Measures of Computing Bond Yield - Case Study Example

ECON 203: Bank and Finance College: Name: Students ID: Date: Course Name: Unit Code: Instructor's Name Measures of Computing Bond Yield Governments and other agencies require sufficient finances to operate effectively. There are numerous ways to source for these funds. Bonds are a form of debt securities that are issued by these bodies to collect funds. A bond is security a guarantee where the issuer promises to shell out a particular rate of interest for the duration of the existence of the bond and to reimburse the principal amount borrowed once it matures. For investors, bonds are an attractive investment opportunity as there are various ways by which they can obtain returns (Gallegati et al. 2011). These include a periodic coupon interest payment forwarded by the issuer, all capital gains or losses just the once the bond matures, is called, or is put on the market, and interest income derived from reinvesting the periodic cash flows. The following are several measures used to calculate the return for a bond yield. I. Yield to maturity (YTM) A bond’s Yield to Maturity (YTM) refers to the discount rate at which the present price of a bond equates the present value of the bond’s upcoming cash flows. It also refers to “promised yield” an investor receives from holding the bond to maturity and the coupons are ploughed back at the Yield to Maturity. The Yield to Maturity is calculated just as the Internal Rate of Return; where the considered cash flows are those that the investor is expected to take in by holding the bond to maturity. A semi-annual pay bond’s, the Yield to Maturity is computed starting with the computation of the periodic interest rate, y, as indicated in the formula below; In the above equation, P = bond price, C = semi-annual coupon interest, M = value upon maturity and n = number of periods. To obtain the Yield to Maturity, for a semi-annual pay bond, the periodic interest rate (y) is doubled up. Nonetheless, performing this action otherwise annualizing the yield minimizes the effective yearly yield. In the face of this, conventionally, in the market the Yield to Maturity is obtained by doubling-up the periodic interest rate, y, in the above mathematical expression. The Yield to Maturity arrived at by the means of this market standard is referred to as the bond-equivalent yield. Working out the Yield to Maturity calls for an iterative procedure. In calculating the Yield to Maturity, it is assumed that the investor ploughs back the coupon imbursements at the Yield to Maturity that is obtained. This is for the reason that the Yield to Maturity arises out of a promise that will be obtained by merely holding the bond to maturity, also the coupon interest imbursements are ploughed back at the Yield to Maturity (Thornton & Poudyal, 1990). Once an investor fails to hold the bond to maturity and the coupon imbursements are ploughed back at the Yield to Maturity, in that case the concrete yield the investor takes home can exceed or fall below the Yield to maturity. The example below illustrates how the Yield to Maturity is calculated. Consider a bond valued at $967.7 and whose coupon rate is 9 percent, suppose the bond is held to maturity for 4 years, its Yield to Maturity is arrived at by; First, we begin by solving for y using the mathematical expression given above. In this case, a trial-and-error method is applied where diverse interest rates have got to be tried up to when the present worth of the bond’s cash flows becomes equal to the bond price. By this means, an interest rate of just about 5 percent is obtained. This rate gives a cash flow value of $967.7 that is just one and the same to the bond price of $967.7. As a result, the yield is approximately 5 percent. To obtain a much exact figure, financial calculator is used, which gives a figure of 5.1108 percent. To obtain the Yield to Maturity, the periodic interest rate of 5 percent is doubled up, which gives a figure of 10 percent (5.1108 percent yields 10.2216 percent as the Yield to Maturity). II. Yield to call (YTC) The Yield to call (YTC) is a measure used to calculate bond yield that assumes that a bond will be called at its most basic promising call date. The formula used to calculate the price a callable bond is: In the formula above, C = the annual coupon amount, CP = the price of calling the bond, T = the time to the earliest promising call date, and YTC = the Yield to call, with semi-annual coupons. If a bond is a straight bond, the Yield to call can be worked out if the price of a callable bond is known. Regularly, participants in the bond market calculate the Yield to Maturity along with the Yield to call, for a callable bond, and draw on the lower yield to price a bond. If bonds are bought and sold at or higher than a specific point of intersection, which is estimates a bond’s par value in addition to one year’s interest, the Yield to call will more often than not present the least yield measure (Semmler & Mateane, 2012). A bond issuer will most probably call back callable bonds as soon as the bond’s price goes up to the price higher than the par-value and the calculated Yield to Maturity falls sufficiently low that it would be lucrative for the issuer to call the bond and fund the call by putting new bonds up for sale. Below is an illustration of how the Yield to call is calculated; Consider the following bond: Coupon rate = 11 percent Maturity = 18 years Par-value = $1,000 First par call in 13 years Suppose that the market price for this bond $1,169 and the given Yield to Call is 8.8 percent, verify if 8.8 is the actual Yield to Call. To confirm that the Yield to Call is 8.8 percent, we can use this rate to work out the bond’s price to substantiate whether it is $1,169. To arrive at this, first the present value of the coupon payments with N = the number of periods up to when the bond is presupposed to be called (= 13 x 2 = 26) is calculated. This gives us $842 as shown below; = 55[15.314] = $842 Then we calculate the present value of the maturity value where the assumption that it will be called in 13 years applies. This gives us $326 as shown below; = 1,000[0.327] = $327 Once a semi-annual interest rate of 8.8 / 2 = 4.4 is used, the present value of the cash flows becomes $842+ $327= $1,169. Accordingly, the Yield to Call for this bond is 8.8 percent Effect of Interest Rate Traditionally, it is approved that increasing interest rates are bad for bonds. Even investors in 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. However, there are a lot of other factors to mull over given today’s varied and worldwide bond markets that present managers with scores of options that may well strategically cushion investors against interest rate variations (Philippon, 2009). Regardless of the question on the implication of interest rate variations for bond prices, the effects are real. For a committed portfolio, an increase in interest rates has two apparent effects: An increases in interest rates will diminish bond prices, but An increase in interest rates will boost the future value of reinvested coupons Also, for a committed portfolio, a decrease in interest rates has two apparent effects: A fall in interest rates will increase bond prices, but A fall in interest rates will shrink the future value of reinvested coupons. Once the price-yield correlation is graphed, it displays a convex shape as shown below: Price Yield This non-linear relationship exists because: Prices move in reverse to the bond yield For a given change in yield, longer maturity bonds report bigger changes in price; therefore, bond price volatility is straightforwardly linked to term to maturity. Price instability goes up at a declining rate as term to maturity goes up Price actions ensuing from equivalent absolute increases or decreases in yield are not proportionate. If yield declines, bond prices rises greater than a swell in yield of the equal sum lowering prices. Elevated coupon issues illustrate minor percentage variations for a given change in yield, that is, price volatility is linked to coupon in reverse. References 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. He, X.-Z., and Westerhoff, F.H. (2005). Commodity markets, price limiters and speculative price dynamics. Journal of Economic Dynamics and Control, 29(9): 1577-1596. Philippon, T. (2009). The Bond Markets, Quarterly Journal of Economics, 124 (3): 1011-1056. Semmler, W. and Mateane, L. (2012). Equity Market or Bond Market—Which Matters the Most for Investment? Revisiting Tobin’s q Theory of Investment, Technology and Investment, 3(4): 203-209. Thornton, J., and Poudyal, S.R. (1990). Money and Capital in Economic Development: A Test of the McKinnon Hypothesis for Nepal. Journal of Money, Credit and Banking, 22(3):395-99. Retrieved 3 December 2013 Westerhoff, F. (2003). Speculative markets and the effectiveness of price limits. Journal of Economic Dynamics and Control, 28(3): 493 - 508. Read More