Ways of Determining Yields - Essay Example

Running Head: BOND YIELDS AND EFFECTS OF INTEREST RATES Measures of Bond Yields and the Effects of Interest Rates on Bond Pricing Name Course Instructor Date BOND YIELDS AND EFFECTS OF INTEREST RATES Measures of Bond Yields and the Effects of Interest Rates on Bond Pricing Introduction Fabozzi (2007), states that bond is an agreement between an investor and a company or government. The investor lends money to the company or government (the issuer) which the issuer pays back at a pre agreed interest rate at a pre arranged date. Bonds are issued when a company wants to expand and are usually borrowed from individual investors, mutual funds, pension funds etc. They may have coupons, which are paid regularly at pre arranged interest rates at regular intervals before maturity when the principle is redeemed. Other bonds have no coupons and interest and principal are all paid to the investor once at maturity. There are different types of bonds which include fixed rate bonds whose interests remains fixed all through the bond’s tenure, due to this fixed nature of the bonds they are not affected by the changes to which the market is prone. Zero interest rate bonds do not pay interest to the investors and the issuer is only supposed to pay back the principal amount at maturity. There other bonds known as floating rate bonds whose coupon rates change with the market reference rates. Perpetual bonds pay interest to their holders perpetually, holders of these bonds are not entitled to redemption of their principal amount since the bonds do not have a maturity date. Recently, there has been intro another type of bond referred to as climate bond, these are issued by governments to raise funds when their country has been affected by climate change (Fabozzi, 2001). To understand the working of bond market, it is imperative to understand the mathematics behind issues like pricing. Once an investor has invested in bonds, it is also necessary for them to know the yields to expect and to evaluate performance of the investment after it has matured. Different factors affect the price of bonds one of the most important of them being interest rates. This BOND YIELDS AND EFFECTS OF INTEREST RATES essay will look into the effects of interest rates in pricing of bonds and how they affect the prices (Diebold et al 2005). Measures of Yield Yield enables a potential investor to compare the bonds available in the market which enables them make informed decisions when deciding which bonds to buy. It is the rate of gain the investor can expect from his bond investment. Yield changes with the change of bond prices in the market which is often due to changing interest rates (Chaudhry, M 2004). There are different ways of determining yields which are listed below; however, current yield and yield to maturity are of the greatest interest. Current Yield Current yield is also known as flat yield, interest yield, and income yield and running yield, it is the simplest measure of yield. it is considered a crude measure since it does not take into consideration gains or losses incurred in the capital. This is because it assumes the price of the bond will not vary during the period it is held. It also does not factor in the time value for money. A calculation of yield using this method is best used to the desired effect when the coupon income is more in the total return than any gain or loss in capital. This situation is only likely when the bond has a much longer than average term to maturity (Chaudhry & Gross, 2003). The formula for this calculation is: Current Yield =Coupon rate (%) x 100 Clean price BOND YIELDS AND EFFECTS OF INTEREST RATES Example: If an investor buys a bond at $1000 par value (clean price) and it has a coupon rate of 10% the yield will be found by: Finding 10% of the clean price i.e. $1000 i.e. 10/100 x 1000 = 100 And then dividing it by 1000. 100/1000 = 1/10 Multiply this by 100 to get the percentage yield. 1/10 x 100 = 10% the current yield of the bond is 10%. Simple yield Simple yield is current yield with a little more sophistication since it recognizes capital gain, it assumes that the capital gain accrues linearly over the life of the bond. It uses clean price in the calculation and thus does not allow compounding of interest and neither does it consider accrued interest (Fabozzi, 2001) Formula for its calculation is Simple Yield = (Coupon Rate + (100 – clean price) x 100) x clean price Years to maturity BOND YIELDS AND EFFECTS OF INTEREST RATES Yield to Maturity (YTM) Yield to maturity is also referred to as Redemption Yield or Internal Rate of Return. It is the most commonly used yield when a bond is listed in the market and it shows total return an investor is likely to get if the bond is held to maturity. It factors in all interest payments due to be received and assumes that they will all be reinvested in the bonds at the same rate as the bonds current yield, it also factors in any gain when the bond is purchased at a discount or loss if it is purchased at a premium. Using the above parameters to calculate shows that YTM gives only the potential yields of the bond and it is not necessarily accurate in the long run (Fabozzi, 2007). This method of determining yield has its limitations, due to the assumption that bonds are held to maturity, it cannot be used to calculate yield of the bond at a time before maturity. Its assumption of a flat yield curve in which coupons received are reinvested at the same rate is erroneous since the reinvestment is done at the market rate that is there at the time coupons are paid to the investor and their reinvestment. In YTM all cash flow is also discounted at the same rate. Yield to Maturity may be calculated as gross, without factoring in the tax element or Net redemption yields in which the taxes levied are deducted from both the coupon payments and redemption payments; sometimes the taxes are levied on both income and gains in capital. The formula for gross YTM is: P = c + c + c …………..+C + R 1 + y (1 + y)2 (1 + y)3 (1+ y)n Where P = dirty price C= Coupon BOND YIELDS AND EFFECTS OF INTEREST RATES R= redemption payment n=number of periods y = redemption yield When the YTM to be calculated is for bonds with bi annual coupons the formula should be modified as follows: P= C/2 + C/2 + C/2 +………..C/2 + M (1+1/2 r) (1+1/2r) 2 (1+1/2 r) 3 (1+1/2r) 2N (1+1/2r) 2N = 2n ∑ C/2 + M n=1 (1+1/2r) n (1 + 1/2r) 2N = C/r 1 - 1 + M (1 + ½) 2N (1 + 1/2r) 2N Worked Example: Description: The bond has a dirty price of $ 98.50 and a 3% coupon rate, it has one year before maturity and therefore three payment periods i.e. two coupon payments and redemption. Once the figures have been substituted into the above formula for gross YTM the equation will be: 98.50 = 1.50 + 103.50 (1+1/2 r m) (1 + 1/2r m) 2 BOND YIELDS AND EFFECTS OF INTEREST RATES This equation can be rearranged to form a quadratic equation thus 98.50x2 – 1.50x – 103.50 = 0, where x = 1 + r m 2 Using the standard formula for solving quadratic equations; i.e. X= -b + √b2-4ac 2a The solution for this is r m = 0.22755 or r m = 4.551% 2 Other types of yields include: Yield to call An issuer of a bond can redeem it before maturity by paying a price referred to as the call price. Call price is usually higher than the face value of the bond. Call protected bonds cannot be called less than five years after they have been issued, callable bonds are usually issued by companies. Yield to call is the return an investor earns when he has invested in a callable bond at its market price and holds it until it is called on the call date. This yield shows the discount rate which shows the relationship between the values of the bonds future cash flow to the prevailing market rate given that the bond is called. It is shown in this equation: BOND YIELDS AND EFFECTS OF INTEREST RATES Where B0 = bond price C= annual coupon payment CP = Call price YTC = yield to call on the bond CD = number of years to call date. Yield to put Some bonds allow the investor to force the issuing company to purchase them at certain preset dates. These dates are referred to as put dates the repurchase price is normally specified at the time when the bonds are issued and it is normally the bond’s par value. These bonds are referred to as putable bonds. Yield to put is the yield that would be realized on a putable bond if it was redeemed on the put date that would result in the highest yield. The formula for calculating the yield to put is similar to the formula for yield to call but instead of using the number of coupons before call, the number of periods before put is used (Chaudhry, 2004). BOND YIELDS AND EFFECTS OF INTEREST RATES Yield to worst This is the lowest possible yield that can possibly be received in without the bond issuer defaulting. To calculate YTW the worst case scenarios on the issue are assumed these scenarios include the possibility that the bond issuer uses all provisions including prepayment and the sinking fund. A calculation is made on all call dates on schedule , an assumption is made that prepayments are made on put and call dates during which payments the issuer offers a coupon rate lower than the one offered during issue, possibly due to a change in the prevailing rates in the market. If the prevailing coupon rates are higher, calculation of the YTW will assume that prepayments are not made. Therefore, yield to worst will be equivalent to yield to maturity. The yield to worst can only be equal to or less than yield to maturity, it can never be more (Chaudhry & Gross, 2003). Nominal yield is the coupon rate of a bond; it is a fixed yield and does not vary with the market price. How changes in interest rates affect bond prices According to Bank of International Settlement (2007) bonds are seen as stable while compared to other securities in the stock market, this is because an investor never loses the principal amount, which is paid at redemption, unless the issuer defaults. Interest rates affect bond prices unless the bonds are index linked, however, there are just a few index linked bonds and therefore most of the bonds in the market are conventional hence the effect interest rates have on them. Conventional Bonds that are already in the market are the ones affected by interest rates when BOND YIELDS AND EFFECTS OF INTEREST RATES interest rates go up, bond prices go down and when the interest rates go down, bond prices go up. It is therefore argued that bond prices move inversely to interest rates. If for example a bond is issued for a certain amount with a 3% coupon interest rate and then interest rates increase to 6% the bond would now be paying 3% less than the market rate. Since the interest rate of the bond is fixed while issuing and cannot be changed the bond can now only be made attractive by reducing its price. This means that the bond must be priced in such a way that annual coupon payments must equal payment at the new interest rate (Dai & Singleton, 2002). This situation was experienced in 1994 – 1995 in the United States of America when the US bond market registered its worst showing ever. The problem started when the Federal Reserve increased short term interest rates due to a projection that the economy that year would produce inflation. By the end of the year, interest rates had grown by 3%. This led to a reduction in bond prices and also very low returns on bonds in which the longer maturity bonds were severely affected even returning negative yields. In 1995 the economy improved and interest rates fell by 2% which led to an increase in bond prices and increased returns for investors. Changes are shown in the table below (Afonso, A. Jalles, T. 2011). 1994 1995 Bond Yield change (%) Return Yield change (%) Return 2 year Treasury + 3.49% +0.26% -2.55% +11.13% 10 year Treasury +2.08% -8.29% -2.28% +23.58 References Afonso, A. Jalles, T. (2011). ―Growth and Productivity: The Role of Government Debt, School of Economics and Management, Technical University of Lisbon, Working Paper No. 13/2011 (Lisbon: Technical University) Bank for International Settlements (2007). ―Financial Stability and Local Currency Bond Markets, Committee on the Global Financial System Papers No. 28, June. Chaudhry, M (2004). Corporate Bonds and Structured Financial products. 1st edn Oxford: Butterworth-Heinemann. Chaudhry, M, & Gross, G (2003). The gilt-edged market. Oxford: Butterworth-Heinemann.  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. Diebold, F, Li, X, Calin, Y & Vivian (2005). “Modeling Term Structures of Global Bond Yields.” Working paper, University of Pennsylvania. Fabozzi, F. (2001). Bond portfolio management. Hoboken, NJ: John Wiley & Sons. Fabozzi, F. (2007). Bond Markets: Analysis and Strategies. 6th edn. Upper Saddle River, NJ: Prentice Hall. Read More