Efficient Frontier and Portfolio Optimization

Abstract

This chapter discusses the (Markowitz, Journal of Finance 7:77–91, 1952) modern portfolio theory and its implication for the finance studies. Importance of both the systematic and unsystematic risk with respect to the risk and return relationship is covered. Why only market risk is important for a reasonably well-diversified portfolio is discussed in detail. Suitable empirical examples related to the calculation of portfolio returns and risk are included. Critical discussion made on “why calculating the expected portfolio return is easy but the harder part is to work out with the calculation of the risk component of the portfolio”? Two important portfolio risk measuring parameters, namely variance and covariance are introduced in detail. Thereafter, critical discussions are made using appropriate examples on the importance of covariances over variances while calculating the portfolio risk. The general formula for computing the portfolio risk is derived theoretically and visually. Then efficient frontier and portfolio optimization are introduced and detailed discussion made using appropriate examples. Further, it is discussed on how (Markowitz, Journal of Finance 7:77–91, 1952) portfolio selection theory becomes the basis for developing (Sharpe, The Journal of Finance 19:425–442, 1964) theory of price formation for financial assets. Critical discussion on the Capital Market Line & Security Market Line is included. Illustration on plotting the Mean–Variance efficient frontier and portfolio optimization is made using the R programming.