Bond Yield Measures Inform Investors of the Rate of Return on Bonds under Different Assumptions - Essay Example

Bond Yield Measures College: Name: Students ID: Date: Course Name: Unit Code: Instructor's Name Introduction A bond is simply a debt security instrument used by governments, municipalities, corporations, federal agencies or other entities all referred to as issuers to collect funds. A bond entails a guarantee to pay a particular rate of interest for the duration of the time of the bond plus paying back the principal amount as soon as it matures, or comes due (Philippon, 2009). Investors who put their money in bonds expect to receive a return from their investment in either one or more of the following forms; (I) a periodic coupon interest that the issuer will pay; (II) capital gain or loss upon maturity of the bond, is called, or is put to the market, as well as; (III) interest income spawn from reinvestment of the periodic cash flows. There exist a number of ways in which returns from bond investments can be measured, some of which are discussed below. However, whichever technique that is used to measure a bond’s potential yield, it has to take into consideration each one of these three potential sources of return (He & Westerhoff, 2005).  Bond Yield Measures Conventional Measure Yield refers to the interest rate that is able to equal the present value of the cash flows to the cost of investment. Mathematically, this yield, denoted by y, has to satisfy the following equation; P = In the above equation; CFx = cash flow of a given year, P = bond price, and N = number of years. In general, this yield that is obtained computed using the above equation is referred to as the Internal Rate of Return (IRR). This method uses a trial-and-error (iterative) system to work out the yield (y). The main aim is to hit upon the yield liken the present value of the cash flows to the cost of investment (bond price). This yield obtained using the above equation is periodic, that is, if the cash flows are semi-annual, the yield is also semi-annual; if the cash flows are yearly; the yield is also yearly; and so on. To work out the simple annual interest rate, the yield that is obtained for a particular year is increase by multiplying it by the amount of periods in that year (Chiang & Wainwright, 2005). Given a situation where the period covers no more than a single future cash flow, the above method may be ignored and a simpler equation indicated below is used not to settle on the yield; . Also to find an effective annual yield linked to a particular period’s interest rate, the formula used is: Where n = the times (rate at which) annual payments are made Yield to Maturity (YTM) The Yield to Maturity is basically the Internal Rate of Return. Conventionally partakers in the bond buying and selling business annualise the Internal Rate of Return by multiplying by a given factor so as to switch the period to a year; for example, a factor of 2 will be used for a semi-annual bond. In the case of semi-annual bonds, given as an example above, the annualized yield that is obtained is referred to as the Bond Equivalent Yield. However, this yield at all times devalues the true yield on a bond (Chiang & Wainwright, 2005). In calculating the Yield to Maturity, the formula used allows for timing of cash flows, therefore it accepts the time value of money. Also, the formula employs the capital gain or loss likely to be made on the investment if the investor holds the bond to maturity. Also considered is the interest-on-interest factor. However, the Yield to Maturity method presupposes that the investor will hold the bond to maturity and ploughs back the entire interim cash flows at the Yield to Maturity rate given that it discounts each and every one cash flow at that rate. This supposition has an effect on the authentic return of a bond by demonstrating a straightforward inconsistence with the coupon rate and the time to maturity of the bond. If the coupon rate as well as time to maturity of a bond is high, the beating in the value of a bond from failure to reinvest at the Yield to Maturity will too go up. For that reason, a higher coupon or longer maturity makes the reinvestment assumption more vital (Westerhoff, 2003).  Yield to Call The call price is the price an issuer pays for calling a bond. For a number of issues, the call price remains unaffected regardless of whichever time the bond is called. The call price could as well rely upon the time the bond is called. In this case, a call programme detailing the call price for apiece call date exists. A Yield to Call, for callable bond issues, is traditionally worked out just like the Yield to Maturity. When computing the Yield to Call, it is assumed that the bond issuer possibly will call the bond at a predetermined calling date where now the call price turns out to be the call price indicated in the call schedule (Choudhry, 2010). The formula used to compute the Yield to Call is: Where W = call price and p = number of periods up to the assumed call date. Just like for a Yield to Maturity, doubling-up the periodic interest rate (y) of a semi-annual bond will give the Yield to Call on a bond-equivalent basis. In calculating the Yield to Call, it is assumed that the investor can plough back the coupon payments at the Yield to Call rate. Moreover, it takes as a fact that the bond will be called by the issuer on whichever supposed call date (Westerhoff, 2003).  Yield to Put A putable bond issue is that which the investor (bondholder) is capable of compelling the issuer to pay money for the issue at a particular price. Just like for a callable bond issue, a putable bond issue can have a put plan that spells out the time at which the bond issue can be put along with the put price. Once a bond issue is putable, a Yield to Put is worked out. The Yield to Put refers to the interest rate at which the present value of the cash flows to the supposed bond put date together with the put price on that date as detailed in the put arrangement is one and the same to the price of the bond. The formula used to calculate the Yield to Put is one and the same as for computing the Yield to Call, save for W which now turns into the put price and p is the number of periods awaiting the supposed put date (Chiang & Wainwright, 2005). Numerical Examples Consider the bond described below: Coupon rate = 11 percent Maturity = 18 years Par value = $1,000 First par call in 13 years Put date in no more than five years and putable at par value. Suppose that the market price for this bond $1,169. (a) Calculate the Yield to Maturity for this bond The first step is to work out the internal rate of return for the cash flows assuming that the investor holds the bond to maturity. The formula described under the conventional measure for the Internal Rate of Return is brought to play. On computation, using a Financial Calculator, the value obtained is 4.539 percent. For a semi-annual bond, doubling-up the periodic interest rate (y) gives the Yield to Maturity on a bond-equivalent basis. Multiplying 4.539 percent by 2 gives us a Yield to Maturity equivalent to 9.078 percent. (b) Calculate the yield to first par call for this bond The first step is to work out the internal rate of return for the cash flows assuming that the issuer calls holds the bond after 13 years. The formula described under the Yield to Call is brought to play. On computation, using a Financial Calculator, the value obtained is 4.397 percent. For a semi-annual bond, doubling-up the periodic interest rate (y) gives the Yield to Call on a bond-equivalent basis. Multiplying 4.397 percent by 2 gives us a Yield to Call equivalent to 8.794 percent. (c) Calculate the Yield to Put for this bond The first step is to work out the internal rate of return for the cash flows assuming that the investor puts the bond for 5 years. The formula described under the Yield to Call is brought to play. On computation, using a Financial Calculator, the value obtained is 3.471 percent. For a semi-annual bond, doubling-up the periodic interest rate (y) gives the Yield to Put on a bond-equivalent basis. Multiplying 3.471 percent by 2 gives us a Yield to Put equivalent to 6.942 percent. Interest Rate Risk The Interest Rate Risk emanates from the general interest rates in the bond markets on one particular day. The interest rates vary depending on the economic variations, Federal Reserve policies along with other factors. There is no distinct dealing interest rate. The interest rates will show a discrepancy based on the time to maturity for a picky bond, the credit quality of the issuer as well as other factors. Holders of bonds have to visage the Interest Rate Risk in view of the fact that variations in interest rates may perhaps end in losses in the bond’s worth. Realized yield is the yield that is in reality earned or “realized” on a bond. Realized yield is more or less certainly not faithfully one and the same to the Yield to Maturity, or promised yield (Semmler & Mateane, 2012). For the most part, one deep-seated factor to mull over in fixed income investing is interest rates, which pretender both risks as well as opportunities, above all in the present low-interest-rate setting. This is vital especially when considering investing in fixed income and are worried on the subject of managing risk in the total portfolio, or else if one invests in bonds for just income on its own. Not considering whether interest rates go up or drop (at present or at whichever time), variations in interest rates also denote variations in bond prices. This in general will not be of concern if an investor intends to hold bonds to maturity and could do without putting them on the market sooner than then, other than it will shock the worth of the bonds and, more crucially, the amount the investor is expected collect if the investor has to sell prior to maturity (Gallegati et al. 2011). Bond prices have a propensity to fall more rapidly for longer-term bonds if interest rates go up, and the reverse is true. This is for the reason that the investor will survive with the fixed coupon imbursement for a longer period of time for a bond that takes long to mature. There will be additional time for the investor to accept a coupon payment that is either higher than or lower than the existing dealing interest rate, and as a result the relatively attractive the bond possibly will be to an investor weighed against the analogous options that will be offered at present (He & Westerhoff, 2005).  Conclusion A bond is a simply debt security for which an investor earns returns through either (I) a periodic coupon interest imbursement paid by the issuer, (II) whichever capital gain or loss as soon as the bond reaches maturity, is called, or is put on the market, or (III) interest income spawn from ploughing back the periodic cash flows. There exist a number of ways in which the returns from bond investments can be measured (Choudhry, 2010). The conventional measure entails the use of the Internal Rate of Return (IRR) where an iterative procedure is used to arrive at the answer. Specific bond yield measures discussed are the Yield to Maturity, the Yield to Call and the Yield to Put. Bond investors face the risk of interest rate variations which affects the price of the bond. References Atje, R., and Jovanovic, B. (1993). Stock Markets and Development. European Economic Review, 37(2-3): 632-640. Chiang, A. C. and Wainwright, K. (2005). Fundamental Methods of Mathematical Economics, 4th ed, McGraw-Hill, New York. Choudhry, M. (2010). An Introduction to Bond Markets, 4th ed. John Wiley & Sons Gallegati, M., Ramsey, J. and Semmler, W. (2011). Bond Prices q: With or without Equity Market’s q? New School University, New York, 1-25. 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