Portfolio insurance, portfolio theory, market simulation, and risks of portfolio leverage

Bruce Jacobs, Ken Levy, and Harry Markowitz shared similar interests and did comple- mentary work. This led to collaboration, debate, and building upon each other’s ideas and research. They had a prodigious relationship of over 30 years, bridging the gap between theory and practice. Bruce individually, and then with Harry, distinguished between portfolio insurance and portfolio theory. Bruce and Ken estimated security expected returns using cross-sectional analysis, and Harry used that methodology for portfolio management. Bruce and Ken used Harry’s methods for portfolio construction, and they jointly explored the value of using constraints in portfolio optimization and addressed the optimality and optimization of long–short portfolios. Bruce, Ken, and Harry jointly developed an asynchronous, discrete-time, dynamic market simulator, JLMSim, to explain the behavior of security prices and to find equilibrium expected returns. Bruce and Ken extended portfolio theory to account for the unique risks of leverage and applied investor volatility aversion and leverage aversion to portfolio choice. The optimal portfolio lies within an efficient region and on a three-dimensional efficient surface. Harry concurred that the mean–variance model is a special case of the mean–variance–leverage model. Bruce and Ken used the mean–variance–leverage model to address the optimal amount of leverage in 130–30-type portfolio strategies. Bruce and Ken would challenge Harry, and Harry would challenge Bruce and Ken, and out of that would often come something interesting and useful.