12.3 Diversification & Markowitz Minimum Variance Portfolio

Chapter-4 from Szylar (2013) provides an easy to follow introduction and futher details.

Objective: Rational investors; maximise the expected return for a given risk, and they minimise the risk for a given return.

  • A minimum variance set is the set of all portfolios that have the least volatility for each level of possible expected return.
  • An efficient set (frontier) is the part of the minimum variance frontier that offers the highest expected return for each level of standard deviation.
  • Given the level of risk or standard deviation, investors prefer positions with higher expected return and given the expected return, they prefer the positions of lower risk.
  • Taking this into account, we can determine the minimum variance set.
  • The point where the standard deviation is at its lowest is the global minimum variance portfolio (GMV).
  • Portfolios that lie from the GMV portfolio upwards provide investors with the best risk–return combinations and thus are the candidates for the optimal portfolio.
  • These portfolios are called the efficient set (frontier); and in order to be on the efficient frontier, the portfolios have to satisfy the following criterion:
  • Given a particular level of standard deviation, the portfolios in the efficient set have the highest attainable expected rate of return.
Efficient Frontier

Figure 12.1: Efficient Frontier


Szylar, Christian. 2013. Handbook of Market Risk. John Wiley & Sons.