Understanding and Optimizing Tracking Error for Better Investment Management
What is Tracking Error?
Tracking error is the divergence between the price behavior of a position or a portfolio and the price behavior of a benchmark. This often occurs in the context of a portfolio like a hedge fund, mutual fund, or exchange-traded fund (ETF), creating an unexpected profit or loss when the investment doesn’t perform as intended. Tracking error is reported as a standard deviation percentage difference, measuring the gap between the return an investor receives and the benchmark they were attempting to mirror.
Key Takeaways
- Tracking error is the difference in performance between a position (usually an entire portfolio) and its corresponding benchmark.
- It serves as an indicator of how actively a fund is managed and its corresponding risk level.
- Evaluating a past tracking error of a portfolio manager may provide insight into the level of benchmark risk control the manager may demonstrate in the future.
Understanding Tracking Error
Since portfolio risk is often measured against a benchmark, tracking error is a crucial metric to gauge how well an investment is performing. Tracking error illustrates an investment’s consistency versus a benchmark over a given period. Even perfectly indexed portfolios exhibit slight differences from their benchmarks. Here’s how tracking error is calculated:
Tracking Error = Standard Deviation of (P - B)
- Where P is portfolio return and B is benchmark return.
For investors, tracking error helps assess portfolio managers’ effectiveness. If a manager has low average returns combined with a large tracking error, it signifies issues that might warrant finding a replacement. Tracking error is also used by quantitative managers to forecast performance and implement risk models.
Factors Influencing Tracking Error
Expense Ratios and NAV Divergence
The net asset value (NAV) of an index fund tends to be lower than its benchmark due to the presence of fund fees. However, exceptional fund management involving rebalancing, managing dividends, or securities lending can counter these fees and enhance performance.
Holdings and Weighting Differences
Funds often hold a representative sample of the benchmark’s securities. Variances in holdings and their weightings can cause tracking errors. Illiquid or thinly-traded securities can worsen this issue, as they lead to significant pricing differences during trading.
Volatility
The volatility level of an index affects its tracking error. Sector, international, and dividend ETFs typically have higher absolute tracking errors, while broad-based equity and bond ETFs exhibit lower ones.
Premiums and Discounts to NAV
Premiums or discounts occur when ETF prices deviate from the NAV of their basket of securities. Authorized participants usually arbitrage these discrepancies away. Premiums and discounts as high as 5% are known, especially in thinly traded ETFs.
Optimization and Sampling
ETF providers may sample the more liquid stocks of a benchmark index to avoid pushing up prices of less liquid stocks. This process, known as portfolio optimization, minimizes large price shifts and errors.
Diversification Constraints
ETFs comply with legal diversification constraints. For example, 75% of their assets must be in diverse securities and no more than 5% in any single security. This constraint can be challenging when tracking indexes with dominant companies.
Cash Drag
ETFs hold cash, unlike benchmarks without cash resources, primarily due to dividend payments, overnight balances, and trading activities. The lag from accumulating and reinvesting cash can lead to performance declines called ‘cash drag.’ High-yield dividend funds are more susceptible to this phenomenon.
Index Changes
Updates in the benchmarks compel ETFs to follow with their portfolio changes, incurring costs and sometimes resulting in discrepancies due to timing and price variations.
Capital-Gains Distributions
Though more tax-efficient than mutual funds, ETFs still distribute taxable capital gains, impacting their tracking error from an after-tax performance perspective. Higher turnover in fund components leads to higher gains distributions.
Securities Lending
To reduce tracking error, some ETF companies engage in securities lending, collecting fees from hedging funds involved in short selling, which can be used to moderate tracking errors.
Currency Hedging
ETFs using currency hedging techniques may not perfectly align with benchmark indexes, with factors like market volatility and differential interest rates affecting performance.
Futures Roll and Maintaining Leverage
Commodity ETFs execute futures roll by buying and selling near-expiry contracts monthly, which could incur losses if in contango. Leveraged ETFs maintain consistency with their benchmarks through daily derivatives rebalancing.
Illustrative Example of Tracking Error
Consider a large-cap mutual fund benchmarked to the S&P 500 index over five years with the following returns:
- Mutual Fund: 11%, 3%, 12%, 14%, and 8%.
- S&P 500 index: 12%, 5%, 13%, 9%, and 7%.
Calculating their differences provides: ‑1%, ‑2%, ‑1%, 5%, and 1%. The standard deviation of these differences, calculated as tracking error, is 2.50%.
Related Terms: standard deviation, net asset value, expense ratio, risk management, portfolio optimization.
References
- U.S. Government Publishing Office. “Investment Act of 1940”, Page 24.
