Tracking Error

Exam items lean on one calculation trap: tracking error is the standard deviation of active return (the return differences), not the average difference itself — students who report the mean active return have computed the wrong statistic. A common L1 item hands you a short series of period returns for portfolio and benchmark, then asks you to subtract pairwise and take the sample standard deviation of those differences. The “tell” is any prompt mentioning active risk or asking for risk “relative to the benchmark”; the answer hinges on dispersion, never on level.

Don’t confuse the three risk-adjusted ratios. Sharpe divides excess return by total risk (standard deviation); Treynor uses beta (systematic risk); the information ratio divides mean active return by active risk (tracking error) — match the denominator to what’s asked. Another classic slip: a near-perfect index fund has very low tracking error yet a Sharpe ratio close to its benchmark’s, so low tracking error never means low total volatility — a tracker of a volatile index is itself volatile. Memory hook: “tracking error tracks the gap’s wiggle, not the gap.”