Different Ways of Measuring Bond Yield - Assignment Example

Name: Student number: Name of Lecturer: Subject: DIFFERENT WAYS OF MEASURING BOND YIELD It is important for any investor to understand the instruments used in money market (Tavella and Randall, 2000). One of such instruments is the bond yielding, this paper tries to explain bond yielding and the different measures of yielding in the security markets. Chambers and Carleton (2001) define bond yielding as that return an investor earns on a bond when it reaches maturity stage in the market. Another scholar, (Bierwang, 2007 p.76) defines bond yielding as, "the percentage on the return on investment on bonds which must be within a given specified period of time". From the above definitions, the yield can also be referred to as that interest rate that equalises the current value of investment of cash flows to the investment cost, known as the internal rate of return for any investment. This can be written mathematically as follows; PI = Where; PI= price of that investment CFN = cash flow for the year N N= number of years There are several bond market yields in the bond market which can be quoted by the investors and the measures of the yield used by portfolio managers. These are cash flow yield, yield to maturity, yield to call, yield spread measures, yield for portfolio, yield to worst, yield to put and current yield. These can further be discussed as follows; Yield to put/Current yield In this situation, the bond issue is putable, that is, the person issuing the bond can be forced by the bond holder to quote the specific bond price (Bank for International Settlements, 2007). We can therefore define yield to put as that rate of interest that can make the current value of inflow cash be overlooked until the put date where after it will be added to the put price of that said date (Tavella and Randall, 2000). Mathematically this can be stated as follows; YP = Where M* is the put price and n* is the time Example Consider the following bonds given that maturity date is 20 years; coupon rate is 15%, per value is $ 1000 and the first call is in the 5th year. Calculate the first call Solution YP = = 1000(1/ (1+0.15)5) = $497.18 Yield to call This can be defined as the return that an investor gets for waiting with the bond until date of call (Audrino, and De Giorgi, 2007). It is therefore assumed that the investor is in a position to call the bond at a particular date making it necessary to calculate the call price – the price at which the bond is called. Yield to call is calculated the same way as yield to put only that the M* in this case represents the call price. Current yield In this case the investor finds the annual percentage rate on the bonds invested. It often relates to the annual market price and the interest rates of the coupons. Current yield can be calculated as follows; CY = IRc / PB Where CY is the current yield IRc is annual interest rate of coupon PB is price of bonds According to Ingersoll et al. (2003), interest rate of the coupon is the main factor to be considered in the calculation of current yield. Example The coupon annual interest rate is 10% and the price of the bonds is $10. Calculate the current yield Mr. Mark, an investor will get in the first year of investment Solution Current yield = annual coupon interest rate/ price of the bonds = 10% / $ 10 = 0.01 = 1% Yield to maturity This is the total amount of the return on investment that an investor expects to get at the end of investment period. In this case, the interest rate is used to equate the present value of the cash invested to the initial cost of on investment. Yield to maturity can be calculated as follows; PB = Where PB is the bond price C is the coupon interest M is the maturity value N is the time period Example Mr. Ken has debt obligation on bond to be paid as follows Number of years Cash flow in $ 1 2000 2 2000 3 3000 4 5000 5 6000 6 7000 Calculate the yield to maturity if the interest rate is 20% annually Solution PB = = 2000/ (1+0.2)1 + 2000/ (1+0.2)2 + 3000/ (1+0.2)3 + 5000/ (1+0.2)4 + 6000/ (1+0.2)5 + 7000/ (1+0.2)6 = 11958.5 Cash flow yield In this case the cash inflow consists of the interest rate and the repayment principle. This interest rate makes the current value of the projected cash be equal to the price in the market. Yield to portfolio This is calculated by finding the total cash flow of the portfolio and interest rate that equate the current value of cash inflow to the floated market value of that same portfolio. Yield to worst This is the case whereby at maturity of the bond or when it is called the investor at this point gets the lowest interest yield. In other words, it is the lowest rate on return an investor can get. The effects on changes in the rate of interest on the prices of bonds It is important for any investor who wishes to invest in bonds to have a complete know how of the bond market. There are risks involved in this type of market even though it has fixed rate of interest on return for a specific period of time as compared to that of the stock market. There are two major risks involved in investing in this type of market; first, the interest rate risk which forms the main focus of discussion in this paper and second is the credit risk, which means that the bond issuer is not in a position to any regular interest on the principle payment. Inflation caused by unstable economic performance of nations is a major factor affecting the security market. There is a constant change of the interest rate, either to the positive or negative side known as interest rate risk. Various research studies have proved that interest rate and bond prices are inversely related, that is, an increase in the interest rate will subsequently lead to a decrease in the bond prices and also that a decrease in the rate of interest will lead to an increase in the price of bond (Akitobi and Stratman, 2008) Example To illustrate the above statement, we take a point where one holds a bond worth $ 10,000 for the next 20 years at an interest rate of 20% and the coupon is paid quarterly. Due to the effects caused by inflation, the rate of interest of the bond increases to 25% after 6 years. To sell these bond in this 6th year, the person willing to buy must be willing to forgo the 5% increase in price since the interest rates are fixed within a given time period. If the rate of interest on the bonds reduces by maybe 10% then the bond buyer will fetch a higher return. It is therefore true to state that time as a factor is a contributor to the bond prices in relation to the rate of interest, that is, long term bonds are more risky than the short term ones. Calculation of changes in yield This is usually calculated in percentages, that is; Absolute change in yield = (1st yield – new yield) x 100 The change in percentage can also be calculated in natural logarithm as follows; Percentage change in the yield = 100 x log (new yield/ 1st yield) There are various challenges associated with measuring the yield using the internal rate of return. To start with is the assumption in the way cash flows in a given period are invested in the market. Second, using annual simple rate of interest in calculating internal rate of return just an estimation and not accurate. Third and lastly, Kidwell et al. (2010) describes this method as being tedious and cumbersome. Read More