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The Rate of Return: Concept, Postulate and Fallacy of Its Implication

Mohan L. Roy
Finance and Accounting Department of Business Administration IBAIS University, Dhaka.

Abstract/ Executive Summary:

This study speculates that this omission occurs since the conventional timeline return definition breaks down in these cases where there is no initial cash outflow, and because there is no well-known consensus on how to pedagogically resolve this issue. We carefully examine the return and the investment, numerator and denominator of the rate.During the investment horizon if market rates, on average, remain constant, then the rate of return (ROR) will be zero; if they rise, the ROR will be negative; and if they fall, the ROR will be positive. When market rates raise (fall), then the time-value of the asset-price-paid increases (decreases) by a larger (smaller) magnitude than the asset-earnings-received, thereby making the ROR negative (positive). These results hold true irrespective of whether the holding period is greater than, equal to, or less than duration; further, it is in stark contrast with the conventional results, where the ROR is dependent on the length of the holding period in relation to duration.This paper, therefore, proposes an amazingly simple and even intuitive remedy using an internal rate of return (IRR) approach which provides a consistent definition for the rate of return using an “encumbrance” definition of investment throughout the major investment types.

Keywords: Market rate, POR, ROI, Gain, Loss

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Program Area: Socio-economic and Policy

Non-commodity: Market analysis

Objectives:

To demonstrate how finance text-literatures (and instructors) can apply a consistent calculation formula based on an expanded opportunity cost viewpoint of “encumbrances” that employs an internal rate of return calculation to resolve this issue. This new definition will be first applied to the traditional investment case to establish the general method, and then it will be applied to short sales, options, and futures contracts.

Methodology:

What are puzzling, however, is why the theme of risk and return gets so much less emphasis as the learners pass through the text-literatures and why in particular the rate of return calculation gets so quickly abandoned in the later parts on short sales, options, and futures trading. It would seem such a natural concept (and calculation) to retain in order to pedagogically unify the presentations with the risk–return theme. Also, maintaining a more constant focus on the return calculation would provide useful and practical direction in the construction of investment performance guidelines involving more uncertain (derivative-based) investment portfolios.The holding period return (Bodie et al., 2005c), an arithmetic return, is calculated: Holding-Period Return (HPR) = (Ending Price – Beginning Price + Cash Dividend) / Beginning Price. Reilly and Brown (2003a) define HPR as the ending value of investment / beginning value of investment. Although they point out (Reilly and Brown, 2003b) short selling concept but do not clarify rates of return. In the later parts of the text-literature, they do calculate (Reilly and Brown, 2003c) per cent returns on buying calls and puts, but not on writing them. Finally, they show no rate of return calculations for futures trades.Finally, Jones (2004) provides an initial definition of total return = yield + price change, and later he extends that with total return (TR) = (cash payments received + price changes over period) / (price at which asset purchased). He too provides no formulas or examples for percentage returns on short sales, options, or futures.

Source of Information: J. Patuakhali Sci. and Tech. Univ. 2010, 2(1):23-33

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Achievement/Findings:

The rate of return concept introduced in this paper evaluates the reinvestment value of the ratio of asset-earnings and asset-price such that the ROR is zero when expectations with regard to the future values of market interest rates are, on average, realized. If the actual rates, on average, exceed their expected levels, then the ROR is negative and vice versa, irrespective of the length of the investment horizon. In the conventional models, the rate of return is dependent on the length of the holding-period in relation to duration and the level of market rate movements. It does not matter at what point in time (initial, intermediate, or maturity) the investment returns are evaluated, the rate of return is shown to be zero under constant market rate conditions, negative under rising market rate conditions, and positive under falling market rate conditions. While evaluating the investment returns, this paper includes all the parametric changes that take place during the investment horizon.

Knowledge Management: Journal