Bond Features and Theories

Bond Features and Prices

Bonds are debt securities – the bondholder is a creditor of the entity issuing the bond. The bondholder makes a loan of the face value to the issuer. The issuer (borrower) promises to repay to the lender (investor) the principal on maturity date plus coupon interest over its life.

Bond terms

Par value (face value): Face amount paid at maturity.

Coupon rate: Percentage of the par value that will be paid out annually in the form of interest.

Annual interest payment on bond = coupon rate  par value

Maturity: The duration of time until the par value must be repaid.

Example

A bond with par value of $1,000 and coupon rate of 8% might be sold to a buyer for ` 1,000. The bondholder is then entitled to a payment of ` 80 (= 8%  ` 1,000) per year, for the stated life of the bond, say 30 years. The ` 80 payment typically comes in two semi-annual instalments of ` 40 each. At the end of the 30-year life of the bond, the issuer also pays the ` 1,000 par value to the bondholder.

Call Provisions on Corporate Bonds

The call provision allows the issuer to repurchase the bond at a specified call price before the maturity date. If a company issues a bond with a high coupon rate, when market interest rates are high, and interest rates later fall, the firm might like to retire the high-coupon debt and issue new bonds at a lower coupon rate to reduce interest payments. This is called refunding. The call price of a bond is commonly set at an initial level near par value plus one annual coupon payment. The call price falls as time passes, gradually approaching par value.

Callable bonds typically come with a period of call protection, an initial time during which the bonds are not callable. Such bonds are referred to as deferred callable bonds. The option to call the bond is valuable to the firm, allowing it to buy back the bonds and refinance at lower interest rates when market interest rates fall. From the bondholder’s perspective, the proceeds then will have to be reinvested in a lower interest rate. To compensate investors for this risk, callable bonds are issued with higher coupon rates and promised yields than non-callable bonds.

Convertible Bonds

Convertible bonds give the bondholders an option to exchange each bond for a specified number of shares of common stocks of the firm. The conversion ratio gives the number of shares for which each bond may be exchanged. Suppose a convertible bond that is issued at par value of $1,000 is convertible into 40 shares of a firm's stock. The current stock price is $20 per share, so the option to convert is not profitable now. However, should the stock price later rise to $30, each bond may be converted profitably into $1,200 worth of stock.

The market conversion value is the current value of the shares for which the bonds may be exchanged. At the $20 stock price, the bond’s conversion value is $800. The conversion premium is the excess of the bond value over its conversion value. If the bond is selling currently at $950, its premium will be $150.

Valuation of Bonds

To value a security, we discount its expected cash flows by the appropriate discount rate. The cash flows from a bond consist of coupon payments until the maturity date plus the final payment of par value.

Where r is the interest rate that is appropriate for discounting cash flows and T is the maturity date. The present value (PV) of a ` 1 annuity that lasts for T periods when the interest rate equals r is:

Price-Yield Relationship

Nominal yield: This is simply the yield stated on the bond’s coupon. If the coupon is paying 5%, the bondholder receives 5%.

Current yield: Current yield = Annual interest/Current price. This calculation takes into consideration the bond market price fluctuations and represents the present yield that a bond buyer would receive upon purchasing a bond at a given price. As mentioned above, bond market prices move up and down with interest rate changes. If the bond is selling for a discount, then the current yield will be greater than the coupon rate. For instance, an 8% bond selling at par has a current yield that is equivalent to its nominal yield, or 8%.

Current Yield = Annual interest/Current price = (8% x ` 1000) / ` 1000 = 8%.

However, a bond that is selling for less than par, or at a discount, has a current yield that is higher than the nominal yield. Thus if you buy a bond with a par value of ` 1000, coupon rate of 8% and the current price of ` 950, the Current Yield= Annual interest/Current price

= (8 % x ` 1000) / ` 950

= ` 80 / ` 950 = 8.42 %

Yield-to-maturity (YTM): This measures the investor’s total return if the bond is held to its maturity date. This includes the annual interest payments plus the difference between what the investor paid for the bond and the amount of principal received at maturity.

YTM is the annual rate of return that a bondholder will earn under the assumption that the bond is held to maturity and the interest payments are reinvested at the YTM. YTM is the same as the bond’s internal rate of return (IRR). YTM or simply the yield is the discount rate that equates the current market price of the bond with the sum of the present value of all cash flows expected from this investment.

Previously, we had calculated the price of bond value when the discount rate (r) was given. This discount rate was the YTM. In YTM calculations, the market price of the bond is given, and we have to calculate the discount rate that equates the present values of all the coupon payments and the principal repayment to the market price.

We do this by using trial and error or an approximation formula.

Yield-to-Call: When a bond is callable, the market also looks to the yield-to-call (YTC). Normally if a bond is called, the bondholder is paid a premium over the face value (known as the call premium). YTC calculation assumes that the bond will be called, so the time for which the cash flows (coupon and principal) occur is shortened. YTC is calculated exactly like YTM, except that the call premium is added to the face value for calculating the redemption value, and the first call date is used instead of the maturity date.

Risks in Debt Securities

Interest rate risk: The cash flows from a bond (coupon payments and principal repayment) remain fixed though interest rate keeps changing. As a result, the value of a bond fluctuates. Thus interest rate risk arises because the changes in the market interest rates affect the value of the bond. The return on a bond comes from coupons payments, the interest earned from re-investing coupons (interest on interest), and capital gains. Since coupon payments are fixed, a change in the interest rates affects interest on interest and capital gains or losses. An increase in interest rates decreases the price of a bond (capital loss) but increases the interest received on reinvested coupon payments (interest on interest). A decrease in interest rates increases the price of a bond (capital gain) but decreases the interest received on reinvested coupon payments.

Thus there are two components of Interest rate risk.

Reinvestment rate risk is the uncertainty about future or target date portfolio value that results from the need to reinvest bond coupons at yields that are not known in advance.

Interest rate increases tend to decrease bond prices (price risk) but increase the future value of reinvested coupons (reinvestment rate risk), and vice versa.

Default risk or credit risk refers to the possibility of having the issuer defaulting on the payments of the bond. It is the risk that the borrower will not honour, in full or in part, its promise to repay the interest and principal. The realised return on a bond will deviate from the expected return if the issuer fails to meet the obligations to make interest and principal payments.

Most investors do not directly assess a bond’s default risk, but instead use the credit ratings provided by credit rating agencies such as CRISIL, ICRA, Moody’s and S&P to evaluate the degree of risk. Credit ratings are the most common benchmark used when assessing corporate bond default risk. These securities are backed by the issuing companies, rather than by government/agency guarantees or insurance. Credit ratings provide an indication of an issuer's ability to make timely interest and principal payments on a bond.

The two most recognised rating agencies, known worldwide, that assign credit ratings to corporate bond issuers are Moody's Investors Service (Moody’s) and Standard & Poor's Corporation (S&P). In India, the credit rating agencies are ICRA and CRISIL among others.

Call risk: If a company issues a bond with a high coupon rate when market interest rates are high, and interest rates later fall, the firm might like to retire the high-coupon debt and issue new bonds at a lower coupon rate to reduce interest payments. If a bond has a call provision, then the company can repurchase the bond at a specified call price before the maturity date. From the bondholder’s perspective it is a disadvantage, as the proceeds will then have to be reinvested at a lower interest rate. This is the call risk faced by the bondholder.

Liquidity risk: Bonds have varying degrees of liquidity. There is an enormous number of bond issues most of which do not trade on a regular basis. As a result, if a bondholder wants to sell quickly, he will probably not get a good price for his bond. This is the liquidity risk.

Duration of Bonds

Bond duration is a measure of bond price volatility, which captures both price and reinvestment risk and which is used to indicate how a bond will react in different interest rate environments.

The duration of a bond is the weighted average maturity of cash flow stream, where the weights are proportional to the present value of cash flows. It is defined as:

Duration = D = {PV (C1) x 1 + PV (C2) x 2+ ----- PV (Cn) x n} / Current price of the bond

Where PV (Ci) is the present values of cash flow at time i.

Steps in calculating duration:

Step 1: Find present value of each coupon or principal payment.

Step 2: Multiply this present value by the year in which the cash flow is to be received.

Step 3: Repeat steps 1 and 2 for each year in the life of the bond.

Step 4: Add the values obtained in step 2 and divide by the price of the bond to get the value of duration.

Generally speaking, bond duration possesses the following properties:

 bonds with higher coupon rates have shorter durations

 bonds with longer maturities have longer durations

 bonds with higher YTM lead to shorter durations

 duration of a bond with coupons is always less than its term to maturity because duration gives weight to the interim payments. A zero-coupon bond’s duration is equal to its maturity.

Duration and Immunisation

If the interest rate goes up, the price of the bond falls but return on re-investment of interest income increases. If the interest rate goes down, the price of the bond rises but return on re-investment of interest income decreases. Thus the interest rate change has two effects (price risk and reinvestment risk) in opposite directions.

Can an investor ensure that these two effects are equal so that he is immunised against interest rate risk? Yes, it is possible, if the investor chooses a bond whose duration is equal to his investment horizon. Forexample, if an investor’s investment horizon is 5 years, he must choose a bond whose duration is equal to 5 years if he wants to insulate himself against interest rate risk. If he does so, whenever there is a change in interest rate, losses (or gains) in price is exactly offset by gains (or losses) in re-investment.

Bond Portfolio Management

The volatility of a bond is determined by its coupon and maturity. The lower the coupon and the higher the maturity, the more volatile are the bond prices. If market rates are expected to decline, bond prices will rise. Therefore, you would want bonds with maximum price volatility. Maximum price increase (capital gain) results from holding long-term, low coupon bonds. (This is the same as saying hold bonds with long durations).

If market rates are expected to rise, bond prices will fall. Therefore, you would want bonds with minimum price volatility. Therefore, invest in short term, high coupon bonds to minimise price volatility and capital loss. (This is the same as saying ‘hold bonds with short durations’).

Bond Theorems

1. Price and interest rates move inversely
2. A decrease in interest rates raises bond prices by more than a corresponding increase in rates lowers the price
3. Price volatility is inversely related to coupon
4. Price volatility is directly related to maturity
5. Price volatility increases at a diminishing rate as maturity increases

 Lets understand the theorems with illustrations:

Theorem-1 : Price and interest rates move inversely

Lets assume 3 year 10% coupon paying bond for illustration

When YTM = 10%	Price = 100
When YTM = 11%	Price = 97.55
When YTM = 9%	Price = 102.53

Hence it can be concluded that as yield increase price of the bond decline and vice-versa.

Theorem-2 : A decrease in interest rates raises bond prices by more than a corresponding increase in rates lowers price

Lets assume 3 year 10% coupon paying bond for illustration

When YTM = 10%	Price = 100
When YTM = 11%	Price = 97.55	Change in price = -2.45%
When YTM = 9%	Price = 102.53	Change in price = +2.53%

This the most important theorem of bond which says that price movement of bond with change is interest rate either side is not equal. Price of the bond increases more than it declines when equal change in interest rate is given. In above illustration you can clearly see that when yield declines by 1% price increases by 2.53% while in case of increase in yield by 1%, price decline is 2.45%. As price curve of the bond is convex, you gain more than you lose.

Theorem-3 : Price volatility is inversely related to coupon

Lets assume 3 year 10% coupon paying bond and 3 year 11% coupon paying bond for illustration.

3 year 10% coupon paying bond

When YTM = 10%	Price = 100
When YTM = 11%	Price = 97.55	Change in price = -2.45%
When YTM = 9%	Price = 102.53	Change in price = +2.53%

3 year 11% coupon paying bond

When YTM = 10%	Price = 102.48
When YTM = 11%	Price = 100	Change in price = -2.42%
When YTM = 9%	Price = 105.06	Change in price = +2.52%

Lets assume current YTM is 10% and then it increases to 11% and declines to 9%. You can clearly see in the above tables that price movement of the 11% coupon bond is lower than 10% coupon bond. It can be concluded that higher coupon bonds are less volatile than smaller coupon bonds.

Bond Investment Strategies

Bond investors can choose from many different investment strategies, depending on the role or roles that bonds will play in their investment portfolios. Passive investment strategies include buying and holding bonds until maturity and investing in bond funds or portfolios that track bond indexes. Passive approaches may suit investors seeking some of the traditional benefits of bonds, such as capital preservation, income and diversification, but they do not attempt to capitalize on the interest-rate, credit or market environment. Active investment strategies, by contrast, try to outperform bond indexes, often by buying and selling bonds to take advantage of price movements. They have the potential to provide many or all of the benefits of bonds; however, to outperform indexes successfully over the long term, active investing requires the ability to form opinions on the economy, the direction of interest rates and/or the credit environment; trade bonds efficiently to express those views; and manage risk.

 Passive Strategies: Buy-and-Hold Approaches Investors seeking capital preservation, income and/or diversification may simply buy bonds and hold them until they mature. The interest rate environment affects the prices buy-and-hold investors pay for bonds when they first invest and again when they need to reinvest their money at maturity. Strategies have evolved that can help buy-and-hold investors manage this inherent interest-rate risk. One of the most popular is the bond ladder. A laddered bond portfolio is invested equally in bonds maturing periodically, usually every year or every other year. As the bonds mature, money is reinvested to maintain the maturity ladder. Investors typically use the laddered approach to match a steady liability stream and to reduce the risk of having to reinvest a significant portion of their money in a low interest-rate environment.

 Another buy-and-hold approach is the barbell, in which money is invested in a combination of short-term and long-term bonds; as the short-term bonds mature, investors can reinvest to take advantage of market opportunities while the long-term bonds provide attractive coupon rates.

Other Passive Strategies

Investors seeking the traditional benefits of bonds may also choose from passive investment strategies that attempt to match the performance of bond indexes. For example, a core bond portfolio in the U.S. might use a broad, investment-grade index, such as the Barclays Capital Aggregate Bond Index, as a performance benchmark, or guideline. Similar to equity indexes, bond indexes are transparent (the securities in it are known) and performance is updated and published daily. Many exchange-traded funds (ETFs) and certain bond mutual funds invest in the same or similar securities held in bond indexes and thus closely track the indexes’ performances. In these passive bond strategies, portfolio managers change the composition of their portfolios if and when the corresponding indexes change but do not generally make independent decisions on buying and selling bonds.

Active Strategies

Investors that aim to outperform bond indexes use actively managed bond strategies. Active portfolio managers can attempt to maximize income or capital (price) appreciation from bonds, or both. Many bond portfolios managed for institutional investors, many bond mutual funds and an increasing number of ETFs are actively managed. One of the most widely used active approaches is known as total return investing, which uses a variety of strategies to maximize capital appreciation. Active bond portfolio managers seeking price appreciation try to buy undervalued bonds, hold them as they rise in price and then sell them before maturity to realize the profits – ideally “buying low and selling high.” Active managers can employ a number of different techniques in an effort to find bonds that could rise in price.

Credit analysis: Using fundamental, “bottom-up” credit analysis, active managers attempt to identify individual bonds that may rise in price due to an improvement in the credit standing of the issuer. Bond prices may increase, for example, when a company brings in new and better management. n Macroeconomic analysis: Portfolio managers use top-down analysis to find bonds that will rise in price due to economic conditions, a favorable interest-rate environment or global growth patterns. For example, as the emerging markets have become greater drivers of global growth in recent years, many bonds from governments and corporate issuers in these countries have risen in price.

Sector rotation: Based on their economic outlook, bond managers invest in certain sectors that have historically increased in price during a particular phase in the economic cycle and avoid those that have underperformed at that point. As the economic cycle turns, they sell bonds in one sector and buy in another.

Market analysis: Portfolio managers can buy and sell bonds to take advantage of changes in supply and demand that cause price movements.

Duration management: To express a view on and help manage the risk in interest-rate changes, portfolio managers can adjust the duration of their bond portfolios. Managers anticipating a rise in interest rates can attempt to protect bond portfolios from a negative price impact by shortening duration, possibly by selling some longer-term bonds and buying short-term bonds. Conversely, to maximize the positive impact of an expected drop in interest rates, active managers can lengthen duration on bond portfolios.

Yield curve positioning: Active bond managers can adjust the maturity structure of a bond portfolio based on expected changes in the relationship between bonds with different maturities, a relationship illustrated by the “yield curve.” While yields normally rise with maturity, this relationship can change, creating opportunities for active bond managers to position a portfolio in the area of the yield curve that is likely to perform the best in a given economic environment.

Roll down: When short-term interest rates are lower then longer-term rates (known as a “normal” interest rate environment), a bond is valued at successively lower yields and higher prices as it approaches maturity or “rolls down the yield curve.” A bond manager can hold a bond for a period of time as it appreciates in price and sell it before maturity to realize the gain. This strategy can continually add to total return in a normal interest rate environment.

Derivatives: Bond managers can use futures, options and derivatives to express a wide range of views, from the creditworthiness of a particular issuer to the direction of interest rates. An active bond manager may also take steps to maximize income without increasing risk significantly, perhaps by investing in some longer-term or slightly lower rated bonds, which carry higher coupons.

Active vs. Passive Strategies

 Investors have long debated the merits of active management, such as total return investing, versus passive management and ladder/ barbell strategies. A major contention in this debate is whether the bond market is too efficient to allow active managers to consistently outperform the market itself. An active bond manager, such as PIMCO, would counter this argument by noting that both size and flexibility help enable active managers to optimize short- and long-term trends in efforts to outperform the market. Active managers can also manage the interest-rate, credit and other potential risks in bond portfolios as market conditions change in an effort to protect investment returns. A word about risk: Past performance is not a guarantee or a reliable indicator of future results. Investing in the bond market is subject to certain risks including market, interest-rate, issuer, credit, and inflation risk; investments may be worth more or less than the original cost when redeemed. Investing in foreign denominated and/or domiciled securities may involve heightened risk due to currency fluctuations, and economic and political risks, which may be enhanced in emerging markets. Mortgage and asset-backed securities may be sensitive to changes in interest rates, subject to early repayment risk, and their value may fluctuate in response to the market’s perception of issuer creditworthiness; while generally supported by some form of government or private guarantee there is no assurance that private guarantors will meet their obligations. High-yield, lower-rated, securities involve greater risk than higher-rated securities; portfolios that invest in them may be subject to greater levels of credit and liquidity risk than portfolios that do not. Duration is the measure of a bond’s price sensitivity to interest rates and is expressed in years.