Different Types of Bond Yields and Effects of Interest Rates on Bond Prices - Case Study Example

Running Head: DIFFERENT TYPES OF BOND YIELDS Different Types of Bond Yields and The Effects of Interest Rates on Bond Prices Name Course Instructor Date DIFFERENT TYPES OF BOND YIELDS Introduction Bond yield is the return an investor receives form a bond they hold. Like in any other investment, an investor in bonds needs to have a very clear understanding of what to expect as a return when the bond he or she holds reaches maturity, or when he or she sells it before maturity if they so decide (Fabozzi & Modigliani, 2002, p.453). To calculate these yields, different factors are considered and the investor needs to have an understanding of these. These factors are as follows: Face value: It is also known as par value or principal, it is what is owed to the bond holder at maturity of the bond. If for example an investor has bought a 15 year bond whose face value is $ 1000 and its coupon rate is 10% the bond issuer will be paying the investor $ 100 per year for the period of 15 years. After 15 years the bond will mature and the issuer will give back to the investor the $1000 principal he had invested. If during the life of the bond, before its maturity, its price falls below the face value, the bond is said to be trading below par, if price increases beyond face value, it is said to be trading above par. The possibility that the price of a bond will decline is referred to as price risk (Buse, (1970, p.813); Caks, (1977, p. 114). In bonds, maturity is the future date when the principal used by an investor to purchase bonds will be repaid. The maturity period has been known to range from a day to up to 100 years, the normal period, however ranges from 1 day to 30 years. A few bonds in the market are nonredeemable which means that the investor draws coupon payments in perpetuity but he or she never gets a return of the principal. Bonds may be categorized by maturity ranges as long term bonds which have maturity of 12 years or more, intermediate bonds whose maturity ranges from DIFFERENT TYPES OF BOND YIELDS five years to 12 years. The ones with the shortest maturity period are known as short term bonds and they have maturities of up to 5 years. Reinvestment risk is the risk that future coupons earned from a bond will be reinvested at interest rates that are lower than the one prevailing at the time the bond was bought. This risk normally affects a bond whose investor intends to hold to maturity this is so because calculation of a bond’s Yield to Maturity, assumes that the coupon rates earned by the bond will be reinvested at the same rate as the rate as the bond’s coupon rate. Some bonds have no interim coupon payments and they are known as zero coupon bonds and they are the only type of bonds without reinvestment risk. Bonds that have a longer maturity period have a higher reinvestment risk than shorter term bonds this is because the long duration increases opportunity for interest rates to adjust. Higher interest rate means bigger coupons to be reinvested and thus the possibility of bigger loss margins in the event that interest rates have been adjusted downwards (Shirvani and Wilbratte, 2002, p. 21; Dai & Singleton, 2002, p. 431). Bonds also present a risk referred to as credit risk this is especially so with corporate bonds which are debentures and therefore do not have secured collateral. There is a risk that the bond issuer will fail to meet their debt obligation. It is very important for an investor to be in a position to assess this risk because it has the capacity of causing a total loss of the investment. Couponed rate: How changes in interest rates affect bond prices A premium bond means a bond that is trading above par because the interest rate it offers is above the general market rate. A bond whose circumstances are the opposite of this i.e. where a bond’s coupon rate is lower than the prevailing interest rate is referred to as a discount bond. A DIFFERENT TYPES OF BOND YIELDS bond can also be issued for the very first time in the market for an amount less than its par value; such a bond is also referred to as a discount bond. The discount amount in a bond is the amount by which the offer price is lower than the bond’s par value. A bond with a high possibility of default (distressed bond) may be offered at very high discounts to par to make it attractive to potential investors the discounts such bonds offer make their yields very high if the issuer does not default. A change in bond prices to either discount or to premium is normally informed by changes in interest rates. If interest rates rise above a bonds coupon rate, the bond’s price in the market falls making it a discount bond, if on the other hand interest rates fall below the coupon rate of a certain bond the price of that bond rises making it a premium bond. Kinds of bond yields Yield to maturity It is also referred to as the promised yield, redemption yield or the internal rate of return. A bond’s Yield to maturity is the total return expected by an investor that is interest accrued from coupons and capital gain that has been earned when the bond has been held to maturity and redeemed at par value. Yield to maturity assumes that all interest earned during the bond’s maturity is reinvested at an interest rate equal to the rate prevailing at the time the bond was purchased (Johnston et al, 2002, p. 21). This assumption is one of the main reasons why YTM is generally inaccurate; interest rates are likely to change during the bond’s maturity period and therefore have the coupon earnings invested at a rate different from the initial one. There has been debate lately on whether reinvestment of coupon earnings is really important in its calculation (Shirvani & Wilbratte, 2009, p. 35). Owing to the fact that YTM assumes the bond is DIFFERENT TYPES OF BOND YIELDS held to its maturity, it is not useful the investor seeking to make decisions regarding bonds that will eventually not be held to maturity. It is a forward looking approximation of the rate of return of a bond. Some scholars have argued that due to the unrealistic assumption of a flat interest rate that does not change, YTM can virtually never be realised and therefore it is of no much economic significance and it only makes sense for zero coupon bonds because they do not have an investment rate problem (Shawn et al, 2008, p. 50). Realised Yield This is an actual return that has been earned from a bond over a certain period of time it factors in even the returns earned from reinvestment of coupons (Johnston et al, 2002, p. 21). Realised yield differs from yield to maturity if the investor holds the bond in question for a period less than maturity. Realised Compound Yield is the yield realised when coupons are all reinvested at the market rates prevailing at the time the coupons are received and held until the bond matures. The relationship between Realised Compound Yield and the Yield to Maturity is the fact that while YTM looks forward from the time when bonds are offered, RCY looks backwards from the time the bond has matured, it can therefore be put that YTM is for planning ahead while RCY is useful as a tool for evaluating performance of a bond. Expected Yield This is a projection of what an investor can expect to get from a bond. The difference between expected yield and expected return is that return is the interest payment on the principal while yield takes into the price of the bond into account. DIFFERENT TYPES OF BOND YIELDS Worked examples Promised yield (YTM) Promised yield calculation formula can be presented as Bond Price = Cash flow1 + Cash flow 2 +…………. + Last Cash flow (1 + yield) 1 (1+yield) 2 (1+ yield) n Or Using the example of a bond with a par value of $100 and a current yield of 5.21% which matures in two and a half years and it has a half yearly coupon of 5%. The cash flow is that every six month there would be a coupon payment of $2.5 and the redemption amount of $1000 Putting the known values into the formula gives the following picture. 1 1- $95.92 = 2.5 x (1 + i) 5 + 100 x 1 I (1+i) 5 To find ‘i’ plug interest rates higher than 5% to the formula to find out which interest rate gives the bond price of $95.92 which gives an interest rate of 6.8%. DIFFERENT TYPES OF BOND YIELDS Realised yield In a bond whose par value is $100 and the coupon rate is 8% and it is held for duration of 4 years. Formula RY= Vt V0 _-1 Vt is the amount in the end and V0 is the amount at the beginning V0 = $ 1000 and t = 4 Therefore RCY = (Vt /$1000)1/4 -1 To find Vt, we take the $80 earned from coupons was reinvested 8% for the four year duration of the bond which gives $ 360.49 $360.49 + $1000 = $1360.49 Vt = $1360.49 Therefore RCY = $1360.491 1/4 $ 1000 -1 = 0.08 How interest rates affect bond price The relationship between bond price and interest rates is inverse, this means when interest rates increase the price of bonds goes down and when interest rates reduce, the price of a bond goes up. The reasons why this happens is because when the general interest rate is higher than the coupon rate of a bond, investors are likely to lose interest in that particular bond likewise when a bond’s coupon rate is higher than the prevailing market rate, investors will be more interested in DIFFERENT TYPES OF BOND YIELDS purchasing it this means that the demand for it will be high. Since the interest rate of a bond is fixed, the price has to move to accommodate changes in the market (Forbes, Hatem and Paul, 2008, p.49). If an investor purchases a bond at 7% coupon and $ 1000 par value, he or she will be receiving $70 coupon per year. If interest rates go up and a new bond is issued at $1000 par and 8% coupon which means investors in this new bond will be earning $80 in coupons buyers will not be interested in buying the old bond offering 7%. To sell the seller would have to offer the bond at a discount to enable the new buyer to make 8% in coupons. In this case the bond would have to be priced at $875. If the rate falls, below the original 7% and bonds are issued at 6%, it will be worth $1666. When it comes to redeeming, the bond will have to be redeemed at face value and the person who bought it at $875 when the interest rates were high will make a capital gain while the one who bought at a higher price when the interest rates were low will lose capital. Conclusion It is quite clear that many of the methods used to calculate what a bond will yield are singularly inaccurate due to the numerous unforeseeable forces that come into play during its maturity. These unforeseeable forces are the reason why even YTM, the most widely used method of calculating yield cannot be relied upon to be accurate. Realised Compound Yield is accurate but it is calculated retrospectively. In light of the above, it would seem that the best way an investor can make a decision whether to invest in bonds or not is to have a keen finger at the pulse of the economy. That way, it would be possible to know whether there is likely to be drastic changes in interest rates during the time he or she intends to hold the bond or not. References Buse, A (1970). “Expectations, Prices, Coupons and Yields,” Journal of Finance, 809-818. Caks, J (1977). “The Coupon Effect of Yield to Maturity,” Journal of Finance, 103-115.  Dai, Q & Singleton, J. (2002). “Expectation Puzzles, Time-varying Risk Premia, and Affine Models of the Term Structure”. Journal of Financial Economics 63, 415–441. Fabozzi, F & Modigliani, F (2002). Capital markets – Institutions and Instruments, 3rd edn, Prentice Hall. Forbes, S, Hatem, J and Paul, C (2008). “Yield-to-Maturity and the Reinvestment of Coupon Payments.” Journal of Economics and Finance Education 7, 48-50. Johnston, Ken, Forbes, S and Hatem, J (2002). “Reinvestment Rate Assumptions in Capital Budgeting: A Note”, Journal of Economics and Finance Education, Volume1, Number 2, Winter, 28-29. Shawn, M, Forbes, Hatem, J, and Paul, C (2008). Yield-to-Maturity and the Reinvestment of Coupon Payment. Journal of Economics and finance education • Volume 7 • Number 1, 48-51 Shirvani, H and Wilbratte B (2002). “Two Pedagogical Simplifications of the Concept of Duration.” Journal of Economics and Finance Education 7, 18-23. Shirvani, H, and Wilbratte, B (2009). “The Relationship between the Promised and Realized Yields to Maturity Revisited”, Journal of Economics and Finance Education. Volume 8 Number 2, 34-37 Read More