The link between the Shapley value and the beta factor

In this article, we provide a link between the Shapley value in cooperative game theory and the capital asset pricing model (CAPM) in finance. In particular, the Shapley value of a suitably defined cooperative game is closely related to the beta factor in the CAPM. The beta factor for any given secu...

Full description

Saved in:
Bibliographic Details
Published in:Decisions in economics and finance 2016-11, Vol.39 (2), p.311-325
Main Author: Ortmann, Karl Michael
Format: Article
Language:English
Subjects:
Capital assets
Capital markets
CAPM
Econometrics
Economic theory
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Finance
Game theory
Games
Investments
Investors
Management
Mathematical analysis
Operations Research/Decision Theory
Public Finance
Risk
Securities markets
Stock exchanges
Studies
Variance analysis
Volatility
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this article, we provide a link between the Shapley value in cooperative game theory and the capital asset pricing model (CAPM) in finance. In particular, the Shapley value of a suitably defined cooperative game is closely related to the beta factor in the CAPM. The beta factor for any given security may be interpreted as the asset’s fairly allocated share of the market risk or as the asset’s average marginal contribution to the market risk, respectively. Other fairness properties and axioms of the Shapley value may be reinterpreted in this context to attain a deeper understanding of the beta factor and the connotation of systematic risk. Our game theoretic approach further allows for a generalisation of the CAPM with respect to arbitrary risk measures other than variance. Last but not least, we discuss the volatility of an asset’s theoretical fair assessment of risk and of its systematic risk, respectively. This result lends itself to face the challenge of an empirical investigation on real stock markets.
ISSN:1593-8883
1129-6569
DOI:10.1007/s10203-016-0178-0