Bond Yield Measures - Report Example

Measures of Yield Your name Name of Assignment 18th December , 2012 Outline Introduction Measures of yield Yield to Maturity Current Yield Yield to Call Yield to Put Interest rate Theories influencing investors in choosing a yield References Introduction Every investor is interested in the return he gets from an investment made. Therefore it is necessary for one to calculate the yield that has a present value equal to the original cost or investment amount. It is expressed as a percentage and the factors in its calculation include the face value of the bond, the years to maturity, coupon rate and the current value of the bond in the market. Investors would prefer to hold on to bonds with positive convexity during increasing market interest rates (Besley and Brigham, 2008). Any cost to be for an investment is calculated as P = Where P is the maximum price that an investor should make when purchasing a bond, CFt is cash flow in year t and y is yield. In most instances y is calculated using internal rate of return methods of trial and error. There are many measure of yield which includes Yield to maturity, realised yield and expected yield, Current Yield, Yield to Call, Yield to Put, Yield to Worst and Cash Flow Yield (Crescenzi, 2010). Measures of yield Yield to Maturity- Yield to maturity is the yield that an investor will have if he holds the bond to maturity and during that period all interest earned is expected to be reinvested. It is considered the present value of all cash flows made from the bond. It is the rate or return expected or promised on a bond if the bond is held by the investor till maturity of the bond. It is expressed as a percentage and the factors in its calculation include the face value of the bond, the years to maturity, coupon rate and the current value of the bond in the market (Fischer and Jordan, 2006). It is calculated as Where: is value of bond, is annual interest, is required rate of interest, is principal value of maturity and n is life of bond It is easy to see that although bonds carry a promise to maintain a constant-dollar interest payment to maturity, I, and pay a fixed principal at maturity, P, the number of years to maturity, N, and the required rate of interest, i, can vary. Assume the bond with the Le us assume a 10-year bond with a principal value of $1,000, bearing a nominal rate of interest of 10 percent. Assume that an investor wishes to purchase this bond for a rate of percent. Because bond interest is normally paid twice a year, $100 of interest per annum would be paid in two semi-annual instalments of $50 each. The 10 percent annual rate is thus 5 percent per six-month period. The bond was purchase at $ 780. One will begin with calculating internal rate of return of the bond using cash flows up to maturity. The present value of the interest-payment stream of $100 per year for 10 years is as follows: V=P+ V=50+ = 952.38 +376.89 = $1,329.27 The present value of the principal at maturity is $1,000/ (1+.05)20= $376.89. The total value of the bond is thus $952.38 + $376.89, or $1,329.27. In other words, a $1,000 bond is worth $1,329.27 today if the nominal rate and the required rate of interest are equal. The $1,000 value is a composite of $952.38 of interest payments and $376.89 of principal. Note that the principal is compounded twice a year, as are interest payments. To find yield maturity for this kind of a bond, we will use trial and error method. However excel software can help in calculating the yield-to-maturity. In this case we have used excel file and found out the yield-to-maturity to be 3%. This is doubled because the interest is paid semi-annually. The excel file is attached. Current Yield- The current yield relates the annual dollar coupon interest to the market price (Bomfim, 2001). Current yield is the yield which can be earned currently and is derived as shown below Where: = annual interest and = current market price Let us take the following example Coupon rate = 10% Current Market Price= 780 Maturity = 10 years Par value = $1,000 First par call in 6 years Only put date in five years and putable at par value The current yield exceeds the coupon when the bond is selling at a discount. The opposite is true when the bond is selling at a premium. In this case the coupon rate is lower than the current yield and the bond is selling lower than the par value. The disadvantage to the current yield is that it does not take into account the two other sources of income—reinvestment of income and capital gain or loss. Yield to Call—this is also called realised Yield. This is the yield if the investor decides to dispose of the bond before it matures. It is the actual return on a bond based on the cash flows that has been received. When a bond is subjected to redemption prior to maturity, the cash flow implicit in the yield-to-maturity figure is subject to possible early alteration (Besley and Brigham, 2008). Most corporate bonds sold today are callable by the issuer, but with a certain period of protection before the call option can be exercised. At the expiration of this period the bond may be called in at a specified call price, which usually involves some premium over par (Brigham and Ehrhardt, 2010). To provide some measure of the return in the event that the issuer were to exercise his call option at some future point, the yield-to-call is often computed and compared with the yield-to-maturity. This computation is based on the assumption that the bond’s cash flow is terminated at the first call date with redemption of principal at the specified call price. For a given rate, the present value of this assumed “cash flow to call” can be determined and the yield-to-call is then defined as that discount rate, which makes this present-value figure equal to the bond’s market value (Brealey, Myers and Marcus, 2007). Let us take the following example Coupon rate = 10% Current Market Price= 780 Maturity = 10 years Par value = $1,000 First par call in 6 years Only put date in five years and putable at par value Callable at 1070 In this bond we have found out that yield-to-maturity is 6% and can be called in five years which means 10 coupon payment Yield-to-call can be calculated by the following general formula: Where: = number of years to first call date = call price = market price Using excel file we find Yield-to-call = 8% The investor would have to choose between the lower yield-to-maturity 6 percent and the higher yield-to-call 8 percent for investment purposes. With the bond selling below par, if interest rates were expected to fall below 3 percent over the next five years, using the lower yield is both prudent and conservative. If interest rates remain unchanged, or increase, there will be no reason for the issuer to call the bond because they will be paying a rate less than what the market is paying. If interest rates fall below 8%, the coupon rate, then the issuer will call the bond so they can reissue at a lower rate. For an investor who assumes that rates will fall, basing expected yield on the yield-to-call rather than the higher yield-to-maturity might be appropriate. In general, it is always wise to pay some attention to the yield-to-call calculation when the bond: (a) sells at or above par, and (b) you expect interest rates to trend lower over time. Yield to Put- Yield to put is the yield if the bond is putable, that is the bond holder can sell the bond to the issuer at a strike price. It is calculated the same way as yield to call (Coombs, Hobbs and Jenkins, 2005). Let us assume the bond in our example is putable at 5 years and the put price is 1020. Yield-to-put can be calculated by the following general formula: Where: = number of years to first call date = put price = market price Using excel file we find yield-to-put as 3.85 percent. Interest rate and Changes in bond prices Interest rates- From the above analysis we have noted that is an inverse relationship of interest rates and bond prices. As interest rates increase, bond prices simultaneously decrease. Thus most investors would prefer to hold on to bonds with positive convexity during increasing market interest rates. This is because as interest rates rise, the price of a bond with positive convexity decreases at a slower rate than for bonds with lower convexity and this increases the return on the bond. On the other hand, investor would prefer bonds with negative convexity times of interest rate volatility as negative convexity means that the bond prices will be less volatile and less susceptible to the interest rate risk. All maturity- when an investor is choosing to invest in, maturity period plays an important role. If the bond has a longer period, then the price is likely to be low. This is because the longer the period of maturity the riskier the bond is. The shorter the period the higher price is expected to be. As the bond approaches maturity, its market price converges towards par value and at the maturity, it equals par value. Since the bond is selling at a premium, the bond price decreases as it approaches par value ($1,000) Coupon rate- it determines the annual or semi-annual cash in flows or returns the investor is likely to receive. The coupon rate determines the interest that is paid by the issuer. If it’s too low it means the interest will be low and vice versa. Risk premiums due to credit rating of issuer- the risk of default is determined by the credit rating of the bond issuer. If a bond issuer has low credit rating, then the investor may require a higher return because the risk is high. Theories influencing interest rate There are a number of theories that influence the yield an investor will choose while making an investment. These theories include expectation theory, liquidity theory and segmental theory. These theories are explained below; The Expectation Theory—this theory assumes that investors are interested in an upward sloping yield that is they accept interest rates which are likely to increase in future thus short term interest rate. The theory assumes that investors will like long term interest rate to be higher than short term interest rate. It further assumes that for an investor to invest in any bond the present value should be greater or equal to interest rate from short term investment. (Ross, Westerfield and Jaffe, 2005). Let us assume an investment in a bond with a maturity period of three years. In this case an investor can choose to invest in the bond or choose a bond that will mature within one year or possibly within two years. If the yield to maturity for a 3 year bond is assumed to be 6 percent and the current yield to maturity for a one year bond is 6.3 percent then the investors return will be determined as follows We will notice that it is more advantageous to purchase a one year bond as compared to a three year bond. A three year bond will give an overall return of 19.1% while a one year bond will give an overall return of 20.11%. This is when re-investing is taken into consideration and the short term bond interest rate is assumed to remain constant without changing. When other investments with similar interest rates are available then the investor will become in different in choosing where to invest his money. The most important assumption in this theory is that the bond market is efficient thus investors do not incur transaction cost giving an investor an opportunity to maximize profit. It also assumes that interest rates for long term investments are geometrically average with the current and expected short term interest rates. The implication here is that the investors are able to earn average returns throughout the investment period since bond issuers are not able to lower the interest rate (Shim and Siegel, 2008). This theory is important because the investor is not certain about the future when a bond has a changing interest rate. When there is constantly changing interest rate, the investor will not be able to predict the future returns. The Liquidity Premium Theory—this theory is crucial to those investors who are interested with liquidity. The theory assumes that investment interest rate is expected to increase in future. This theory offers an explanation that investors will wish to have a higher return in future since the risk is high. Unlike the expectation theory which did not give an explanation for these changes. This theory has offered an explanation. According to Correia, Flynn, Uliana and Wormald,( 2007) liquidity theory assumes that long term bonds should have a higher interest rate than the shorter term bonds. These theory is only favourable to the investors but unfavourable to bond issuers. This is because if an issuer issues a long term bond, he will inccur a higher cost in the long run as compared to the cost of refinancing continous short teerm bonds. In this case a critical assumption that there are no costs except interest rates. The yield curve, which depicts the relationship between yield and maturity, has a number of implications for the financial manager in financing and in investing funds. Either zero coupon or coupon Treasury yield curves are used, depending on the situation. The longer the maturity, the greater the volatility of bond price with a given change in yield. Also, the lower the coupon rate the greater the volatility, holding other things constant. The duration measure combines maturity and coupon effects, and serves as a guide to bond volatility. The Segmented Markets Theory—this theory assumes that the capital market where bonds are traded is sub-divided into several market segments based on maturity periods of bond and in each segment the yield-to-maturity of a bond is determined by forces of demand and supply. According to the theory, investors will enter into a segment since they want to maximize their returns by matching maturities of bonds and liabilities associated with them. This means that there should be enough bonds to match the liabilities investors will incur in raising funds. In simple terms investors will borrow from an institution with lesser interest rate and invest in a bond with higher returns but both the bond and the loan have equal maturity periods. The other critical assumption of this theory is that investors do not shift from one segment to another since only forces of demand and supply are able to determine the yield-to-maturity (Fischer and Jordan, 2006). Practically, government long term bonds always have highest returns as compared to short term bonds. This explains the risk associated with these bonds although they are default free bonds. A long term government bond has a risk premium which is not associated with t-fold but with extension of bonds maturity period when the government has liquidity problems like in the case of Greece and Spain (Correia, Flynn, Uliana and Wormald, 2007). Yield-to-maturity of any bond has basic component which include influential premium, default risk, liquidity risk, real interest rate and interest rate risk premium. The mentioned methods of yield measures are important to investors who are operating in the market. References Besley, S., & Brigham, E. (2008). Principles of Finance (4th ed.). Mason: Cengage Learning. Bomfim, A.N. (2001). Measuring equilibrium real interest rates: What can we learn from yields on indexed bonds? Retrieved on July 31, 2012 from http://www.federalreserve.gov/pubs/feds/2001/200153/200153pap.pdf Brealey, R, Myers S. & Marcus, A. (2007). Fundamentals of corporate Finance. Boston: McGraw-Hill Irwin. Brigham, E. F., & Ehrhardt, M. C. (2010). Financial Management Theory and Practice. New York: Cengage Learnings. Coombs, H. M., Hobbs, D., & Jenkins, D. E. (2005). Management accounting: principles and applications. New York: Sage Publications. Correia, C., Flynn, D., Uliana, E., & Wormald, M. (2007). Financial Management. Juta and Company Ltd. Crescenzi, A. (2010). The Strategic Bond Investor: Strategies and Tools to Unlock the Power of the Bond Market. Sidney: McGraw-Hill Companies. Fischer, D. & Jordan, R. (2006). Security Analysis and Portfolio Management. New York: Prentice Hall Ross, S., Westerfield, R., & Jaffe, J. (2005). Corporate finance. New York: McGraw Hill Company Shim, J. K., & Siegel, J. G. (2008). Financial Management. New York: Barron's Educational Series. Read More