Duration and Bond Investment Management - Essay Example

?Duration and Bond Investment Management Task Duration is the concept that is used to demonstrate and quantify the element of risk present in fixed-income securities. There are numerous kinds of fixed-income securities, different in nature due to their coupon rate, yields, prices, maturities, etc. It becomes a complex task to compare the risk of one specific kind of bond with the other. Under these situations, the duration is the technique which provides a parameter to compare the risk of fixed-income securities having different maturities. According to the concept of duration, the longer the maturity of a fixed-income security, the greater will be the amount of volatility present in that security in case of a given change in the yield of that security. From this point, bond portfolios can be restructured in a systematic manner outlined as under: In the events when interest rates are expected to decrease, it would be advisable to restructure the bond portfolios drifting towards securities constituting long-term maturities. This will allow the portfolios to earn maximum capital gain because there is a stronger likelihood that the price of the bonds having long maturities are expected to increase by a greater amount than that of bonds having short maturities in case of a decrease in the yields. Conversely, in the events of an increase in the interest rates, it would be advisable to restructure the bonds portfolios drifting towards short-term securities as it may likely to result in decreasing the capital losses from a decrease in the prices of long-term maturities compared to the increase in the prices of securities having short-term maturities. Task 2 Clean Prices of Bonds Task 3 Estimation of Expected Yields after 1Year E (y1(2)) = 0.23% + 0.1(3.10% - 0.23%) = 0.52% E (y1(5)) = 0.85% + 0.1(3.61% -0.85%) = 1.13% E (y1(10)) = 2.03% + 0.1(3.99% - 2.03%) =2.23% E (y1(20)) = 3.19% + 0.1(4.17% - 3.19%) = 3.29% Estimation of Expected Yields after 2Years E (y2(2)) = 0.52% + 0.1(3.10% - 0.52%) = 0.78% E (y2(5)) = 1.13% + 0.1(3.61% - 1.13%) = 1.37% E (y2(10)) = 2.23% + 0.1(3.99% - 2.23%) =2.40% E (y2(20)) = 3.29% + 0.1(4.17% - 3.29%) = 3.38% Task 4 Impact of the estimated yield changes on the market prices of the four bonds Price of Bond 1 (2yr) after 1 year Price of Bond 2 (5yr) after 1 year Price of Bond 3 (10yr) after 1 year Price of Bond 4 (20yr) after 1 year Price of Bond 1 (2yr) after 2 years Price of Bond 2 (5yr) after 2 years Price of Bond 3 (10yr) after 2 years Price of Bond 4 (20yr) after 2 years Bond Current Price P1 P2 2yr 109.5 104.4599 105 5yr 120.23 115.0694 109.2377 10yr 126.63 122.9504 118.6706 20yr 126.46 123.9087 121.6928 Holding Period Returns Bond 1 (2yr) Return for 1 year: 0.23 - 5.04006 = -4.81 Bond 2 (5yr) Return for 1 year: 0.85 - 5.16058 = -4.31 Bond 3 (10yr) Return for 1 year: 2.03 - 3.67964 = -1.64 Bond 4 (20yr) Return for 1 year: 3.19 - 2.55135 = 0.638 Bond 1 (2yr) Cumulative Return for 2 years: [0.23(1.0113) + 0.23] -4.5 = -4.0374 Bond 2 (5yr) Cumulative Return for 2 years: [0.85(1.0113) + 0.85] -10.99 = -9.2804 Bond 3 (10yr) Cumulative Return for 2 years: [2.03(1.0113) + 2.03] -7.96 = 3.877 Bond 4 (20yr) Cumulative Return for 2 years: [3.19(1.0113) + 3.19] -4.76 = 1.656 Bond 1-year Return 2-year Return 2yr -4.81 -4.0374 5yr -4.31 -9.2804 10yr -1.64 3.877 20yr 0.638 1.656 Task 5 Holding period return is considered as quite significant because the period covering this return pertains to the time horizon for which the investment is to be held in the portfolio. In the light of the holding period returns generated for the four bonds, it can be closely observed that if the time horizon is kept as 1 year, securities having short-term maturities, are unable to provide any returns, rather they are incurring losses. Only 20-year bond is providing the holding period return of 0.638 while rest of the other three securities, are in negative zone. On the other hand, if the 2-year time horizon for holding the securities in the portfolio is taken into consideration, it can be noted that the short-term securities are incurring greater losses such that the 5-year bond’s losses are increased to more than double in just 2-year time. The 2-year bond is however reached to its maturity, therefore its losses are reduced marginally which can be ignored. The longer maturity securities have shown a decent performance in 2-year time horizon such that both the 10-year and 20-year bonds have provided the cumulative returns of 3.877 and 1.656 respectively. From the above analysis, there are few implications that should be accounted for such that the shorter the maturity of the securities, the greater the losses and volatility of the securities. The longer the maturity of the securities, the narrower will be the returns and lesser will be volatilities. This shows that the portfolio of recent UK government bonds should be constituted and restructured in such a manner that it must contain fewer amount of securities having short-term maturities and there should be more number of long-term maturities as they provide although narrow returns but are less volatile to the risk of interest rate changes. It is advisable to focus more on the long-term maturity securities over short-term securities, especially if the holding period is kept for a shorter tenure. Task 6 Estimation of Expected Yields after 1Year E (y1(2)) = 0.23% + 0.5(3.10% - 0.23%) = 1.665% E (y1(5)) = 0.85% + 0.5(3.61% -0.85%) = 2.23% E (y1(10)) = 2.03% + 0.5(3.99% - 2.03%) = 3.01% E (y1(20)) = 3.19% + 0.5(4.17% - 3.19%) = 3.68% Estimation of Expected Yields after 2Years E (y2(2)) = 1.67% + 0.5(3.10% - 1.67%) = 2.38% E (y2(5)) = 2.23% + 0.5(3.61% - 2.23%) = 2.92% E (y2(10)) = 3.01% + 0.5(3.99% - 3.01%) =3.50% E (y2(20)) = 3.68% + 0.5(4.17% - 3.68%) = 3.93% Impact of the estimated yield changes on the market prices of the four bonds Price of Bond 1 (2yr) after 1 year Price of Bond 2 (5yr) after 1 year Price of Bond 3 (10yr) after 1 year Price of Bond 4 (20yr) after 1 year Price of Bond 1 (2yr) after 2 years Price of Bond 2 (5yr) after 2 years Price of Bond 3 (10yr) after 2 years Price of Bond 4 (20yr) after 2 years Bond Current P1 P2 2yr 109.5 103.2804 105 5yr 120.23 110.4888 103.2901 10yr 126.63 115.4871 110.3109 20yr 126.46 117.8177 113.7472 Holding Period Returns Bond 1 (2yr) Return for 1 year: 1.665 – 6.2197 = -4.5547 Bond 2 (5yr) Return for 1 year: 2.23 – 9.7412 = -11.9712 Bond 3 (10yr) Return for 1 year: 3.01 – 11.1429 = -8.1329 Bond 4 (20yr) Return for 1 year: 3.68 – 8.6422 = -4.9622 Bond 1 (2yr) Cumulative Return for 2 years: [1.665(1.0223) + 1.665] -4.5 = -1.13287 Bond 2 (5yr) Cumulative Return for 2 years: [2.23(1.0223) + 2.23] -16.94 = -12.4303 Bond 3 (10yr) Cumulative Return for 2 years: [3.01(1.0223) + 3.01] -16.32 = -10.2329 Bond 4 (20yr) Cumulative Return for 2 years: [3.68(1.0223) + 3.68] -12.71 = -5.2679 Bond 1-year Return 2-year Return 2yr -4.5547 -1.13287 5yr -11.9712 -12.4303 10yr -8.1329 -10.2329 20yr -4.9622 -5.2679 The above table produced highlights the holding period returns of the four bonds in the event when theta is increased from 0.1 to 0.5. From these values, it can be very well observed that all the bonds have generated negative returns in the holding period of 2 years. As the securities are moving from short-term to long-term, it can be clearly seen that the magnitude of the negative return is becoming smaller showing that the losses are on a decreasing trend with the increasing maturity. Interesting thing that can be noted over here is that 1-year losses are less than 2-year losses due to a significant increase in the value of theta. This shows that as the expectation of rising interest rates, becomes stronger, it tends to decrease the losses especially if the holding periods of the securities are increased. Conclusion From the above calculations and workings for holding period returns, there are some basic implications which must be taken into consideration while restructuring a bond portfolio guided as under: The maturity of the securities plays a significant role in establishing the holding period returns such that the securities having short-term maturities tend to forward more losses as compared to the ones having longer maturities given a level of interest rate. In the events when there is a greater expectation of increasing interest rates (higher value of theta), the cumulative losses tend to increase as the holding periods increase but with a decreasing rate. It means that after two or three holding periods, the securities may start providing positive returns once they cross the negative zone swiftly. References Barnhill, T.M., Maxwell, W.F. and Shenkman, M.R. 1999. High Yield Bonds: Market Structure, Portfolio Management, and Credit Risk Modeling, Washington: McGraw Hill Professional. Dynkin, L. .2007. Quantitative management of bond portfolios, California: Princeton University Press. Fabozzi, F. J., 2001. Bond Portfolio Management. 2nd ed. New York: John Wiley & Sons. Fabozzi, F.J. and Mann, S.V. 2011. The Handbook of Fixed Income Securities, 8th edn., Washington: McGraw Hill Professional. Fabozzi, F.J., Martellini, L. and Priaulet, P. 2006. Advanced Bond Portfolio Management: Best Practices in Modeling and Strategies, New York: John Wiley & Sons. Read More