Benchmark Selection

Indexes for Index-Based Strategies

There are a number of key factors an investor should consider when selecting an appropriate benchmark for an equity portfolio. Benchmarks are crucial for measuring performance, guiding investment decisions, and ensuring accountability. The following explore the characteristics of index-based strategies, the importance of transparency and investability, the role of index providers, and the concept of stock migration.

Three Requirements for an Index-Based Strategy

Rules

• Index composition and rebalancing must follow clear, objective, consistent, and predictable rules, such as criteria for including constituent stocks and the frequency of rebalancing.
• Unlike active managers whose decision processes are often non-replicable, index rules must be straightforward and replicable by others.
• The index must be replicable in real markets, allowing investors to buy and hold (or sell) the same constituents in the same proportions as the index.

Transparency

• Transparency is critical as index-based managers must understand the rules underlying their investment choices.
• Benchmark providers must clearly disclose:
  • The rules used to determine index constituents and weightings.
  • The constituent stocks included in the benchmark.
• This ensures that investors can verify the methodology and confirms that the index aligns with its stated objectives, avoiding black-box approaches.

Investability

• Investable Index Example: The FTSE 100 is an investable index because:
  • All constituent securities trade on the London Stock Exchange.
  • These securities have sufficient liquidity and transparency, making them easy to purchase.
• Non-Investable Index Examples:
  • HFRI Hedge Fund-of-Funds Indexes: Constituents are hedge funds that are not easily accessible to most investors.
  • Value Line Geometric Index: This index uses a multiplicative average price, making it difficult to replicate in a real-world portfolio.

Understanding Individual Securities (Free-Float Adjustments)

• Some stocks may have low free-float (i.e., shares available for public trading). For example:
  • In a startup, founders might hold a large portion of the shares, leaving few shares to trade publicly.
  • Low free-float can lead to low liquidity and high trading costs.
• Most equity indexes, such as the S&P 500, use a “free-float adjust” method:
  • Only counts shares available for public trading when calculating a company’s weight in the index.
  • Requires stocks to maintain float and average trading volumes above specific thresholds.

Role of Equity Index Providers

• Main Providers: CRSP, FTSE Russell, Morningstar, MSCI, and S&P Dow Jones.
• Responsibilities:
  • Establishing and publicizing rules: Ensures transparency and consistency.
  • Communicating changes in constituents: Investors need to track additions/removals and rebalancing details.
  • Reporting performance: Allows for benchmarking of portfolio returns and risk metrics.
• Data from providers is often offered for a fee. Over time, these providers refine their rules to keep their indexes more investable and representative of their target market.

Steps to Enhance Index Investability

Stock Migration Between Indexes

Stocks may transition from one index to another as their market capitalization changes, such as moving from small-cap to mid-cap to large-cap indexes, or vice versa if their market capitalization decreases. Managing this migration effectively is critical to maintaining investability and reducing trading costs.

Techniques to Manage Migration

Buffering

Buffering establishes ranges around breakpoints that determine index membership, ensuring that stocks remain in their current index unless they exceed specific thresholds. This approach reduces frequent changes and ensures smoother transitions:

• For example, in the MSCI USA Large Cap Index, which includes the 300 largest US companies, a stock in the MSCI USA Mid Cap Index must rank as the 200th largest company to move up to the Large Cap Index.
• Conversely, a large-cap constituent must drop to the 451st rank to move down to the Mid Cap Index.
• Buffering helps mitigate the impact of daily market price fluctuations, ensuring gradual and orderly transitions.

Packeting

Packeting involves splitting a stock’s position into parts across different indexes to manage transitions more effectively:

• If a stock in a mid-cap index increases in capitalization and breaches the breakpoint for large-cap status, a portion of its holding moves to the large-cap index, while the rest remains in the mid-cap index.
• On the next reconstitution date, if the stock continues to meet large-cap qualifications, the remainder of the shares are transferred to the large-cap index.
• Packeting reduces portfolio turnover and lowers trading costs, providing a more efficient approach to index management.

Considerations When Choosing a Benchmark Index

Desired factor exposure

When selecting a benchmark index, the primary consideration is the desired factor exposures. These are determined by the objectives and constraints outlined in the investor’s investment policy statement (IPS). For equity portfolios, decisions include the geographic market segment, size, style, and other constituent characteristics that are considered risk factors. These factors are similar to those discussed in equity investment universe segmentation.

Geographic Market

The choice of geographic market is influenced by the investor’s circumstances, such as their domicile, risk tolerance, liquidity needs, and legal considerations. For instance, a Japanese institutional investor may have different considerations than a UK-based individual investor. The size of the domestic equity universe and the complexities of cross-border transactions are also factors to consider.

Size

Historical market data and empirical studies indicate that small-cap stocks tend to be riskier and provide a higher long-term return than large-cap stocks, making size an important consideration. Size classifications range from mega-cap to micro-cap, and many indexes aim to provide equity exposure to both small- and mid-cap companies. Investors desiring exposure across the capitalization spectrum may opt for an “all-cap” index.

Style

Equity benchmark selection also involves the investor’s preference for exposure on the growth versus value style spectrum. Growth stocks exhibit characteristics such as high price momentum, high P/Es, and high EPS growth, while value stocks may exhibit high dividend yields, low P/Es, and low price-to-book value ratios. Depending on their basic philosophy and market outlook, investors may have a strong preference for growth or value.

Broad Market Exposure

Broad market exposure is provided by nearly 79% of all indexes. Developed market indexes are about four times as common as emerging market indexes. The majority of total-return global equity indexes cover the all-cap space or are otherwise focused on large-cap and mid-cap stocks.

Index Construction and Maintenance

Once the investor has settled on the market, capitalization, and style of benchmark, the next step is to explore the method used in constructing and maintaining the benchmark index.

Equity Index Construction and Weighting Methodologies

Equity index providers utilize various methodologies for stock inclusion, which can be broadly classified into exhaustive and selective strategies. For instance, the FT Wilshire 5000 Index, a market-cap-weighted index, employs an exhaustive strategy by including approximately 5,000 publicly traded stocks from various market-cap ranges, making it one of the most comprehensive sets of constituents in the US market.

Conversely, selective strategies focus on securities with specific characteristics. The S&P 500 Index, which aims to provide exposure to US large-cap stocks, is an example of a selective approach. The index’s constituent securities are chosen through a committee process based on size and broad industry affiliation.

Weighting Method

The weighting method significantly influences an index’s performance. Market-cap weighting is a common method where each constituent company’s weight in the index is calculated as its market capitalization divided by the total market capitalization of all constituents of the index. This method is integral to the development of the capital asset pricing model, implying that the capitalization-weighted market portfolio offers the highest return for a given level of risk.

Moreover, a capitalization-weighted equity index can be a reasonable proxy for the market portfolio, and the tracking portfolio may be close to mean–variance efficient. This approach also reflects a strategy’s investment capacity, as a cap-weighted index can be considered a liquidity-weighted index. Many investor portfolios tend to be biased toward large-cap stocks and use benchmarks that reflect that bias.

Free-Float Weighting: Most Common Form of Market-Cap Weighting

Free-float weighting is a widely used method for determining a company’s weight in an index by adjusting its outstanding shares for those not generally available to the public. Unlike traditional market-cap weighting, which considers the total market value of all outstanding shares, free-float weighting excludes shares that are strategically held and unlikely to trade on the open market.

This adjustment process relies on publicly available information to identify shares held by governments, affiliated companies, founders, or employees, as these holdings are rarely traded. Free-float weighting ensures that the index more accurately reflects the investable portion of the market.

For example, consider Toyota Motor Corporation. A significant portion of Toyota’s shares might be held by the founding family, related entities, or strategic partners. These shares are not freely available for public trading. Therefore, in a free-float weighting methodology, these shares would be excluded when calculating Toyota’s weight in an index like the MSCI Japan Index. This adjustment ensures the index reflects only the portion of shares available to most investors and avoids distortions caused by strategic holdings.

Price-Weighted Index

A price-weighted index assigns weights based on the price per share of each constituent company. For example, in the Dow Jones Industrial Average, a well-known price-weighted index, each company’s share price is divided by the sum of all share prices in the index to determine its weight. However, this method is less common due to complications arising from stock splits.

Equally Weighted Indexes

Equally weighted indexes are a type of stock market index where each constituent stock is given the same weight. This means that the performance of each stock has an equal impact on the index’s total value. However, due to market fluctuations, these indexes require regular rebalancing to maintain equal weights. For example, the S&P 500 Index, offered by Standard & Poor’s, is rebalanced to equal weights every quarter. Despite this, for a 91-day quarter, the index remains unequally weighted for 99% of the time, highlighting a potential drawback of equally weighted indexes.

Drawbacks and Advantages of Equal Weighting

One major drawback of equal weighting is its limited investment capacity. Smaller-cap constituents in an equally weighted index may have low liquidity, making it difficult for investors to purchase large quantities of shares without affecting the price. For instance, a study by Zeng and Luo (2013) estimated the total investment capacity for tracking each of the S&P equally weighted equity indexes, revealing potential liquidity issues.

On the other hand, equally weighted portfolios can have an advantage over cap-weighted portfolios. If any constituent stocks are mispriced, equally weighted portfolios can yield superior returns as stock prices adjust to their correct intrinsic value. However, this advantage may diminish when considering taxes and transaction costs.

Non-Cap-Weighted Indexes

Besides equally weighted indexes, there are other non-cap-weighted indexes that are weighted based on a company’s fundamental characteristics such as sales, income, or dividends. This method, known as fundamental weighting, separates a stock’s portfolio weight from its market value, operating on the belief that stock prices will eventually align with their fundamental attributes.

Market-cap-weighted Indexes and Fundamentally Weighted Indexes

When it comes to investing, two popular strategies are the use of market-cap-weighted indexes and fundamentally weighted indexes. Both of these strategies offer benefits such as low cost, rule-based construction, transparency, and investability. However, they differ in their underlying philosophies. Market-cap-weighted portfolios are based on the efficient market hypothesis, which suggests that market prices reflect all available information. On the other hand, fundamentally weighted indexes aim to exploit potential inefficiencies in market pricing, such as undervalued or overvalued stocks.

Portfolio Concentration and Benchmark Selection

Choosing the right benchmark is crucial in investing. One important factor to consider is the concentration of the index. This is where the concept of the effective number of stocks comes into play. It indicates portfolio concentration and can provide crucial information. For instance, a high degree of stock concentration or a low effective number of stocks may suggest a relatively undiversified index, like the Dow Jones Industrial Average which only includes 30 companies.

Herfindahl–Hirschman Index (HHI)

The Herfindahl–Hirschman Index (HHI) is a measure of stock-concentration risk in a portfolio. The HHI is calculated using:

$$HHI = \sum_{i=1}^{n} w_i^2$$

where \(w_i\) is the weight of stock i in the portfolio. The HHI can range from 1/n, where n is the number of securities held, to 1.0. An HHI of 1/n signifies an equally weighted portfolio, while a value of 1.0 signifies portfolio concentration in a single security, such as if an investor put all their money into Apple stocks.

Effective Number of Stocks

The effective number of stocks for a portfolio is calculated as the reciprocal of the HHI. This can estimate the effective (or equivalent) number of stocks, held in equal weights, that would mimic the concentration level of the chosen index. For example, cap-weighted indexes like the S&P 500 have been shown to have a surprisingly low effective number of stocks due to the heavy weighting of large-cap stocks.

Example: Effective Number of Stocks

A market-cap-weighted index contains 60 stocks. The largest five stocks have the following weights: \(0.10, 0.085, 0.075, 0.065, 0.055\). The bottom 55 stocks collectively have a total weight of \(0.62\), and the sum of the squares of their weights is \(0.0125\).

Calculate the HHI

Sum of squares of the largest five stocks:
$$ \begin{align*} HHI_{\text{Top 5}} & = (0.10)^2 + (0.085)^2 + (0.075)^2 + (0.065)^2 + (0.055)^2 \\
& = 0.01 + 0.007225 + 0.005625 + 0.004225 + 0.003025 = 0.0251 \end{align*} $$

Sum of squares of the bottom 55 stocks is \(0.0125\).

$$ HHI = HHI_{\text{Top 5}} + HHI_{\text{Bottom 55}} = 0.0251 + 0.0125 = 0.0376 $$

Calculate the Effective Number of Stocks (ENS)

$$ ENS = \frac{1}{HHI} = \frac{1}{0.0376} \approx 26.60 $$

The ENS is derived as the reciprocal of the HHI and provides an estimate of the “effective” diversification in the portfolio. Although the index contains 60 stocks, the ENS of approximately \(26.60\) means that the portfolio’s concentration is equivalent to holding 26.6 equally weighted stocks. This highlights the disproportionate influence of the largest-cap stocks on the overall portfolio, despite the larger number of constituents.

Investment Strategies

Post the stock market crises of 2000 and 2007, defensive or volatility reducing investment strategies gained prominence. For instance, income-oriented investors might prefer strategies that weight benchmark constituents based on the dividend yield of each stock, such as the Dogs of the Dow strategy. Another strategy is volatility weighting, which calculates the volatility of each constituent stock and weights the index based on the inverse of each stock’s relative volatility. A related method produces a minimum-variance index using mean–variance optimization, a technique used in Modern Portfolio Theory.

Index Reconstitution and Rebalancing

Index reconstitution and rebalancing are key considerations in index construction. Reconstitution often involves the addition and deletion of index constituents, while rebalancing refers to the periodic reweighting of those constituents. For example, the S&P 500 index is rebalanced quarterly and reconstituted annually. The turnover for developed-market, large-cap indexes that are infrequently reconstituted tends to be low, while benchmarks constructed using stock selection rather than exhaustive inclusion have higher turnover.

Effects of Reconstitution

Reconstitution can produce additional effects. For instance, when a company like Tesla is added to the S&P 500, index-tracking portfolios, mutual funds, and ETFs will want to hold the newly included names and sell the deleted names. This demand can push up the stock prices of added companies while depressing the prices of the deleted ones. Depending on the reconstitution method used by index publishers, arbitrageurs may be able to anticipate the changes and front-run the trades that will be made by index-based managers.

Reconstitution Methods

Reconstitution methods vary. In some cases, the index rules are written such that the decision to add or remove an index constituent is voted on by a committee maintained by the index provider. Where a committee makes the final decision, the changes become difficult to guess ahead of time. In other cases, investors know the precise method used for reconstitution, so guessing is often successful. Stocks near the breakpoint between small-cap and large-cap indexes are especially vulnerable to reconstitution-induced price changes.

Investability

Investability is a final consideration. An effective benchmark must be investable in that its constituent stocks are available for timely purchase in a liquid trading environment. Indexes that represent the performance of a market segment that is not available for direct ownership by investors must be replicated through derivative strategies, which may be sub-optimal for many investors.

Practice Questions

Question 1: Transparency is a crucial requirement for an index to be used in an index-based investment strategy. This is because index-based managers need to understand the rules underlying their investment choices. In this context, what does transparency in an index mean?

1. The index rules and constituents are disclosed without any hidden methodologies.
2. The index is visible and well-known in the market.
3. The index is based on clear and simple rules that are easy to understand.

Answer: Choice A is correct.

Transparency in an index means that the index rules and constituents are disclosed without any hidden methodologies. This is crucial for index-based investment strategies because the managers need to understand the rules underlying their investment choices. The index rules include the criteria for selecting the constituents of the index, the weighting methodology, the rebalancing frequency, and any other rules that govern the construction and maintenance of the index. The constituents of the index are the individual securities that make up the index. Transparency in these aspects allows the managers to replicate the index in their portfolio, track the performance of the index, and understand the risks associated with the index. It also promotes trust in the index and its provider, as it shows that the index is constructed and maintained in a fair and objective manner.

Choice B is incorrect. While visibility and recognition in the market can be beneficial for an index, they do not constitute transparency. An index can be well-known and yet lack transparency if its rules and constituents are not fully disclosed.

Choice C is incorrect. While simplicity can enhance the understandability of an index, it does not equate to transparency. An index can have complex rules and still be transparent if these rules are fully disclosed. Conversely, an index can have simple rules but lack transparency if these rules are not fully disclosed.

Question 2: Equity index providers such as CRSP, FTSE Russell, Morningstar, MSCI, and S&P Dow Jones have adopted various policies to manage the migration of stocks between different indexes. One such policy is “packeting”, which involves splitting stock positions into multiple parts. How does the policy of packeting help in managing the migration of stocks between different indexes?

1. It increases portfolio turnover and trading costs.
2. It keeps portfolio turnover and trading costs low.
3. It has no impact on portfolio turnover and trading costs.

Answer: Choice B is correct.

The policy of packeting helps in managing the migration of stocks between different indexes by keeping portfolio turnover and trading costs low. Packeting is a process where a stock’s position is split into multiple parts or ‘packets’ and these packets are then gradually moved from one index to another over a period of time. This gradual migration helps to spread out the impact of the migration on the market, reducing the potential for price volatility and market disruption. By doing so, it also helps to keep portfolio turnover low, as it reduces the need for large, sudden trades that can result in high transaction costs. Furthermore, by spreading out the trades over time, packeting can also help to reduce the impact of trading costs on the overall performance of the index. Therefore, packeting is a useful tool for index providers to manage the migration of stocks between different indexes in a cost-effective and efficient manner.

Choice A is incorrect. Packeting does not increase portfolio turnover and trading costs. On the contrary, it is designed to reduce these factors by spreading out the migration of stocks over a period of time, thereby reducing the need for large, sudden trades that can result in high transaction costs.

Choice C is incorrect. Packeting does have an impact on portfolio turnover and trading costs. As explained above, it helps to keep these factors low by spreading out the migration of stocks over a period of time, thereby reducing the need for large, sudden trades and the associated trading costs.

Glossary

• Price-weighted index: An index in which each company’s weight is determined by its share price.
• Equally Weighted Index: A type of stock market index where each constituent stock is given the same weight.
• Rebalancing: The process of realigning the weights of a portfolio’s assets to maintain an intended level of risk or asset allocation.
• Cap-Weighted Index: A type of stock market index in which each constituent stock is weighted according to its total market capitalization.
• Fundamentally Weighted Indexes: A type of equity index in which components are chosen based on fundamental criteria as opposed to market capitalization.
• Herfindahl–Hirschman Index (HHI): A measure of the concentration of the constituents of a portfolio.
• Effective Number of Stocks: An estimate of the number of stocks, held in equal weights, that would mimic the concentration level of a chosen index.
• Volatility Weighting: An investment strategy that calculates the volatility of each constituent stock and weights the index based on the inverse of each stock’s relative volatility.

LOS 1(f): discuss considerations in choosing a benchmark for an equity portfolio