Different Measures of Yields - Essay Example

Measures of Yield Student’s Name Institution Measures of Yield Bond yield is a measure of the proceeds that an investor will earn from the investment on the bond. The less the amount paid for a bond, the higher the returns from the bond and also the higher the bond yield. The higher the amount paid for the bond, the lower the earnings gained and the lower will be the bond yield. Bond yield and bond prices have an inverse relationship. When the bond prices increase the bond yields tend to go down and when the bond prices reduce the bond yields tend to go up. The understanding of this relationship will help investors to avoid the confusion associated with the dealing of bonds. Bond yields are a good indicator of the strength of the stock market and the level of interest generated from the amount of money invested. If there is an increase in the demand for bonds by the investors then the bond prices will go up. With bonds, the cash flows are always positive and the variations rate at which income can be re-invested is much lower. Bond yield is the profits from an investment expressed as a yearly percentage. For example, a 10% yield means that the investment averages 10% earnings every year. Therefore it is necessary for an investor buying bonds to seek high yielding bonds all the other factors held constant. Many types of securities and a great number of dealers are found in the bond market. Bonds are of many types ranging from junk bonds to corporate bonds, zero coupon bonds, municipal bonds, agency bonds and asset backed securities. Bonds have certain characteristics that define them such as maturity dates, face value or par value, the yield and the coupon payments. A bond measure is a scheme to sell bonds for the purpose of raising funds for the various government projects such as research and development, building of government schools and hospitals, provision of public goods and services, transportation, social welfare services among other projects. There are three commonly quoted measures by the dealers and used by the investors or the portfolio managers. They are outlined below as follows; 1. Current Yield This is a measure that is important to the income oriented investors. It relates to the annual coupon interest to the current market price of the bond. The formula for the current yield is Current yield (CY) = annual dollar coupon interest(c) ÷ price (p) Where CY= Current bond yield C=annual dollar coupon interest P=prevailing market price of a bond For example, standard chartered bank has a ten year bond at a rate of 5% and a market price of 98. The annual dollar coupon interest will be 0.05×$100= $5 Current yield= $5÷98×100=5.1% When the bond is selling at a discount the current yield is greater and when the bond is selling at a premium the current yield is lower. At par selling of a bond, the current yield is equivalent to the coupon rate (Fabozzi, 1996). The limitation with the current yield calculation is that it only accounts for the coupon interest and nothing else hence no other source of return will affect the investor’s yield. This method is straight forward since the bond prices increases with declining market interest rates. A bond has a fixed coupon rate and the only way to change the bond’s yields with changing rates of interest is to change the price of the bond. The method also ignores the time value of money since the cash flows are computed until the maturity date of the bond. This method does not consider capital gain or loss and the reinvestment income. It is a useful yield measure to those investors seeking to earn proceeds from their portfolio. For those investors seeking a capital gain, it is not a good measure of return and it is a useless statistic for zero coupon bonds which do not pay annual coupon payments to their holders (Place, 2000). 2. The Bond Yield To Maturity On A Payment Date This is the internal rate of the bond that a buyer would earn if he bought the bond at prevailing market value. It is also known as the redemption yield. The aim of this calculation is to find the rate of interest that will formulate the present value of the flows of cash similar to the value of the investment. An inverse correlation exists between the prices of bonds and the bond yields. When the bond price goes up, the bond yield goes down and vice versa. This method measures both current income and the expected capital gain or losses unlike the current yield. There is no technique that can be utilized in the computation of the actual yield to maturity on a bond. The calculation can only be done using a trial and error basis which is very tedious. Unlike other methods used to measure the bond yield, this is probably the most accurate method. When investing in bonds, a full evaluation of the bond investment needs to consider whether the gains earned are adequate compensation for the risk of invested funds and how it compares with alternative investment over the same term (Zipf, 2002). The disadvantage of the yield to maturity is that it assumes that the coupon rate will be re-invested at a rate of interest similar to the yield to maturity. Therefore, a higher coupon and a longer maturity date make the reinvestment assumption more important. This method takes into consideration the time value of money thus the timing of the cash flows, the capital gains or losses by holding the bond until maturity and the current coupon income. Formula for a semi- annual pay bond (P) = C÷ (1+y) ^1+ C÷ (1+y) ^2……. + C÷ (1+y) ^n +M ÷ (1+y) ^n where P = price of the bond, C= semi-annual interest coupon (in dollars), m= maturity date value (in dollars) and n= periodic numbers (year number×2) Formula for yield to maturity of a zero coupon bond (p) =C÷ (1+Ym÷2) 2n Where C is the cash flow, (Ym) is the yield to maturity and n is the number of years to maturity. Consider a case whereby a bond has a face value $1,000, a coupon rate of 8% per year paid semi annually and has 3 years to maturity. The current value of the bond is $961.63. The bond is called in one year with a call premium of 3% of the face value (Choudhry, 2010). Price of the bond=0.08÷ (1+0.08) ^1+0.08÷ (1+0.08) ^2+ 0.08÷ (1+0.08) ^3×2+ $240÷(1+0.08) ^6=4.75×2=9.50% 3. The Yield to Call on a Payment Date This method applies to a bond that may be called before its stated maturity date necessitating a yield measure to be commonly quoted by the dealer; the Yield to call (YTC). The method for calculating the yield to call is similar to that of calculating the YTM except that the cash flows used in the computation are those that are expected to occur before the first call date. This method grants a dealer a buying back right before the maturity date at a specified price. The call price will usually be set at par or a little above the par value. Bonds with call options will usually sell at a higher yield (lower price) than comparable non callable bonds. YTC is the yield that makes present value of the flows of cash till the first call date equal to the price of the bond assuming that the bond is held to its first call date. The yield to call like the YTM assumes that the bond is held to its first call date and the reinvestment of the interim cash flows at the yield to call date (Dynkin, 2007). Formula for YTC= (P) = C÷ (1+y) ^1+ C÷ (1+y) ^2……. + C÷ (1+y) ^n +M ÷ (1+y) ^n where P = price of the bond, C= semi-annual coupon interest (in dollars), n= the period number until the first call date and m= the call price for the bond (in dollars). Consider a case whereby a bond has a par value of $1,000, a coupon rate of 8% per year paid semi annually and has 3 years to maturity. The current value of the bond is $961.63. The bond is called in one year with a call premium of 3% of the face value. Price of the bond=0.08÷ (1+0.08) ^1+0.08÷ (1+0.08) ^2+ 0.08÷ (1+0.08) ^3+$30÷ (1+0.08) ^12= 15.17%. OTHER BOND YIELD MEASURES 1. Yield to Worst The investor can commonly calculate the yield to maturity, the yield to every possible put date and the yield to every possible call date. The minimum of all these yields is what is known as the Yield to Worst. This measure is supposed to measure the worst possible return a shareholder will earn if the bond is put or called before the maturity date (Choudhry, 2010). 2. The Cash Flow Yield Market participants calculate a cash flow yield for amortizing securities. It’s the rate of interest that will create the present value of the forecasted flows of cash similar to the market value. The difficulty involved in calculating a cash flow yield is determining what the prepayments will be for each period. Periodic cash flows are made up of the coupon interest, the prepayments and the scheduled principal repayments. Cash flow yield deals with asset backed and mortgage backed securities (Campbell & Taksler, 2002). 3. Yield (internal rate or return) for a Portfolio The yield on a portfolio is calculated by predicting the cash flows for the portfolio and coming up with the interest rates that will formulate the present value of the cash flows similar to the market price of the assortment. 4. Nominal Yield The nominal yield on a bond means the rate of the coupon on the bond. A bond having 7% coupon has a 7% nominal yield. This method provides an efficient way of describing the coupon characteristics of the bond. This method does not consider capital gain or loss or the reinvestment income of an investment (Diebold & Li, 2003). 5. Yield to Refunding This technique applies when bonds are callable currently, but there exists barriers from the funds origin utilized to purchase back the arrears when a call is being exercised. The date of refund is the first date a bond can be called using a lower cost debt. Its calculation is the same as that one for the yield to maturity. 6. Yield to First Call It is calculated for a callable bond that is not currently callable. The actual computation is similar to that of the yield to maturity with the only difference being that the analysts use the call price and the first call date in calculating the yield instead of the face value and the stated maturity date of the bond. How Changes in Interest Rates Affect Bond Prices The variations in the current interest rates in the economy will affect bond prices in a major way. The interest rate is the rental price of money expressed as an annual percentage of the amount borrowed. For the borrower, interest is the penalty incurred for consuming income before it is earned. Interest for the lender is the reward for postponing current consumption. An inverse relationship exists between the bond prices and the level of interest rates. When interest levels rise, the bond prices in the market fall and when the interest levels decrease, the bond prices in the market rise. This has an effect of raising yields of older bonds when interest rates increase and matching them with newer bonds with high coupons and lowering the yield of the older bonds when the interest rates decrease and matching them with newer bonds with lower coupons. If there is an increase in demand for the bonds, the bond prices will go up and if there is a decrease in demand for bonds then the bond prices will go down. This is a good indicator of how strong the stock market is and an increase in the interest rates will raise the value of a country’s currency against other world majors. The fundamental determinant of the rate of interest rates is the interaction of saving and investment. The higher the return on an investment, the more likely investors are to undertake a particular investment project. At higher interest rates, fewer business projects can earn the required rate of return. Therefore, the demand for capital will be lower. The lower the interest rates and the demand for capital will be higher and many business ventures will earn the required rate of return. When it comes to saving, many people prefer to consume goods currently than on the following day. At lower levels of interest, most people will postpone very little consumption for saving and thus the supply of saving will be higher. With higher interest rates, most people will not postpone consumption for saving and thus the supply for saving will be much lower (Place, 2000). In order to avoid massive fluctuations due to interest level changes, interest rates can be projected using the economic modeling. Economic modeling predicts interest rates by estimating the statistical relationship between economic variables and the level of interest rates. The key assumption being that the causality among variables is highly stable (Zipf, 2002). There is also an interest rate risk that exists and consists of price risk and reinvestment risk. Price risk is a risk that arises out of the inverse correlation that exists between the prices of bonds and the interest rates. Reinvestment risk is more complex and arises because interest rate changes cause fluctuations in investors’ realized yield. The rise in returns makes bond prices fall but coupon rate reinvestment increases and vice versa. Therefore, a measure that accounts for both risks is needed. Duration matching is a technique used to eliminate the price and reinvestment risk (Choudhry, 2010). References Campbell, J. Y., & Taksler, G. B. (2002). Equity volatility and corporate bond yields. Cambridge, MA.: National Bureau of Economic Research. Choudhry, M. (2010). An introduction to bond markets (4th ed.). Chichester, West Sussex: Wiley. Diebold, F. X., & Li, C. (2003). Forecasting the term structure of government bond yields. Cambridge, Mass.: National Bureau of Economic Research. Dynkin, L. (2007). Quantitative management of bond portfolios. Princeton: Princeton University Press. Fabozzi, F. J. (1996). Bond markets, analysis and strategies (3rd ed.). Upper Saddle River, NJ: Prentice Hall. Place, J. (2000). Basic bond analysis. London: Centre for Central Banking Studies, Bank of England. Zipf, R. (2002). How the bond market works (3rd ed.). New York: New York Institute of Finance. Read More