Does Macaulay Duration Provide The Most Cost-Effective Immunization Method – A Theoretical Approach
In the following, we offer a theoretical approach that attempts to explain (Comments 1-3) why and when the Macaulay duration concept happens to be a good approximation of a bond’s price sensitivity. We are concerned with the basic immunization problem with a single liability to be discharged at a fu...
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| Format: | Article |
| Language: | English |
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Sciendo
2017-02-01
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| Series: | Foundations of Management |
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| Online Access: | https://doi.org/10.1515/fman-2017-0008 |
| _version_ | 1818583534361640960 |
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| author | Zaremba Leszek |
| author_facet | Zaremba Leszek |
| author_sort | Zaremba Leszek |
| collection | DOAJ |
| description | In the following, we offer a theoretical approach that attempts to explain (Comments 1-3) why and when the Macaulay duration concept happens to be a good approximation of a bond’s price sensitivity. We are concerned with the basic immunization problem with a single liability to be discharged at a future time q. Our idea is to divide the class K of all shifts a(t) of a term structure of interest rates s(t) into many classes and then to find a sufficient and necessary condition a given bond portfolio, dependent on a class of shifts, must satisfy to secure immunization at time q against all shifts a(t) from that class. For this purpose, we introduce the notions of dedicated duration and dedicated convexity. For each class of shifts, we show how to choose from a bond market under consideration a portfolio with maximal dedicated convexity among all immunizing portfolios. We demonstrate that the portfolio yields the maximal unanticipated rate of return and appears to be uniquely determined as a barbell strategy (portfolio) built up with 2 zero-coupon bearing bonds with maximal and respective minimal dedicated durations. Finally, an open problem addressed to researchers performing empirical studies is formulated. |
| first_indexed | 2024-12-16T08:06:48Z |
| format | Article |
| id | doaj.art-90d692e351b44872a815d2806c54fdab |
| institution | Directory Open Access Journal |
| issn | 2300-5661 |
| language | English |
| last_indexed | 2024-12-16T08:06:48Z |
| publishDate | 2017-02-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Foundations of Management |
| spelling | doaj.art-90d692e351b44872a815d2806c54fdab2022-12-21T22:38:27ZengSciendoFoundations of Management2300-56612017-02-01919911010.1515/fman-2017-0008fman-2017-0008Does Macaulay Duration Provide The Most Cost-Effective Immunization Method – A Theoretical ApproachZaremba Leszek0Academy of Finance and Business Vistula, Institute of Finance, Warsaw, PolandIn the following, we offer a theoretical approach that attempts to explain (Comments 1-3) why and when the Macaulay duration concept happens to be a good approximation of a bond’s price sensitivity. We are concerned with the basic immunization problem with a single liability to be discharged at a future time q. Our idea is to divide the class K of all shifts a(t) of a term structure of interest rates s(t) into many classes and then to find a sufficient and necessary condition a given bond portfolio, dependent on a class of shifts, must satisfy to secure immunization at time q against all shifts a(t) from that class. For this purpose, we introduce the notions of dedicated duration and dedicated convexity. For each class of shifts, we show how to choose from a bond market under consideration a portfolio with maximal dedicated convexity among all immunizing portfolios. We demonstrate that the portfolio yields the maximal unanticipated rate of return and appears to be uniquely determined as a barbell strategy (portfolio) built up with 2 zero-coupon bearing bonds with maximal and respective minimal dedicated durations. Finally, an open problem addressed to researchers performing empirical studies is formulated.https://doi.org/10.1515/fman-2017-0008barbell strategyconvexitydedicated durationmacaulay durationunanticipated rate of return |
| spellingShingle | Zaremba Leszek Does Macaulay Duration Provide The Most Cost-Effective Immunization Method – A Theoretical Approach Foundations of Management barbell strategy convexity dedicated duration macaulay duration unanticipated rate of return |
| title | Does Macaulay Duration Provide The Most Cost-Effective Immunization Method – A Theoretical Approach |
| title_full | Does Macaulay Duration Provide The Most Cost-Effective Immunization Method – A Theoretical Approach |
| title_fullStr | Does Macaulay Duration Provide The Most Cost-Effective Immunization Method – A Theoretical Approach |
| title_full_unstemmed | Does Macaulay Duration Provide The Most Cost-Effective Immunization Method – A Theoretical Approach |
| title_short | Does Macaulay Duration Provide The Most Cost-Effective Immunization Method – A Theoretical Approach |
| title_sort | does macaulay duration provide the most cost effective immunization method a theoretical approach |
| topic | barbell strategy convexity dedicated duration macaulay duration unanticipated rate of return |
| url | https://doi.org/10.1515/fman-2017-0008 |
| work_keys_str_mv | AT zarembaleszek doesmacaulaydurationprovidethemostcosteffectiveimmunizationmethodatheoreticalapproach |