Passive Portfolio Construction

Full Replication

Full replication entails purchasing all the individual securities within an index with weightings that closely mirror the index itself. Some indices are better suited for full replication than others, depending on certain factors. Several factors contribute to making full replication a more viable strategy:

• Smaller total shares traded within the index.
• Higher similarity between the shares.
• More liquidity in the shares.

The advantage of full replication is its ability to mimic index performance closely. However, the drawback lies in its potentially high cost. As the portfolio purchases more stocks from the underlying index, the initial reduction in tracking error occurs as the portfolio aligns more closely with the actual index. Yet, including less liquid securities increases transaction costs, affecting returns and causing the portfolio to deviate from the index.

In the graphic, the values on the left side illustrate the swift initial decline in tracking error as securities are added to the portfolio, moving away from the origin. As you move further along the x-axis (showing more securities in the portfolio), trading costs go up, and tracking error, not counting trading costs, goes down. This interplay results in an initial decrease in ‘net’ tracking error, reaching its lowest point and then gradually rising again.

Stratified Sampling

Stratified sampling breaks down an equity index into smaller groups. The most liquid securities from these groups are then added to the portfolio. The aim is for the portfolio to closely match the index's performance while controlling trading costs by excluding less liquid securities.

To do stratified sampling properly:

• Each security must belong to only one group.
• Each security must not belong to more than one group.

Meeting these conditions ensures effective stratified sampling. The index constituents can be categorized using NAICS or GICS codes.

Here's an example: The chart below categorizes companies by industry and sorts them from low to high bid-ask spread. In the tech industry, Company \(X\) has the highest bid-ask spread. In the home builders industry, Company \(C\) has the highest bid-ask spread. Excluding \(X\) and \(C\) from the portfolio could reduce transaction costs without significantly affecting tracking error. These less liquid firms often make up a small part of the index anyway.

$$ \begin{array}{c|c|c}
\textbf{Industry} & \textbf{Company} & \textbf{Bid-Ask} \\
\textbf{Classification} & & \textbf{Spread} \\
\text{TECH} & W & \$0.01 \\
\text{TECH} & Y & \$0.01 \\
\text{TECH} & Z & \$0.02 \\
\text{TECH} & X & \$0.11 \\ \\
\text{HOME BUILDERS} & D & \$0.02 \\
\text{HOME BUILDERS} & B & \$0.02 \\
\text{HOME BUILDERS} & A & \$0.02 \\
\text{HOME BUILDERS} & C & \$0.07
\end{array} $$

Optimization

Optimization in portfolio management is a method closely related to stratified sampling but with a more automated approach. Like stratified sampling, the goal is to minimize tracking error while closely representing index performance.

The distinction between stratified sampling and optimization lies in the use of modern portfolio theory tools in the latter. Optimization is a software-driven process that selects the best combination of securities to include in a portfolio to achieve two primary goals:

• Minimize tracking error.
• Reduce trading costs.

The process involves setting constraints for the software to work within, such as ESG considerations or portfolio size. The software then identifies the optimal set of shares to purchase. Studies indicate that adding constraints on portfolio volatility enhances outcomes, maintaining mean-variance efficiency under the extra constraint.

Advantages include accounting for correlations between securities without needing specific strata, such as industry classification. A limitation is that optimization relies on historical data, and its predictive power depends on how well the past reflects the future.

Blended Approach

The blended approach merges full replication with either stratified sampling or optimization. This technique is effective when an index includes numerous securities with diverse characteristics, such as a wide range of market capitalizations.

In this method, the most liquid securities are fully replicated, while the smaller, less liquid securities are included using stratified sampling or an optimization approach.

 

Question

Which attribute among the following does not contribute to the effectiveness of a full-replication approach?

1. Larger total shares traded on the index.
2. More similarity between shares.
3. More liquid shares.

Solution

The correct answer is A.

This attribute does not necessarily contribute to the effectiveness of a full-replication approach. In a full-replication strategy, the focus is on holding all the individual securities in the index, not on the total trading volume of the index itself. The effectiveness of full replication is more dependent on the availability and accessibility of all the index constituents, the ability to maintain the correct proportions, and the costs associated with trading and holding these securities. The total shares traded on the index may be unrelated to these factors.

B is incorrect. Having shares that are more similar in characteristics (e.g., market capitalization, sector, geographic location) can be advantageous when implementing a full-replication approach. This similarity can make it easier to replicate the index because the securities are more interchangeable. Therefore, this attribute can contribute to the effectiveness of a full-replication approach.

C is incorrect. The liquidity of shares is an important consideration for the effectiveness of a full-replication approach. Liquidity refers to how easily shares can be bought or sold in the market without impacting their price. More liquid shares are generally easier to trade and may result in lower transaction costs. Therefore, having more liquid shares can contribute to the effectiveness of a full-replication approach as it can help minimize trading costs.

Reading 24: Passive Equity Investing

Los 24 (d) Compare the full replication, stratified sampling, and optimization approaches for the construction of passively managed equity portfolios