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Article Teaching CAPM for a Pre-Finance Graduate Program at the STEM Undergraduate Level: Linear Algebra Perspective
Chi-Lu Peng 1@, Wen-Kuei Chen 1 and An-Pin Wei 2,*
Business Intelligence School, National Kaohsiung University of Science and Technology, Kaohsiung 82445, Taiwan; chilupeng@nkust.edu.tw (C.-L.P.); rexchen@nkust.edu.tw (W.-K.C.) School of Economics, Guangxi University for Nationalities, Nanning 530006, China Correspondence: anpinwei@gmail.com or anpinwei@gxun.edu.cn
Abstract: Students considering a masters in Finance Engineering or Artificial Intelligence in Finance are usually required to have an undergraduate background in science, technology, engineering, or mathematics (STEM). STEM students have a good capacity in mathematics and science, but they may not have studied financial theory. To facilitate the classroom teaching of the Capital Asset Pricing Model (CAPM) for STEM students, this paper seeks to expound on the essence of the theory starting at a two-asset framework. Adopting the concepts proposed by Merton (1972), this paper accomplishes the derivation by virtue of basic mathematical tools such as linear algebra, geometry, and statistics except for calculus. We show that the major aspects of Merton's derivation of the CAPM for a universe of N assets may also be obtained in a two-asset world. Through the methods of this article, students will learn the in-depth theory of CAPM and its hands-on empirical tool. For example, students will realize that even if investors specify different threshold rewards, their different CAPMs will yield identical pricing for assets and portfolios.
Citation: Peng, C.-L.; Chen, W.-K.; Wei, A.-P. Teaching CAPM for a Pre-Finance Graduate Program at the STEM Undergraduate Level: Linear Algebra Perspective. Mathematics 2021, 9, 1668. https://doi.org/ 10.3390/math9141668
Keywords: capital asset pricing model; benchmark portfolio; threshold portfolio; market portfolio; securities market line
1. Introduction Business schools are racing to add concentrations in STEM to their MBA programs ([1]. STEM students have a good capacity in mathematics and science, but they may not Academic Editor: Miltiadis Chalikias have studied financial theory. The Capital Asset Pricing Model (CAPM) has been one of the cornerstones of modern finance. Despite its controversial empirical performance, the Received: 12 June 2021 model remains a valuable tool to introduce students of economics and finance into the Accepted: 11 July 2021 world of trade-off between risk and reward [2-4]. For that reason, scholars have attempted Published: 15 July 2021 to facilitate the exposition of the theory in a simplified universe 5-7]. We assume that Publisher's Note: MDPI stays neutral pre-finance graduated STEM students possess a fundamental knowledge of linear algebra with regard to jurisdictional claims in The propose of this study is to introduce vector-matrix proofs of theoretical concepts of published maps and institutional affil- CAPM based on the parabola nature. To the best of our knowledge, this article is the first iations. effort that tries to discriminate CAPM within principles of geometry. Starting with the setting of a two-asset market, this paper seeks to derive the famous CAPM by adopting the matrix approach introduced by Merton 3] and Roll [9]; this cc ? paper acquires all theory results only counting on basic mathematic