discount rate is used to discount the various cash flows of the bond to present time.

Bond Valuation using Spot Rates:

In view of the yield curve however, the interest rates relevant for different maturities will not be the same. It would therefore be more appropriate to discount the various cash flows using the particular discount rate relevant to each maturity. The appropriate discounts rates to use for each maturity are called the spot rates for the maturity

Absolute Yield Spread:

Absolute Yield Spread is also called the Nominal Spread. This measure is calculated as the simple difference in the yield between two bonds expressed in basis points.

Relative Yield Spread:

The Relative Yield Spread simply expresses the nominal difference in yields as a percentage of the yield level of the lower yield.

Yield Ratio:

This is simply, the yield of the higher yielding bond, divided by the yield of the lower yielding bond.

Credit Spread:

This is the difference in yields between two bonds which is solely due to the difference between their credit qualities. A credit spread can be calculated between a corporate bond and a treasury security’s yield. Similarly a credit spread could exist between two corporate bonds due to the difference between their credit rating.

Economic Signals:

Credit spreads provide signals regarding the state of the economy. The credit spread between corporate bonds and treasuries will decrease during economic booms. On the other hand, recessionary periods will increase the inherent risk of corporate initiatives which will translate into a higher yield requirement from corporate bonds. This will increase the credit spread between corporate bonds and treasuries during recessions.

Yield Spreads of Bonds with Embedded Call Options:

For bonds with embedded call options, the bondholder is exposed to three additional risks; upward price compression, cash flow uncertainty and reinvestment risk. Thus the yield spread of a bond with an embedded call option will be higher relative to a benchmark yield, due to the call option.

Yield Spreads of Bonds with Embedded Put Options:

For bonds with embedded put options, the bondholder effectively has lower risk since the bondholder owns the Put option which can be exercised if interest rates rise. Thus the yield spread of a bond with an embedded put option, will be lower relative to the benchmark yield.

Yields of Larger Issues:

In general, larger issues are more liquid than smaller issues. Larger issues will be in greater demand, due to their higher liquidity which will mean that these will be more expensive, and the resultant yields will be lower relative to a benchmark treasury yield.

Yields of Smaller Issues:

For smaller bond issues liquidity will be lower, consequently the level of risk will be higher due to the lower liquidity. This will imply a lower price for smaller issues, translating into a higher yield relative to a benchmark treasury yield.

After-Tax Yield on Taxable Bonds:

For any investor the yield earned on a taxable bond will be effectively reduced after the investor has paid taxes on income earned from the bond. The Marginal Tax rate relevant to the investor will determine how much the investor will be left with, after paying taxes. The after tax yield to the investor will be given as:

After Tax Yield = The Yield on the Taxable Bond x ( 1 – Marginal Tax Rate)

Yield on Tax Exempt Bonds:

Certain bonds are tax exempt and the investor does not become liable to pay taxes from the income earned through such bonds. As a result, tax exempt bonds will generally offer lower yields due to the tax benefit. In order to draw a comparison between this yield and the yield of a taxable bond, the tax equivalent yield will be calculated.

 Taxable Equivalent Yield = Yield on Tax Free Bond / ( 1 – Marginal Tax Rate)

Funded Investor:

A funded investor borrows funds for the purpose of investing in various securities. LIBOR is the interbank borrowing rate, and other investors pay a mark-up over that. The cost of borrowing for a funded investor can be determined based on the spread that he is charged over LIBOR to be added on to the base rate.

End of Quick Review