Yield Approximations: A Historical Perspective

Hawawini, Gabriel; Vora, Ashok

doi:10.1111/j.1540-6261.1982.tb01100.x

Cited by 9 publications

(5 citation statements)

References 15 publications

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“…This was the question of how to determine the rate of compound interest underlying an annuity transaction, when given the purchase price, the annual payment and the period for which it was to be paid. The various attempts which were made to find a solution are described in detail by Hawawini and Vora (1962), starting with a pioneering method proposed by Dary (1677), which used a systematic trial and error approach. Unfortunately, Dary's method approached the unknown true value of the rate of interest only slowly and was therefore not of great practical use.…”

Section: Interest Rates Underlying Annuity Transactionsmentioning

confidence: 99%

The emergence of compound interest

Lewin¹

2019

Br. Actuar. J.

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Compound interest was known to ancient civilisations, but as far as we know it was not until medieval times that mathematicians started to analyse it in order to show how invested sums could mount up and how much should be paid for annuities. Starting with Fibonacci in 1202 A.D., techniques were developed which could produce accurate solutions to practical problems but involved a great deal of laborious arithmetic. Compound interest tables could simplify the work but few have come down to us from that period. Soon after 1500, the availability of printed books enabled knowledge of the mathematical techniques to spread, and legal restrictions on charging interest were relaxed. Later that century, two mathematicians, Trenchant and Stevin, published compound interest tables for the first time. In 1613, Witt published more tables and demonstrated how they could be used to solve many practical problems quite easily. Towards the end of the 17th century, interest calculations were combined with age-dependent survival rates to evaluate life annuities, and actuarial science was created.

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Section: Interest Rates Underlying Annuity Transactionsmentioning

confidence: 99%

The emergence of compound interest

Lewin¹

2019

Br. Actuar. J.

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“…Compared to the approximations given in Hawawini and Vora's (1982) historical survey of yield approximation methods, the power-law approximation is more accurate.…”

Section: Yieldmentioning

confidence: 99%

Power law bond price and yield approximation

Barber

2021

JRF

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PurposeThis paper determines a simple transformation that nearly linearizes the bond price formula. The transformed price can be used to derive a highly accurate approximation of the change in a bond price resulting from a change in interest rates.Design/methodology/approachA logarithmic transformation exactly linearizes the price function for a zero coupon bond and a reciprocal transformation exactly linearizes the price function for a perpetuity. A power law transformation combines aspects of both types of transformations and provides a superior approximation of the bond price sensitivity for both short-term and long-term bonds.FindingsIt is demonstrated that the new formula, based on power-law transformation, is a much better approximation than either the traditional duration-convexity approximation and the more recently developed approximations based on logarithmic transformation of the price function.Originality/valueThe new formula will be used by risk managers to perform stress-testing on bond portfolios. The new formula can easily be inverted, making it possible to relate the distribution of prices (which are observable in the market) to the distribution of yields (which are numerical solutions that are not directly observable).

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“…In contrast, new DuPont extensions keep appearing to examine the ROE under certain conditions and eliminate the flaws of earlier iterations. Hawawini and Viallet (1999) proposed modifications to the three-factor model to account for managerial income levels, which have been widely used and adopted as a building block for other modifications such as the 5-, 7-, and 10-factor models. The 5-factor model from Gujjar and Manjunatha (2021) perspective considers the additional impacts of the tax burden (also referred to as the tax ratio, measured as the ratio of net income to earnings before tax) and the impacts of the interest burden (also called the financial cost ratio, measured as the ratio of earnings after tax to earnings before tax).…”

Section: Theory Of the Dupont Modelmentioning

confidence: 99%

Evaluating the financial performance of listed REIT firms in South Africa: A 7-step DuPont model technique

Ayaba,

Amo-Bediako,

Takawira

2023

IJAEFA

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This research paper presents empirical information about the use of the 7-step DuPont model in the context of publicly traded Real Estate Investment Trust (REIT) firms operating in South Africa. The DuPont model is a crucial paradigm for performance analysis, however, scholars have given its numerous parts varying ratings. As a result, it is now very necessary to examine it. The Generalized Least Square models (fixed effect and random effect) are used to evaluate the financial performance in a DuPont model context. The empirical study uses panel data from six REIT companies that are publicly traded on the Johannesburg Stock Exchange and spans the years 2005 through 2021. The findings of the study suggest a strong positive relationship between return on sales and return on equity. Additionally, a correlation was found, indicating a negative association between various operational items and return on equity. However, a notable positive correlation is shown between total asset turnover and return on equity. Contrary to the aforementioned findings, the fixed charge ratio, tax return, equity multiplier, as well as sales and management expenses, all reported an insignificant association with return on equity. The study avows that the seven-step DuPont model is the most appropriate model for assessing performance as it better explains the performance of listed REIT companies in South Africa. It may be inferred that the seven-step DuPont model provides a more comprehensive explanation of parameters associated with firms.

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Yield Approximations: A Historical Perspective

Cited by 9 publications

References 15 publications

The emergence of compound interest

The emergence of compound interest

Power law bond price and yield approximation

Evaluating the financial performance of listed REIT firms in South Africa: A 7-step DuPont model technique

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