Explain the main ways active equity portfolios are put together

Construction approaches differ along two axes: systematic against discretionary, and bottom-up against top-down. Systematic managers apply rules and optimisers across broad universes; discretionary managers rely on judgement and conviction. Bottom-up managers let exposures emerge from stock choices, while top-down managers set macro or factor exposures first. Within these, position weights can be set by heuristics such as equal weighting or conviction tiers, by constraints relative to the benchmark such as sector and stock deviation limits, or by optimisation that maximises expected alpha minus penalties for risk and cost. Hybrids are common. The trap is treating an optimiser as objective: it magnifies errors in expected return estimates, so its output is usually tightly constrained or blended with judgement.