Explain how transactions-based, holdings-based and returns-based attribution work, with the strengths and weaknesses of each

Returns-based attribution regresses the portfolio's total returns on a set of factor or style index returns. Needing only a return series, it is quick, cheap and usable where holdings are hidden, as with many hedge funds, but it is the least precise, cannot identify individual decisions and can mislead when exposures change. Holdings-based attribution uses positions at the start of each period; it is more accurate, especially with frequent snapshots and low turnover, but it ignores trades within the period, so trading effects and transaction costs leak into a residual. Transactions-based attribution uses holdings plus every trade, so it reconciles fully to the actual return and captures trading decisions; it is the most accurate but the most data-hungry and costly.