Portfolio management aims to take positions in financial instruments that achieve the desired risk-return trade-off regarding a benchmark. In each period, a manager selects positions that optimize diversification to reduce risks while achieving a target return. Across periods, the positions will be rebalanced to account for changes in weights resulting from price movements to achieve or maintain a target risk profile.
Diversification permits us to reduce risks for a given expected return by exploiting how price movements interact with each other as one asset's gains can make up for another asset's losses. Harry Markowitz invented Modern Portfolio Theory (MPT) in 1952 and provided the mathematical tools to optimize diversification by choosing appropriate portfolio weights. Markowitz showed how portfolio risk, measured as the standard...