Measures of Bond Yield - Essay Example

Measures of Yield Name: Course Name and Code: Professor’s Name: Date: Abstract The current yield is a representation of interest rate of securities, and is commonly linked with bonds. It is annual return rate which an investor buying a security at the market price will realize. In order to attain the current yield, the formula to be used is dividing annual coupon interests by market price. The yield on a given investment is the rate of interest which will formulate present values of cash flows from investment to be equal to investment price. A bond which is callable always has the chance of being called before the date of maturity. Investors are able to notice slightly high yields when the bonds that have been called are paid at premium. Several bonds, particularly those which are issued by corporations are said to be callable. The prices of bonds move inversely to the rates of interest. When the rates of interest increase, the prices of bonds decrease, and when they decrease, the prices of bonds increase, and this is applicable when bonds that have been issued previously trade in an open market. Measures of Bond Yield Bonds are said to be debt instruments that are taken out by some companies. Investors therefore provide money to a company when they purchase its bonds. In exchange of this, the company is able to pay its interest which is a ‘coupon’ at intervals that are predetermined (semiannually or annually), and also returns principals on date of maturity, thereby terminating the loan (Apedjinou, 2004). Since the issue of each bond is not the same, it is significant to comprehend the terms prior to investment. In that regard, this paper will determine the three measures of yield and the way in which changes in interest rates affect bond prices. There are three measures of yield that are commonly stated by dealers, as well as utilized by investors. These include current yield, the yield to maturity, and yield to call. Current Yield The current yield is a representation of interest rate of securities, and is commonly linked with bonds. It is annual return rate which an investor buying a security at the market price will realize (Boukrami, 2002). In order to attain the current yield, the formula to be used is dividing annual coupon interests by market price. The difference between current price of a given bond and the annual interest provides the measurement that the investor expects to make in certain numbers of years. This kind of calculation takes into consideration the coupon interest, as well as no other return source which will have an impact on the yield of an investor. The gain on capital that investors realize when the bond is bought at discounts or capital loss, which the investor eventually realizes when a bond is bought at premium, and is maintained to mature levels are not considered. Further, time value of money is ignored. The following is the formula used to determine the current yield: Current Yield= Annual Bond Coupon/Current Bond Price For instance, if a given bond has the price of 110.45 dollars, and the rate of the coupon is 7.83 dollars, the current yield will be equal to 7.08 per cent. The current yield affects the investor in certain ways. A trader is highly likely to monitor current yields when seeking to leave the position in a year’s time. In the formula above, when the trader has the intention of purchasing the bond, one will receive 7.83 dollars from the investment. Since the investor receives the dividends from that bond, the gain of the trader will be dependent on bond price in one year. If an assumption is made that the rate of interest dropped, and bond price increased to 114.50 dollars when the investor is ready to close position. The actual return rate from the bond will be 3.6 per cent (that is, 4.05 dollars divided by 110.45 dollars). The basics that follow the current yield are that whenever the bond sells as a discount, this implies that the current yield is going to be more than discount rates (Nielson, 2010). When current yield is lesser than coupon rate, it means that the bond will be bought at premium. Further, whenever the rates of interest increase, the prices of the bond decrease, and when the rates of interest decrease fall, the prices of the bond increase (Bond Basics, 2008). Yield to Maturity The yield on a given investment is the rate of interest which will formulate present values of cash flows from investment to be equal to investment price (Bond Investment Strategies, 2010). On a particular bond, the yield to maturity is rate of return which an investor will gain from if the bond is bought at current market prices, and held to maturity. It is a representation of discount rate, which discounted value of future cash flow of bonds, is equated to the current market price. The equation below is an illustration of this explanation: Bo= C/2 [ 1-(1+YTM/2)-2T] + F/ (1+YTM/2)2T YTM/2 Where, Bo = the bond price, C= annual coupon payment, F= face value of bond, YTM= yield to maturity on bond, t= number of years that remain until maturity. Source: (Investment Advisory, 2007) It is important to note that yield to maturity cannot be directly solved. In general, it has to be determined by the use of trial and error, or as mentioned before, the iterative technique. An example to illustrate the calculation of yield to maturity is when one is told to give the yield to maturity on a coupon bond which is semiannual, and has a face value of 1000 dollars, a 10 per cent coupon rate, as well as 15 years that remain until maturity, when bond price is given as 862.35 dollars. $862 = 100/2 [1- (1+ YTM/2)-2(15)] + 1000/ (1+YTM/2)2(15); therefore, the YTM=12% YTM/2 In order to find a value that is more accurate, a procedure that is iterative is utilized (Sunders, 1998). The main objective of this is to determine interest rate that will make present values of cash flows to be in equal values with the price. This calculation has many assumptions deemed to be significant. First and foremost, the bond is going to be held to maturity, and the second is that the cash flows of the bond can be invested again at yield to maturity. As a measure of IRR, yield to maturity is exposed to certain flaws. Nevertheless, the flaws are not very serious in this instance, as a result of the characteristics of the bonds. The cash flows are always said to be positive, as well as the rate variation where the income to be reinvested is not high. All in all, the yield to maturity is better as compared to flat yield, and is an accurate measure to be used in bond yield (Kim & Koppenhaver, 2005). The maximum evaluation of any given bond has to be considered if the spread of the yield is enough compensation of the risk, as well as the way in which it is compared with other alternatives in the same term. Yield to Call A bond which is callable always has the chance of being called before the date of maturity. Investors are able to notice slightly high yields when the bonds that have been called are paid at premium (Simons, 2003). An investor with such a bond might wish to find out the yield that will is going to be realized when such a bond is called at certain call dates, to find out if the prepayment risk is worth it. Several bonds, particularly those which are issued by corporations are said to be callable. This implies that the one that issues the bond is able to redeem it before it mature, and this is done through payment of the call price. The amount paid is more than the bond’s face value. In normal circumstance, callable bonds are not called until five or ten years after issue. When this happens, the bonds are considered to be call protected (Liang, 2007). The call date is then that day when the bonds are called. The yield to call is that rate of return, which investors earn if they purchased callable bonds at current market prices, and held to the call date provided that the bond is called on call date. It is a representation of discount rate which equates a bond’s discounted value cash flows of the future to the current market price provided that such a bond is called on a call date. The formula below is a representation of how to calculate the yield to call: Bo=C/2 [1- (1+YTC/2)] + CP YTC/2 (1+YTC/2)2d Source (Bond Basics, 2008). Where; Bo=bond price, C=annual coupon payment, CP=call price, YTC=yield to call on bond, and CD=number of years that remain until call date. The yield to maturity is the same as yield to call since it cannot be directly solved. In general terms, it has to be determined by the use of iterative or trial and error techniques. An example to illustrate this is when one is asked to determine the yield to call on a coupon bond that is semi-annual, and has face value of 1000 dollars, a 10 per cent coupon rate, and 15 years that remain to maturity provided a bond price of 1175 dollars. The bond can be called five years from now at 1100 dollars as the call price. This is given by: $1175= 100/2 [1- (1+YTC/2)-2(5)] + 1100 YTC/2 (1+YTC/2)2(5) Therefore, YTC=7.43% Another illustration is given a 30 year callable bond that has been issued with coupon of 7 per cent and is callable after a total of five years. It is assumed that five years later, the rates of interest for any new 30 year bonds are 5 per cent. In this case, the issuer will recall bonds since the debt can be refinanced at low rates of interest. On the contrary, if rates are increased to 10 per cent, the issuer is not in a position to do anything, because the bond is considered to be cheap in comparison to the rates in the market. Interest Rates and Bond Prices The prices of bonds move inversely to the rates of interest. When the rates of interest increase, the prices of bonds decrease, and when they decrease, the prices of bonds increase, and this is applicable when bonds that have been issued previously trade in an open market. In order to understand the inverse relationship, an illustration will be used. A given bond is issued for an amount of 10000dollars, for a period of five years, and has a 5 per cent interest rate or coupon, which is paid every six months. The rate of interest rises to 6 per cent. If an investor wants to sell a bond, the number of people that will purchase it when it pays at 1 per cent under the market rates (that is, 5 per cent versus 6 per cent) is low. Therefore, one is forced to make it attractive so that the buyer is able to get a market rate of the particular bond. One is also not in a position to modify the rate of interest of the bond that is fixed at the percentage of 5 per cent. However, one is able to modify the price that will be taken for that bond. The yearly payment of 500 dollars (that is, 10,000 multiplied by 5 per cent) has to be equal to a 6 per cent payment. In calculating this, it is discovered that the bond’s face value has to be discounted to 8333 dollars so that 500 dollars fixed payment will be equal to a 6 per cent yield on investment of the buyer (that is, $8333 multiplied by 6 per cent, which is equal to 500 dollars). When the rates of interest decrease instead of decreasing, then one is able to sell the bond at premiums which are more than face value. This is because the rates of interest which are fixed will be more than market rates (Liang, 2007). Conclusion The purpose of this paper was to determine the three measures of yield and the way in which changes in interest rates affect bond prices. It was shown that there are three measures of yield that are commonly stated by dealers, as well as utilized by investors. These include current yield, the yield to maturity, and yield to call. The current yield is a representation of interest rate of securities, and is commonly linked with bonds. It is annual return rate which an investor buying a security at the market price will realize. The difference between current price of a given bond and the annual interest provides the measurement that the investor expects to make in certain numbers of years. The current yield affects the investor in certain ways. A trader is highly likely to monitor current yields when seeking to leave the position in a year’s time. On a particular bond, the yield to maturity is rate of return which an investor will gain from if the bond is bought at current market prices, and held to maturity. The yield on a given investment is the rate of interest which will formulate present values of cash flows from investment to be equal to investment price. A bond which is callable always has the chance of being called before the date of maturity. An investor with such a bond might wish to find out the yield that will is going to be realized when such a bond is called at certain call dates, to find out if the prepayment risk is worth it. The prices of bonds move inversely to the rates of interest. When the rates of interest increase, the prices of bonds decrease, and when they decrease, the prices of bonds increase, and this is applicable when bonds that have been issued previously trade in an open market. References Apedjinou K. M. (2004) “What Drives Interest Rate Swap Spreads”, Columbia Business School working paper. Boukrami, L. (2002). The Use of Interest Rate Swaps by Commercial Banks. Manchester Metropolitan University – Graduate Business School. Bond Basics (2008). Bond Basics: What are Interest Rate Swaps and How Do They Work. Global Investment Authority PIMCO Bond Investment Strategies (2010). Interest Rate Swaps. Investing in Bonds. Retrieved July 16, 2010, from http://www.investinginbondseurope.org California Debt and Investment Advisory Commission (2007). Understanding Interest Rate swap and Math Pricing. Kim, S. and Koppenhaver, G.D. (2005). An Empirical Analysis of Bank Interest Rate Swaps. Journal of Financial Services Research, 7 (1), 57-72. Liang, B. (2007). The Driving Force of Swap Spreads. An Empirical Analysis of the US Dollar Interest Rate Swap Spreads. Nielson, J. (2010). Fraud Charges on Interest-Rate Swaps. Retrieved July 16, 2010, from http://www.bullionbullscanada.com Saunders, T. (1998) The Interest Rate Swap: Theory and Evidence. United States. Simons, K. (2003). Interest Rate Derivatives and Asset-Liability Management by Commercial Banks. New England Economic Review Read More