Macaulay Duration Research Articles

The mean–variance (in)efficiency of duration‐based immunization

AbstractEmpirical studies report inconclusive assessment of duration‐based immunization, notably showing that more sophisticated strategies do not outperform immunization relying on Macaulay duration. This article provides a mean–variance framework to explain this puzzle. We characterize the efficient portfolio allocations for a stylized barbell strategy trading off reinvestment risk with discounting risk. We show, in a model‐free setting, that barbell allocations form a convex set in the mean–variance space, and the endpoints of the efficient frontier can switch as time passes, reversing the set of efficient allocations. Consequently, duration‐based immunization, which is not minimum variance, can exhibit temporary inefficiency. This result is numerically illustrated in a one‐factor Gaussian and a two‐factor non‐Gaussian model. Using yield curve scenarios resampled from U.S. data over the 1977–2020 period, we further corroborate our conclusions non‐parametrically, and find that duration‐based immunization is sometimes inefficient.

Performance persistence and style consistency of Indian fixed income mutual funds – A longitudinal study

In this study, we evaluate the performance of Indian fixed-income mutual funds using a comprehensive sample over a ten-year period from April 2010 to March 2020. We examine performance persistence of 190 fixed income funds across 16 fund categories and analyze investment style of the most persistent and top performing funds. We assess performance persistence using recursive portfolio formation test, and analyze investment style using Sharpe's (1992) asset class factor model supplemented with Lobosco and diBartolomeo (1997) approach for statistical robustness. We also study the correlation between performance persistence and style consistency and find persistent funds to be less consistent in style. Our findings indicate that a substantial proportion (73%) of the funds considered were under-performers. Our results pertaining to style analysis indicate substantial drift in investment style from regulator-mandated investment objectives. Further, the study nudges regulators to revisit the prevailing practice of fund classification based on Macaulay's duration. In light of the growing prominence of Indian fixed income securities, the findings of this study are all the more pertinent to investors, asset management companies and policy makers.

Assessing the Market Risk on the Government Debt of Kazakhstan and Bulgaria in Conditions of Turbulence

The purpose of this publication is to quantify and compare the market risk on the external government debt of Kazakhstan and Bulgaria in the conditions of COVID-19, the emerging energy crisis, and the coup attempt in the first country. In particular, the authors invest the market risk of sovereign bonds issued on global financial markets. Market risk is assessed both as a single issue and at a portfolio level using the Value-at-risk approach. Sixteen samples with historical observations of all issues of Kazakhstan’s and Bulgarian Sovereign Bonds issued on the international financial markets were formed. The duration method was used in the calculation of Delta normal bond VaR and CVaR. It was found that with the same credit rating, similar portfolio duration levels, similar GDP per capita, Debt (% of GDP), and Debt Per Capita, the market risk on their portfolio differed significantly. The comparison of risk levels between the two portfolios was made by six indicators–two indicators measuring linearly the sensitivity of bond prices to changes in market interest rates (Weighted average Macaulay duration and Weighted average modified duration) and four downside indicators (Undiversified VaR, Diversified VaR, Undiversified CVaR, amd Diversified CVaR). The return/risk performance of both portfolios was assessed by the Sharpe ratio in three variants (SR Undiversified VaR, SR Diversified VaR, and SR Diversified CVaR). When evaluating the bond portfolio VaR and CVaR, a practical version of the Duration method was proposed, which allows the use of an unlimited number of assets, taking into account the correlations between yield returns and historical price volatility.

An Exploratory Pledging Framework of Crowdfunding for Utilities Tunnel Engineering Project

This paper gives an exploratory mathematical framework for crowdfunding pledging of utilities tunnel engineering project. For two typical types of “All-or-Nothing” and “Keep-it-All” platforms, it analyzes the crowdfunding process how to operate on the platforms for the project. There are four types of crowdfunding modes, and a utilities tunnel project can flexibly choose one or several crowdfunding types analyzed in this paper to improve project construction according to the status of the project. Debt crowdfunding should design rational interest payment mechanism and Macaulay duration, and equity crowdfunding should consider the backers may get dividend and capital revenue for a utilities tunnel project. Simulation analyses of debt crowdfunding and equity crowdfunding give some cases for project fulfillment. The founder of reward crowdfunding can give free or low price energy products to the backers, while the backers of donation crowdfunding are completely philanthropic to supply the pledged capital.

INTEREST RATES SENSITIVITY ARBITRAGE – THEORY AND PRACTICAL ASSESMENT FOR FINANCIAL MARKET TRADING

Purpose – Nowadays popular algorithmic trading uses many strategies which are algoritmizable and promise profitability. This research assess if it is possible successfully use interest rates sensitivity arbitrage in bond portfolio (also known as convexity arbitrage) in financial praxis. This arbitrage is sparsely described in literature and an assessment about its practical success is missing. Research methodology – Methodology steps: mathematical definition of given arbitrage; construction of sufficient portfolio; backtesting on USD zero-coupon curves. Portfolio of two bonds is constructed (theoretically and practically) to have the same Macaulay duration and price, but a different convexity at certain YTM point. Therefore, being long the first bond while shorting the second (of higher convexity) would result in a market-directional bet for parallel zero-coupon yield curve shifts. Findings – To construct practically the portfolio which is sufficient for the convexity arbitrage could be unrealistic on markets with low liquidity; the presumptions necessary to practically succeed are not fulfilled enough to ensure the arbitrage is profitable. Research limitations – The backtesting is limited to USD market, testing other markets is recommended, but different result is not expected. Practical implications – The research helps practitioners considering this strategy for its implementation to algorithmic trading. Originality/Value – New important results for financial practitioners; states that practical and profitable utilization of convexity arbitrage is unrealizable and save costs during implementation of the strategy.

Inferring Stock Duration Around FOMC Surprises: Estimates and Implications

AbstractDiscount rates affect stock prices directly via the discount-rate channel or indirectly via the cash-flow channel because expected future cash-flow growth varies with the discount rate. The traditional Macaulay duration captures the effect from the discount-rate channel. I propose a novel duration measure, the effective equity duration, to capture the effects from both channels. I estimate it around unexpected policies in the federal funds rates. I find that the equity yield curve is hump-shaped because expected future cash-flow growth increases with the discount rate. The effective equity duration captures information other than monetary policy risk.

Macaulay’s theory of duration: 80-year thematic bibliometric review of the literature

PurposeThe purpose of this research is to propose a framework for research on Macaulay duration and establish future research directions.Design/methodology/approachThematic, bibliometric and content analyses have been used to review 168 research papers published between 1938 and 2019 taken from ISI Web of Science and Scopus contributed by leading authors, journals and regulatory bodies.FindingsIdentification and integration of themes of duration theory, duration model development and duration model implementation leading to unattended research gaps, and framework for research on Macaulay duration.Research limitations/implicationsThe study is based on an extensive review of the literature to extract important themes, research gaps and frameworks. It does not empirically investigate significance of Macaulay duration and various sectors.Practical implicationsThis research has several aspects that are helpful for practitioners. Macaulay duration has been the subject of empirical research only without any guiding framework. This research provides a platform to initiate profound researches in various areas of finance. Various proposed models are required to be tested under holistic approach in conventional and emerging fields, especially in Islamic settings.Originality/valueThis research highlights, research themes leading to framework, research gaps and factors that are crucial in developing, extending and testing duration models leading to enhancement of theoretical base of Macaulay duration.

Using Expected Geometric Values to Calculate the Cost of Interest in Hyper-inflationary Environments: the Case of Venezuela

It is of vital importance to explore the relationship between pensions and inflationary levels because this forms a link between social policy and economic development in the context of Venezuela’s challenging economy and its impact on the development of pension systems. With such rampant inflation, companies must adjust the rates of salary increases to avoid a significant decrease in the purchasing power of income from defined benefit plans. Our research seeks to find the possibility of using an average geometric rate of future interest rates expressed as an expected value to discount obligations. Consequently, the cost of interest associated with the actuarial liability of the Benefit plans increases substantially in the next fiscal period to the actuarial valuation, sometimes compromising its sustainability over time. In order to minimize this problem, two scenarios for calculating the interest rate are proposed to smooth out this volatile effect; both are based on a geometric average with the expectation of working life or with the duration of the obligations. We are careful to use a reasonable interest rate that is not so high as to compromise the cash flow, resulting in skewed annual results of the companies. Our research seeks to find the possibility of using an average geometric rate of future interest rates expressed as an expected value to discount obligations. We formulate and actuarially evaluate two different scenarios, based on job expectations and Macaulay's duration, of the obligations that allow the sustainability of the plan in an environment of extremely high inflation. To illustrate the impact of the basic annual expenditure of the period, the results of an actuarial valuation of an actual Venezuelan company were utilized. Despite some companies adjusting their book reserves increasingly through a geometric progression, the amounts associated with the costs of interest would be huge in any such adjustment pattern. Therefore, we suggest adoption of one of the alternatives described in the research.

Pricing a Lease Contract in Presence of Late Payment Extra-Charges

Partial insolvency in leasing contracts may entail to afford additional late payment costs. In this paper we focus on the case that the lessee makes partial payments in due time and settles the debt augumented by the late payment interests later. The presence of the extra-costs drives the lease Effective Annual interest Rate (EAR) to deviate from the lease contract rate. The aim of this work is to illustrate how design the contract payback amortization to stick EAR to the lease contract rate, when the lease contract rate, the late payment rate and the contract term are exogeneously fixed. First we achieve a proxy for EAR given by the lease contract rate plus an extra-charge rate addendum. We show that this latter addendum is sensitive to the payback Macaulay Duration, a weighted size and timing average. Specifically, the longer the Macaulay Duration, the smaller the extra-charge rate addendum. As a consequence, two general rules to drive EAR close to the lease contract rate roll out, specifically: (1) the payment pattern should be set with a long Macaulay Duration; and (2) the surrender value of the leased good should be put large. As the contract settlement is given, we show that EAR is delimited by a lower bound and an upper bound. Then the payback amortizations with fixed instalments are studied. To get insight on the importance of EAR inputs we roll sensitivity analysis out through illustrative applications. The results of the paper are useful to provide policymakers a better knowledge about the effects on EAR of the contract conditions on the pattern of payments.

A\xa0duration approach for the measurement of biometric risks in life insurance

Duration concepts are standard methods for measuring interest rate risks of portfolios, liabilities or other cash flows. Macaulay duration, effective duration and key-rate duration are widely used in practice according to different types of yield curves. In this paper, we will present a formulation for a forward rate duration measure by using multi-dimensional Taylor series approximation. It allows to measure the interest rate risk based on arbitrary forward rates. This approach can easily be adopted for biometric risk management, allowing the definition of a biometric duration. The biometric duration will be applied to actuarial present values of premiums and benefits as well as the actuarial reserve to quantify the corresponding biometric risk. It proves to be an easy-to-use tool in the actuarial practise.

Medición de riesgo tasas de interés en las instituciones financieras

El artículo presenta de una manera resumida las metodologías existentes para la medición del riesgo tasa de interés de las instituciones financieras, que se deriva de las operaciones activas6 y pasivas que realizan. Algunas de esas medidas, como la duración de Macaulay y la duración modificada fueron introducidas en 1938 y otras, como el valor en riesgo, se remontan a la introducción del concepto de varianzas y covarianzas, que básicamente tuvo su origen formal en el trabajo pionero de Harry Markowitz. La decisión de qué métrica utilizar depende básicamente de las características de las operaciones que realiza el banco. Por ejemplo, en una institución donde la mayor parte de sus ingresos se generan en la operación de trading se debe utilizar el plazo, la duración y el valor en riesgo como métricas relevantes para estimar el riesgo tasa de interés. Por el contrario, en los bancos donde los ingresos netos provienen de las operaciones de crédito y de la captación minorista y mayorista, las medidas más apropiadas deben ser el GAP de tasas de interés o de repreciación y el GAP del capital del banco

Количественная оценка процентного риска портфеля облигаций

This article considers the sensitivity to interest rates changes of market value of the bonds. In order to address this problem the model developing F. Macaulay's approach based on the analysis of elasticity of present value of the cash flows on the bond expected to receiving is offered. The research leans on such general scientific methods as observation, comparison and formalization and such special methods as economic-mathematical modeling and the statistical analysis. Modern approaches to definition and analysis of interest rate risk based on perspective (Macaulay duration, complimentary duration) and retrospective (Value-at-Risk) analysis considered. The disadvantages and limitations of using these models described. The present article considers the model based on comparing the duration as a bond's length of economic life with the extension to its maturity. Relative duration could be interpreted as a relative payback of investments in bonds rate. On the other hand, this indicator rather than Macaulay's duration could be interpreted as a interest risk comparison ratio which does not depend on bonds terms and structure of the maturities which is the novelty of this methodology. This interpretation is proved by the statistical analysis of sample of 20 bonds with different levels of duration. The technique of the evaluation of interest rate risk of portfolio of debt market-base instruments is suggested.

The Macaulay Duration: A Key Indicator for the Risk-Adjustment in Fair Value

International Financial Reporting Standards (IFRS) 13 Fair Value Measurement lays down two methods to adjust Expected Present Value (EPV) for risk. According to Method 1, expected cash inflows should be risk-adjusted by subtracting a risk-premium and discounted at the market risk-free rate, see (IFRS 13, B25). In contrast according to Method 2, expected cash inflows should be discounted at the risk-free rate augmented by a risk-premium addendum, see (IFRS 13, B26). Standard IFRS 13, B29 leaves the freedom to choose between the two methods. The aim of this note is to identify the relationship between the Risk-Adjusted EPVs rolled out from Method 1 and Method 2. First we introduce a theoretical solution to risk-adjustments compliant with the Standard IFRS 13, B29. Then, we set up a user-oriented proxy to connect the risk-premium present in Method 1 with the risk-adjusted rate present in Method 2. This proxy spots light on the key role played by the Macaulay Duration of expected inflows, rather than that of the lifetime of the project. As a consequence, projects expiring at the same redemption date and endowed with the same EPV and/or the same total inflow may differ considerably in risk-adjustments, due to different Macaulay Durations. A user-oriented method to properly to fast evaluate risk-adjustments for multi-cash inflow projects is provided. Sensitivity analysis of the impact of the Macaulay Duration on Risk-Adjusted EPV is also rolled out through numerical examples.

AN EMPIRICAL DEMONSTRATION OF LOAN TRACKING USING DURATION

ABSTRACT Macaulay's Duration can be used as an objective measure for evaluating the repayment performance of loans, borrowers and also loan officers, lending institutions and economies. This paper explores the use of Duration and demonstrates through a numerical example the Duration Ratio as it changes over time with loan payments. The method is simple and require elementary computing power. Further, it is amenable to aggregation over units, divisions, regions and economies. Keywords loan repayment performance, loan tracking, uses of Duration.

Perbandingan Sensitivitas Harga Obligasi Berdasarkan Durasi Macaulay dan Durasi Eksponensial dengan Pengaruh Konveksitas (Studi Empiris pada Data Obligasi Korporasi Indonesia yang Terbit Tahun 2015)

Macaulay duration has often been used as a measure of the bond prices sensitivity to changes in interest rates. For a small change in interest rates, the duration provides a good approximation of the actual change in price. As the change in interest rates gets larger, the duration approximation has larger errors. The convexity of bond prices change is often used as a way to improve the accuracy of the approximation. Several authors have pointed out that the natural logarithm of bond price is a better measure of percentage changes in bond prices as interest rates change. Based on this idea, this paper derives an accurate method of estimating percentage bond price changes in response to changes in interest rates, which is called exponential duration. This paper gives new estimation of bond prices using exponential duration with convexity approach. It will be shown that the new estimation bond prices is always more accurate than by Macaulay duration with convexity approach. For empirical study, it is used corporate bond data, which is published by Indonesian Bond Pricing Agency in 2015. The result support the theory that error value of Macaulay duration with convexity is more than the error value of exponential duration with convexity.Keywords:Bond Price, Convexity, Exponential Duration, Macaulay Duration, Modified Duration

Does Macaulay Duration Provide The Most Cost-Effective Immunization Method – A Theoretical Approach

Abstract 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.

Risk and Return: Bonds and Sukuk in Indonesia

The aim of this research is to compare the degree of risk and return of bonds with sukuk, using several calculations magnitudes, which are, yield to maturity (YTM), Macaulay's duration, and Value at Risk (VaR). The results of this study show that there is no significant difference between the YTM bonds and the YTM of emitted sukuk. Using the Macaulay’s duration formula to evaluate the duration of bonds and sukuk, the research found out that there is no significant difference in the duration of bonds and sukuk. However, the calculation and comparison of the VaR, showed a significant differences between bonds and sukuk , likewise either the comparison of the VaR of a sample group of bonds with a sample group of sukuk using k sample test. But by testing each group of the VaR of bonds sample group and sukuk sample group,the results show no significant differences . DOI: 10.15408/aiq.v8i2.3159

The IRR of a project with many potential outcomes

ABSTRACTThis article shows that the internal rate of return (IRR) of a project's expected cash flow stream is a weighted average of the IRRs offered by the project's (many) possible future outcomes, where the weights are calculated using the outcome probabilities and invested capital balances. Because the invested capital associated with a particular realization is a function of the Macaulay duration of the cash flows in that outcome, the weights depend on the outcome probabilities and the effective length of each cash flow stream.

Implementation of Stochastic Yield Curve Duration and Portfolio Immunization Strategies

In this paper, we propose an implementation method for a new concept of stochastic duration which can be used to measure the sensitivity of complex bond portfolios with respect to the fluctuations of the yield surface. Our approach relies on a first order approximation of a chaos expansion in the direction of the yield surface, whose dynamics is described by the Musiela equation. Using the latter technique, we obtain an infinite-dimensional generalization of the classical Macaulay duration, which can be interpreted as the derivative of a first order approximation of a Taylor series on locally convex spaces.

Sovereign risk and its changing effects on bond duration during financial crisis

We examined the effects of sovereign risk on bond duration in European and Latin American sovereign bond markets over the period 1996 to 2011. We compared the sovereign risk-adjusted duration with the Macaulay duration for both investment- and speculative-grade US dollar-denominated sovereign bonds. We found that the sovereign risk-adjusted duration is significantly shorter than its Macaulay counterpart for all ratings, and the ‘shortening’ effect is stronger for lower rated bonds, which generally intensified during the recent financial crisis. Results are robust when credit default swap (CDS) prices are used as a proxy for changes in sovereign risk. This study provides evidence for advocating the importance of adjusting the bond duration for sovereign risk. More important, this study provides a practical methodology for estimating a sovereign risk-adjusted duration measure for managing international bond portfolios.