PROJECT III (MATH4181) 2014-15


On Capital Asset Pricing Model

Hasanjan Sayit

Description

Consider a portfolio consisting of a risk-free security and a specified risky security with expected return m and variance v. Such portfolios form a broken line on the m, v, plane consisting of two rectilinear half-lines. By taking portfolios containing risk-free security and a security with m_1, v_1, anywhere in the attainable set represented by the Markowitz bullet on the m, v, plane, we can construct any portfolio between the two half-lines. The efficient frontier of this new set of portfolios, which may contain the risk-free security, is the upper half-line tangent to the Markowitz bullet and passing through the point with coordinates 0, r, where r is the return of the risk-free asset. According to the assumptions of the capital asset pricing model, every rational investor will select his or her portfolio on this half-line, called the capital market line. This argument works as long as the risk-free return r is not too high, so the upper half line is tangent to the bullet. The purpose of this project is to study the capital asset pricing model in detail. We will derive the equation of the capital market line joining the risk-free security and the market portfolio. We will estimate the beta factor of a given portfolio and analyze the corresponding security market line.

Prerequisites

No previous knowledge in finance is required.
  • Calculus & Probability 1 (MATH1061)
  • Linear Algebra 1 (MATH 1071)
  • Resources

  • Mathematics for Finance by Marek Capinski and Tomasz Zastawniak
  • email: H.Sayit


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