Measuring the Sensitivity of a Bonds Price to Changes in the Market Interest Rates - Essay Example

? MEASURING THE SENSITIVITY OF A BOND’S PRICE TO CHANGES IN THE MARKET INTEREST RATES ------------ ------------ ------------ Course: ------------ Date: ------------ A bond is a long term debt issued by government or firms to individuals that yields returns known as coupons on the principal value. It is a security issued to the public as a source of funds to the government or firms. If bonds are issued by the government, then the funds realized are used in provision of public goods. But the most important reason why governments issue bonds is to use the funds to carry out the fiscal policies in case the economy is in any kind of a macroeconomic problem. On the other hand, bonds issued by companies are used for long term financing of the firm since they mature after a long period of time, usually more than ten years. Coupons are mostly paid out twice in a year but some could be payable once in a year. On maturity of a given bond, the bondholders are entitled to the principal amount initially invested at the present value at maturity. A bond may be issued at a discount or at a premium. If it is issued at a discount, the amount realized from such an issue is less than the face value of the bond. This occurs mostly when the interest rates of the bonds are low; therefore the government or the firms have to induce investors to invest in such a bond by lowering the prices of the bonds. On the other hand, if the amounts of funds realized from a bond issue are more than the face value of the bond, the bond is said to have been issued at a premium. This mostly occurs when the rates of return of the bond in question are relatively high and the bond is expected to yield some high returns in terms of the coupons. Investors will take into account the high amount of returns expected in the future and many will be interested in buying the bonds. These investors will be willing to pay a higher price for the bond, higher than the bonds face value. A bond’s price will change with changes in the market interest rate. There are different reasons for the changes in price. One of the most significant reasons is the fact that increase in market price denotes a higher rate of return on a given bond. Investors will inject their funds in an investment that has potential of yielding maximum returns for them. Given that they are rational individuals, the investors will rank a bond with a high rate of return at a higher position in their priorities of investment. This will drive the price of the bond up since the demand for it has gone up. This leads to the bond being issued at high price. The sensitivity of a bond’s price to interest rate movements is dependent on the bonds characteristics (Madura 2001). This is clearly the case since there are many kinds of bonds and each of them exhibit different unique characteristics according to its nature. Some of these unique characteristics are the different maturity periods. Some bonds mature after only ten years while others might mature at thirty years. The frequencies at which bonds pay out coupons also differ accordingly. The convex relationship between bond price and yield illustrates that the changes in prices for a given change in interest rates is not constant and nor is it identical, for all but very small amounts, for both upward and downward change in yields (Cima 2000). The two common methods of assessing the sensitivity of a bond to a change in the required rate of return on bonds are: Bond price elasticity Duration The above methods are computed as follows: 1. Bond price elasticity The sensitivity of bond prices to changes in the required rate of return is commonly measured by the bond price elasticity (Madura 2001). The computation is given as follows; Pc = percentage change in p / percentage change in k where; Pc is the bond price elasticity P is the bond price K is the required rate of return This method is significant especially when measuring the sensitivity of a bonds price on the market interest rate over a given period of time. There exists an inverse relationship between interest rate movements and bond price movements (Madura 2001). This implies that as interest rates increases in the bond market, the prices of these bonds tend to be dropping or decreasing. The most probable explanation of the above phenomenon is the situation that would prevail in cases of high interest rates. As investors and the general public realize that the required rate of return on bonds is increasing, they would be willing to buy the bonds at all costs. This increase of interest in investing in bonds will increase the demand for bonds. Due to market forces, the prices of these bonds will have to fall so that the market clears. This results to declining bond prices and hence the inverse relationship of bond prices to the market interest rates. 2. Duration Madura (2001, p.185) observes that an alternative measure of bond price sensitivity is the bond’s duration which is a measurement of the life of the bond on a present value basis. According to him, the longer a bond’s duration is, the greater its sensitivity to interest rate changes. The common measure used in this method (DUR) is given below: DUR: dG /G=-D*dy + 1/2C (dy) 2; where D* = - (1/G) dG/dy; and C=dD*/dy D* is the governments securities modified duration. C is the governments securities modified convexity. The duration gap of a net portfolio value is a measure of the interest rate sensitivity of a portfolio of financial instruments and is the difference between the weighted-average duration of assets and liabilities adjusted for the net duration of any off-balance sheet instruments (Choudhry 2001). First, we use a duration/ convexity method to estimate the government’s portfolio interest rate risk and from the price-yield relationship of bonds, this method estimates bond price changes for a change in yields (Amadou 2005). Amadou also points out that the duration of a bond is a linear approximation of a bond price change. He also agrees to the fact that the longer the duration of a bond-measured in years- the more interest sensitive it is. In some economies, the policy makers of a country will respond to the various business cycles in the economy, thereby influencing the level of returns on a bond and also generally the level of the market interest rates. In this case, investors will try and use different economic indicators to forecast the levels of yields on bonds according to the business cycle and anticipate how these yields are going to change over time. When the rates are set by policy makers, they directly influence those rates that are short term in nature but will have a much insignificant effect on those yields that are expected over a long period of time. The above information can be represented on yields curve as shown below: Source: BondSquack The shape of the above curve indicates that as funds increases in the short run, the short run interest rates are seen to rise more than those long term interest rates. This results to the flattening of the yields curve as shown above. Another way that can be used to measure the sensitivity of a bond’s price to changes in the market interest rate is what the investors call the measure of DV01. This measure is used to the change in price experienced by a bond when interest rates change by a single basis point. An illustration of the use of measure DV01 is as follows: for instance if the DV01 of a given two year bond is $0.0515, and at the same time, the DV01 of another thirty year bond is given as $0.1919, the hedge ratio of the two bonds will be given as 0.1919/0.0215, or 8.9256 to 1.  For each $1,000,000 position the investor takes during the thirty year period, he will assume an opposing position of $8,925,600 in the two-year.  As the interest rates change with time, the investor will calculate time and again the DV01 of every bond and readjust the various positions according to the steps indicated above. Models exhibit different levels of sensitivity to changes in market prices and rates (Choudhry 2001). This indicates that the different models used to measure the sensitivity of bonds to the changes in interest rates can be used efficiently to determine the extent of the sensitivity of bonds. Some of the other factors that can affect the price sensitivity are: The lower the coupon on a bond, the more sensitive it is to changes in market interest rates-the bigger its percentage price change for a given change in yield (Choudhry 2009). If a certain bond offers relatively lower coupon payments to bondholders, it is likely to respond to changes in the market interest rates with a higher magnitude than one that pays higher coupon payments. The interest rate environment also affects the price sensitivity on a bond. Choudhry also states that in a low interest rate environment, a given change in yield produces a larger change in the price of a bond than in a high interest rate environment. Conclusively, we can say that there are several factors that affect price sensitivity to changes in market interest rates as discussed above. The various ways of measuring this sensitivity are also clearly stated above and all of them will help investors or other interested parties in decision making on whether to invest in short term bonds or long term bonds according to the existing variables and conditions of market interest rate. References Chisholm, A 2002, An introduction to capital markets products, strategies, participants, J. Wiley, New York. Chisholm, A 2009, An introduction to international capital markets: products, strategies, participants, 2nd edn, John Wiley & Sons, Chichester. Choudhry, M 2001, The bond and money markets: strategy, trading, analysis, Butterworth-Heinemann, Boston. Cima, 2000, Management Accounting Information Strategy Beyond 2000 Pilot Paper, Elsevier, Washington D.C. Madura, J 2001, Financial markets and institutions, 5th edn, South-Western College Publishers, Australia. Amadou, S.R 2005, Managing the interest rate risk of Indian banks' government securities holdings, International Monetary Fund, Monetary and Financial Systems Department, Washington, D.C. Read More