Different Measures of Bond Yield using Practically Worked Examples - Example

Bond Yield Measures Name Professor Institution Course Date Introduction The bond yield measures are the ones that advise investors about the bond’s rate of return under different assumptions. In describing the different measures of bond yield, practically worked examples have been used for proper and good explanation. Bond pricing is common term under bond yield measures. In order to price a bond, we use the formula of its present value and information about the magnitude and timing of cash flows alongside bond contract terms. The bond contract terms includes the principal and coupon payments as the two cash flows of a bond. Also, a bond pays coupons periodically to the bondholder and, at maturity, the bond has to pay the bondholder the face value, and the principal of the bond. A bond’s coupon rate is determined by the coupon payments’ size. For instance, in a case where a coupon rate is 7% per annum for a bond whose face value is $1000, interest per year is given by: Bond yield is a reflection of rate that a bond holder earns. It depends on price risk, reinvestment risk and credit or default risk. The Yield to Maturity (YTM) refers to the yield that is promised to a bondholder for the bond held to maturity and the coupon reinvested at a yield that is promised. Realized yield is, also, the actual return that is earned on a bond for cash flows that the investor actually receives, assuming there was reinvesting at the rate of the coupon. Also, expected yield is a forecast yield and is based upon the expected sale price. Different Measures of Bond Yield using Practically Worked Examples Several ways are used to describe the return rate of a bond, and this includes the coupon rate, the yield to maturity, the current yield, the modified yield to maturity that is modified, the realized yield and yield to call. In the pricing of a bond, present value formula is applied together with information on the amount of cash flows and the timings. The amount of cash flows and timing is also better understood by looking by further understanding the bond contract terms. There are two cash flows in a bond: The principal and coupon payments. A bond pays some periodic interest payments to its holder. At maturity, the bond also pays the bondholder the par value of face value of the bond and the principal. The rate of the coupon of a bond is a stated interest rate that would pay. Thus, The bond yield basics entail the bond’s coupon rate and also its current yield. We find the price of a bond by adding together the bond’s present value to the present value of that bond’s face value. The Yield to Maturity (YTM) of a Bond YTM is simply a discount rate that equates the bond price for today with the bond’s present value future cash flows. Further, the YTM is like the bonds Internal Rate of Return (IRR). YTM is the yield which a bondholder is promised if a bond is held to maturity and all its coupons reinvested at the yield promised. YTM equates the present value (PV) of the cash flows of a bond to its price. There are situation the YTM is not equal to the investor’s return. Such circumstances arise when a bondholder sells a bond before its maturity and the bond issuer defaults. The actual returns earned under such circumstances are what is called realised yield. At times, the investor may wish to compute yield that would be earned if interest rates where to be altered. The predicted or forecast yield that results is called expected yield. It is based on an expected sale price. Assumptions behind Calculation of YTM Reinvestment is assumed The resulting measures of yield are the same as the MIRR for that bond. The formula for bond price is simply the coupon’s present value added to the present value of the bond’s face value. To allow for semi-annual compounding, all values are divided by two in the formula. In this formula Annual coupon payments the bond’s face value the maturity of the Bond (Measured in years) Example 1 Thus, using this formula based on bond pricing, we can calculate a straight bond price given the face value as USD 1000, YTM as 9%, coupon rate as 8%, and maturity of 20 years. When one buys a bond between coupon dates, the person will receive next coupon payments and might even have to pay taxes on that bond. However, when buying a bond between the coupon payments, then the seller must be compensated for all the accrued interest. The convention for bond prices quotes differs, in that, the bond prices’ quotes ignore all the accrued interest, and this leads to what we call a clean price. Callable Bonds These bonds are the most and give the issuer the option of buying back a bond at a call price that is specified, anytime after the first call protection period. As a result, YTM is not useful at this point for callable bonds. Yield to call (YTC), A measure for yield which assumes that a bond will be called at earliest call date, is instead considered. From this formula The Annual coupon The Call Price of that given bond The Time to the call date that is earliest possible. The call yield with semi-annual coupons Types of Yield Curves Example 2 As a second example for the calculation of bond return measures, the following is considered: Consider a 2-year bond purchase, and a semiannual interest payment, coupon rate is 8% , and the current price is USD 964.54. Assume further that the payments of interest will be reinvested at a rate of 9% per year, and the most recent payment of interest is said to have occurred immediately before the purchase of the bond. Before calculating the various returns, we assume the bond matured. 8.294% Thus, YTM = 5% per period, or 10% per year. Modified YTM = 4.971% per period, or 9.943% per year YTC = 7.42% per period, or 14.84% per year Realized Yield: If realized yield is not called = 4.971% per period, or 9.943% per year If realized yield is called = 7.363% per period or 14.725% per year Bond Theorems The theorems about bonds communicate about the relationship between the changes in interest rates and the prices for bonds. Some of these theorems which are of significant interest include: Theorems on bond yield and prices Theorems on maturity and volatility of the bond price Theorems on coupon rate and volatility of the bond prices Focusing on bond yield and price theorem, the argument is that this is the most straight forward. The theorem holds that as interest rate at the market declines, the bond prices also decline. This results from the fact that since the coupon rate is fixed, then the only available option that can alter a bond’s yield is the change of the bond’s price. Besides, the theorem on volatility and maturity of a bond price refers to the bond’s price sensitivity to changes in interest rate. The relationship that exists between the maturity and volatility of a bond price holds that the longer the maturity terms of a bond, then the greater the bond’s volatility price. Also, coupon rate explains the bond price sensitivity to changes in the interest rates. Thus, the lower the coupon rate of a bond, then the greater that bond’s price sensitivity to alterations in the interest rates. Duration and Interest Rate Risk The risk on interest rate consists of the reinvestment risk and the price risk. Reinvestment risk arises from changes in interest rate which in turn lead to rise and fall of the realized yield of investors. Price risk is also associated with an inverse relationship between the interest rates and the bond prices. When the yields go up, the prices of bonds decrease but the rate of reinvesting coupons increases and vice versa. However, both investment risk and price risk offset each other to some level. Consequently, we require a figure of interest rate risk which can account for both reinvestment risk and price risk. Duration also refers to a risk measure of interest rate that takes into consideration, both the maturity of the bond and its coupon rate. Short-duration bonds are those that have higher coupon rates. For bonds having a single payment, their duration is equal to their term to maturity. Still, most notable is that the higher the sensitivity of a bond to alterations in interest, the greater the duration of that bond. Using duration, we can manage interest rate risk through three principle ways: The approach of zero coupons The approach of maturity matching The approach of matching duration Duration matching is helpful in the elimination of interest rate risk for both reinvestment and price risks. The duration is matched with the bond’s holding period. This sees to it that the capital losses and gains from changes in interest rates are offset by alterations in invested income. Explain how Changes in Interest Rates would Affect Bond Prices There are several variations in the prices of bonds due to variations in the rates of interests. If the rates of interest rise, then the bond values will decrease and vice versa – if the rates of interest decrease, then the bond value will also increase. As a general rule, if a bond takes more time to reach maturity, then more of the bond’s value will be affected by the current interest rates at the market. In fact, for a bond whose maturity is a year or two, then it will not change so much in its value once there is change of interest rates. A bond that has matured for a long duration will have large changes in its value if the rates of interest do change. It is a matter of opportunity cost when buying a bond. If the market interest rates are 6% and the coupon is 5%, then the investor would not opt to purchase it because it is 1% under the rates at the market. Besides, if the rates of interest fall, we would prefer to sell bonds at a premium that is over the face value. This is because the fixed interest rate will be higher than market rate. References Andrew, M. (2003). An Introduction to Capital Markets: Products, Strategies, Participants. John Wiley & Sons: West Sussex, UK. Bob, R. (2007). Corporate Finance and Valuation. Patrick Bond: UK. Brimble, M. (2011). Financial Markets, Institutions and Money. 2nd ed. Laxmi Publications LTD: New Delhi. Charles, P. (2009). Investments: Analysis and Management. Blackwell Publishing: New York. Eugene, F., & Michael, C. (2011). Financial Management. Theory and Practice. Frank, F. & (2005). The Handbook on Fixed Income Securities. Pearson Education Limited: England. Frank, J. (2007). Fixed Income Analysis. Prentice Hall: Harlow. John, T. (2012). 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