Managing Tracking Error - CFA, FRM, and Actuarial Exams Study Notes (2024)

FAQs

How to calculate tracking error in CFA? ›

Given a sequence of returns for an investment or portfolio and its benchmark, tracking error is calculated as follows: Tracking Error = Standard Deviation of (P - B) Where P is portfolio return and B is benchmark return.

Active risk (tracking error) is a function of the portfolio's exposure to systematic risks and the level of idiosyncratic, security-specific risk. It is a relevant risk measure for benchmark-relative portfolios. Absolute risk is the total volatility of portfolio returns independent of a benchmark.

In finance, tracking error or active risk is a measure of the risk in an investment portfolio that is due to active management decisions made by the portfolio manager; it indicates how closely a portfolio follows the index to which it is benchmarked.

To reduce tracking error, portfolio managers aim to invest cash flows at valuations similar to those used by the benchmark index provider.

Three indicator rule. If the model has factor complexity 1, the covariance matrix of the error terms, V (δ) = Θ, is diagonal, and each factor has at least three indicators (observed variables associated with that factor), then the CFA model is identified.

In an ideal case scenario, an index fund must have a tracking error of zero when comparing performance to its benchmark. But in reality, index funds lean towards the 1%, -2% range.

For example, a manager outperforming its benchmark by 5% each and every year would have the same tracking error - 0% - as a manager underperforming the benchmark by -5% each year.

Tracking Error

It is defined as the standard deviation of the excess return, that is, the difference between the return on a portfolio and the return on its benchmark. Unlike VaR, which is usually measured for shorter periods, tracking error is typically meas- ured in terms of monthly returns.

What are the factors affecting tracking error? ›

Here are some of the other factors that influence tracking error: Portfolio size. Variations in market capitalization, investment approach, timing, and other portfolio features. Alterations in index constituents.

Active risk, also known as tracking error, represents the standard deviation of active returns. Portfolios with substantial fluctuations in active returns will exhibit high active risk.

A case study with three muni index ETFs

The excess returns measure a straight arithmetic performance deviation over the given period. The tracking error—the more meaningful metric—shows the consistency of keeping the fund's returns in line with its benchmark.

Limited Scope: Tracking error only measures the deviation of a portfolio's return from its benchmark. It does not provide any information about the quality of the portfolio's investments. For example, a portfolio with a low tracking error may still have poor investment choices that result in low returns.

Standard Error of the Sample Mean Formula

Where S is the sample standard deviation; and S2=∑(Xi−X)2n−1 S 2 = ∑ ( X i − X ) 2 n − 1 .

Sampling error (also called error of estimation) is the difference between the observed value of a statistic and the quantity it is intended to estimate. For example, sampling error of the mean equals sample mean minus population mean.

To calculate IR, subtract the total of the portfolio return for a given period from the total return of the tracked benchmark index. Divide the result by the tracking error. The tracking error can be calculated by taking the standard deviation of the difference between the portfolio returns and the index returns.

The score needed to pass the exam is approximately 70%. I observed that students who scored near 70 in all subjects passed. There were some cases where a person missed 70 in one subject but still passed. The score required for the 90th percentile is around 85%.