The First Difference Property of the Present Value Operator

Stephen A. Buser, Bjarne Astrup Jensen

Research output: Contribution to journalJournal articleResearchpeer-review

59 Downloads (Pure)

Abstract

This paper identifies a fundamental relationship between the present value of a given cash flow and the present value of the period by period change in that cash flow. The new relationship is shown to be highly useful for the identi.fication of analytic expressions for present value and related measures such as duration and convexity; expressions that continue to play an instructive role by helping to relate the quan­titative outcomes of numerical calculations to the driving forces behind those cal­culations. This new method applies only simple arithmetic operations and avoids the use of differential calculus and advanced series summation in order to derive these analytic results.
We apply the method to a variety of nontraditional cash flows, including cash flows with linear growth or decay, cash flows that are subject to different true effects for dividends and capital gain, and cash flows that are projected to exhibit cyclical variation over time.
Original languageEnglish
Article number1750012
JournalQuarterly Journal of Finance
Volume7
Issue number4
Number of pages41
ISSN2010-1392
DOIs
Publication statusPublished - 2017

Keywords

  • Present value
  • First difference property
  • Recursive calculation
  • Duration
  • Convexity

Cite this

@article{1a3393883ec5496dacd68634c9ea2138,
title = "The First Difference Property of the Present Value Operator",
abstract = "This paper identifies a fundamental relationship between the present value of a given cash flow and the present value of the period by period change in that cash flow. The new relationship is shown to be highly useful for the identi.fication of analytic expressions for present value and related measures such as duration and convexity; expressions that continue to play an instructive role by helping to relate the quan­titative outcomes of numerical calculations to the driving forces behind those cal­culations. This new method applies only simple arithmetic operations and avoids the use of differential calculus and advanced series summation in order to derive these analytic results. We apply the method to a variety of nontraditional cash flows, including cash flows with linear growth or decay, cash flows that are subject to different true effects for dividends and capital gain, and cash flows that are projected to exhibit cyclical variation over time.",
keywords = "Present value, First difference property, Recursive calculation, Duration, Convexity, Present value, First difference property, Recursive calculation, Duration, Convexity",
author = "Buser, {Stephen A.} and Jensen, {Bjarne Astrup}",
year = "2017",
doi = "10.1142/S2010139217500124",
language = "English",
volume = "7",
journal = "Quarterly Journal of Finance and Accounting",
issn = "1939-8123",
publisher = "World Scientific",
number = "4",

}

The First Difference Property of the Present Value Operator. / Buser, Stephen A.; Jensen, Bjarne Astrup.

In: Quarterly Journal of Finance, Vol. 7, No. 4, 1750012, 2017.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - The First Difference Property of the Present Value Operator

AU - Buser, Stephen A.

AU - Jensen, Bjarne Astrup

PY - 2017

Y1 - 2017

N2 - This paper identifies a fundamental relationship between the present value of a given cash flow and the present value of the period by period change in that cash flow. The new relationship is shown to be highly useful for the identi.fication of analytic expressions for present value and related measures such as duration and convexity; expressions that continue to play an instructive role by helping to relate the quan­titative outcomes of numerical calculations to the driving forces behind those cal­culations. This new method applies only simple arithmetic operations and avoids the use of differential calculus and advanced series summation in order to derive these analytic results. We apply the method to a variety of nontraditional cash flows, including cash flows with linear growth or decay, cash flows that are subject to different true effects for dividends and capital gain, and cash flows that are projected to exhibit cyclical variation over time.

AB - This paper identifies a fundamental relationship between the present value of a given cash flow and the present value of the period by period change in that cash flow. The new relationship is shown to be highly useful for the identi.fication of analytic expressions for present value and related measures such as duration and convexity; expressions that continue to play an instructive role by helping to relate the quan­titative outcomes of numerical calculations to the driving forces behind those cal­culations. This new method applies only simple arithmetic operations and avoids the use of differential calculus and advanced series summation in order to derive these analytic results. We apply the method to a variety of nontraditional cash flows, including cash flows with linear growth or decay, cash flows that are subject to different true effects for dividends and capital gain, and cash flows that are projected to exhibit cyclical variation over time.

KW - Present value

KW - First difference property

KW - Recursive calculation

KW - Duration

KW - Convexity

KW - Present value

KW - First difference property

KW - Recursive calculation

KW - Duration

KW - Convexity

U2 - 10.1142/S2010139217500124

DO - 10.1142/S2010139217500124

M3 - Journal article

VL - 7

JO - Quarterly Journal of Finance and Accounting

JF - Quarterly Journal of Finance and Accounting

SN - 1939-8123

IS - 4

M1 - 1750012

ER -