CoachA benchmark is the reference portfolio, usually a published index, against which a mandate is measured. If and are the returns of the portfolio and the benchmark, the active return is , and the tracking error is the annualised standard deviation of .
Exemples
Example 3.7 (Twenty overweight bets)
A manager overweights 20 stocks by 1% each and underweights 20 others by 1% each. If stock-specific returns are independent with volatility 25% and the common factors cancel, . A mandate that caps the tracking error at 3% leaves room for little more than this: an “active” portfolio is mostly the index.