Tracking error in index funds
Tracking error is the annualised standard deviation of the difference between a mutual fund’s periodic returns and the returns of its benchmark index over the same period. It is the primary metric for evaluating how accurately an index fund or exchange-traded fund (ETF) replicates its target benchmark. A tracking error of zero would imply perfect replication, in practice, every fund has some non-zero tracking error driven by costs, cash drag, and rebalancing lags.
In India, tracking error has grown in importance as the passive fund category has expanded rapidly since 2019, with index fund and ETF AUM surpassing ₹10 lakh crore by 2024.
Formula
The standard definition (ex-post, computed from historical return differences):
\[ \text{TE} = \sigma\left(R_p - R_b\right) = \sqrt{\frac{\sum_{t=1}^{N}\left[(R_{p,t} - R_{b,t}) - \overline{d}\right]^2}{N-1}} \]
Where:
| Symbol | Meaning |
|---|---|
| \(R_{p,t}\) | Fund return in period \(t\) |
| \(R_{b,t}\) | Benchmark return in period \(t\) |
| \(d_t = R_{p,t} - R_{b,t}\) | Active return (return difference) in period \(t\) |
| \(\overline{d}\) | Mean active return over all periods |
| \(N\) | Number of periods |
To annualise from daily data: \(\text{TE}{\text{annual}} = \text{TE}{\text{daily}} \times \sqrt{252}\)
To annualise from monthly data: \(\text{TE}{\text{annual}} = \text{TE}{\text{monthly}} \times \sqrt{12}\)
Tracking difference vs tracking error
These two terms are related but distinct:
- Tracking difference is the gap between the fund’s cumulative return and the benchmark’s cumulative return over a given period. It is a single signed number (fund return minus benchmark return). See tracking difference for a dedicated treatment.
- Tracking error is the standard deviation of periodic tracking differences. It measures consistency of replication, not just the average deviation.
A fund can have low tracking difference (i.e., it roughly matches the index over a year) but high tracking error (the daily differences are erratic). Conversely, a fund with a consistent 0.15 per cent monthly underperformance would have a low tracking error (very consistent) but a meaningful negative tracking difference over time.
Both metrics are needed for a complete assessment of passive fund quality.
Sources of tracking error in Indian index funds
1. Total expense ratio drag
The total expense ratio (TER) is a guaranteed source of tracking difference: the fund always underperforms the total return index by approximately the TER per year. However, if the TER drag is perfectly constant, it contributes to tracking difference but minimally to tracking error (the deductions are smooth and predictable).
2. Cash drag
Index funds hold some cash to meet redemptions. Cash earns less than the equity index, creating day-to-day differences. SEBI permits funds to hold up to 5 per cent of AUM in cash/debt for liquidity management.
3. Dividend accrual timing
When index constituents pay dividends, the total return index (TRI) credits them immediately (or at the ex-date), but the actual cash received by the fund may take 1–2 days to settle and be reinvested. This creates temporary mismatches.
4. Corporate actions and index rebalancing
Additions, deletions, and weight changes to the index (quarterly reconstitution for most NSE/BSE indices) require the fund to trade. Large funds trading in illiquid midcap or smallcap stocks face market impact costs that widen tracking error.
5. Security lending income
Many ETFs engage in securities lending, receiving income that can offset TER and actually reduce tracking difference below zero (fund outperforms the index net of fees). SEBI regulations permit mutual fund ETFs to lend securities subject to SEBI (Securities Lending Scheme) norms.
6. Sampling in large indices
For indices with many constituents (e.g., Nifty 500), funds may use stratified sampling rather than full replication, holding a representative subset. Sampling introduces additional stock-level tracking error.
Typical tracking error in India (2023–2024 data)
| Fund type | Typical annualised tracking error |
|---|---|
| Nifty 50 index fund (large AUM) | 0.05–0.15% |
| Nifty 50 ETF (liquid, large AUM) | 0.03–0.10% |
| Nifty Next 50 index fund | 0.10–0.25% |
| Nifty Midcap 150 index fund | 0.15–0.40% |
| Nifty Smallcap 250 index fund | 0.20–0.60% |
| International fund of funds | 0.50–1.50% |
| Gold ETF | 0.10–0.30% |
Midcap and smallcap funds have higher tracking error because their constituent stocks are less liquid and corporate actions (splits, bonuses, demergers) are more frequent and complex to execute.
Tracking error and TER
For index funds, TER is the most controllable driver of both tracking difference and tracking error. SEBI’s January 2022 circular capped index fund TER at 1.00 per cent, but the most competitive Nifty 50 funds now charge 0.05–0.15 per cent. The Nifty 50 TRI has delivered approximately 12–14 per cent per annum over 10-year periods; a 0.10 per cent TER fund keeps 99.2 per cent of that gross return, while a 0.50 per cent TER fund keeps 96.4 per cent.
Benchmark: total return index requirement
SEBI circular SEBI/HO/IMD/DF2/CIR/P/2018/007 (4 January 2018) mandated that equity mutual funds benchmark their performance against the total return index (TRI) of their stated benchmark, not the price-return index. Index fund tracking error must therefore be measured against the TRI (e.g., Nifty 50 TRI, not Nifty 50), because the TRI includes dividend reinvestment and represents what the fund is actually trying to replicate.
Prior to this mandate, performance was benchmarked against price-return indices, systematically understating tracking difference by the dividend yield of the index (approximately 1.0–1.5 per cent for Nifty 50).
How to evaluate tracking error for fund selection
- Compare tracking error within the same index and fund type (e.g., all Nifty 50 funds, not mixed categories).
- Prefer funds with at least 3 years of data, 1-year tracking error estimates are noisy.
- Examine both tracking difference (average deviation) and tracking error (consistency). A fund with a tracking difference of −0.20 per cent (slightly underperforms the index by 0.20 per cent per year, equal to its TER) and a tracking error of 0.08 per cent is well-managed. A fund with a tracking difference of −0.25 per cent and a tracking error of 0.50 per cent is inconsistent in its replication despite a similar TER.
- Look at the rolling 1-year tracking error over several years, not just the point estimate.
Tracking error for active funds
The term “tracking error” is also used for actively managed funds relative to their benchmark, but in the active context it measures the degree of active positioning. A large active fund with a tracking error of only 1–2 per cent against its benchmark is a “closet indexer”, it charges active management fees but takes little active risk. The information ratio divides alpha by tracking error to assess whether the active bets are worth the active risk taken.
SEBI disclosure requirements
SEBI and AMFI require that ETFs and index funds disclose tracking error in their scheme information documents and monthly factsheets. The AMFI circular of 2013 standardised the computation methodology (standard deviation of daily NAV returns vs daily benchmark TRI returns, annualised over the previous year). Some AMCs additionally disclose rolling tracking error in quarterly investor presentations.
See also
- Tracking difference in index funds
- Total return index benchmarking
- Total expense ratio
- Information ratio
- Portfolio turnover ratio
- Alpha (Jensen’s alpha)
- Mutual fund
- SEBI
References
- SEBI circular SEBI/HO/IMD/DF2/CIR/P/2018/007 dated 4 January 2018, TRI benchmarking mandate.
- AMFI circular on tracking error computation methodology, 2013.
- SEBI circular on index fund and ETF TER ceiling, January 2022.
- NSE Indices, Index methodology documents for Nifty 50 TRI and other indices.
- Value Research, Tracking error and tracking difference data for Indian index funds, valueresearchonline.com.