Tracking Error & Tracking Difference

Tracking error (%)

Tracking error measures the level of consistency or divergence between the performance of a passive mutual fund (Index fund or ETF) and its target Index. Mathematically, it is calculated as the annualised standard deviation of the difference in returns between the passive fund and its underlying Index.

Mathematical formula:

$\text{Tracking error}=\frac{\Sigma {(R_f-R_i)}^2}{(n-1)}\times \sqrt{250}$

where,

$\Sigma$	is symbol for summation of each instance of the fund returns considered
$R_f$	is each instance of daily return of the fund portfolio
$R_i$	is each instance of daily return of the benchmark index
$n$	is number of daily instances considered

Tracking error is typically expressed as a percentage that indicates the variability of the fund's performance relative to the index over a specific time period (1-month, 3-month, 1-year, 3-year, 5-year, etc.).

A higher tracking error suggests that the passive fund has deviated more from its benchmark, resulting in a greater difference in performance. It indicates that the fund's returns are less predictable and may vary significantly from the performance of the benchmark that it "tracks".

This can arise due to factors such as the fund's expenses or how closely the fund manager is able to replicate the weightages of the stocks in the Index in the passive fund’s portfolio.

Thus, a fund with lower tracking error is more desirable. However, it's important to note that tracking error alone does not determine the overall quality of a passive mutual fund.

Tracking difference (%)

Tracking difference refers to the discrepancy between the returns of a passive mutual fund (Index fund or ETF) and its underlying benchmark index. Mathematically it is nothing but the absolute difference in returns between the passive fund and its underlying Index.

Mathematical formula:

$\text{Tracking difference}=R_f-R_i$

where,

$R_f$	is return of the fund portfolio for the given period
$R_i$	is return of the benchmark index for the given period

Tracking difference is typically expressed as a percentage and represents the difference in returns over a specific time period (1-month, 3-month, 1-year, 3-year, 5-year, etc.). It can be positive or negative, indicating outperformance or underperformance relative to the index, though generally it tends to be negative due to its expense ratio.

It is a metric that is related to tracking error, but differs in their measurement and interpretation. Tracking difference measures the difference in returns between the passive fund and its benchmark index whereas tracking error measures the volatility or standard deviation of the difference in their returns.

In simpler terms, tracking difference tells you whether a passive fund is performing better or worse than the index for a given period, while tracking error tells you how consistently the fund's performance deviates from the index.

Both tracking difference and tracking error provide insights into the ability of a passive mutual fund to replicate its benchmark index. Investors should consider both metrics when evaluating a passive fund's performance and assessing its ability to deliver the desired investment outcomes.