12.3 Diversification & Markowitz Minimum Variance Portfolio
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.
Szylar, Christian. 2013. Handbook of Market Risk. John Wiley & Sons.