Equity Portfolios.

Equity portfolio management is a crucial aspect of investment management. It involves the strategic allocation of funds into different equity securities to achieve specific investment objectives. There are three principal approaches that equity portfolio managers use when building an indexed portfolio by transacting in individual securities. These approaches are Full Replication, Stratified Sampling and Optimization.

Full Replication

Full replication involves holding all securities in an index with weightings that match the actual index weightings to mimic its performance closely.

Advantages: Effectively achieves the primary goal of matching index performance. Simple and straightforward strategy.

Requirements: Sufficient asset size, liquidity, and availability of index constituents for trading are necessary for successful full replication.

Applicability: Not suitable for all indexes due to the high number of constituents in some (e.g., MSCI ACWI Investable Markets Index). More feasible for indexes with readily available constituents for trading (e.g., S&P 500).

Impact on Tracking Error: Tracking error decreases as the number of securities held increases, improving index replication accuracy. Adding smaller, less liquid stocks increases trading costs (brokerage fees, price pressure), which can negatively affect tracking performance. A U-shaped relationship exists between tracking error and the number of securities held due to increased transaction costs with less liquid stocks.

Portfolio Creation and Management in Full Replication

Portfolio managers seeking to match an index’s performance through full replication start by gathering detailed data from the index provider. This includes information on constituent stocks, their identifiers, shares outstanding, price, dividends paid, and total returns. Using data compilers like Charles River, Moxy, or other Order Management Systems (OMS), managers replicate the index constituents and their weights to construct the portfolio.

Utilizing Technology for Efficient Portfolio Construction

The portfolio construction process often involves spreadsheet and database programs, such as Excel and Access, for modeling. The OMS is crucial for not only constructing the portfolio but also for executing trades using protocols like FIX or SWIFT, ensuring pre-trade compliance, and adapting to index changes in a timely manner to maintain accurate performance tracking.

Adherence to Compliance and Execution Protocols

Pre-trade compliance checks are essential to address client-specific restrictions, front-running issues, and other regulatory requirements. The OMS facilitates these checks and the delivery of buy and sell orders, underscoring the importance of technology in modern portfolio management.

Maintenance and Adjustment for Index Changes

Following the initial portfolio creation, managers must promptly adapt to any changes announced by the index provider. This includes updating their models in the OMS and adjusting the number of shares to buy or sell. Accurate performance tracking requires trading at the market-on-close price to match the index provider’s performance calculations closely.

Stratified Sampling

Stratified sampling is a technique employed by portfolio managers when it becomes impractical to hold all the constituent securities of an index. This impracticality could arise due to a variety of reasons such as a large number of constituents, low trading liquidity of some constituents, high trading costs, or excessive brokerage fees. Instead of holding all constituents, a limited sample is held that closely tracks the index return and risk characteristics. Stratified sampling is not done randomly. It involves arranging a population into distinct strata or subgroupings. These strata should be mutually exclusive and exhaustive, and they should closely match the characteristics and performance of the index. Common stratification approaches include using industry membership and equity style characteristics.

Application in Portfolio Management:

For instance, consider a portfolio manager tracking the FTSE 100 index. Instead of investing in all 100 companies, the manager might divide the index into sectors such as technology, finance, healthcare, etc., and then select a few representative companies from each sector. This way, the portfolio still reflects the overall performance of the FTSE 100 index, but with fewer holdings and potentially lower costs.

Multi-Dimensional Stratification:

For multinational indexes, stratification is often done first on the basis of country affiliation. Indexes can be stratified along multiple dimensions, such as country affiliation and then industry affiliation, within each country. This multi-dimensional stratification can result in closer index tracking. For example, a global index might be divided first by country, then by sector within each country, and finally by company size within each sector.

Usage and Advantages:

Stratified sampling is most frequently used when the portfolio manager wants to track indexes that have many constituents or when dealing with a relatively low level of assets under management. For instance, the MSCI World Index consists of more than 1,600 constituents. Most investors would prefer not to trade and maintain 1,600 securities when a significantly smaller number of constituents would achieve most portfolios’ tracking objectives.

Weighting in Portfolio Management:

Regardless of the stratified sampling approach used, index-based equity managers tend to weight portfolio holdings proportionately to each stratum’s weight in the index. This means that if the technology sector makes up 20% of the FTSE 100 index, then around 20% of the portfolio would be invested in technology companies.

Optimization

Optimization is a fundamental approach in the construction of index portfolios. The primary objective of optimization is to either maximize a desirable characteristic or minimize an undesirable one, all while adhering to certain constraints. The ultimate goal of optimization is to achieve the lowest possible tracking error in an indexed portfolio, thereby ensuring the portfolio closely follows its benchmark index.

Constraints in Optimization

When constructing an optimized portfolio, there are several constraints that need to be considered. These constraints can significantly influence the composition and performance of the portfolio. They include:

The number of security holdings: For example, a portfolio may be constrained to hold no more than 50 constituent securities. This is similar to the S&P 500 index, which is composed of 500 large companies listed on stock exchanges in the United States.

Market capitalization: The portfolio may only include stocks with a market capitalization above a certain level. For instance, the Russell 2000 Index focuses on the smallest companies in the Russell 3000 Index, representing approximately 8% of the total market capitalization of that index.

Style characteristics: The portfolio may be required to mimic the style characteristics of the benchmark. For example, a growth fund may be required to invest in stocks that exhibit characteristics of high growth companies, such as high price-to-earnings ratios.

Trade restrictions: Trades may be restricted to round lots, which are standard trading units as defined by the exchange. For example, one round lot of stock is 100 shares.

Rebalancing costs: The portfolio may be limited to stocks that keep rebalancing costs low. This is particularly important for index funds that aim to track a benchmark index as closely as possible.

Optimization and Portfolio Volatility

While optimization aims to minimize tracking error, it can sometimes lead to portfolios that are mean-variance inefficient versus the benchmark. This means the optimized portfolio may exhibit higher risk than the benchmark. To address this, a constraint on total portfolio volatility can be added, aiming to make the portfolio’s total volatility equal to that of the benchmark. This is similar to the approach used by risk parity funds, which aim to allocate risk equally among different asset classes.

Post-Optimization Stage

After conducting a mean-variance optimization using all the index constituents, managers may delete the lowest-weighted stocks in a post-optimization stage. This is because investing in these stocks may involve transaction costs that exceed the diversification benefits. For example, a fund tracking the S&P 500 may choose not to hold the smallest companies in the index due to their higher trading costs and lower liquidity.

Optimization and Stratified Sampling

Optimization can be conducted in conjunction with stratified sampling or alone. When run without constraints, optimization programs do not consider country or industry affiliation but use security level data. This is similar to the approach used by global index funds, which aim to replicate the performance of a global benchmark index without considering country or industry weights.

Technical Sophistication

Optimization requires a high level of technical sophistication, including familiarity with computerized optimization software or algorithms, and a good understanding of the output. This is similar to the skills required by quantitative analysts, who use mathematical and statistical methods to solve complex financial problems.

Advantages of Optimization

Lower tracking error compared to stratified sampling: By considering the covariances among the portfolio constituents, optimization can achieve a lower tracking error compared to stratified sampling.

Explicit accounting for the covariances among the portfolio constituents: Optimization takes into account the relationships between different securities, which can help improve portfolio performance.

Limitations of Optimization

Despite its advantages, optimization has its limitations. The results of optimization are usually based on past market data, and may not apply to future periods due to variations in returns, variances, and correlations between securities. This means that optimization would need to be run frequently and adjustments made to the portfolio, which can be costly. This is similar to the challenges faced by active managers, who need to constantly adjust their portfolios to keep up with changing market conditions.

Blended Approach

This approach is particularly beneficial for indexes that cover a wide range of capitalizations, from large to small. Examples of such indexes include the Russell 3000, the S&P 1500, and the Wilshire 5000.

Full Replication for Larger Indexes:

In the context of these indexes, full replication is generally recommended for indexes with fewer constituent securities. To illustrate, consider the S&P 500, which is composed of 500 large-cap companies. The largest constituents, approximately 1,000 or so, are quite liquid. This liquidity implies that brokerage fees, bid-ask spreads, and trading costs are low. Therefore, for the largest-cap portion of an indexed portfolio, full replication is a sensible and desirable approach.

Alternative Approaches for Small-Cap Indexes:

However, when it comes to index constituents that have smaller market capitalizations or less liquidity, a different approach is needed. For instance, a small-cap index like the Russell 2000, which is composed of smaller, less liquid companies, may require a different strategy. In such cases, a stratified sampling or optimization approach can be useful. These methods are preferred for the reasons mentioned previously, which include the potential for lower costs and greater efficiency.

Practice Questions

Question 1: An equity portfolio manager is tasked with creating an index-tracking equity ETF portfolio. The manager wants to ensure that the portfolio’s characteristics match those of the index. To achieve this, the manager plans to divide the market into segments, or strata, and then select securities from each stratum. Which of the following portfolio management approaches is the manager likely to use in this scenario?

1. Full Replication
2. Stratified Sampling
3. Optimization

Answer: Choice B is correct.

The portfolio management approach that the manager is likely to use in this scenario is Stratified Sampling. Stratified sampling is a method used in index tracking where the market is divided into segments, or strata, and securities are selected from each stratum. The aim is to create a portfolio that mirrors the characteristics of the index, without necessarily holding all the securities in the index. This approach is often used when full replication is not feasible due to the large number of securities in the index or other constraints. By selecting representative securities from each stratum, the manager can ensure that the portfolio’s characteristics, such as sector allocation, market capitalization, and other factors, closely match those of the index. This approach can reduce tracking error and improve the portfolio’s performance relative to the index.

Choice A is incorrect. Full Replication is a method where the manager buys all the securities in the index in the same proportions as they are in the index. This approach ensures a perfect match with the index, but it may not be feasible if the index contains a large number of securities or if some securities are illiquid or hard to obtain.

Choice C is incorrect. Optimization is a method where the manager uses mathematical models to select a subset of securities from the index that is expected to provide the best possible match with the index’s characteristics. This approach can be more complex and requires more computational resources than stratified sampling. It also relies on the accuracy of the models used, which can be a source of risk.

Question 2: A portfolio manager is considering using mathematical models to select securities for an index-tracking equity ETF portfolio. The goal is to maximize the portfolio’s expected return for a given level of risk, or minimize risk for a given level of expected return. Which of the following portfolio management approaches is the manager considering?

1. Full Replication
2. Stratified Sampling
3. Optimization

Answer: Choice C is correct.

The portfolio manager is considering the Optimization approach. Optimization is a mathematical technique used in portfolio management that seeks to maximize a portfolio’s expected return for a given level of risk, or minimize risk for a given level of expected return. This is achieved by selecting the optimal combination of securities that provides the highest expected return for a given level of risk, or the lowest risk for a given level of expected return. The optimization process involves the use of mathematical models and algorithms to determine the optimal weights for each security in the portfolio. This approach is often used in the management of index-tracking equity ETF portfolios, where the goal is to replicate the performance of a specific index as closely as possible while managing risk and return.

Choice A is incorrect. Full Replication is a portfolio management approach where the manager buys all the securities in the same proportion as they are in the index. This approach does not involve the use of mathematical models to select securities and does not aim to maximize expected return for a given level of risk or minimize risk for a given level of expected return.

Choice B is incorrect. Stratified Sampling is a portfolio management approach where the manager selects a representative sample of securities from each sector or category within the index. This approach also does not involve the use of mathematical models to select securities and does not aim to maximize expected return for a given level of risk or minimize risk for a given level of expected return.

Glossary

• Full Replication: Holding all securities in an index in the same proportions as they appear in the index, aiming for exact index performance replication.
• Index Replication: Aiming to match the performance of a specific index through portfolio management techniques.
• Sampling: Holding a representative sample of securities from an index instead of full replication.
• Tracking Error: The divergence between the performance of a portfolio and its benchmark index.
• OMS: Software for tracking orders and securities across a portfolio.
• FIX or SWIFT Protocol: Standardized communication protocols for trade-related messages.
• Stratified Sampling: Dividing the market into segments and selecting securities from each to match the index’s characteristics.
• Optimization: Using mathematical models to select a portfolio aiming to maximize return for a given risk level or minimize risk for a given return level.
• Synthetic Replication: Using derivatives and other financial instruments to replicate an index’s performance.
• Over-the-Counter Derivatives: Financial instruments traded directly between parties, outside of exchanges.
• Blended Approach: Combining full replication for liquid issues with stratified sampling or optimization for less-liquid issues.
• Liquidity: The ease with which an asset can be bought or sold in the market without affecting its price.
• Market Capitalization: The total market value of a company’s outstanding shares, calculated by multiplying the share price by the number of shares.
• Global Industry Classification Standard (GICS): A classification system for equities, facilitating consistent investment research and reporting.
• Assets Under Management (AUM): The total value of the investments managed by a person or entity on behalf of clients.

Portfolio Management Pathway Volume 1: Learning Module 1: Index-Based Equity Strategies; LOS 1(d): Compare the full replication, stratified sampling, and optimization approaches for the construction of index-based equity portfolios.