Choosing a Benchmark

• Rules Based: A benchmark should have well-defined criteria for including and excluding stocks, including how they are weighted and rebalanced. These rules need to be objectively implemented to allow investors to replicate the index's performance.
• Transparent: The rules mentioned above should be easily accessible and comprehensible to the public.
• Investable: The assets of the underlying index should be available for investors to purchase. If the index is not investable, replication becomes impossible.

Considerations for Choosing a Benchmark

Determining Desired Exposure

Investors have a wide range of options when it comes to selecting stock characteristics, including:

• Industry: Determining whether exposure to technology or consumer sectors discretionary is desired.
• Company size: Evaluating market capitalization from large to small-cap stocks.
• Investment style: Deciding between growth and value stocks.
• Other factors: Considering liquidity, momentum, and more.

Identifying Methods Used in Constructing and Maintaining Index

Various methods are employed in constructing and maintaining indices. These methods are covered in greater detail in other segments of the curriculum. Here's a recap of the major index composition methods:

• Market-cap weighting: This method assigns index representation based on a firm's total outstanding equity value. Larger companies receive greater representation due to their higher market capitalization, aligning with liquidity benefits.

  $$ \text{Market Capitalization} = \text{Price per share} \times \text{total shares outstanding} $$

• Price weighting: Simpler but less common, this method uses share prices to determine index representation, ignoring total shares outstanding. Smaller firms can gain more representation if they have fewer shares outstanding.
• Equal weighting: Every firm gets the same index representation, regardless of size. This method benefits smaller firms but can increase volatility.
• Fundamental weighting: This method considers factors like sales or EBITDA for assigning weights to firms.

Stock Concentration – Herfindahl-Hirschman Index

Stock concentration explains the degree of competition within a market or index. Indexes with high concentration have higher risk, meaning fewer companies have an increasing influence on a market.

The Herfindahl-Hirschman Index is the sum of the squared weights of the individual stocks in a portfolio.

$$
HHI = S^2_1 + S^2_2 + \dots S^{2}_{n} $$

Where:

\(HHI\) = Herfindahl-Hirschman Index

\(S_n\) = Market share of firm in index (as a percentage)

A market with an HHI of:

\(\lt 1,500\) = Competitive marketplace.

1,500 to 2,500 = Moderately concentrated marketplace.

\(\gt 2,500\) = Highly concentrated marketplace.

Effective Number of Stocks

Calculating the reciprocal of the HHI provides a value that reflects the effective number of stocks needed in an equally weighted index to replicate the concentration of the actual market being analyzed. This is useful because various markets utilize different weighting methods (e.g., price vs. market-cap weighted), allowing for a meaningful comparison of concentration levels across different indexes.

\(\frac {1}{HHI}\) = Effective number of stocks in an equally weighted index.

Question

Given the following data on a market, calculate the HHI of the market:

1. A market share = 60%.
2. B market share = 10%.
3. C market share = 15%.
4. D market share = 15%.

1. 415.0.
2. 100.0.
3. 4,150.0.

Solution

The correct answer is C.

The HHI is calculated as:

$$ HHI = 60^2+10^2+15^2+15^2 = 3,600+100+225+225 = 4,150 $$

A and B are incorrect. From the calculation the correct answer is 4,150.

Reading 24: Passive Equity Investing

Los 24 (a) Discuss considerations in choosing a benchmark for a passively managed equity portfolio