Official Blog – Cleantech, Investments, Bonds

A derivative instrument (or simply derivative) is a financial instrument which derives its value from the value of some other financial instrument or variable. For instance, a stock option is a derivative because it derives its value from the value of a stock. An interest rate swap is a derivative because it derives its value from one or more interest rate indices. The value(s) from which a derivative derives its value is called its underlier(s).

Derivative instruments can be an excellent means of maximizing return on an investment, as well as successfully hedging a financial portfolio.

Since derivative instruments depend on the strength of an underlying security or set of securities, it is important to assess the current status of those securities, as well as accurately project their future movement. For example, if a bond option carries a variable rate that is tied directly to the performance of an underlying stock, the investor would want to look closely at the past history of that stock. Along with the history, the potential investor should also consider the standing of the issuer within its particular industry, and assess the potential for that stock to increase in value during the life of the option. If the prospects seem attractive, investing in the derivative is likely to be a good idea.

Derivative instruments are sometimes issued with the potential for the investor to eventually acquire shares of the underlying security. From this perspective, this means that an investment of this type can be an excellent way to hedge a portfolio against future purchases. Experienced investors often make use of hedging strategies of this type in order to maximize return while also increasing the scope and general value of the portfolio.

In order to identify derivative instruments that show promise of earning a significant return, it is a good idea to work closely with a broker who understands the nature of derivatives. This makes it easier to sort through the many options on the market, and focus on derivatives that are likely to help the investor achieve his or her personal financial goals. A competent broker is usually able to quickly identify strengths and weaknesses associated with the underlying security or securities, and accurately advise the investor of what to expect if the derivative is purchased.

By contrast, we might speak of primary instruments, although the term cash instruments is more common. A cash instrument is an instrument whose value is determined directly by markets. Stocks, commodities, currencies and bonds are all cash instruments. The distinction between cash and derivative instruments is not always precise, but it is a useful informal distinction.

Derivative instruments are categorized in various ways. One is the distinction between linear and non-linear derivatives. The former have payoff diagrams that are linear or almost linear. The latter has payoff diagrams that are highly non-linear. Such non-linearity is always due to the derivative either being an option or having an option embedded in its structure.

A somewhat arbitrary distinction is between vanilla and exotic derivatives. The former tend to be simple and more common; the latter more complicated and specialized. There is no definitive rule for distinguishing one from the other, so the distinction is mostly a matter of custom. Usage does vary.

Exhibit 1 lists some standard derivatives and indicates the categories they fall into as stand alone (as opposed to embedded) instruments.

Standard Derivatives
Exhibit 1

Asian option: non-linear – exotic
Barrier option: non-linear – exotic
Basket option: non-linear – exotic
Binary option: non-linear – exotic
Call: non-linear – vanilla
Cap: non-linear – vanilla
Chooser option: non-linear – exotic
Compound option: non-linear – exotic
Contingent premium option: non-linear – exotic
Credit derivative: non-linear – exotic
Floor: non-linear – vanilla
Forward: linear – vanilla
Future: linear – vanilla
Lookback option: non-linear – exotic
Put: non-linear – vanilla
Quanto: non-linear – exotic
Rainbow option: non-linear – exotic
Ratchet option: non-linear – exotic
Swap: linear – vanilla
Swaption: non-linear – vanilla

Standard derivatives are listed. They are categorized as linear/non-linear and as vanilla/exotic. Usage of the vanilla/exotic distinction does vary, so some of the exotics listed above might be considered vanilla by some professionals. Basket options are an obvious example. Among rainbows, most are exotic, but spread options might be considered vanilla.

Many bonds include a call feature that allows the issuer to redeem or “call” all or part of the issue before the maturity date.

The call option has value to the issuer for several reasons. In the future the borrower may wish to remove restrictions placed on him by the bond indenture. For a corporation these might be restrictions on merger, the sale of assets, or the payment of dividends. Without the call provision, the bondholders by hard bargaining might be able to utilize their monopoly position to extract a large premium from the issuer before selling back the bonds or agreeing to change these clauses.

A second source of value is that the borrower may find that he wants to decrease the amount of his borrowing before the bonds mature. Essentially the same effect as retiring his own bonds could be obtained by buying on the market similar bonds issued by someone else. However, because of the transaction costs involved in making interest payments, the cost of bonds to the issuer will always be somewhat greater than their value on the market. There will therefore be some saving to the issuer in retiring his own bonds rather than buying someone else’s.

The third and probably most significant source of value of the option to the issuer is the ability it gives him to refinance the issuer in the future if interest rates should fall. This implies three risks from the investor:
(a) The cash flow pattern becomes uncertain;
(b) The investor becomes exposed to reinvestment risk because the issuer will call the bond when interest rates drop;
(c) The capital appreciation potential of a bond will be reduced, because the price of a callable bond may not rise much above the price at which the issuer will call the bond.

Option writing for bonds is used both for risk and hedge purposes. Bond call options provide liquidity with little cash requirement. Bond options also have a finite life and can be expensive to purchase and hold until maturity.

Mechanics of Bond Option Writing

The seller of the contract must have on account securities or funds equal to the amount of the potential sale until the contract expires. The seller is also called the writer of the contract. The incentive for writing a bond call option is the premium payment reflecting the risk of loss of the bonds. The premium payment is in addition to the strike price. The strike price is the market value the bond call option must reach in order to be exercised, or called.

Trading on an Exchange

For a stated par, or maturity value, the bond call writer initiates a contract through his broker on a nationally recognized exchange. The exchange provides a uniform bond option contract detailing the responsibilities of both the bond call option buyer and seller, including the length of the call and what bonds constitute good value for delivery. Rarely are bonds ever delivered. Instead contracts are offset by cash payments at maturity. The contract also denotes an exercise price. The fee received, the premium, is determined by market conditions. This includes the current level of interest rates, the price volatility of the bonds and the number of business days the bond option seller is at risk.

Leverage

Rather than incur the price volatility and cash payment for bonds, traders often use bond call options. Traders know from the beginning of the trade the absolute amount of loss they may incur while freeing up cash for other trading purposes. The cost of a bond option varies depending on the premium charged, but a one month bond call option may cost as little as 2 percent of the face value of the bonds. This implies that a 1 percent increase in bond values on a $1 million call would increase bond option values by nearly $10,000.

Hedging

Bond options are popular as hedging vehicles to reduce risk. Traders can buy options and use them to hedge, or offset, an equal amount of futures contracts, bonds and other options, such as bond put options. Bond call options are also used like stock options in a variety of mathematical strategies. By buying and selling different bond call and bond put options, income can be derived from the time to maturity, the difference in coupon or even bond prices. Bond call options, with their liquidity, and known maximum loss, provide traders many opportunities to employ profitable, leveraged, strategic portfolio outcomes.

Ai = number of accrued days for the ith, or last, quasi-coupon period within odd period counting forward from last interest date before redemption.
DCi = number of days counted in the ith, or last, quasi-coupon period as delimited by the length of the actual coupon period.
NC = number of quasi-coupon periods that fit in odd period; if this number contains a fraction it will be raised to the next whole number.
NLi = normal length in days of the ith, or last, quasi-coupon period within odd coupon period.

Bonds often are referred to as being short-, medium- or long-term. Generally, a bond that matures in one to three years is referred to as a short-term bond. Medium or intermediate-term bonds generally are those that mature in four to 10 years, and long-term bonds are those with maturities greater than 10 years. Whatever the duration of a bond, the borrower fulfills its debt obligation when the bond reaches its maturity date, and the final interest payment and the original sum you loaned (the principal) are paid to you.

Not all bonds reach maturity, even if you want them to. Callable bonds are common: they allow the issuer to retire a bond before it matures. Call provisions are outlined in the bond’s prospectus (or offering statement or circular) and the indenture – both are documents that explain a bond’s terms and conditions. While firms are not formally required to document all call provision terms on the customer’s confirmation statement, many do so.

Bond maturities usually range from one day up to 30 years or even more. But this maturity date must be seen as the last future date (except if the borrower is in default) on which the investor will receive the principal amount from to the issuer. Depending on redemption features, the real reimbursement date can be very different (much shorter). These redemption features usually give the right to the investors and/or the issuer to advance the maturity date of the bond:

Call

This is a provision that allows or require the issuer to repay the bond before the maturity date. The issuer will ‘call’ his bond if the interest rate index is lower than when he issued the bond. On the investor point of view, it means that the bond will be prepaid if the bond brings him too much interest compared to the current market conditions. If you purchase a bond with a ‘call option’, you have to pay less (get a premium) than without call because if the bond is prepaid, you will reinvest the money at a lower rate.

Put

The put is a provision that gives to right to the investors to require from the issuer to redeem the bond before the maturity date. Investors usually exercise this option when the current market rates are higher so that he can reinvest his money at a higher rate. The put feature is a protection for the investor against an increase of the interest rate on the market and, consequently, should pay more (pay a premium) for a bond with a put than without.

Conversion

Some corporate bonds, known as convertible bonds, contain an option to convert the bond into common stock instead of receiving a cash payment. Convertible bonds contain provisions on how and when the option to convert can be exercised. Convertibles offer a lower coupon rate beacuse they have the stability of a bond while offering the the potential upside of a stock.

Partial Prepayment (Paydown)

This kind of feature is usually seen with mortgage-backed securities. Without entering into details, a mortgage-backed security is anything else but the securitisation of a pool of mortgage loans. In mortgage loans, you have a regular (often monthly or quarterly) payment of principal and also the ability for the borrower the prepay the loan before maturity. Mortgage-backed securities prepay the principal to the investors in parallel the underlying mortgage loans. That’s the reason why mortgage-backed securities are traded on the basis of their ‘average life’.

Mortgage-backed bonds prices are more volatile than fixed rate bonds because the speed of redemption increases when the interests go down (when you have to reinvest at a lower rate) but decreases when interests go up. An increase in interest rates will increase the average life (the real maturity date) of your investment.

In the early 1990s, a product called fixed-rate capital securities was introduced to meet the needs of income-oriented investors and provide a cost efficient source of capital for issuers.

These securities combine the features of corporate debt securities and preferred stock: generous yields compared with other investment vehicles, regular income disbursement, predictable investment time frames, liquidity and investment grade quality (in almost every case).

Fixed-rate capital securities (aka hybrids) are like preferred stock, but with a few peculiarities. There is no DRD tax advantage; thus, they pay a higher yield than preferred stocks or bonds from the same issuer. The have a lien status that is higher than preferreds but below creditors, and they carry the credit rating of the issuer. They are traded in the OTC market and most are also listed on the NYSE and AMEX stock exchanges. Most are priced at $25 per share, they have a stated maturity, and are callable after 5 to 10 years. Most issuers are utilities, industrial companies, and financial institutions.

FRCS are also classified based on how they are issued:
1.Junior subordinated debentures are issued directly by the parent company.
2.Trust preferred FRCS are issued by a trust.
3.Partnership preferred FRCS are issued by a partnership.

Specific FRCS are known by acronyms and names which describe the frequency of the payments, or how they are issued, such as:
•MIDS – Monthly Income Debt Securities
•QUICS – Quarterly Income Capital Securities
•QUIDS – Quarterly Income Debt Securities
•QUIPS – Quarterly Income Preferred Securities
•SKIS – Subordinated Capital Income Securities
•TOPrS – Trust Originated Preferred Securities
•TruPS – Capital Trust Pass-through Securities

The main difference between preferreds and FRCS is that FRCS pay interest—not dividends—monthly, quarterly, or semi-annually, but can be deferred if the company is in financial trouble. However, payments can be deferred only if no dividends are being paid for the issuer’s common or preferred stock, and if the interest payments are deferred, then interest continues to accumulate until it is paid. Sometimes FRCS are issued as zero coupon bonds, which are original issue discount (OID) instruments.

However, these securities can have tax complications, either because of interest payment deferral or because they are OIDs. In these cases, interest accrues, and if it is not paid in the year earned, then the investor in these securities must pay taxes on the accrued interest, which is calculated according to complex laws and formulas.

Besides the deferral risk mentioned above, there is also a special event risk, which allows the issuer to redeem the FRCS, at any time, for face value, if the tax law changes that disallows the tax deduction for the interest payments for the issuer’s parent company.

Features and Benefits

Priority of Claims
• FRCS typically offer a higher security claim than preferred and common stock, but rank junior and are subordinate in right of payment to all senior debt of the issuer.

Potential for Attractive Yields
• FRCS typically provide yield advantages relative to preferred stock and corporate bonds of the same issuer, partly to compensate investors for claims with a lower priority in addition to payment deferral risk.

Liquidity
• Certain FRCS trade on the OTC and listed markets, and generally have easily attainable quotes. Many FRCS are also listed on the NYSE®.

Credit Ratings
• FRCS may be rated by investment rating agencies such as Moody’s® and Standard & Poor’s® to assist investors in their evaluations of the securities.

Low Investment Minimum
• Many FRCS are issued at $25 a share (although some are issued with a $1000 par value). This feature enables investors to buy and sell in smaller increments. The actual price paid by the investor may be more or less than $25, particularly when the security is purchased in the secondary market.

Risks

While it may seem appealing to look at securities that offer higher yields, investors should consider those higher yields to be a sign of potentially greater risk.

Market Risk
• FRCS are subject to price fluctuation due to material events affecting the issuer or the market. Additionally, FRCS prices typically decline on ex-dividend days (the dates that buyers of FRCS are not entitled to receive the dividend).

Interest Rate Risk
• FRCS tend to rise in value when interest rates fall, and decline in value when interest rates rise.

Credit and Default Risk
• Investors should consider the possibility of risk that a corporation might default on its payments of interest or principal. Purchasing top–rated securities from companies with a stable or good credit history may help reduce credit risk.

Call Risk
• FRCS generally have a call provision which entitles the issuer to redeem the shares prior to maturity. Typically an issuing corporation will call its securities when interest rates fall, leaving the investor with potentially less favorable reinvestment possibilities. When evaluating FRCS, an investor should know whether call options exist and when these options may be exercised by the issuer.

Special Event Risk
• Many FRCS include a “special event” redemption option, allowing the issuer to redeem the securities at the liquidation value if a tax law change disallows the deductibility of payments by the issuer’s parent company, or subjects the issue to taxation separate from the parent company.

Deferral Risk
• FRCS permit the deferral of payments without declaring default, if the issuer experiences financial difficulties. Payments may be deferred or suspended for some stipulated period. If the issuer defers payments on a cumulative FRCS issue, the deferred income typically continues to accrue for tax purposes, even though the investor does not receive cash payments. Investors should consult with a tax professional regarding the tax treatment of investment income.

Inflation Risk
• FRCS are subject to the risk that the rate of the yield to call or maturity of the investment may not provide a positive return over the rate of inflation for the period of the investment.

Bonds provide an important component of many financial plans. Most investors buy bonds for two basic reasons: safety and/or income. Bonds can provide some stability for your portfolio to counter the volatility of stocks while generating current or future income.

Every year, bondholders receive their annual 1099-INT forms and dutifully report the numbers that are listed there on their tax returns. However, there is often more to what appears on these forms than the income that is generated from the stated rate of interest. Many fixed income investors are unaware of a number of factors that can impact the amount of taxable interest that they must report at the end of the year.

The interest earned from bonds is taxed as ordinary income. However, if the bond is sold before maturity, or if the bond was bought in the secondary market for other than par value, then there will also be a capital gain or loss, depending on whether the sale or redemption price was greater or less than the purchase price. The capital gain is not recognized until the sale or the redemption of the bond.

However, taxes on interest must be paid in the year earned, whether it is received or not. For bonds that make regular coupon payments, taxable interest for the year is the interest received or payable for that year.

Nevertheless, for original issue discount (OID) bonds, the bondholder must pay interest that was earned, but not received, which is based on the imputed interest — the interest that the OID bond earns based on a constant yield method, or straight-line amortization. For a zero-coupon bond, which is issued at a deep discount, but pays no interest, the imputed interest rate, which is simply the yield to maturity, is determined by the purchase price, the par value, and the term of the bond, so the IRS requires the use of this rate regardless of changes in the bond’s price in the secondary market.

Some OID bonds do pay regular interest periodically, but the coupon rate was below prevailing interest rates when issued, and so was sold at a discount to its par value. Thus, these bonds pay a stipulated amount of interest, but also have an imputed interest that must be added yearly to determine taxable income. The coupon rate and the imputed interest rate will equal the yield to maturity for the bond. The imputed interest will be proportional to the original issue discount. 

Original Issue Discount = Redemption Value – Purchase Price

When a bond with imputed interest is sold, the capital gains or loss is determined by adding the imputed interest to the purchase price of the bond, and subtracting this value from the sale or redemption price.

The major exceptions to reporting OID as interest includes:

• debt securities with a term of 1 year or less;
• United States savings bonds;
• most tax-exempt securities.

De Minimis OID

The interest can be treated as zero if the discount is less than the de minimis OID:

De Minimis OID = 0.0025 x Redemption Value x Number of Years from Issue to Maturity

The de minimis OID will, however, have to be reported as a capital gain if held to maturity.

Bonds Acquired At Original Issue

Generally, a bond that you acquired at original issue is not a market discount bond. If your adjusted basis in a bond is determined by reference to the adjusted basis of another person who acquired the bond at original issue, you are also considered to have acquired it at original issue.

Exceptions

A bond you acquired at original issue can be a market discount bond if either of the following is true.

• Your cost basis in the bond is less than the bond’s issue price;
• The bond is issued in exchange for a market discount bond under a plan of reorganization (this does not apply if the bond is issued in exchange for a market discount bond issued before July 19, 1984, and the terms and interest rates of both bonds are the same).

Accrued Market Discount

The accrued market discount is figured in one of 2 ways:

1. ratable accrual method;
2. constant yield method.

Ratable Accrual Method

Treat the market discount as accruing in equal daily installments during the period you hold the bond. Figure the daily installments by dividing the market discount by the number of days after the date you acquired the bond, up to and including its maturity date. Multiply the daily installments by the number of days you held the bond to figure your accrued market discount.

Constant Yield Method

Instead of using the ratable accrual method, you can choose to figure the accrued discount using a constant interest rate (the constant yield method). Make this choice by attaching to your timely filed return a statement identifying the bond and stating that you are making a constant interest rate election. The choice takes effect on the date you acquired the bond. If you choose to use this method for any bond, you cannot change your choice for that bond.

The international bond market has greatly expanded in recent years because of the readily available information provided over the Internet, and more deregulation in financial markets throughout the world. There is greater opportunity to not only diversify a portfolio, but to also earn higher yields. Furthermore, new financial instruments, such as interest rate swaps and currency swaps, allow issuers of bonds to take advantage of foreign markets, and to pay out lower rates than would otherwise be possible.

However, there are two additional risks in holding international bonds that are not found in domestic bonds: sovereign risk and foreign-exchange risk. Sovereign risk (synonyms: country risk, political risk) is the risk associated with the laws of the country, or to events that may occur there. Particular events that can hurt a bond are the restriction of the flow of capital, taxation, and the nationalization of the issuer. Foreign exchange risk is the possibility that the foreign currency will depreciate against the domestic currency. Currency exchange rates are changing all of the time, so if the bond currency depreciates against the investor’s domestic currency during the term of the bond, then the investor will either lose money or not make as much profit.

The world of bonds can be subdivided based on domicile of the issuer and the buyers, and currency denomination.

Domestic bonds are issued by a company or bank within a country, in the country’s currency, and traded within the country, and are subject to that country’s rules and regulations.

Foreign bonds are issued by a foreign entity, but are underwritten and sold in a domestic market.

Eurobonds are underwritten by an international syndicate to be sold primarily outside the domestic market, which does not necessarily include Europe, but usually does.

Global bonds are underwritten by an international syndicate to be sold both domestically and internationally.

Another way to classify international bonds is whether they pay in United States dollars (USD) or a foreign currency. U.S.-pay bonds are sensitive to interest rates in the United States, while foreign-pay bonds are sensitive to the interest rates of the currency’s country of origin. With the exception of the emerging market debt, U.S.-pay bonds have a risk profile similar to domestic U.S. bonds. With foreign-pay bonds, however, the investor must consider currency exchange risk, trading hours and procedures, the laws of the country (for instance, what happens if a company goes bankrupt?), and especially taxation.

U.S.-Pay International Bonds

U.S.-pay bonds are bonds that are from issuers domiciled in other countries, but that are denominated and pay in USD. Foreign pay bonds pay in foreign currency, and so there is a foreign exchange risk with these bonds. If the dollar strengthens against the bond’s currency, then the value of the bond will decline; but if the dollar declines, then the bond’s value increases.

Yankee Bonds

Because the United States market is large and safe, many foreign companies and banks choose to issue bonds in this country to raise capital. Yankee bonds are issued in the United States by foreign companies and banks, but are underwritten by a United States syndicate, and are sold in the United States and pay interest semi-annually in U.S. dollars. They are also registered with the Securities and Exchange Commission (SEC), so they are much like domestic bonds. Many Yankee bonds are sovereign or sovereign-guaranteed issues, so they are of high credit quality. Supranational agencies and Canadian companies and agencies have been the major issuers of Yankee bonds. The size of the Yankee bond market increased substantially after the abolition of the interest equalization tax  (effective 1963-1974), which taxed U.S. buyers of foreign securities.

Eurodollar Bonds

Eurodollar bonds are usually issued, mostly by sovereigns, supranational agencies, such as the World Bank, corporations, and banks, outside of the United States, and are mostly traded in foreign markets, in the so-called Eurobond market — the major trading center is London. Eurodollar bonds are usually of high quality, many are sovereign or sovereign-guaranteed issues, but they are not registered with the SEC. Eurodollar bonds constitute most of the Eurobond market and are denominated in United States dollars. They are bearer bonds, which are unregistered—like cash, possessing them is owning them. They are underwritten by an international syndicate and marketed in many different countries.

Because they are not registered with the SEC, new issues cannot be sold in the United States. Thus, Eurodollar bonds can only be purchased in the secondary market after they have been seasoned — SEC  Regulation S arbitrarily defines seasoned as a security that’s been on the market for 40 days (recently reduced from 90 days).

The Euro medium-term note is similar to the Eurodollar bond, but is issued in different currencies and maturities under a single agreement.

International Bond Market is very big and has an estimated size of nearly $47 trillion. The size of the US bond market is the largest in the world. The US bond market’s outstanding debt is more than $25 trillion.

The International Bond Market has grown double in size since the year 2000. By the end of the year 2006 it has been recorded that nearly $10 trillion of the bonds were outstanding as far as International Capital Market Association data are concerned. This rapid growth of the International Bond Market is due to the bonds that are issued by the various multi national companies.

In International Bond Market, markets that are looked after by the government of a particular country are actually taken into account. These markets are big in size, there is liquidity in the market. They lack credit risk, which make them sensitive to the interest rates.

Convexity means a measure of the curvature in the relationship between bond prices and bond yields that demonstrates how the duration of a bond changes as the interest rate changes. Convexity is used as a risk-management tool, and helps to measure and manage the amount of market risk to which a portfolio of bonds is exposed.

In the example above, Bond A has a higher convexity than Bond B, which means that all else being equal, Bond A will always have a higher price than Bond B as interest rates rise or fall.

As convexity increases, the systemic risk to which the portfolio is exposed increases. As convexity decreases, the exposure to market interest rates decreases and the bond portfolio can be considered hedged. In general, the higher the coupon rate, the lower the convexity (or market risk) of a bond. This is because market rates would have to increase greatly to surpass the coupon on the bond, meaning there is less risk to the investor.

Convexity is the rate that the duration changes along the price-yield curve, and, thus, is the 1^st derivative to the equation for the duration and the 2^nd derivative to the equation for the price-yield function, and is calculated by the following equation:

Convexity Formula

P = bond price

y = yield to maturity in decimal form

T = maturity in years

CF_t= cash flow at time t

The equation for duration can be improved by adding the convexity term:

Calculating the Change in Bond Prices with Interest Rates Using Duration + Convexity Adjustment

∆y = yield change

∆P = bond price change

Convexity can also be estimated with a simpler formula, similar to the approximation formula for duration:

Convexity Approximation Formula

Convexity = P₊ + P_- – 2P₀
─────────────
2 x P₀(Δy)²

P₀ = bond price
P_- = bond price when interest rate is incremented
P₊ = bond price when interest rate is decremented
∆y = change in interest rate in decimal form

However, that this convexity approximation formula must be used with this convexity adjustment formula, then added to the duration adjustment:

Convexity Adjustment Formula

Convexity Adjustment = Convexity x 100 x (Δy)²

∆y = change in interest rate in decimal form

Hence:

Bond Price Change Formula

Bond Price Change = Duration x Yield Change + Convexity Adjustment

Convexity is usually a positive term regardless of whether the yield is rising or falling, hence, it is positive convexity. However, sometimes the convexity term is negative, such as occurs when a callable bond is nearing its call price. Below the call price, the price-yield curve follows the same positive convexity as an option-free bond, but as the yield falls and the bond price rises to near the call price, the positive convexity becomes negative convexity, where the bond price is limited at the top by the call price. Hence, similar to the terms for modified and effective duration, there is also modified convexity , which is the measured convexity when there is no expected change in future cash flows, and effective convexity , which is the convexity measure for a bond for which future cash flows are expected to change.

Bonds primary and secondary markets are a vital source of finance for governments, cities, and corporations. They also provide investors with a wide range of opportunities. At the start of 2004, the global bond market had an estimated value of nearly $40 trillion. This market is divided into primary and secondary markets.

Primary Bond Market

When bonds are originally issued to the public, this is known as the primary bond market. When a company decides that it needs to raise money for a large project, it will potentially decide to issue bonds. The companies that issue the bonds will typically work through an investment bank to help them. The investment bank will be in charge of finding buyers for the bonds and actually issuing them. In return for their services, the investment bank will receive a specific commission for each bond that is sold. Investors purchase bonds directly from issuers or their agents.

Secondary Bond Market

The secondary market is where bonds are traded between investors after issue on the primary market. Investors can liquidate their bonds before maturity here. The majority of transactions in the bond market take place in the secondary market. The secondary market represents when an individual that owns a bond sells it to another investor. Many times, institutional investors will purchase bonds through the primary market and then turn around and sell them to investors in the secondary market. In order to purchase bonds in the secondary market, an individual will need to open an account with a bond broker. A bond broker will facilitate the process of purchasing the bonds that are needed. They will help the investor research the different bonds that are available in the market and then make the purchase.

Purchase Amount

One of the biggest differences between the two different bond markets is in the amount that is paid for the bonds. In the primary market, investors are only going to pay the face value of the bond. For example, if the bond has a par value of $1000, the investor is going to pay $1000 for it in most cases.

In the secondary market, this is not the case. Bonds rarely sell for exactly the par value in the secondary market. The value of bonds is drastically impacted by interest rates in the market. If interest rates are higher than what the coupon rate of the bond is, the value of the bond is going to decrease. If interest rates are lower than the par value, the bond is going to increase in value.

Skill

In order to invest in both of these markets, investors have to have a certain amount of skill. In the secondary market, you have to be able to properly value the bonds that you are buying and selling. This requires a certain amount of skill and practice to calculate how much the bond should be sold for.

In order to get involved in the primary market, you do not need to necessarily understand how to calculate bond values, but you do need to know the right people. Most of the time, bond sales in the primary market occur between investment banks and institutional investors.

In fact, callable bonds are more risky for investors than non-callable bonds because an investor whose bond has been called is often faced with reinvesting the money at a lower, less attractive rate. As a result, callable bonds often have a higher annual return to compensate for the risk that the bonds might be called early.

Fixed income investors and financial advisors face a dilemma in the current environment; either invest in short-term bonds and earn virtually nothing in return, or invest in longer-term bonds and risk significant losses in the event that future interest rates rise substantially. The cushion bond – a callable bond trading at a premium to par value – offers the potential for higher return in a low rate environment, while providing protection against the potentially damaging consequences of future rate increases.

Most investors know that bond prices move inversely to changes in interest rates (i.e. when rates increase, bond prices fall). Most investors may also be aware that long-term bonds are more sensitive to changes in rates than short-term bonds. However, most investors do not fully appreciate one of the biggest factors that may reduce a given bond’s sensitivity to changes in interest rates – an embedded call option.

The investor has to determine the value of the option and the level of compensation required for the associated risks in a callable security.

Three forms of embedded options

The type of embedded option in a callable security affects the option’s value.

• American options are continuously callable at any time after the lockout period expires.
• Bermudan options give the issuer the right to call the bond on specified dates after the lockout period that typically coincide with coupon dates.
• European options have a one-time call feature coinciding with the expiration of the lockout period.

Importance of lockout periods

Coupled with the time to maturity, the lockout period also affects the option’s value. For example, the embedded option in a 10-year noncallable for six months (10nc6M) can be likened to a 6-month European option on a 9.5-year security. The embedded option in a 10nc3 European callable is the same as a 3-year option on a 7-year security. The uncertainty or risk associated with 7-year rates three years from now is higher than the uncertainty of 9.5 year rates 6 months from now, so the first option should have a higher value.

The call option feature of a bond is the most significant characteristic that may reduce interest rate sensitivity because it is the only feature that can actually accelerate the maturity date of a given bond. The call option allows the issuer of a bond – a corporation or municipal agency – the right to call back the bond at a fixed price, typically at par value or slightly more. Thus, if interest rates decline after original issuance, the issuer may repurchase the bonds at a fixed price and subsequently reissue new bonds at lower prevailing market rates. Obviously, the call option embedded in such bonds is a benefit to the issuer, not the investor.

A callable bond can therefore be viewed as a combination of a non-callable bond, plus a call option. Yet, while the investor owns the bond, the issuer owns the call option. In other words, the investor has effectively sold the call option to the issuing agency, and therefore the call option has negative value to the bondholder as it reduces the overall market value of the callable bond. Formulaically, this can be expressed as follows:

Value of Callable Bond = Value of Noncallable Bond – Value of Call Option

So, why do callable bonds represent an opportunity in the current market environment? Well, over the past couple of years as interest rates have declined, investment-grade bonds have generally appreciated in value, but much less so for callable bonds. As rates declined, it became more likely that many such bonds would be called by their issuers at or near par value, so these bonds simply could not appreciate in price to any meaningful degree. Referring back to our formula, this means that the value of the call option increased significantly as interest rates fell, dampening any overall increase in the value of the bond itself.

For the same reason, if rates begin to rise in the coming year or two, these callable bonds are less likely to lose much value because they are already trading at levels that are relatively close to par. Such callable bonds, which have coupon rates that are higher than current market rates and trade at slight premiums to par value, are known as “cushion bonds” – the name being derived from the fact that these bonds are not as sensitive to overall changes in interest rates; they do not appreciate very much when rates fall, nor do they depreciate very much when rates rise. Thus, these bonds can cushion, or buffer, a fixed income portfolio against the affects of changing interest rates.

Discount Bonds

Discount bonds are bonds that sell for less than the face value of the bond. In many cases, a discount bond will also be a zero-coupon bond. Like many bond issues, a discount bond normally pays the original purchase price plus a fixed or variable amount of interest over the life of the bond.

Understanding how a discounted bond functions is not difficult. Assuming that a bond has a face value of $2,000.00 and is sold for $1,800.00, it can be said that the bond sold for a discount of $200.00. The new owner of the bond can look forward to earning a return on both the principal and any interest that is generated according to the terms and conditions surrounding the bond issue.

Discount bonds could trade for less than the face value for a number of reasons. In some cases, discount bonds can be very attractive to investors because they provide an opportunity to increase the yield on the investment.

Interest Rates

One of the reasons that a bond could be trading for a discount is fluctuations in interest rates in the market. Bonds have an inverse relationship to interest rates in the market. If interest rates increase above the interest rates that are paid by the bonds, the bond values will decrease. This happens because investors will try to sell the bonds in order to get locked into bonds that pay a higher rate of interest. This concept also works in reverse, as the value of bonds will increase if interest rates in the market go down.

Default

Another reason that a bond could potentially trade for a discount is that the company is close to defaulting on the debt. If the company is close to default, investors may be trying to get anything that they can of the bonds that were issued by the company. Many investors will like to purchase these bonds at a deep discount because that provides them with a huge upside. If the company does not go into default, the bond would provide them with a great return on investment.

While many examples of the discount bond do pay interest, that is not always the case. When there is no interest involved, the investment is known as a pure discount bond. In this scenario, the buyer purchases the bond for less than the face value, but ultimately earns a return by eventually receiving the face value of the bond.

Zero Coupon Bonds

Zero coupon bonds also trade at a discount to the face value of the bond. With a zero coupon bond, the investor does not receive any regular interest payments, as he would with a traditional bond. Instead, he purchases the bond for a deep discount at the beginning of the bond term. He can then hold the bond until maturity and cash it in for the full face value. This gives him all of the interest that he would have earned at once. The bonds are called zero coupon because the interest is paid at maturity.

Benefit of Zero Coupon Bonds

The main benefit of zero coupon bonds is that you can invest for specific goals in the future. If you want to invest a certain amount of money and know exactly what you will get back in the future, this could be a great tool. For example, if you were investing so that you could purchase a home or pay for a child’s education at a certain point, this could be a very valuable tool to use.

Tax Implications

One thing that you will have to consider about zero coupon bonds is the tax implications that come with them. With this type of bond, you are actually responsible for the interest payments on your taxes, even though you receive no payments. This is referred to as “phantom interest” and it has to be accounted for along the way. This requires you to come up with money to pay the taxes from other sources besides the bond. Then when you get to cash in the bonds, you will not have to pay any taxes on the money.

Ways to Minimize Taxes

• Retirement accounts- Coupon bonds can be a great addition to a retirement account. When you buy them with your retirement account funds, you do not have to worry about taxes on the bonds. Your account is allowed to grow tax free. Then when you retire, you can worry about paying the taxes for them.
• Education savings- When you use zero coupon bonds for education, you can actually put the bonds in the children’s names. This will allow make the interest taxable at the child’s rate, which will usually be much less than what your tax rate would be.