A fresh look at the time value of money equation

Osborne, Mike (2002) A fresh look at the time value of money equation. In: 15th Australasian Finance & Banking Conference, University of New South Wales, Sydney, Australia.

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The time value of money (TVM) equation is the Swiss army knife of finance. It is often differentiated to obtain the interest rate sensitivity of whatever is being valued. The process is so common in finance that it could be said to be automatic it is never questioned. In fixed income analysis the result is incorporated into the concept known as duration. It is well known that the various versions of duration yield approximate answers. Considerable extra effort is necessary to improve the approximations by adding concepts such as convexity, or incorporating a duration vector. But the results remain approximations. This paper summarises an entirely new approach based on the fact that the TVM equation is a polynomial, and a polynomial does not have one root, it has many, distributed around the complex plane. The result of taking the multiple solutions into account is a solution to the problem of inaccuracy that has existed in the duration literature since the time of Macauley (1938). A new equation for duration is derived that provides precise results for the measure of interest rate sensitivity, no matter what the change in the rate. The paper describes the computational issues presented by the new approach and suggests a way to deal with them. The analysis also provides a new, more general, perspective to the TVM equation that may be a launch pad for further research into the many other financial concepts that depend on the equation.

Item Type: Conference or Workshop Item (Paper)
Schools and Departments: University of Sussex Business School > Business and Management
Depositing User: Michael Osborne
Date Deposited: 06 Feb 2012 20:36
Last Modified: 21 Oct 2014 13:30
URI: http://sro.sussex.ac.uk/id/eprint/26877
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