Bond Yield Measures - Case Study Example

Bond yield measures Student’s name: Instructor’s name: Course code: Date of submission: 1.0 Introduction A bond is a debt investment by an investor whereby he loans money to a corporate of government entity that borrows fund to conduct its businesses for a given time period and the investor earns an interest rate that is usually fixed (Hearth, Jarrow and Morton, 2006). Mostly the interest rate is computed as a percent of the principal amount of the bond. A bond is also called fixed income securities and together with cash equivalents and stock, they make up the three main classes of assets. An investor uses different methods to determine the rate of return on different bonds so as to make their investment decisions appropriately (Korajczk and Levy, 2009). The prices of bonds are usually influenced by the prevailing interest rates in the markets. When interest rates are rising, bonds are priced differently compared to when they are falling (Bekaert, Harvey and Lumsdaine, 2009). This report outlines the different yield measures that can be used by investors and the effects of changes in interest rates on bond prices. 2.0 Types of bond yield measures 2.1 Current yield Current is basically a measure used to approximate the rate of return of a coupon bond (Black and Scholes, 2011). Simply it is the coupon payment made annually divided by the bond price (C/P, C stands for annual coupon payment while P stands for the price of the bond). Among all yields measure, the current yield measure is the simplest measure to use (Bekaert, Harvey and Lumsdaine, 2009). It is a better approximation for bonds that have a long maturity period and mostly preferred when the bond price is closer to the bond’s face value. Example Calculate the current yield of a treasury note with duration of two years, it has a face value of $ 1,000, its coupon rate is 6% and the price of the Treasury note is $ 975. Annual coupon payment= 6% * 1000 = 60 Current yield= annual coupon payment/bond price 60/975 = 6.15% 2.2 Yield to maturity Yield to maturity refers to an interest rate that makes the price of the bond and the cash flow present value equal (Hearth, Jarrow and Morton, 2006). The yield to maturity of a semiannual pay bond is determined by first calculating periodic interest rate denoted ‘y’ and satisfies the following relationship: P = P= bond price, C= semiannual coupon interest, M= maturity value, N= number of periods (since its semiannual pay bond). The yield to maturity is given by doubling the discount rate or periodic interest rate (Bekaert, Harvey and Lumsdaine, 2009). For a bond that is a zero coupon one, computing its yield to maturity is much easier (Davis and stone, 2009) and the formula used is: When calculating yield to maturity, one not only takes into consideration coupon rate income, the capital loss or gain is also considered that will be realized by the investor for holding the bond up to maturity (Hearth, Jarrow and Morton, 2006). Furthermore, timing of cash flows is also taken into account when calculating the yield to maturity of a bond. Example Consider a treasury bond with a par value of $ 10,000, a coupon rate of seven percent and a maturity period of 5 years. The interest is paid semi-annually ant the price of the bond is 8842. Calculate the yield to maturity of the bond. Formula used is P = Since it is a semiannual pay bond, the cash flows totals to ten $350 coupon payments made for every six month. $ 10,000 principal is supposed to paid in a period of six months for a total of ten times from now. From the above equation, to get y, various interest rates have to be attempted until the price of the bond is equal to cash flows present value. The periodic interest rate will be 5 percent as shown below: Coupon payments = 7% * 10,000 / 2 (since interest rates are paid semiannually) = 350 Number of years from now Promised Annual Payments PV of Cash Flow at 5% 1 $350 $333.3 2 $350 $317.5 3 $350 $302.3 4 $350 $287.9 5 $350 $274.2 6 $350 $261.2 7 $350 $248.7 8 $350 $236.8 9 $350 $225.6 10 $10,350 $6354.0 Present value = $8841.7 The present value (8841.7) is almost equal to the price of the bond (88842) if 5 percent interest rate is used. Therefore, we can conclude that the periodic interest rate of the above bond is close to 5 percent and using a financial calculator or excel to be precise; the periodic interest rate is 4.99964 percent. The yield to maturity is given by doubling the interest rate that is 5 percent times two and it gives 10%. Therefore the yield to maturity of the above bond is 10 percent. 2.3 Yield to call The call price simply refers to the price of a bond when it is called (Taggart, 2007). Mostly, the call price is constant irrespective of when the bond is called. In other callable issues, a bond’s call price basically is determined by the date of calling the issue. This simply means that a call schedule is put in place to specify the bond’s call price when the issue is called on different dates (Tse, 2010). ` For callable issues, the yield to maturity and the yield to call are always calculated (Sharma, 2005). In the yield to call practice, it is assumed that the investor at an assumed call date will call the bond and the call schedule specifies the call price. The formula to calculate the yield to call is as below: P = M= Call price n* = Number of years times two N/B: the yield to call for a bond that is semiannual pay is given by multiplying the periodic interest rate by two. Example Consider a treasury bond with a par value of $ 10,000, a coupon rate of seven percent and a maturity period of 5 years. The interest is paid semi-annually ant the price of the bond is 8842. The bond is called in 5 years at 100% face value. Calculate the yield to call of the bond. Since it is a semiannual pay bond, the cash flows totals to ten $350 coupon payments made for every six month. $ 10,000 principal is supposed to paid in a period of six months for a total of ten times from now. From the above equation, to get y, various interest rates have to be attempted until the price of the bond is equal to cash flows present value. The periodic interest rate will be 5 percent as shown below: Coupon payments = 7% * 10,000 / 2 (since interest rates are paid semiannually) = 350 Number of years from now Coupon payments PV of Cash Flow at 5% 1 $350 $333.3 2 $350 $317.5 3 $350 $302.3 4 $350 $287.9 5 $350 $274.2 6 $350 $261.2 7 $350 $248.7 8 $350 $236.8 9 $350 $225.6 10 $10,350 $6354.0 Present value = $8841.7 The present value (8841.7) is almost equal to the price of the bond (88842) if 5 percent interest rate is used. Therefore, we can conclude that the periodic interest rate of the above bond is close to 5 percent and using a financial calculator or excel to be precise; the periodic interest rate is 4.99964 percent. The yield to call is given by doubling the interest rate that is 5 percent times two and it gives 10%. Therefore the yield to maturity of the above bond is 10 percent. 3.0 Effects of interest rates changes on bond prices Interest rate refers to the rate of paying interest on loan given to a debtor by a lender. It is usually a percent of the principal amount that is paid at a certain number of times for every period given by the lender (Brennan and Schwartz, 2007). Interest is usually charged per year and hence the interest rate is quoted per annum. Interest charged on bonds can be applied either semiannually or annually in most cases of bonds. The issuer is given a certain interest mainly a percent of the principal amount of the bond. It is very vital for bond buyers to know the process of calculating the bond price since it will show the bond yield if the bond is purchased (Lumsaide, 2009). The bond price can be simply described as the amount of money paid to purchase a bond. A bond can be sold either at par, premium or discount. A bond said to be trading at par simply means that the bond’s price is its face value. A bond is said to be trading at a premium when its price is above its face value. The coupon rate of such a bond is always much higher than the prevailing interest rates since the investor will pay more so as to earn higher yields. In the market, prevailing rates of interest are continuously changing and this force existing bonds to be adjusted in terms of prices to their YTM approaches the YTM on new bonds that are being issued (Black and Scholes, 2011). For example, if the coupon rate of a bond is 3% and interest rates that are prevailing rise to 4%, the price of the bond will have to fall so that the bond yield will rise and move in line closely with the prevailing interest rates. Note that the bond yields and bond prices moves in opposite directions. A bond tends to trade at discount when the prevailing interest rates are higher than the coupon rate of the bond while a bond is said to trade at a premium if prevailing interest rates are lower than the coupon rate of the bond (Korajczk and levy, 2009). Due to this fact, the proportion of bonds trading at premium in the market will be much higher when prevailing interest rates are decreasing. On the other hand, a higher percentage of bonds will trade at a discount when the prevailing interest rates are rising. In the case of callable bonds (bonds that can be redeemed before maturity date), the bond issuer is likely to redeem a bond if the prevailing interest rates fall because the issuer does not to keep on paying rates that are above the market rates therefore the most likely bonds to be called away are premium bonds (Boniface, 2010). The premium paid by the investor could disappear and at the high coupon, he (investor) would receive small interest payments. 4.0 Conclusion Investors use the bond yield measures to determine the rate of return on different bonds. The three yield measures that are mostly preferred by investors are current yield, yield to maturity and yield to call. The simplest measure to use is the current yield. Both the yield to maturity and the yield to call are calculated through the same process. For semiannual pay bonds, the yield to maturity and yield to call are given by multiplying the periodic interest rate by two. Bonds are trade either at par, premium or discount. If the price of the bond is above the face value the bond is said to be trading at premium and it said to trade at par if the face value equals the price of the bond. Changing interest rates affect the prices of bond and therefore determines how the bond is going to trade. A bond tends to trade at discount when the prevailing interest rates are higher than the coupon rate of the bond while a bond is said to trade at a premium if prevailing interest rates are lower than the coupon rate of the bond. Before an investor decides on where to invest, he should conduct a bond yield measure using the current yield, yield to maturity or yield to call criteria so as to make the right investment decision. The investor should also consider the prevailing interest rates and how they might affect the bond price in the market. References Bekaert, G., Harvey, C. R., & Lumsdaine, R. L. (2009). The dynamic of emerging market equity flows. Journal of International Money and Finance, 21, 295–350. Black, F. and M. Scholes (2011), “The Pricing of bonds and Corporate Liabilities”, Journal of Political Economy, 81, 637-654. Bonface, G. D. (2010). Determinants of corporate debt securities in the Euro Area. The European Journal of Finance, 11(6), 493–509. Brennan, M. J. M. and E. S. Schwartz (2007), “A Continuous Time Approach to the Pricing of Bonds”, Journal of Banking and Finance, 3, 133-155. Davis, E. P., & Stone, M. R. (2008). Corporate financial structure and financial stability. Journal of Financial Stability, 1, 65–91. Heath, D., R. Jarrow and A. Morton (2006), “Bond Pricing and the Term Structure of Interest Rates: A New Method for Contingent Claim Valuation”, Econometrica, 60(1), 77-105. Korajczyk, R., & Levy, A. (2009). Capital structure choice: Macroeconomic conditions and financial constraints. Journal of Financial Economics, 68(1), 75–109. Sharma, K. (2005). The underlying constraints on corporate bond market development in Southeast Asia. World Development, 29(8), 1405–1419. Taggart, R. (2007). A model of corporate financing decisions. Journal of Finance, 32, 1467– 1484. Tse, Y. K. (2010), “Some International Evidence on the Stochastic Behaviour of Interest Rates”, Journal of International Money and Finance, 14(5), 721-738. Read More