Bond Yield Measures Inform Investors of the Rate of Return on Bonds Under Different Assumptions - Assignment Example

Bond Yield Measures Inform Investors of the rate of return on bonds under different assumptions. Describe the different measures of yield using practical examples. Name Professors Name Institution Course Date Introduction A bond is a long term debt security sold to investors particularly by large companies or the government (Bodie & Marcus, 1996). Bonds are some of the means used by large companies to raise capital. Investors always go for the bonds with the highest rate of expected return. Determining the bonds with the highest expected rate of return is one of the major task investors have to face when deciding whether to buy or sell particular bonds. The investors have to measure the yield of the bond. Bond yield refers to the figure showing the return the investor gets on the bond. Bond yield is always expressed as a percentage. Return on investment on bonds by investors come from first from coupon payments received annually or semi annually except for zero coupon bonds. Secondly, they come from reinvestment gains earned from coupon receipt received periodically (Shape, 1999). Thirdly, the returns arise from capital gain or loss upon the sale of the bond before maturity. There are three measures used to measure bond yield. Current yield measure/ Realized Yield This measure of bond yield measures the rate of return of the bond in connection to the current market price. To get the current yield, the coupon interest (annual) is dived by the prevailing market price. This measure does not take into consideration the capital gain or loss investors will realize if the bond is sold at a premium or at a loss (Bodie & Marcus, 1996). The current yield calculation measure therefore takes into consideration only the coupon interest. Current yield measure ignores other sources through which a bond obtains returns and does not take into account the time value of money. Current yield measure cannot be used for zero coupon bonds. Current yield is calculated using the formula below: Current yield= Annual coupon payment/ Market price (as a % of the face value/par value of the bond) For example if an investor purchased a 3-year bond for $951.90 with a coupon interest of 10% annually with per value of $1000. The current yield will be calculated as follows. Coupon interest is10% Coupon Payment= Coupon interest * face value 10% * 1000= 100 Market Price as a % of the face value= 951.90/1000 * 100 =95.19% Current yield= Current yield= Annual coupon payment/ Market price (10/95.19)* 100 =0.1051*100 =10.51% Thus the current yield measure of for this bond is 10.51% The investor will obtain a 10.51% gain upon investment on this bond. Yield to Maturity (YTM) This yield is also referred to as the internal rate of return (IRR). Yield to maturity refers to the discount rare which equates present values of the bonds cash flows to the bond market value. The yield to maturity measure calculates the bonds total expected cash flows or expected rate of return taking into account the coupon interest, time value of money, capital gains and reinvestment income. For this measure to hold investors should hold their bonds until maturity and reinvest their capital payments received annually or semi annually in securities offering the very same rate of return. Most investors prefer YTM measure since it reflects all the return you will receive from your investment in a particular bond. This measure reflects every payment upon interest you will receive plus the principal amount which will be repaid back to you upon maturity (Campbell, 1993). This measure is highly valuable since it reflects total income an investor will receive from the bond. YTM is calculated using the following complex formula Before looking at an example, first we will review the relationship between bonds price and Bonds yield. As the bond price increases the bond yield decreases yielding a negative curve as shown below Yield Curve Adapted from (Fama et al, 1987) For example if an investor purchased a 3-year bond for $951.90 with a coupon interest of 10% annually with per value of $1000. The YTM yield will be calculated as follows. We calculate the cash flow Total Coupon payments= 10% * 1000 =$100 Then plug the known amount into the formula 951.90= 200 *(1-(1/ (1 + i)3/i) + ( 1000* (1/(1+i)3). The (i) in this equation is the bond yield/ interest rate. From this we will use the method of guess and check to determine the “i”. Bonds can either be sold at a discount or a premium. The bond we are looking at in this case is sold at a discount; $951.90 instead of $1000 therefore considering the relationship between yield and bond price. When bond is sold at a premium the interest rates is less than coupon rate but if the bond is priced at a discount like in our case the interest rate is more the coupon rate. Therefore the expected rate of return is more than 10%. Since we know that the expected rate of return is more than 10% then we will calculate the expected rate of return using the method of guess and check. This will be done by guessing interest rate figure which are above 10% and then check whether by plugging them in the formula 951.90= 200 *(1-(1/ (1 + i)3/i) + ( 1000* (1/(1+i)3) until we get the interest rate that gives us bond price of $951.90. Expected rate of return Bond price 20% 999.987 22.5% 959.15516 23% 939.608 Since the price of our bond is $951.90 then our interest rate lies between 22% and 22.5% to get the exact rate of return we create another guess and estimation table of figures between the restrains we have developed. Interest rate Bond price 22.5% 949.33 22.4% 951.59 From the above table using the guess and check method, we can estimate the bond yield to be approximately 22.4%. This is the return the investor will get upon investing on this bone. YTM=22.4% Yield to Call (YTC) This measure is used when the owners of the bond call for the bond before the maturity date. To compute YTC, the cash flows obtained upon the first call are used (Bodie & Marcus, 1996). The method used to calculate the YTC is similar to the method used to calculate YTM but in the case of Yield to call only the cash flows obtained before the call date are used. YTC thus refers to the return that will equate present value cash flows up to the date of the first call to the price of the bond. The main assumption of this measure is that the investors will hold the bond up to the first call and reinvestment is done using similar rate of return (Barsky, 1989). To calculate for this call bond only few adjustment are made to the yield to maturity formula as follows:- For example if example if an investor purchased a 3-year bond for $951.90 with a coupon interest of 10% annually with per value of $2000 paid in and the first call is done after 1 and a half years for $1000. The YTC will be calculated using the following formula; adjusted from the YTM formula. The calculation will be done using the guess and check following the formula used in the yield to maturity. The Maturity value in the YTM will be replaced by the call value. The call value in our example is $1000, and the coupon rate is 10%. Plugging into the formula it becomes 951.90= 200 *(1-(1/ (1 + i)3/i) + ( 1000* (1/(1+i)3) and try to estimate the interest rate that will give us 951.90. Using the guess and check method as calculated in the yield to maturity above. We will obtain the YTC to be approximately 22.4% the same with what we obtained in the YTM. However in this case the bond has per value of $2000. YTC=22.4$ Part 2 How Changes in Interest Rates Affect Bond Prices Investors who are willing to expand their horizons and profit in the bond market should strive to fully understand the relationship between bonds prices and the interest rates. High quality bond prices are directly connected to the interest rates (Boudoukh, 1993). Bond prices are inversely related to the interest rates. When the interest rates rise, the prices of the bonds go down. Since most investors do not put their bonds on hold till the maturity date; they are ever trying to maximize their profits upon changes on bond prices, they prefer the interest payments they receive from their bonds (Barsky, 1989). Changes in interest rates thus affect the bond prices and the yield. The effect the interest rates have on bond prices is also determined by the maturity date, coupon payments and the volatility of the bond as explained below. Bond Yield and Prices Investors should first measure the yield of a bond before purchasing it. There is an inverse relationship between the price and yield of a bond. If the interest rates rise, the prices of bonds fall, and then the yield of the bond increases to compete or match the prevailing market interest rates (Andersen et al, 2006). On the other hand when the interest rates fall, the price of the bond increases, and then the bond’s yield decreases to match or compete with the prevailing market interest rates. For example if an investor purchased a bond for $1000 with a coupon interest of 5% and the interest rates happen to rise by 7% it will have an effect on the bond values as shown in the calculations below. When the coupon interest is 5%, the investors receives coupon payments of 5% * 1000= 50 He receives= $50 each year Investors want to maximize their profits therefore they will not purchase a bond for $1000 with a coupon payment of 5% when they can buy the same bond with a coupon interest of 7%. To remain competitive with the secondary market the bond will be sold at a discount from the face value of $1000. To encourage investors to purchase the bond due to the rise in interest rates the price of the bond will have to drop by $50/7%= $714.29 Thus with a rise in interest rates from 5% to 7%, the bond price will drop from $1000 to $714.29. The fall in price of the bonds increases the yield of the bond. Bond Price Volatility and Maturity Bond price volatility refers to the measure that measures how bond prices react to changes in the interest rates. As observed above bonds prices are inversely related to interest rates. Holding all other factors in the bond market constant, the risk of the bonds interest rates rises along with the length of time remaining before maturity. There is a direct relationship between the bond price volatility and the maturity date (Fama et al, 1987). For example a 1 year bond will be less price volatile compared with a 20 years bond, though the volatility will be the same to the interest rates of the 20 years bond when only one year is remaining before maturity. The longer the maturity date the more price volatile the bond. Bonds that have a long time before maturity are highly volatile compared to bonds with short maturity period. Bond Price Volatility and Coupon Rate The bond’s interest risk and the coupon rate are inversely related. Low coupon rate and long maturity leads to high bond price volatility. On the other hand, high coupon rate and short maturity leads to low bond price volatility. Bonds with long maturity are highly risky and highly price volatile than bonds with short maturity (Glosten et al, 1993). The change on a bonds price as a result of change in the expected yield depends on the coupon rate of the bond. For example if we have two bonds having the same face value and the same maturity date; let’s say two investor purchased each a 3-year bond with a coupon interest of 10% and 12% respectively with per value of $1000 each. The bond with the low coupon rate of 10% will be highly volatile compared to the same bond with a high coupon rate of 12%. Conclusion Investors purchase bonds with the aim of making huge profits. However to decide which bond they should purchase with the highest return on investment, they have to measure the bonds yield in order to determine the bond with the yield. The returns investors get upon investment on bonds come from coupon payments they receive annually, the capital gains upon reinvestments and the capital gains or loss obtained upon selling the bond before maturity. Bond yield can be measure either by the current yield measure, the yield to maturity measure which is the most preferred measure since it includes all the payments the investor will receive from the bond and lastly incase the bond is a callable bond, it can be measured by the yield to call formula. Wise investors should determine the relationship between bond price and interest rates before investing in the bond market. The bond price and the interest rates ate inversely correlated. References Andersen, T.G., Bollerslev, T., Christoffersen, P.F., and Diebold, F.X., (2006)a, “Volatility and Correlation Forecasting,” in G. Elliott, C.W.J. Granger, and Allan Timmermann (eds.), Handbook of Economic Forecasting. Amsterdam: North-Holland, 778- 878. 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