Based on historical performance: Also called backward-looking or ex post tracking error.There are two types of tracking error models:
an index fund) that always matches its benchmark's actual return (zero active returns) would have a tracking error of zero. Ī portfolio created to match the benchmark index (e.g. Tracking error is measured as the dispersion of a portfolio's returns relative to the returns of its benchmark, and is expressed as the standard deviation of the portfolio's active return (annualized). Tracking error is a measure of how closely a portfolio follows the index to which it is benchmarked. In other words, the three-factor model can help determine the effectiveness of a fund manager. An alpha greater than this suggests that the fund manager is adding value beyond the underlying factor exposures. If the fund manager captures the factor exposures perfectly, the expected alpha would be zero, minus the expense ratio (ER) of the fund. r i t − r f t = α i + β i m ( r m t − r f t ) + β i s S M B t + β i h H M L t + ϵ i t factors. To represent the market cap ("Size") and book/market ratio ("Value") returns, Fama and French modified the original CAPM model with two additional risk factors: size risk and value risk.
In summary, Fama-French viewed both size and value as risk factors, for which one is rewarded with extra return. In their paper, high book/market is acronymed "HBM." "Book/market ratio" is the inverse of the more familiar "price/book ratio." In other words, a high book/market ratio is the same as a low price/book ratio- a "value". Note: The terminology by Fama-French is different than common usage. The three-factor model explains up to 95% of returns for a cross-section of equity portfolios of various sizes and styles. Therefore, a portfolio with a small median market cap and a high book/market ratio will have a higher Expected return than a portfolio with a large median market cap and a low book/market ratio.
3.2 Specifying risk factor helps investor choices.3.1 Classifying funds into style buckets.