Index Construction Methodologies
When it comes to constructing a home, there's a simple design with the necessary basics like a kitchen, bedrooms, and bathrooms. And then there are extras, like entertainment areas, special features, and unique add-ons.
This is somewhat similar to building a stock index. For some indexes, only certain stocks are chosen that meet certain criteria, but other indexes are at the opposite end of the spectrum.
No.
That's an index that's limiting its stocks based upon capitalization.
Definitely not.
A large-cap value index is limiting stock inclusion to only large-cap value stocks, so it's using specific criteria.
Once the index builders select the foundation of stocks that are included in the index, it's time to create the index. For practically all index providers, the goal is to capture the market—in particular, those stocks that are driving sentiment. So what do you think the weighting of indexes is based upon?
No.
The relation of fees to weighting isn't a good way to capture the market's status.
Not quite.
Liquidity doesn't capture how the market does, as some small stocks do well while others don't.
This simple approach can be advantageous for investors because the capitalization-weighted index is mean–variance efficient, meaning that it offers the highest return for a given level of risk. Why might the capitalization-weighted index be mean–variance efficient?
Within market-cap weighting, the most common approach is free-floating weighting, where each stock's shares are adjusted for closely held shares that aren't available to the investing public. These adjustments are made to account for strategic holdings by key individuals, corporations, or even foreign governments. This process can be complex, with different index providers reporting different shares outstanding for a company due to weighting differences.
No.
The absolute lowest risk would be the risk-free rate, but that's not the relationship between risk and return here.
Not quite.
The mean–variance-efficient portfolio produces the highest return per a level of risk, so that's not always the absolute highest return.
In comparison to the other weighting methods, why would an equally weighted index potentially be more diversified?
No.
That's a market-cap weighting index, and it's focused on the largest companies, so it's not broadly diversified.
Why might investor capacity be an issue for small-cap stocks?
That's not it.
That's a price-weighted index, which is focused on the company with the highest price.
Given this, what type of investor may receive benefits from using an equal weighting approach?
That's not it.
There are more small-cap companies that large-cap companies, so there are plenty of companies to invest in.
No.
Since the market cap of small-cap stocks is small, there's a greater market price impact from investing large amounts in them.
No.
Taxes will remove the benefits associated with mispriced securities in an equally weighted index once rebalancing occurs.
No, actually.
Individual investors can't achieve the necessary investment amounts to ensure that the mispriced stocks generate satisfactory returns.
Speaking of intrinsic value, another type of weighting system is fundamental weighting, where stocks are weighted based upon a fundamental characteristic. Although fundamental weighting and market-cap weighting share characteristics like low cost, transparency, investability, and being rules based, market-cap weighting is based upon efficient market hypothesis, while fundamental weighting is based upon market inefficiencies.
Given that $$\frac{1}{n}$$ is how an equally weighted index is calculated, what do you think an HHI value of 1 indicates?
No.
The value $$\frac{1}{n}$$ is used to create the equally weighted index, which is the least-concentrated portfolio.
That's right!
An HHI value of 1 indicates a security concentration in a single stock. That's some pretty high concentration. In addition to using HHI to calculate the concentration, you can also use it to calculate the effective (or equivalent) number of stocks held in equal weights that matches the concentration level of the chosen index. That equation is
$$\mbox{Effective number of stocks} = \frac{1}{\sum^n _{i=1} w^2_i} = \frac{1}{HHI}$$.
You can see that the effective number of stocks is the reciprocal of the HHI. Studies have shown how important the HHI and the effective stock calculation can be. In fact, many market-cap weighted indexes have a surprisingly low number of effective stocks.
That's not it.
The value $$\frac{1}{n}$$ is used to create the equally weighted index, so 1 isn't an equally diversified portfolio.
Think about an index using stock selection versus exhaustive inclusion. Which do you think would have the higher turnover in general?
Some index providers use a committee to help prevent investors from increasing the prices of securities. What's another way to describe the process of using a committee?
That's not it.
Exhaustive inclusion incorporates all stocks into the index, so it's going to have limited turnover.
No, actually.
An index with narrower criteria will have higher turnover in general.
No.
Objective criteria don't change, which allows investors to predict the additions and subtractions to the index.
Exactly!
A committee is another way to introduce subjective criteria into the index reconstitution process. In contrast, well-established reconstitution procedures allow investors to predict the inclusion or subtraction of securities, which impacts the price. In particular, stocks close to the break point between small-cap and large-cap indexes are especially at risk for price changes. For example, stocks that move down to the small-cap index are going to have the some of the largest weights in the index, making their price increase, while stocks that move to the large-cap index will have smaller weights, reducing their demand.
The final consideration in index construction is investability—stocks within the index must be available for timely purchase in liquidity markets.
To summarize:
[[summary]]
Exactly!
If some indexes limit inclusion, then the opposite of that is full inclusion of all securities. That's called an exhaustive index because it includes every constituent of a universe, while a selective index only includes securities with specific characteristics.
That's right!
Performance is the most common way to weight an index because it captures stocks that are driving returns. You're probably familiar with the market-cap weighting method, where a stock's weighting is determined by its market cap divided by the index's total market cap.
Right!
Since the market capitalization-weighted index is based upon market performance, it's essentially the market portfolio, which makes it mean–variance efficient. Plus, it will capture a strategy's investment capacity, meaning that it's weighted so that it captures the investor's natural need for liquidity.
That's it!
There's limited liquidity for small-cap stocks because the market capitalization doesn't allow for large amounts to be invested. That's one drawback of equally weighted indexes. However, research has shown that equally weighted portfolios have a natural advantage over market-cap weighted portfolios, as mispriced stocks will move up or down to their intrinsic values. Yet, after taxes and transaction costs in rebalancing, this advantage hardly remains.
Right!
Institutional, tax-exempt investors may experience superior returns because the tax exemption helps protect the gains from the rebalancing. Plus, the amounts invested can help the institutional investor achieve greater returns.
Exactly!
In general, the equally weighted index is the least concentrated index of the weighting methods because every stock has an equal impact on the performance of the index. Studies have shown that since equally weighted indexes are factor indifferent, they tend to have higher volatility than cap-weighting indexes because small-cap stocks have an equal weighting in the index.
Yes!
An index constructed with stock selection criteria will have greater turnover in general because stocks will need to meet the criteria consistently. In contrast, an exhaustive inclusion index tries to incorporate the entire stock universe, so there's limited turnover.
Incorrect.
A rules-based process will make it easier to predict the change in prices, so that's not a strategy that's associated with a committee.
Unlike only selecting special stocks, what would the opposite index include?
Another type of index weighting is a price-weighted index, where (just as the name implies) each stock is weighted by its price per share divided by the sum of all shares' prices in the index. Essentially, a price-weighted index owns one share of each security, but that's not really practical because investors don't invest that way. That's why this weighting isn't commonly used by portfolio managers, and it's difficult to implement due to stock splits, which impact the divisor.
A third type is equally weighted indexes. Equally weighted indexes are calculated by weights of $$\frac{1}{n}$$, where $$n$$ represents the number of stocks in the index. Since this approach doesn't show any preference to one stock, it's attractive to investors, especially when you consider diversification.
Additionally, equal weighting requires frequent rebalancing, since the weights will change once the market starts trading. Most investors use a regular rebalancing format (like once a quarter), but that can be an issue since the index isn't equally weighted 99% of the time. Equally weighted indexes also have investor capacity issues when it comes to the equality of small-cap stocks.
Another consideration when building an index is the stock concentration. For example, an index with a low number of stocks may be relatively undiversified. To examine this, you can use the Herfindahl–Hirshman Index (HHI), calculated as
$$\displaystyle \text{HHI} = \sum^n _{i=1} w^2_i$$
where $$w$$ is the weight of the stock $$i$$ in the portfolio. This calculation can range from $$\frac{1}{n}$$ (where $$n$$ is equal to the number of securities in the portfolio) to 1.
Additional considerations for index construction include strategies that are defensive or that reduce volatility. For example, some investors use indexes that weight stocks based upon their dividend yield, while volatility weighting calculates the volatility of each stock and weights the index based on the inverse of each stock's relative volatility.
Plus, it's important to consider the index's periodic rebalancing and reconstitution schedule. Reconstitution is the addition or deletion of index stocks, while rebalancing is the periodic reweighting of those stocks. Rebalancing and reconstitution both create turnover amongst stocks, but not all indexes have the same amount of turnover.
But an index's reconstitution can produce turnover for all indexes, and it can be significant for those that can correctly predict the stocks that are added and deleted. For example, stocks that are added to an index are in demand, so the price of the security usually goes up. In contrast, stocks that are deleted have lower demand, so their price goes down. This is particularly the case when an index has published rules that allow investors to anticipate the change.
Fees
Liquidity
Performance
It captures the market portfolio
It takes the absolute lowest risk
It produces the absolute highest return
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It places more emphasis on the largest companies
It's the least concentrated of the weighting methods
It places the most emphasis on the number of shares outstanding
There's low liquidity for small cap stocks
There's a limited number of companies to invest in
There's no market impact from investing large amounts in small-cap stocks
Individual, taxable investor
Individual, tax-exempt investor
Institutional tax-exempt investor
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A completely diversified portfolio
A portfolio concentration in a single security
An equally diversified portfolio amongst all securities
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Stock selection
Exhaustive inclusion
Both have the same turnover
Objective criteria
Subjective criteria
Rules-based criteria
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Only small-cap stocks
Only large-cap value stocks
Every single constituent in the stock universe
