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.
Highlights
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
We assume that pre-finance graduated STEM students possess a fundamental knowledge of linear algebra
Summary
Business schools are racing to add concentrations in STEM to their MBA programs CAPM by adopting the matrix approach introduced by Merton [8] and Roll [9]; this paper acquires all theory results only counting on basic mathematical tools, such as linear algebra, geometry and statistics, except for calculus or higher mathematics. We believe this approach further facilitates STEM students’ understanding of the formal structure of the CAPM theory, as well as the rich economic implications therein even with a basic understanding of the parabola nature. Almost all mathematical details are relegated to the Appendix A
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