The mean-semivariances approach to realistic portfolio optimization subject to transaction costs

Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review

“…Kaplan and Alldredge (1997) used a specific risk-based index, which could maintain a certain level of risk in different periods of time, to make a series of trade-offs between risk and return and studied its properties and performance in the case of semi-variance. Hamza and Janssen (1998) took transaction cost into consideration and applied the mean-semi-variance model to the portfolio selection problem, introduced a series of binary variables and separable constraints, and finally solved the portfolio optimization problem using separable techniques. Grootveld and Hallerbach (1999) analyzed the similarities and differences of using variance and downside risk as risk measures from empirical data and theory.…”

Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review

“…Kaplan and Alldredge (1997) used a specific risk-based index, which could maintain a certain level of risk in different periods of time, to make a series of trade-offs between risk and return and studied its properties and performance in the case of semi-variance. Hamza and Janssen (1998) took transaction cost into consideration and applied the mean-semi-variance model to the portfolio selection problem, introduced a series of binary variables and separable constraints, and finally solved the portfolio optimization problem using separable techniques. Grootveld and Hallerbach (1999) analyzed the similarities and differences of using variance and downside risk as risk measures from empirical data and theory.…”

Two-sided coherent risk measures and their application in realistic portfolio optimization

“…q a;p ðXÞ also extends the risk measure in Hamza and Janssen (1998) since, instead of adopting both semivariances, it uses the 1-norm of ðX À E Q ½XÞ þ and the p-norm of ðX À E Q ½XÞ À . Our new measure looks like the deviation measures in Rockafellar et al (2006) in that the positive deviation and negative deviation from the mean are treated asymmetrically.…”

“…Preferably, such a measure will satisfy coherency conditions. The only ''two-sided" risk measure we have seen so far is that in Hamza and Janssen (1998), where the risk is measured through the convex combination of semivariances of the portfolio rate of return. Although the degree of risk aversion can be reflected by selecting the combination coefficient, the corresponding adjustment is only linear.…”

Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review

“…Kaplan and Alldredge (1997) used a specific risk-based index, which could maintain a certain level of risk in different periods of time, to make a series of trade-offs between risk and return and studied its properties and performance in the case of semi-variance. Hamza and Janssen (1998) took transaction cost into consideration and applied the mean-semi-variance model to the portfolio selection problem, introduced a series of binary variables and separable constraints, and finally solved the portfolio optimization problem using separable techniques. Grootveld and Hallerbach (1999) analyzed the similarities and differences of using variance and downside risk as risk measures from empirical data and theory.…”

Two-sided coherent risk measures and their application in realistic portfolio optimization

“…q a;p ðXÞ also extends the risk measure in Hamza and Janssen (1998) since, instead of adopting both semivariances, it uses the 1-norm of ðX À E Q ½XÞ þ and the p-norm of ðX À E Q ½XÞ À . Our new measure looks like the deviation measures in Rockafellar et al (2006) in that the positive deviation and negative deviation from the mean are treated asymmetrically.…”

“…Preferably, such a measure will satisfy coherency conditions. The only ''two-sided" risk measure we have seen so far is that in Hamza and Janssen (1998), where the risk is measured through the convex combination of semivariances of the portfolio rate of return. Although the degree of risk aversion can be reflected by selecting the combination coefficient, the corresponding adjustment is only linear.…”

Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review

“…Kaplan and Alldredge (1997) used a specific risk-based index, which could maintain a certain level of risk in different periods of time, to make a series of trade-offs between risk and return and studied its properties and performance in the case of semi-variance. Hamza and Janssen (1998) took transaction cost into consideration and applied the mean-semi-variance model to the portfolio selection problem, introduced a series of binary variables and separable constraints, and finally solved the portfolio optimization problem using separable techniques. Grootveld and Hallerbach (1999) analyzed the similarities and differences of using variance and downside risk as risk measures from empirical data and theory.…”

Two-sided coherent risk measures and their application in realistic portfolio optimization

“…q a;p ðXÞ also extends the risk measure in Hamza and Janssen (1998) since, instead of adopting both semivariances, it uses the 1-norm of ðX À E Q ½XÞ þ and the p-norm of ðX À E Q ½XÞ À . Our new measure looks like the deviation measures in Rockafellar et al (2006) in that the positive deviation and negative deviation from the mean are treated asymmetrically.…”

“…Preferably, such a measure will satisfy coherency conditions. The only ''two-sided" risk measure we have seen so far is that in Hamza and Janssen (1998), where the risk is measured through the convex combination of semivariances of the portfolio rate of return. Although the degree of risk aversion can be reflected by selecting the combination coefficient, the corresponding adjustment is only linear.…”