Bond Yield Measures Inform Investors of the Rate of Return on Bonds under Different Assumptions - Assignment Example

Measures of Bond Yield Name: Institution: Measures of Bond Yield Yield to maturity/promised yield The yield to maturity, also known as the promised yield, can be found from calculations involving the known purchase price of a bond using the formulas of bond pricing. The yield to maturity is a type of yield that is pledged to the holder of the bond while assuming that it will be held till it matures, and that the principal and coupon payments will be adhered to as promised (Alliance Consulting, n.d; Ireland, n.d). In addition, it is assumed that the coupon payments made would be plowed at the promised yield of the bond for the remainder of the maturity period. A reinvestment risk occurs when the yield to maturity is more than the actual yield of the bondholder. This is as a result of reinvesting coupon payments at a lesser rate. The trial and error method is used to calculate the promised yield (Alliance Consulting, n.d). In most cases, a number of iterations are required in order to complete the calculation. To illustrate this, an example is given as follows: a person purchases a person purchasing a bond that has a purchase price of $90, a face value of $ 100, a 2-year maturity term, a 7 per cent coupon rate, as well as an interest payment every six (6) months. The given market interest rate is 9 %. Find the yield to maturity of this bond. The bond’s cash flows include: Four periods of interest payments which earns = 3.50 = (0.5 * 0.07 * 100) it is important to find the value of the rate of discount (i), which would solve for the current purchase price ($ 90) PV (90) = 3.50 { } +  The yield ought to be greater than the coupon rate of 7 % since the face value is greater than the price value. We could try using 8 % with 4 per cent for each 6 months PV (90) = 3.50 { } + 100 At 12 per cent PV is equal to 91.33 At 13 per cent PV is equal to 89.72 The real rate was 12.826 %. Without a calculator, it would take a number of attempts to come up with that solution. The approximation technique could also be employed. I =  I =  I =  = 6.3157 % As a result, the approximated yield will be given by 2 * 6.3157 % = 12.63 per cent Realized yield The amount of return that a bond earns can easily be shown by the yield to maturity in the event that the borrower of the bond, not only promises but also makes all required cash payments, the rate of interest does not change over the maturity of the bond, as well as the bond being held to maturity by the investor (Ireland, n.d). In case an investor decides to sell the bond at a lower purchase price before it matures, the return earned on this bond would most certainly be different from the yield to maturity. The realized yield is defined as the return a bond earns given the actual cash flows that the investor receives on assumption that all coupon payments are plowed at the yield to maturity. An example to illustrate this realized yield is provided. Assuming that one purchases a 10-year, 8 % coupon (annual payments) bond at par (the yield to maturity is similar or equal to the coupon rate). After three years, this investor decides to go on a vacation in Nepal and decides to sell the bond in order to acquire the needed means of achieving this. During this time, there exist 7-year bonds that have the same features, for instance default risk, whose selling yields, are at 10 per cent. For that reason, the realized yield will be totally different from the 8 per cent yield to maturity. This is as a result of the market yields on corresponding bonds increasing to 10 per cent. To calculate the actual yield that is earned on the investment, it is important to calculate the rate of interest that links the cut-rate sum of the actual cash flows that the investor receives from the original price he used to purchase the bond. The first step involves calculation of the present bond price, or the bond’s market price on the actual date of sale. From the above example, $ 1000 was used to pay for the bond. The investor received $ 80 coupon payments annually for the three years that he held the bond. The market, or current, price of the bond on the date of sale is equivalent to the current value of the seven remaining coupon payments, as well as the eventual principal repayment. This is calculated as follows:  +  + …. +  The next step involves solving for the value of the rate of interest. Before this is done, the initial $ 1000 purchase price is set to be equivalent to the current value of the actual cash flows that the investor receives. This present value is equal to the three $ 80 coupon payments and the $ 902.63 sale price. $ 1000 =  +  + …. +  The use of trial and error or a financial calculator to solve the above equation, gave rise to an annual 4.91 per cent realized yield. The selling of the bond before it reached maturity led to a $ 97.37 capital loss, whose explanation is derived from the difference between the yield to maturity and the realized yield ($ 902.63 - $ 1000). Importance is attached to knowing the realized yield. It helps an investor, who could either be an individual or a financial institution; assess the returns of his bonds at the end of the investment horizon or holding period or ex-post. In conclusion, the realized yield can simply be taken to mean the rate of return that is earned on a bond using the original purchase price and the actual cash flows that are received by the investor. Expected yield Majority, if not all, financial institutions or individual investors who plan on selling their bonds before expiry of the maturity period, would like to be informed on the impact that changes in the rates of interest would have on the returns on their bond investment before the detail, or ex-ante. A number of forecasting techniques are usually employed in the estimation or prediction of impending rates of interest. The basis for such predictions more often than not lies within the boundaries of money supply, economic activities, the rates of inflation, as well as the preceding characteristics of interest rates. Having such information enables the investor to envisage the bond’s market price at the end of an applicable investment horizon. With knowledge on the predicted future price of the bond, an investor is able to calculate the expected yield that is a reflection of the anticipated sale price. The previous case in point of a 10-year, 8 % coupon bond, would be used to illustrate this. This investor had anticipated selling the bond after 2 years at the current market prices. At the time of purchasing the bond, his investment adviser had foreseen that analogous bonds that had 8 years before they could mature would generate 6 per cent after a two year period. The forecast on the rate of interest signified that the expected price of the bond would be $ 1124.40. This is found from the calculation below. PB = $ 1124.20 =  +  + …. +  From the preceding calculation, it is important to note the presence of eight (8) coupon payments, as well as the remaining principal payment at the point in time when the sale would take place. In order to calculate the value of the expected yield over the investor’s 2-year investment horizon, it is necessary to find the value of the rate of interest that links the initial purchase price, In this case $ 1000, to the cut-rate summation of the cash flows the investor is expected to receive. These include the expected selling price of the bond and the coupon payments. $ 1000 =  +  + …. +  The expected yield is also found using trial and error method or by use of a financial calculator. In the given example, the expected yield is found to be 13.81 per cent. The selling of the bond before it reached maturity led to a $ 124.20 capital gain, whose explanation is derived from the difference between the yield to maturity and the expected yield ($ 1124.20 - $ 1000). In conclusion, the expected yield can be taken to indicate the projected return on bonds after the appropriate holding period has run out and it derives its basis from forecasts made from rate of interest predictions. There exist three bond theorems which are employed in offering explanations in regards to the existing relationships linking the prices of bonds to the changes in the amount of interest rates. The relationship between interest rates and bond prices is vital in the management of not only bond portfolios but also fixed-income securities, which are financial contracts with fixed interest payments until the expiry of the contract’s life. Fixed-income securities include the usual fixed-rate house mortgage loans; government, treasury and corporate bonds; and car loans. How changes in interest rates would affect bond prices The three theorems are Yield and Bond Prices, Maturity and Volatility of Bond Prices, as well as Coupon Rate and Volatility of Bond Prices. Yield and bond prices The relationship between the prices of bonds and yields is an inverse one (Alliance Consulting, n.d ). As the market yield, or interest rate, increases, the market price of a bond drops; as the market yield, or interest rate, decreases, the market price of a bond increases (Ireland, n.d; Federal Accounting Standards Advisory Board, n.d). The existence of this inverse association is attributed to the fact that the rate of interest or the coupon on a bond is usually fixed at the point in time when the bond is being issued. When there is an increase in the market rate of interest, it is important to reduce the price of the bond with the intention of increasing the yield on a bond to be equivalent to the market interest rate. In this situation, the investor of this bond receives an extra interest given in the form of capital gain. In the similar manner, a reduction in the market rates of interest leads to an increase in the price of bonds so as to reduce the yield of the bond to the market rate. It is worth noting that this inverse correlation in not limited to bonds only, but has applications in all financial contracts that have fixed interest rates payments till maturity of the contract. Maturity and Volatility of Bond Prices This relationship is affected by the mathematics applied in the present value formulae. In particular, short-term bonds experience less volatility in prices of bonds than long-term bonds, in case other characteristics of the bond are held constant (Sill, 1996). Consequently, short-term bonds have lower rate of interest risk than equivalent but long-terms bonds have (Houweling, Mentink & Vorst, 2003; Federal Accounting Standards Advisory Board, n.d). The volatility in bond prices is defined as the change in the prices of bonds for a particular yield change or change in the rates of interest (ABC, n.d). It is usually measured in percentages. Sill (1996) notes that the volatility in bond prices is an assessment of the sensitivity of the price of a bond to the changes in the rates of interest. The price volatility is calculated using the formula below. % ΔPB =  * 100 Where % ΔPB is the percentage price change  is the final price after time t is the price just before the new price An example to illustrate this is as follows: A bond is being sold at par and has an eight (8) % annual coupon. Assume that the market interest rates on equivalent bonds rise by 25 basis points (1 bps = 1 %) to reach 8.25 %. There is a decrease of $ 16.59 in the bond price, which declines from 1000 dollars to 983.41 dollars. Using the above equation, the volatility in bond prices is found to be:  * 100 = - 1.66 % Coupon Rate and Volatility of Bond Prices The coupon rate also poses a significant amount of influence on the volatility of bond prices. In particular, a reduction in the coupon rate leads to an increase in the percentage change in bond prices for a particular amount of change in interest rate. Several examples have been provided in a number of texts to prove that lesser coupon rate bonds usually exhibits a higher percentage change in price (the bond’s volatility in price) for a particular change in the market rate of interest and consequently, increase the levels of the rate of interest risk (Federal Accounting Standards Advisory Board, n.d). Price – yield reports, which are plots of price of bonds against market rate of interest, are some examples of profiles that show the effect that coupon rates have on the volatility of bond prices (ABC, n.d). References ABC. (n.d). How do interest rate changes affect bond prices? Retrieved from: http://www.abcsofinvesting.net/how-do-interest-rate-changes-affect-bond-prices/ Alliance Consulting. (n.d). Bond yields & duration analysis. Retrieved from: http://www.waifem-cbp.org/v2/dloads/BOND%20YIELDS-DURATION.pdf Barry, N. (2009). How bond market pricing works. Retrieved from: http://www.investopedia.com/articles/bonds/07/pricing_conventions.asp Federal Accounting Standards Advisory Board. (n.d). The need for market valuation of your portfolio. Retrieved from: www.treasurydirect.gov/govt/apps/fip/.../dfimarket_valuations_duration.ppt Houweling, P., Mentink, A., & Vorst, T. (2003). How to measure corporate bond liquidity? Discussion paper. Rotterdam: Tinbergen Institute. Ireland, P. N. (n.d). Understanding interest rates. Lecture notes on money, banking, and financial markets. Retrieved from https://www2.bc.edu/~irelandp/ec261/chapter4.pdf Sill, K. (January-February, 1996). The cyclical volatility of interest rates. Federal Reserve Bank of Philadelphia Business Review. Read More