Tracking Error and Excess Return in Portfolio Management
In the field of portfolio management, two key metrics stand out – Tracking Error and Excess Return. These metrics are used by investors to differentiate performance among portfolio managers.
Tracking Error
Tracking error is a measure of how closely a portfolio mimics its benchmark. It is a reflection of a manager’s ability to replicate the benchmark return. It is calculated as the standard deviation of the difference between the portfolio return and its benchmark index return. For instance, if a portfolio manager is managing a fund that is supposed to mimic the S&P 500, the tracking error would measure how closely the fund’s returns match the S&P 500’s returns.
The tracking error for a portfolio p is given by:
$$\text{Tracking error} = \sqrt{\text{Variance}_{R_{p} – R_{b}}}$$
Where \(R_{p}\) is the return on the portfolio and \(R_{b}\) is the return on the benchmark index.
Excess Return
On the other hand, excess return measures the difference between the portfolio returns and benchmark returns. For example, if a portfolio manager’s fund returns 10% in a year, and the benchmark index (like the S&P 500) returns 8%, the excess return would be 2%.
Excess return for portfolio p is calculated as:
$$\text{Excess return} = R_{p} – R_{b}$$
It is crucial to note that tracking error and excess return are distinct measures and should not be used interchangeably. Tracking error measures the manager’s ability to closely track the benchmark over time. Excess returns can be positive or negative and tell the investor how the manager performed relative to the benchmark. Tracking error, which is a standard deviation, is always presented as a non-negative number.
Index fund managers aim to have low tracking error and excess returns that are not negative. Low tracking error is important in measuring the skill of the index fund manager because the investor’s goal is to mimic the return stream of the index. Avoiding negative excess returns versus the benchmark is also important because the manager will want to avoid underperforming the stated index.
Tracking error varies according to the manager’s approach to tracking the index. An index that contains a large number of constituents will tend to create higher tracking error than those with fewer constituents. This is because a large number of constituents may prevent the manager from fully replicating the index. For an index fund, the degree of tracking error fluctuates over time. Also, the value will differ depending on whether the data frequency is daily or less frequent.
Potential Causes of Tracking Error and Excess Return
Tracking Error
Tracking error in an indexed equity fund can arise due to several reasons:
Fees: For instance, if a mutual fund charges a 2% management fee, this cost will reduce the fund’s returns and increase its tracking error. Higher fees contribute to lower excess returns and higher tracking error.
Number of Securities: For example, the S&P 500 index, which is highly liquid and investable, can be fully replicated by a fund. However, an index that includes small-cap stocks or international securities may be more difficult to replicate, leading to a higher tracking error.
Intra-day Trading: For instance, if a fund manager buys a stock at a higher price than its closing price on the index, this will contribute to the fund’s tracking error.
Trading Commission: For example, if a fund manager trades frequently, the commission costs paid to brokers can add up and contribute to the fund’s tracking error.
Cash Holding: For instance, if a fund receives dividends from its holdings, this cash balance can create a tracking error since equity indexes do not have a cash allocation.
Excess Return
The following factors can affect the excess return:
Trading Costs: For example, an index fund that passively tracks the S&P 500 will likely have lower trading costs than an actively managed fund, which can lead to a higher excess return.
Cash Drag: For instance, if a fund has a large cash balance due to uninvested investor contributions, this can create a cash drag that reduces the fund’s excess return, especially in a rising market.
Dividend Drag: For example, if a fund accrues cash dividends that are not immediately reinvested, this can create a dividend drag that reduces the fund’s excess return.
Practice Questions
Question 1: An index fund manager is considering two different indexes to track. Index X contains a large number of constituents, while Index Y has fewer constituents. The manager’s goal is to minimize tracking error. Based on this information, which index should the manager consider tracking?
- Index X, because a larger number of constituents will result in a lower tracking error.
- Index Y, because a smaller number of constituents will result in a lower tracking error.
- Index X, because a larger number of constituents will result in a higher tracking error.
Answer: Choice B is correct.
Index Y should be considered for tracking by the index fund manager because a smaller number of constituents will result in a lower tracking error. Tracking error is a measure of how closely a portfolio follows the index to which it is benchmarked. The smaller the tracking error, the closer the portfolio is following the benchmark index. When an index has fewer constituents, it is easier for the fund manager to replicate the index in the portfolio, thereby reducing the tracking error. This is because with fewer constituents, the fund manager has fewer securities to buy and sell, which reduces transaction costs and makes it easier to match the weights of the securities in the index. Therefore, if the manager’s goal is to minimize tracking error, it would be more advantageous to track an index with fewer constituents.
Choice A is incorrect. While it might seem intuitive that a larger number of constituents would provide more diversification and thus lower tracking error, this is not necessarily the case. A larger number of constituents can actually increase tracking error because it is more difficult for the fund manager to replicate the index accurately. This is due to the increased transaction costs and the difficulty in matching the weights of a larger number of securities.
Choice C is incorrect. While it is true that a larger number of constituents can result in a higher tracking error, this is not the desired outcome for the fund manager. The goal of the fund manager is to minimize tracking error, not to increase it. Therefore, choosing an index with a larger number of constituents would not be the best choice in this scenario.
Question 2: A portfolio manager is trying to understand the impact of cash drag on his portfolio’s value. In which of the following market conditions would the effect of cash drag on portfolio value be positive?
- When the market is rising
- When the market is falling
- When the market is stable
Answer: Choice B is correct.
The effect of cash drag on a portfolio’s value would be positive when the market is falling. Cash drag refers to the negative impact on investment returns caused by holding cash or cash equivalents in a portfolio. This is because cash typically earns a lower return than other investments. However, in a falling market, holding cash can actually be beneficial. This is because cash does not lose value when market prices fall. Therefore, a portfolio with a higher cash allocation would lose less value in a falling market than a fully invested portfolio. This is why the effect of cash drag would be positive in a falling market. It’s important to note that while cash can provide a buffer against losses in a falling market, it can also limit potential gains in a rising market.
Choice A is incorrect. In a rising market, the effect of cash drag on a portfolio’s value would be negative. This is because cash earns a lower return than other investments. Therefore, a portfolio with a higher cash allocation would earn less in a rising market than a fully invested portfolio.
Choice C is incorrect. In a stable market, the effect of cash drag on a portfolio’s value would likely be negative. This is because cash typically earns a lower return than other investments. Therefore, even in a stable market, a portfolio with a higher cash allocation would likely earn less than a fully invested portfolio. However, the impact of cash drag in a stable market would likely be less severe than in a rising market.
Glossary
- Tracking Error: A measure of how closely a portfolio mimics its benchmark. It is calculated as the standard deviation of the difference between the portfolio return and its benchmark index return.
- Excess Return: The difference between the portfolio returns and benchmark returns.
- Benchmark Index: A standard against which the performance of a portfolio is measured.
- Tracking Error: The deviation of the portfolio’s returns from its benchmark index.
- Excess Return: The return that an asset achieves over a period of time compared to a benchmark index.
- Cash Drag: The tracking error caused by temporarily uninvested cash.
- Dividend Drag: Cash drag attributable to accrued cash dividends paid to shareholders.
Portfolio Management Pathway Volume 1: Learning Module 1: Index-Based Equity Strategies;LOS 1(e): Discuss potential causes of tracking error and methods to control tracking error for index-based equity portfolios