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Which is the Correct Discount Rate? Arithmetic Versus Geometric Mean

Which is the Correct Discount Rate? Arithmetic Versus Geometric Mean
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Year:    2020

Author:    Kipp, Martin, Koziol, Christian

Credit and Capital Markets – Kredit und Kapital, Vol. 53 (2020), Iss. 3 : pp. 355–381

Abstract

The paper revisits the two major concepts for average historical returns, i.?e., the arithmetic mean and the geometric mean, in order to clarify which approach must be used for which application. Conducting a rigorous derivation with a geometric Brownian motion, we can explain that the appropriate discount rate refers to the mean discrete return and, therefore, to the arithmetic mean rather than the often wrongly applied geometric mean. Likewise, the prominent CAPM relationship between the expected asset return and the expected market return is only valid for the arithmetic mean rather than the geometric mean. Using historical data for the German stock index, we illustrate that an inconsistent application can cause severe deviations from the meaningful ex-ante expected performance of an asset, the true discount rate, the true CAPM risk-adjusted return, and the intended performance scenarios of packaged retail and insurance-based investment products (PRIIPs) within the key information documents (KIDs).

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.3790/ccm.53.3.355

Credit and Capital Markets – Kredit und Kapital, Vol. 53 (2020), Iss. 3 : pp. 355–381

Published online:    2020-09

AMS Subject Headings:    Duncker & Humblot

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

Keywords:    Asset returns Arithmetic mean Geometric mean Geometric Brownian Motion Discount rate CAPM PRIIPs G12

Author Details

Kipp, Martin

Koziol, Christian

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  30. Koller, T./Goedhart, M./Wessels, D. (2015): Valuation: Measuring and Managing the Value of Companies, 6th edition, John Wiley & Sons.  Google Scholar
  31. KPMG (2019): Cost of Capital Study 2019, 14th ed.  Google Scholar
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  33. Stehle, R. (2004): Die Festlegung der Risikoprämie von Aktien im Rahmen der Schätzung des Wertes von börsennotierten Kapitalgesellschaften, Die Wirtschaftsprüfung, Vol. 57(17), 906–927.  Google Scholar
  34. Tsay, R. S. (2005): Analysis of Financial Time Series, Vol. 543, John Wiley & Sons.  Google Scholar

Section Title Page Action Price
Martin Kipp / Christian Koziol: Which is the Correct Discount Rate? Arithmetic Versus Geometric Mean 1
Abstract 1
I. Introduction 1
II. Theoretical Background 3
1. Basic Principles of Asset Returns 3
2. Geometric Brownian Motion as Stock Price Process 6
III. Arithmetic and Geometric Mean of Discrete Returns 9
1. Geometric Mean of Discrete Returns 9
2. Arithmetic Mean of Discrete Returns 1
IV. The Proper Discount Rate 1
V. Capital Asset Pricing Model 1
1. Proof of the CAPM 1
2. Analysis of a Potential Inaccuracy 2
VI. PRIIPs 2
VII. Conclusion 2
References 2