The Concept of Bond Duration - Assignment Example

 The Concept of Bond Duration The concept of duration is widely applied in the financial and investment sectors for bond analysis, determining interest rates among other applications. This discourse tends to explain or simplify two basic duration concepts. It provides different concepts for students with strong and weak mathematical understanding. It employs the principle of the dynamic or shifting of the flagpole’s center of gravity (physical metaphor) to explain the principles of bond duration, to students with weaker mathematical understanding. However, those with good mathematical understanding are made to understand the concepts behind bond duration through some proven mathematical formula, and this imply the correlation between changes in the bond values and the fluctuations in the interest rates. There are two basic applications of the duration principles and these greatly vary with the kind of risk involved as well as the investment strategy put in place. Duration could be used as a measure of bond values persistent investors or those willing to take deadly business risks. Such investors are known to embrace active business strategies and benefit from the anticipated alterations or fluctuations in the interest rates due to changes in the bond durations. However, for non risk takers, duration act as a tool of protecting bond values from certain fluctuations due to fluctuations in the interest rates. Bond protection in this case is kind of a assurance that the bond value is likely to remain stable irrespective of changes in the prevailing interest rates, hence it encourage investors to buy certain bonds as they are not scared of changes in interest rates. Majority of financial analysts assumes that the graph of bond prices verses interest rates is flat, meaning there is major effects of fluctuations in the interest rates on bond prices, and this is not correct as various mathematical formulas can be employed to certify this. However, this can only be understood with students with mathematical trainings. Flag pole as physical metaphor to explain the concept of duration This is used to explain the concept of duration as it applies in the changes in bond prices. It does not involve the applications of complex mathematical or financial formula hence appropriate for students with shallow mathematical understanding. This method applies the basic mechanical principles to verify the relationship between duration and changes or fluctuations in bond prices. Various sketches of a flagpole could be used to give different visuals to represent the differences in bond durations, which is also associated to the changes in center of gravity of various physical objects (flagpoles). Each object has a single center of gravity, and the same principle is applied to explain the single accumulation of bonds’ value after certain duration. Stable objects tend to have a lower center of gravity and the same applies to stable bonds or rather those with stable values which tend to have a shorter duration. This concept could also be explained using Macaulay duration formulae which is weighted average of maturity bond , attained from this formula = [ΣtCFt/(1+k)t]/ ΣCFt/(1+k)t , where D is the Macaulay duration, t is time period in months or years, n is the maturity periods, K is the prevailing market interest rates, CF is the cash flow. The formula is an indication that bond duration is subject of four basic factors namely; bond maturity (n), coupon size (C), value of each bond (M) and the prevailing interest rates in the market (k). However, changes in M are usually not included in the analysis in major occasions. The above formula would work well with students with different majors in mathematics or those with deep mathematical understanding. For students with poor mathematical understanding, the concepts of bond durations could be demonstrated using various images of flagpoles. Bond maturity could be represented with the length of the flagpole; the flagpole diameter represents the annual coupon and the bond’s par value is represented with the spherical head of the pole. The effect on changes on market interest rates on bond values can be indicated with decrease in the flagpole diameter as from the base to the pole end. The figure below indicates that after some time which is portrayed by the length of the flagpole, duration concepts depend on the center of gravity of the pole. Just as the duration depends on the prevailing market interest rate, coupon and maturity, the same applies with relationship between the center of gravity, diameter, length as well as the shape of the pole. The center of gravity of the flagpole tends to shift to the base as the pole becomes: longer, thinner and less conical. With the same concept, the bond’s duration becomes longer as its maturity lengthens, as coupon rates reduces and finally market interest rates reduces. Figure two represents two flagpoles with different lengths. Suppose the first bond has duration of 10 periods while the second has duration of twenty periods. From Macaulay equation, the 20 period duration is the greatest among the two. The longer pole is less stable compared to the shorter one, hence bonds with the highest duration has the most dynamic, or unstable bond prices. The third figure represents two different flagpoles with different diameter (coupon). The narrow flagpole represent bond with lowest coupon, and from Macaulay equation, bond D is greater than C. Using the flagpole concept, pole D is less stable as its center of gravity is away from the base. The final figure represents tow poles with different shapes. The upper pole tends to become sharper at a high rate (higher interest rates) compared to the second pole which represents low interest rates. The two poles represent different discounts on future coupons. The pole with a bigger head tends to shift its center of gravity away from its base, making it less stable. While that with a narrow head or high interest rate tends to shift the center of gravity towards its base, making it more stable. Calculating bond prices changes For bonds with low interest rates, Macaulay formula changes to ΔP/P = - D* (Δk) and here, D* = D/ (1 + k), is the modified value of Macaulay duration. As k becomes greater, D reduces or rather approaches zero. However, for k with greater values, the principle of convexity is introduced and the equation changes to [Σt (t + 1) CFt/ (1+k)t+2]/ ΣCFt/(1+k)t, all variables is discussed above. Conclusion Both the physical metaphor and the mathematical calculations have proven to be helpful among students without mathematical understanding and those with mathematical majors respectively. The physical metaphors applies the shifting of the center of gravity to define the stability of certain flagpole while the mathematical calculations use numerical variables to a certain the exact value of bond durations. The physical metaphor variables include the length, thickness and the shape of the head of the pole while the mathematical variables include coupon, prevailing interest rates and bond durations. Figure 1 Figure 2 A B C D FIGURE 3 E F FIGURE 4 Work cited Wilbratte Barry and Shirvani Hassan. "Two Pedagogical Simplifications of the Concept of Duration." JOURNAL OF ECONOMICS AND FINANCE EDUCATION (2002): 18-23. Read More