BBK3413 Investment AnalysisRM50 and at the end of the third year, he will get back RM1,000. • A zero coupon bond will not pay any coupon. However, when it is sold for the first time,

Topic 4

Fixed Income Securities

BBK3413 | Investment Analysis

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Content

7.1 CHARACTERISTICS OF BOND

7.2 RISKS ASSOCIATED WITH BONDS

7.3 BOND PRICING

7.4 BOND YIELDS

7.5 VOLATILITY IN BOND PRICES

7.6 BOND PORTFOLIO MANAGEMENT

By the end of this topic, you should be able to:

1. Identify the characteristics of bonds;

2. Explain the risks associated with bonds;

3. Compute the price of a bond;

4. Differentiate between yields to maturity, current yield and yield to call;

5. Formulate bond portfolio management strategies; and

6. Summarise the concepts of duration and immunisation.

Learning Objectives


Bonds are normally issued by firms and governments. It allows the issuer to tap funds from the financial markets for various purposes which may include business expansion.

In its simplest form, it may be regarded as a loan. Some of the key characteristics of bonds are:

(a) Maturity PeriodMaturity period refers to a time period when the issuer fulfils the obligations of the bond to the investor. The shortest time period for a bond is six months.

(b) Maturity ValueMaturity value is also known as the principal value, redemption value or face value. It is the value that has to be paid by the firms when the bond matures.

(c) Coupon RatesA coupon rate is the rate quoted on the bond. It will be used as a basis to determine the interest that has to be paid to the investor. The interest payment is known as coupon payment. It is paid either annually, semiannually, quarterly or monthly as stipulated in the bond agreement. Bonds are normally issued at a coupon rate attractive enough to induce potential investors. Rates would normally take into account various types of risks that will be faced by the issuer and investor. The coupon payment is determined by multiplying the rate with the face value of the bond.


(d) Floating Rate

A floating rate indicates that the coupon rate may change according to the current interest rate. This current interest rate is dependent on the state of the economy. [Base Rate (BR)/Base Lending Rate (BLR)

(e) Zero-coupon Bonds

Zero-coupon bonds are bonds which do not pay any coupon.

(f) Embedded Options

Embedded options are specific characteristics stipulated in the bond indentures. These characteristics may include the option to call the bond at an earlier date before maturity. Another type of option is when bonds can be converted to equity. The latter is known as convertible bond.


• To further clarify the characteristics of a bond, let’s use an example of a bond that matures in 3 years, with a face value of RM1,000, and a coupon rate of 10% paid semi-annually.

• Based on this information, every six months the investor will get RM50 and at the end of the third year, he will get back RM1,000.

• A zero coupon bond will not pay any coupon. However, when it is sold for the first time, the price is below the face value. For example, a one-year zero coupon bond with a face value of RM1,000 can be sold for RM900. At the end of the year, the investor will get back the RM1,000.


Bonds may promise a periodical fixed income but not without risks. Investors may be exposed to the following types of risk:

(a) Interest Rate Risk

• The uncertainty in income for the investor may result from the change in bond price as a result of changes in market interest rates.

• An increase in current market rates will make the existing bond unattractive since an alternative investment now can fetch a higher rate of return.

• An increase in the demand for an alternative security will motivate investors to dispose of their existing bonds, hence pushing down the price of the bonds.


(b) Reinvestment Risk

The yield from a bond is always under the assumption that the coupon amount is reinvested. This stems from the idea of compounding interest. However, an investor is faced with the risk that the current rate of interest might fall. Should this happen, the coupon payment that they receive will be reinvested at a lower rate.

(c) Redemption Risk (or Risk of a Call)

A bond that allows the issuer to redeem or recall the security, poses risks to its investors. A bond that is recalled earlier than maturity will deprive the investors of the potential income that they may otherwise receive. A bond may be recalled because the market interest rates have fallen and the issuer now wants to issue a new bond with a lower coupon payment. The investor will therefore lose potential income since they are offered a new but lower coupon rate.


(d) Default Risk

The uncertainty of income as a result of the failure of the bond issuer to pay its coupon and principal payments.

(e) Inflation Risk

Income that will be received from a bond is fixed. However, if the level of

price in the economy rises, say from 5% to 7%, then in real terms, the

purchasing power that can be derived from the income will be actually

reduced. In short, you have less income to buy what your heart desires.


(f) Liquidity Risk

• The ability to convert the bond into cash immediately without eroding its value is very important for an investor who does not wish to hold the bond until maturity.

• Unless an economy has a liquid secondary market for bonds, investors will be faced with this type of risk.

• These are some of the types of risks related to bonds. As the markets and purpose of the bonds become more complex, other types of risks may exist.


• The price/value of a bond is the present value of the expected cash flow from the bond. The expected cash flows are the coupon payments and the face value.

• These cash flows are then discounted at the required rate of return. This rate of return is normally called the yield of the bond. This yield will depend vastly on the present market interest rate.

• The present market interest rate will consider the risk-free rate of return and compensate its investor for the expected inflation. Depending on the risk structure of the bond, the investor will also be compensated for additional risks faced throughout the life of the bond. These risks may include liquidity, default or call risk which are normally specific to the security and firms.

7.3 BOND PRICING

• For example, a three-year RM1,000 bond with 10% coupon rate with a yield of 8% will have a value of:

• Specifically the value of a bond is:

7.3 BOND PRICING

• We can call the maturity date T and the discount rate r, hence the bond value can be expressed as below:

• The summation sign in Equation 7.1 indicates that the periodical coupon payments must be discounted until the maturity time T.

• The first term in the equation also indicates that the present value of an annuity is discounted at a rate r.

• The second term is the present value of a single amount, which is the final payment of the bond’s par value.

7.3 BOND PRICING

• Now let us see the model of valuation if the coupon rate is paid semi-annually.

• Using the above three-year bond above and coupon paid semi-annually, the price of the bond is:

7.3 BOND PRICING

• The rate of return earned from investing in bonds until the bond matures is termed yield to maturity. Yield to maturity is also viewed as the promised rate of return accruing to investors.

• However, investors can only expect the promised return if:

(a) The probability of the issuer defaulting in payment is zero; and

(b) The bond cannot be called before maturity.

• If there is some default risk, or if the bond may be called, then there is a probability that the promised payments to maturity will not be received, in this case the calculated yield to maturity will differ from the expected return. From equation (7.1) the YTM is the rate r.

7.4 BOND YIELDS7.4.1 Yield to Maturity

• Let’s say in the market there is a three-year RM1,000 bond, with a coupon rate of 10%, and it is going at a price of RM951.97. Fitting these values into equation (7.1) will show:

• You could substitute values for r until you find a value that forces the sum of the PVs on the right side of the equal sign to equal RM951.97. It involves finding r by trial-and-error and is a tedious process, but as you may have guessed, it is easy with a financial calculator. The answer is 12%.


• The YTM for a bond that sells at par consists entirely of an interest yield.

• If the bond is priced at RM1,000, we will get a YTM of 10%. This is the same rate as the coupon rate.

• But if the bond sells at a price other than its par value, the YTM consists of the interest yield plus a positive or negative capital gains yield.

• As above, the YTM is 12% which is 2% higher than the coupon rate.

• Yields are normally reported on an annualised basis. For semi-annual bonds, the calculated YTM can be multiplied by two to get the annual YTM.


• The effective annual yield of the bond however, accounts for compound interest.

• If one earns 3% interest every six months, then after one year, each dollar invested grows with interest to $1x (0.03)2 = 1.0609, and the effective annual interest rate on the bond is 6.09%.

• The bond’s yield to maturity is the internal rate of return on an investment in the bond. YTM can be regarded as the compound rate of return over the life of the bond under the assumption that all bond coupons can be reinvested at an interest rate equal to the bond’s yield to maturity. YTM therefore is an accepted proxy for average return.


• As in the example above, the current yield is:

7.4 BOND YIELDS7.4.2 Current Yield

• If you purchased a bond that is callable, where issuers can call or redeem their bond when the market interest rate is generally falling, you would not have the option of holding the bond until it matures.

• Thus, you lose the chance to earn YTM. For example, suppose KFC Holdings originally issued a 10% coupon bond and then decides to save its coupon payment when market interest rates fall to 5%. The company will call in the 10% coupon bond, pay off the investor and replace the bond with a new 5% bond. KFC will save 5% interest per bond per year. This will be beneficial to the issuer but not to investors.

• The investor should understand that if the current interest rates are well below the coupon rate, there would always be a possibility that the bond will be called.

• Investors will therefore estimate its expected return as the yield to call (YTC) and not YTM.

7.4 BOND YIELDS7.4.3 Yield to Call

• To calculate the YTC, we solve the following equation for r:

• Here, N is the number of years until the company can call the bond.

• The call price is the amount the issuer has to pay in order to call the bond. The price is normally set above the par value.

• At least it is the face value plus one-year coupon payment. This will normally compensate investors for the reinvestment risk faced when bonds are recalled.

7.4 BOND YIELDS7.4.3 Yield to Call

• You should be able to differentiate and not be confused by the difference between rate of return on a bond over any particular holding period and the Bond’s yield to maturity.

• The yield to maturity is that discount rate that equates the present value of payments to the price of bonds when purchased. It is the measure of an average return over the bond’s life if it is held until maturity.

• The return can be calculated for any holding period based on the income generated over that period.

7.4 BOND YIELDS7.4.4 Holding-Period Return Versus YTM

• As an illustration, if a 30-year bond paying an annual coupon of $80 is purchased for $1,000, its yield to maturity is 8%.

• One year later you decided to sell the bond with a market price of RM1,050.

• With the latest price, the yield to maturity will no longer be 8% (the bond is now selling above par value, so the YTM must be less than the 8% coupon rate). However, your holding period return for the year is greater than 8%:

7.4 BOND YIELDS7.4.4 Holding-Period Return Versus YTM

• Generally, the price of bonds will move counter cyclical to the movements in interest rates. In other words, if the price of bonds has a tendency to fall, then it may be due to the upward movement of interest rates in the market.

• To illustrate, if we have a five-year 8% coupon bond, the behaviour of its price in relation to the market interest rate is as follows:

7.5 VOLATILITY IN BOND PRICES7.5.1 Bond Prices Move Inversely with Interest Rates

• Notice that as interest rates increase, the price of the bond falls.

• Diagrammatically the relationship can be observed in the following Figure 7.1:


• Table 7.1 shows a few more examples of how bonds with different maturities react to changes in interest rates.

• Table 7.1 above shows that as the market interest increases, prices of bonds will decrease irrespective of the maturity periods.


Investors can put their money in more than one bond to create a bond portfolio. There are two types of management strategies, namely passive and active.

(a) Passive Strategy

In this approach, there are basically two types of strategies which include:

(i) Buy and Hold Strategy

• In this strategy, the portfolio is managed based on the objectives and constraints dictated by the investor.

• The bonds will be bought and held until maturity. After choosing a bond that is considered good, the investor will match the maturity and the duration of the bond during the investment period.

• An aggressive investor will normally invest at the right market timing.


Investors can put their money in more than one bond to create a bond portfolio. There are two types of management strategies, namely passive and active.

(ii) Index Strategy

• In this strategy, an investor will form his portfolio based on one index. Normally, the index will be formed from bonds with varying types of risk structures combined together in a portfolio.

• The first important step is to develop a reasonably good index. Bonds to be purchased will be matched with the index.

• The proportion of portfolio investment will be almost similar to the index constructed. The portfolio manager will compare its portfolio to that of the index.


(b) Active Strategy

There are four sources of active management strategies, namely:

(i) Interest Rates Forecasting

• This strategy is the riskiest strategy as it involves the forecasting of future interest rate movements.

• The main idea here is to maintain existing capital when interest rates are forecasted to rise and increase capital gains when interest rates are predicted to fall. This is done by adjusting the maturity and duration period of bonds held in the portfolio.


(ii) Choosing a Sector

• In this strategy, the manager will pick the sectors that are believed to give high returns. A manager may pick a sector having a high credit risk.

(iii) Movements Between Sectors

• This strategy involves movement of funds from one sector to another. The bond market can basically be divided into government and corporate, long-term and short-term sectors.

(iv) Choosing a “Wrongly” Priced Bond

• In this strategy exist two situations. Firstly, to assume that the bond is priced correctly and then to find the best bond within the category.

• Bonds ranking AAA are said to be the best and choosing the best from this category will be appropriate. Secondly, find a bond that is wrongly ranked; it should have been an AA bond but is ranked BB instead.


Documents

BBK3413 Investment AnalysisRM50 and at the end of the third year, he will get back RM1,000. • A zero coupon bond will not pay any coupon. However, when it is sold for the first time,