Bond Yield Measures and Interest Rates - Assignment Example

Bond Yield Measures and Interest Rates Students Name Institution Bond Yield Measures and Interest Rates It is important to note that the value of bonds is reduced once the interest rates increases and the bond value goes up once the interest rates reduces. The yield of these bonds can be measured using several methods(Rosen, 1995). This paper aims at giving a detailed information on these yield methods and the effects the interest rates has on the value of bonds. Measuring bond yield The interest rate can be referred to the yield of any investment and equalizes the current value of the anticipated cash flow that is from the entire investment to its cost. This can be expressed in the following equation. P =  CFt / (1+y) n Where CFt is equals to the cash flow in period t, p is the investment price, and n represents the number of periods represents the interest rate. On the other hand the bond expression can be as follows, P =  C i / (1+y) n + P/ (1+y) n One thing to note from the yield calculation represents a certain period ,or the period in which the interest is paid. However, to under take the yield calculation process a trial and error is the most appropriate method to use. In the case of zero coupon bond this method is relevant because the intermediate cash flows are not available and yield determination is a straight forward issue(Rosen, 1995). The Yield Measures There are several bond yield measures that are used, which includes the following. Nominal, current, yield to call, yield to maturity and realized yield measure (Jarrow, 2002). Nominal yield This stands for a rate of a coupon of a certain issue. For example a bond with a coupon of 8% means that it has a nominal yield of 8%, Therefore, a convenient ways of expressing the characteristics of the bond coupon are provided. The following is a numerical example of this measure NY=income per year/par value*100 For example, Bond income per year=$ 20 Par/face value=$ 100, therefore, NY=20/100= 0.2*100 =20% Current yield measure This form of measure relates the yearly coupon rate to the bond price as illustrated in the following equation. CY =equals to the yearly Dollar Coupon Interest/price For example, A bond has face value = $100 Interest rate of 5 percent, Annual interest = $50. Bond currently selling price = $945. Therefore, CY=50/945= 000529 or 5.29% Current yield measure attributes the yearly total actual values of the coupon cash flow to the bond price (Jarrow, 2002). Therefore the timing of these cash flows is not taken into account or any other source of return in the bond. For example, loses or capital gains. This form of yield measure is important to the investors who are income oriented. Yield to Maturity This form of yield refers to the internal rate of return/.The equation used above can also be used in analyzing this measure. In the bond market the convention annualization is done by multiplying the convention with a straight factors that helps in converting the whole period to one year(Kugler,1996). After multiplying the results obtained are a bond equivalent yield that helps in understating the effective yield on the bond.YTM accounts for the time of the money value through the inclusion of the cash flows and the related forms of capital gain that any investor is likely to realize once the bond reaches maturity. The formula used in this approach is For example For example, a company issued the following information 1st Jan 2012, $5000, 5 year bond Par value = $1,000 per bond. Current bond price $975 Coupon rate = 9 % Interest rate in year 3, 4, and 5 = 10, 8 and 9%, therefore YTM would be as shown below $976 = $90 ×1-(1+r) ^-5/r+$1,000/ (1+r) ^5 From the above information YTM = 9.65% The formula used in YTM takes in the assumption that the bond reaches maturity and the interim cash flows are reinvested in the rate of YTM because the measure discounts all cash flow discounts at that reinvested rate(Macaulay,1938). The reinvestment hypothesis impact on the real return of a bond has direct variation with the bonds coupon together with the term to maturity. It is note able that a coupon rate that is high and the maturity term will hike the loss in value from a failure of reinvesting at the YTM. The reinvestment hypothesis of will be significant based on a higher coupon or a prolonged bond maturity Yield to Call (YTC) This measure is commonly quoted to a kind of bond that has not reached its maturity date. The method used to calculate this kind of measure is the same with that of YTM. The only difference is that the used cash flow are those that are anticipated to arise a head of the first call date(Fase,1999).YTC makes the current cash flow value up to the first call date equivalent to the bond price. In this case the assumption made is that the bond is on hold up to the its first call date.YTC can be calculate as shown below, Bond price =coupon payment × 1-(1+r) ^-n /r+ call price/ (1+r) ^n Coupon payment =Bond rate/annual no of payments × debt par value r = call yield/no of periods annually For example, a company issued the following information 1st Jan 2012, $5000, 5 year bond Par value = $1,000 per bond. Current bond price $975 Coupon rate = 9 % Interest rate in year 3, 4, and 5 = 10, 8 and 9% $976 = $90 ×1-(1+r) ^-4/r+$1,000/ (1+r) ^4 r= YTC of 10.48%. Horizon Yield The last form of bond yield measure is the horizon yield, which measures the bond rate of return that is expected to sell before its maturity date. This measures the expected rate of return of a bond that you expect to sell before its maturity (Fase, 1999). This is the overall return measure that enables the portfolio manger project on the bond performance based on the investment planned horizon. A portfolio manager is able to evaluate and indentify the bond that once considered for investment will have the best performance over the planned investment horizon. The demerit of using this measure is that the portfolio manger is expected to come up with assumptions on the reinvestment rates, future yields and think of a specific horizon (Fase,1999). However, the manager is able to evaluate the bond performance under diverse interest rate scenarios thereby being able to get an assessment of the bond sensitivity in relation to the changes in interest rate. The following is a numerical example, Interest rates effects on bond prices It is clear that since the bottom of 2008 stock market there have been money shifts from the stocks to bond. The logic explanation from this kind of trend is that investors have been attempting to seek for safety and income. This raises the question on the bond safety. In order to answer the question it is important to focus on the current state of interest rates, the anticipated future state, and the effects that changes in interest rates will have on these bonds. The funds were lowered by the Federal Reserve to a level of 0% – 0.25%.This rate is expected to remain this low until the unemployment level goes down to 6.5% predicted to happen in 2015(Batten, & Fetherston, 2002). The point to note is that interest rates are currently low, but their next change they will rise. Once thus takes place the bond investors will find their portfolios in trouble. The rule between the interest rates and bonds is simple, which is whenever the interest rates are high the bond price goes down. For example, incase a person purchases a bond at $1000 that pays an interest of 5 %.The bond will pay $ 50 every year until it matures giving back a total of $10000, from an investment point of view this means that the bond is purchased at par value(Batten, & Fetherston, 2002). However, suppose the bond issuer hikes its rate to 6%, the bond would pay$ 60 per year until the par value is returned to the investor. In such a case if another is looking to buy a bond, they would go for the 6% bond for $1000 over the previous 5%.Therefore the 5% bond can only be sold $ 100 less to some discounted amount he 5% is as attractive as 6% bond. Risks of a bond There are investors who think that bonds are risk free, however the have the following risks. Default risk where the bond issuer defaults on debt, rate in reinvestment, this is where the coupon payments will be reinvested at a low interest rate in future. Another risk is the purchasing power risk , and the interest rate risk, that cause the value of the bond market. The following tables shows a summary of the relationship between interest rates and bonds. Coupon Bond of 4% Maturity time in years 1% Change in Interest Rates 2% Change Interest Rates Rise in Rates Fall in Rates Rise in Rates Fall in Rates 1 –1.0% 1.0% –1.9% 2.0% 5 –4.4 4.6 –8.5 9.5 10 –7.8 8.6 –14.9 18.0 20 –12.6 15.0 –23.1 32.8 30 –15.5 19.7 –27.7 45 Coupon Bond of 6% Maturity in years 1% Change in Interest Rates 2% Change in Interest Rates Rise in Rates Fall in Rates Rise in Rates Fall in Rates 1 –0.9% 0.9% –1.8% 1.9% 5 –4.1 4.3 –8.1 8.9 10 –7.1 7.7 –13.5 16.3 20 –10.6 12.5 –19.7 27.3 30 –12.4 15.4 –22.6 34.7 Conclusion There is persistent and a rapid economic growth which can lead into inflation. This can eventually force the Fed to come up with tight polices by increasing the rates affecting the value of bonds. Therefore investors should be more conversant with the bond prices and the influence they get from economic cycles like these ones. One of the way to avoid bond risks is take control or the duration of a bond where by investors considers portfolios that has a duration of less than 5 years. References Batten, J., & Fetherston, T. A. (2002). Asia-Pacific fixed income markets: An analysis of the region's money, bond, and interest derivative markets. New York: Wiley. Fase, M. M. G. (1999). On interest rates and asset prices in Europe: The selected essays of Martin M.G. Fase. Cheltenham, UK: E. Elgar. Jarrow, R. A. (2002). Modeling fixed-income securities and interest rate options. Stanford, Calif: Stanford University Press. Kugler, P. (1996). Long term bond yields, monetary policy and the expectations hypothesis of the term structure of interest rates. Bern: Universität Bern Macaulay, F. R. (1938). Some theoretical problems suggested by the movements of interest rates: Bond yields and stock prices in the United States since 1856. New York: National Bureau of Economic Research. Rosen, L. R. (1995). The McGraw-Hill handbook of interest, yields, and returns. New York: McGraw-Hill. Sundell, P., Denbaly, M., & United States. (1992). Modeling long-term government bond yields: An efficient market approach. Washington, DC: U.S. Dept. of Agriculture, Economic Research Service, Agriculture and Rural Economy Division . Read More