Bond Yield Calculations - Essay Example

Student’s name) (Course code+name) (Professor’s name) (University name) 1.0. Bond yield Bond is a long term security on the financial markets. An investor gets return when he or she invests in bonds (Kidwel et al., 2010). There are three sources for return for an investor who has invested in bonds. These returns are; A periodic coupon payment of an interest Reinvestment income of the periodic coupon interest Capital gain when the bond is sold or when it matures up The measure and analysis of any bond yield depends on the above three sources of return. a. Yield definition David (2012) defined bond yield as the measure of return potentiality of a given bond taking certain considerations and assumptions on the future happenings of the bond in the market. 2.0. Types of yield There are different forms of yield. First one is current yields which normally relate to the annual dollar coupon interest compared to the market prices and in most cases it fails to recognize any gain in capital or loss in capital and also it does not take reinvestment income into consideration (David, 2012). Second bond yield is yield to maturity which is the interest rates that have the potentiality of making the present value of the cash flow from invested bond equal to the accrued interest plus the bond price (Kidwel et al., 2010). Bond equivalent yield is the annualized or semi annualized that can double and result into annual yield. Others include yield to call, yield worst, cash flow yield among others. 2.1. Current yield This relates to the annual coupon interest rates to the current market prices of the same bond as stated by Kidwel et al. (2010). In its calculation, it considers coupon interest income but does not consider loss or gains in capital and also income which has been reinvested. The current yield is normally greater than the coupon when it sells at premium and less when it sells at discount (Basu, 1999). The current measure of yield is normally a weak bond measure since it does not measure any cash flow apart from the payment of coupon. It does not give any consideration to loss or gain in capital hence does not give an investor an opportunity to analyses the return in investments. Current yield does not consider reinvested income hence it is not holistic in its bond measurement. The current yield also does not follow the time value of money hence is not easy for an investor to estimate or forecast the returns on a given bond using current yield (Kidwel et al., 2010). Current yield = Annual interest payment/clean price Examples; Bond face value is $ 100 Rate is 10% Clean is$ 95 Therefore yield = (100X10%)/95 = 1.05% 2.2. Yield to maturity It is also called the internal rate of return of a bond and it is one of the most commonly used measures of yield. It is the interest rate that will normally make the present value of the cash flow of the bond to be equivalent to its price (Burstein and Rebelo, 2003). Yield to maturity is the same as the internal rate of return (IRR). It can either be calculated using calculator, Trial and error method or Excel spread sheet. It is calculated as below; Where; P is the bond price C is the periodic coupon payment N is the number of years to maturity M is the (face value) payment at maturity y is the “risk-adjusted discount rate” (or yield to maturity, or IRR) When calculating yield to maturity of the bond interest semiannually, the common market convention of annualizing them is adopted hence they are being multiplied by two. This concept is called bond equivalent yield (Kidwel et al., 2010). For bonds which are selling in the market at a discount, the coupon rate is usually less the current yield while the ones which are selling at premium are greater than yield to maturity. Yield to maturity normally takes into account the three sources of returns in its calculation but at the same time assumes that the coupon payments plus any other principal payment can be at the same time be reinvested at an interest rate which is equivalent to yield to maturity bond held (Kidwel et al., 2010). Unlike current yield, yield to maturity will only be realize only if the interim cash flow can be reinvested at the yield to maturity and yield to maturity bonds held, if the bond is purchased at this point then the reinvestment risk will be less than the maturity yield of the bonds. There is relationship which exist between coupon yield, current yield and yield to maturity; the table below gives the summary of the relationship 2.3. Yield convention and bond equivalent The idea behind annualizing the semiannual yield is mainly to double it and the outcome of it is the bond equivalent yield. And in case any market player refers to the yield return measure as to be calculated on bond equivalent basis then this simply means that the return on yield are doubled (Bakshi, 2000). 3.0. Short comings of YTM It is better than current yield in measuring yield return this is because it measures the coupon, reinvestment income and loss or gain on capital. Its concept is also based on time value of money which is very important concept for investors. The yield to maturity assumes that the coupon payment from the bond can be again be reinvested at the same interest rate equal to the yield to maturity. This assumption can be really misleading due to reinvestment risk since the structure of interest rates exists hence may result to different yield at different times (Bakshi, 2000) Example calculated A 10 year bond with 8% semiannual coupon bond was purchased at a per value of $100, calculate yield; Solution Yield to maturity is 8% Of it is calculated into future dollars then = 100x (1.04)20 = 219 Decomposition this $100 of principal of the total dollar returns is = $ 219-100 = $ 119 If the reinvestment is ignored then the return on investment would be $ 80 of the coupon and zero capital gain since the bond was purchased at par value. The shortfall on the return on the dollar investment would be; = $119-$ 80 = $39 The shortfall here is made up of the coupon payment yield if reinvestment would have taken place which is the interest rate of the bond when it was purchased. In this case, an investor will only realized yield to maturity of 8% only if the bond is held to maturity and the coupon payment can be reinvested ta the yield to maturity of 8%. Therefore, the assumptions used in calculating yield to maturity are questionable (Burton, 2003). 4.0. Factors affecting the reinvestment risk of the bond Reinvestment risk can be defined as the risk which the investors would face in the future reinvestment rates in case it will be less than the yield to maturity rate at the time when the bond was purchased (Burton, 2003). Another factor is the interest rate risk which can be defined as the risk that in case a bond is not held by the investor to maturity then, the investor may sell it for a rate which is lesser than the purchase price. Lastly time factor, the longer the maturity of the bond and the higher the coupon rate, the more probable higher the return since the return is dependent on the reinvestment income of the realized yield to maturity during time of purchase. 4.1. The reinvestment risk There are two major factors which affects reinvestments risks; firstly, time, the longer the yield to maturity the more the bond‘s dollars return since it depends on the reinvestment income in order to realize the yield to maturity at the time when the bond was purchased (Kidwel et al., 2010). The implication of this to investor is that at long term, a large amount of the dollar returns might be realized hence more risky to the investor. Secondly, the higher the coupon rate the more dependent the bond’s total dollar return will be in the reinvestment of the coupon payments in order for it to produce the yield to maturity during the time of the purchase (Kidwel et al., 2010). This has more adverse implication to the investor since if the selling is at premium then it will highly depend on the reinvestment income so that it can make up for the loss of capital due to the amortization of the price at the premium when holding the bond till the maturity date and in case the said bond sells at a discount then it will be less dependent on the reinvestment income. The exhibit 1 below shows the reinvestment risk at 8% 5.0. Yield to call This is a yield on a bond at an interest rate that will actually make the present value of the expected cash flow to the assumed called date to be equivalent to the accrued interest plus the bond price. The measure to the callable bonds includes yield to the first par call. Yield to the next call, yield to the first call and yield to refunding (Burton, 2003). In most cases, yield to call is calculated like yield to time. It assumes that the bond issuance will call the bond at a specified time in the future and at a specified price. Yield to refunding in most cases are used when the bond are currently callable but have some specific restrictions on the source of fund to be used in carrying out the exercise. If the yield to call for an 8-years bond at a rate of 7% coupon bond which is having maturity value of $100 the call date will be at the end of the three year and is having a call price of 103. The exhibit II below shows the calculation. 6.0. Effect of interest rates on bond prices If rates are high in long term bond then their prices tend to fall this is due to the fact the an investor will stay long with the coupon with a longer maturity period than the one with a shorter period hence the price of long term bonds are inversely related to their interest rates (Basu, 1999). Example 30 year treasury bond purchased in January 2012 at interest rates of 3.0% and the rates are expected to rise to 7% then there will be price decline in the subsequent weeks, A new 10-year Treasury bond with a yield of 1.8% when purchased at the beginning of 2012, however, only experienced a 4% price decline. The market interest rate (or yield) on the 10-year Treasury bond over that period of time (Lewis, 2000). An illustration on how bond prices fluctuates with changes in interest rate, consider the table below. period (holding years) 1 2 3 coupon payment 150 150 256.00 discounted value of coupon 131.80 7866.53 173.67 PV 8172.00 i 0.138087     From the table above the coupon payment changes during different years of holding times, The changes and the bond prices fluctuates as shown below. Yield Coupon maturity 6% for 2years Coupon 6% maturity 10years 7% 98.15 93.90 6% 100 100 5% 101.90 108.90 The table above shows how the bond prices, yield rates and time fluctuates 7.0. Conclusion Yield to maturity is the actual bond yield or the return which an investor will receive after investing in the bond incase the bond was held to maturity. It is the bond which the bond manager should always consider whenever he is considering a fixed income investment as it is better than all other types of bond yields. Yield to maturity not only accurate bond measurement methods but also gives an investor an opportunity compare different types of mutual bond funds in the market based on the yield to maturity calculation. Current yield on the other hand is useful in obtaining a general about the size of the coupon of the bond divided by the bond price. The only problem with it is that it forces the investor to calculate the true earning of the bond. Therefore current yield is not good in making investment decision. Reference Bakshi, G., C. Cao, and Z. Chen, (2000), ``Do Call Prices and the Underlying Stock Always Move in the Same Direction? ‘Review of Financial Studies, 13, 549±584. Basu, S (1999). “The Relationship between Earnings’ Yield, Market Value and the Returns for NYSE Common Stocks: Further Evidence.” Journal of Financial Economics Burton G. Malkiel (2003) Critics of EMH: Perspectives of Economic Journal—Volume 17, Number 1—winter 2003—Pages 59 – 82 Burstein, Ariel, Joao Neves, and Sergio Rebelo (2003) “Distribution Costs and Real Exchange- Rate Dynamics during Exchange-Rate-Based Stabilizations,” Journal of Monetary Economics, David S. Krause (2012) Yield Measures, Spot Rates, and Forward Rates Ph.D., Marquette University Lewis, A. L., (2000), Option Valuation under Stochastic Volatility, Finance Press, Newport Beach, CA. Kidwell, D.S. and others, John Wiley 2nd ed. (2010) Financial Markets, Institutions and Money ISBN: 9781742166629  . Read More