How Changes in Interest Rates Would Affect Bond Prices - Example

Explain how changes in interest rates would affect bond prices Your name:   Course name:         Professors’ name: Date: Introduction Bonds play a vital role in an investor portfolio. However, bonds are susceptible to economic changes that can affect their value. An investor with bonds is able to reduce his or her overall risk through diversifying his or her holdings. The biggest threat to bonds yield is raising interest rates. Before investing in the stock market, people need to understand the fundamentals- including the rewards and potential risks. When bonds are compared to shares, they sit at the middle to lower end of the risk spectrum; cash is seen as a lower risk investment than bonds (Amihud, 2002). The price of bond may go up and down in response to two factors: change in credit quality and interest rates. Investors in bond market tend to worry about the safety of their investment. Many Australians who have invested in bonds do not comprehend how a change in the interest rate will have an effect on the bond price (Ripley, 1997). Since early 1980s, interest rates have been widely used to determine return on bond investments. The paper will use practical worked numerical examples to explain how changes in interest rates would affect bond prices. Bond Yield For an investor, bond yield is the anticipated return on investment, the yield is usually expressed as a yearly percentage. For example, a 7 % bond yield means that the investment on the bond average 7% per every year. There are many ways in which bond yields can be calculated, but whichever way bond yields are calculated, the relationship between bond yields and price remains constants: Rule # 1: the price of bond is opposite to the interest rates (Park and Reinganum, 1986). In other words, if the interest rate of a bond is increased the bond value will decline, and if the interest rate is failing the bond value will increase. Change in interest rates is always the largest factor in the total return performance calculation of a bond yield. There are three measures of yield used in bond markets: current yield, Current Yield The current yield is mostly associated with bonds and represents the interest rate of a bond security (Amihud, 2002). The current yield is calculated by dividing the yearly interest rates payments by the current bond value or price. By comparing the difference of the current price of the bond and the annual interest, it will help an investor to measure on what to expect in a year’s time (Amihud, 2002). Current yield formula is the simplest way to calculate bond yields: Current yields = (Annual Interest/Current Bond Price) x 100. Current yield is the interest rate that is based on the amount an investor will paid for the bond. A 2,000 dollar bond that is bought at par its value receiving 6 per cent interest would earn a current yield of 6 per cent. If an investors plans to buy this bond at a price that is lower or higher than par price, the current bond yield will differ (Ripley, 1997). For example, if an investor bought the bond of 2000 dollars with an interest rate of 6 per cent for 1,800 dollars, the investor will be required to pay less than par price and buy the bond at a discount. Therefore, the yield of that investor will be higher than the straight interest rate pegged at 6.67 percent instead of the actual interest rate which stand at 6 per cent. The bond yield is calculated as follows: = 2,000 dollars x 0.06 (the stated interest rate) = 120 (the annual interest payment). the amount an investor would paid for the bond= 120/ 1,800 = 6.7 % current yield. An investor is able to closely monitor the current bond yield when looking at the position of the bond within one year (O'Hara, 2012). In the example given above, if an investor was to buy the bond, he will receive 7.83 dollars from investing in the bond. When the investor received dividend from the bond, the gain the investor will receive will depend on the bond price at the end of the year. Let make assumption that the interest rate fell and the bond’s price increased to 114.50 dollars when an investor wanted to close the position. The actual rate of return for the bond would be 3.6 per cent (4.05/110.45 dollars). Yield to maturity (YTM) YTM is the rate of return that a person would earn if he purchased a bond at its current market value and held it until the bond matures. YTM measures the yearly return until the bond matures. This can be demonstrated by the following equation: Yield to maturity for a bond measures the yearly return a person receives if he waited until the bond reach the maturity period. In order to understand yield to maturity, a person must first know that bond price is equal to the present bond value of its future cash flows. This formula is stated as:  Where: P = bond price C = the yearly coupon payment F = maturity value r = required rate of return on this investment t = the number of years remaining until maturity. The above formula is based on the current value or price on the market, and is used to calculate the effectiveness of a bond (Park and Reinganum, 1986). For example, the price of a bond is 920 dollars and its face value is set to 1000 dollars. The assumption in this example is that the annual bond value or price is at 100 dollars with 10 % interest rate, and the maturity date is in 10 year time.  Approx YTM =11.25 % The maturity yield is estimated to be at 11.25 %. However, if the interest rate is used as “r” in the bond yield formula, the present price of the bond will be 927.15 dollars which is near to the present bond value or price, of 920 dollars. Another example is that, a higher bond yield to maturity is seen to have a lower value of a bond (Park and Reinganum, 1986). In the example given above, the estimated bond yield to maturity show a purchase price of 927.15 dollars and this is higher than actual purchase price, at 920 dollars. Equivalent taxable yield (ETY) ETY is the return on bond that is required on a taxable investment to make it equal to the return on a tax-exempt investment (Temal, 2001). ETY is commonly used when municipal bond returns are being evaluated. The formula that is used to in ETY is: R(te) = R(tf)/(1- t)     Where: t= investor's marginal tax rate R (tf) = return on tax-free investment R (te) = taxable equivalent yield for the investor For example, a person who belong to a tax bracket of 28%, has made up his mind whether to invest municipal bond that has a 10 per cent interest rate or not. When using the formula stated above, the taxable municipal bond will be: R(te) = 0.10 / (1 - 0.28) In this example, in order for an investor to get a higher return, the taxable interest rate should be more than 13. 8%. In order for an investor to invest in a municipal bond (Ripley, 1997). A tax-free municipal bond can have an impact on an investor’s overall investment returns, especially if the investor is found a high tax bracket (Park and Reinganum, 1986). For example, let assume an investor has a marginal tax rate of 20% , and the investor has not made up his mind whether to go ahead and invest in a 10% municipal bond. ETY of this investor can be calculated as follows: R (te) = 0.10 / (1 - 0.20)     R (te) = 0.125 = 12.5% In the first example, it is viable to invest in a bond if taxable return is more than 13.89% more than the tax free bond offered by the municipality. But in the second example, in which an investor is found in a lower tax bracket, this investor must earn more than 12.5% from the taxable bond in order the bond yield to be favorable than the same 10 % municipal bond (Temal, 2001). In another example, a person has not yet decided whether to invest in a 4.5% tax-free yield or a 5 % taxable yield. Let assume the person is found in a 28% tax bracket. The person would be first be forced to calculate the ETY so that he can be in a position to choose which between the two has high returns. By using the formula above: 4.50 ÷ (1 – .28) 4.50 ÷0 .72 6.25% tax-equivalent yield So, the results of this calculation tells us is that a person in a 28 per cent tax bracket needs to find a fixed income investment that will yield for him at least 6.25 per cent before tax in order to get the same after-tax yield of a 4.50% tax-free. Conclusion Rapid economic growth can lead to inflation, thereby provoking the government to tighten its monetary policy by increasing its interest rates (Temal, 2001). From the discussion, such a policy will erode a bond’s value. We have seen bonds with longer maturity time are more risky than bonds with shorter maturity time (O'Hara, 2012). Therefore, an investor needs to understand how bond price may be influenced by such economic cycles. But regardless of the direction of interest rates on a bond, an investor should consider bond portfolio that have maturity time that is less than five years. References Amihud, Yakov, 2002, Illiquidity and stock returns: cross-section and time-series effects, Journal of Financial Markets 5, 31-56. Houweling, Patrick, Mentink, Albert, and Vorst Ton, 2005, Comparing possible proxies of corporate bond liquidity, Journal of Banking & Finance 29, 1331-1358 Park, S.-Y. and M. Reinganum, 1986, “The Puzzling Price Behavior of Treasury Bills that Mature at the End of Calendar Months,” Journal of Financial Economics, 16, 267-283. Ripley, William, 1997, Railroads: Finance & Organization. New York: Longmans, Green, & Co.. pp. 106–107. Temal, J. Wesalo, 2001, The Fundamentals of Municipal Bonds: The Bond Market Association. John Wiley and Sons, Inc.. p. 49 O'Hara, Neil, 2012, The Fundamentals of Municipal Bonds. Hoboken, NJ: John Wiley & Sons, Read More