Modern Portfolio Theory

The basic elements of modern portfolio theory are covered in this Chapter. Starting from the basics of price return time series, the authors introduce Markowitz’s mean variance optimization and the central concept of the efficient frontier. Extensions to other risk measure optimization methods within the portfolio theory framework are covered, including: tangent portfolio optimization which exploits the relationship between the efficient frontier and the capital market line; minimization of the conditional value-at-risk, a tail-risk measure replacing the variance; and the Black–Litterman model, designed to address issues appearing in mean variance optimization. The classical implementation of these optimization techniques using moving windows of historical asset return data is developed.