Question

What is the global minimum variance portfolio? How does it vary with correlation coefficient?

Answer 1

Solution.

once the efficient frontier is known, an investor can make asset allocation decision that meets the risk and return he/she desired efficiently. Thus, a successful efficient asset allocation hinges upon the existence of the minimum variance portfolio. In this paper, we use data samples from the US stock markets to investigate the minimum variance portfolio, and the stability of this portfolio, from a practical point of view. Section II provides a brief review of 3 the Markowitz Portfolio Theory. Section III outlines the methodology and data. We discuss the result in section VI and conclude the paper in section V. II: The Minimum Variance Portfolio of Two Risky Assets It is easier to understand the modern portfolio with a two-security portfolio. Most popular textbooks (see Bodie, Kane and Marcus, 2009; Jordan and Miller, 2009; Strong, 2009; Reilly and Brown, 2009) for investment course all present very similar examples. We can think of these two securities as combinations of a bond fund and an equity fund, or a mixture of two equity funds (or simply as two equities). The derivation of the minimum variance portfolio is available in all investment textbooks and is easily accessible for anyone interested in investing on their own. The following derivation is taken from one of the most common investment textbook, Bodie, Kane and Marcus (2009). Consider an individual investor who is considering how much he/she would invest in two securities, A and B. Let the portion of the fund invested in security A as waand the remainder of the fund be invested in security B (wb).