# Value-Weighted Index: Definition, Calculation & Examples Video with Lesson Transcript

## Breaking Down the Capitalization-Weighted Index

Capitalization-weighted indexes are widely used because the values change proportionally to the price changes of each component (since market capitalization is determined by the stock price multiplied by the number of shares outstanding). The indices also consider the shareholder base of each component.

Since some companies own shares that are not fully available to the public, most of the indices use the free float factor to adjust calculations. The free float is the percentage of the shares available for trading.

Some investors criticize capitalization-weighted indexes for providing a distorted view of the stock markets

Stocks, also known as equities, represent fractional ownership in a company. Many believe that the primary reason for the distortion is the overweighting toward companies with the largest market capitalization.

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Market-capitalization weighted indexes (or market cap- or cap-weighted indexes) weight their securities by market value as measured by capitalization: that is, current security price * outstanding shares.

In a cap-weighted index, changes in the market value of larger securities move the index’s overall trajectory more than those of smaller ones. Let’s look at the same hypothetical five-member index, this time cap-weighted:

 Security Current Price Outstanding Shares Market cap Weighting A \$3 50 150 15% B \$1 50 50 5% C \$7 70 490 51% D \$9 20 180 19% E \$10 10 100 10% Total market cap 970 100%

At \$7/share, Security C doesn’t have the highest price, but it does have the largest market capitalization and thus the highest weighting in our index. Meanwhile, Security E, the highest priced security but also the one with the smallest number of outstanding shares, has fallen from the largest piece of the pie to second smallest.

The advantage of a cap-weighted index is obvious: It reflects the way markets actually behave. Larger companies do in fact have more dramatic effects on the overall market than smaller companies. It’s also a self-rebalancing methodology, in that as a company’s price or outstanding share quantity changes, so too does the proportions of stocks in the index basket.

But cap-weighted schemes aren’t perfect. For example, sometimes companies have shares that aren’t fully available for trade on the open market (such as government-held shares, or large privately-controlled holdings).

Most index providers adjust their cap-weighted indexes accordingly using a freefloat factor, or the percentage of shares available for trading.

Free Float Shares = (Shares x Free Float Factor)

So the free float market cap would be:

Float Market Cap = (Price x Shares x Free Float Factor)

There’s a more systemic downside to cap weighting, in that such indexes inherently assume that the EMH always holds—which isn’t necessarily true. Recent research shows that cap-weighted indexes tend to give too much weight to securities the market has overvalued and too little weight to ones it has undervalued. As a result, true market value is skewed.

Alternative weighting schemes to cap-weighting have gained more favor in recent years. These are covered briefly in the next section.

The CWI Composite is a capitalization-weighted index. It consists of four companies only: Company A, Company B, Company C, and Company D. The summary of the current stock prices and the total number of the shares outstanding for each company is given in the table below:

Using the information from the table above, we can calculate the market capitalization of each index component. The market capitalization can be found through the following formula:

Thank you for reading CFI’s explanation of a capitalization-weighted index. CFI is the official provider of the global Financial Modeling {amp}amp; Valuation Analyst (FMVA)™

Valuation Analyst (FMVA)® accreditation is a global standard for financial analysts that covers finance, accounting, financial modeling, valuation, budgeting, forecasting, presentations, and strategy.

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• Common Stock
• Diluted Shares Outstanding
• Nikkei Index
• Weighted Average Shares Outstanding

## Lesson Summary

Let’s take a few moments to recap what we’ve learned about value-weighted indexes…

An index tracks the performance of a group of securities and expresses it as a single number. Securities the index tracks can be assigned a weight, which determines how much each individual company has on the index number.

Market capitalization is the market price of a security time the number of shares outstanding. To calculate the value of a value-weighted index, sum the market capitalization for each company and divide it by a divisor which is set initially to make the index a round number.

## Market Capitalization = Stock Price x No. of Shares Outstanding

Thus, the market capitalization of each company in the index is:

• Company A = \$5 x 5,000,000 = \$25,000,000
• Company B = \$10 x 1,000,000 = \$10,000,000
• Company C = \$25 x 500,000 = \$12,500,000
• Company D = \$15 x 1,500,000 = \$22,500,000

The total market capitalization of the index is the sum of the market capitalization of all the components. Therefore, the market capitalization of the CWI Composite is:

CWI Composite = \$25,000,000 \$10,000,000 \$12,500,000 \$22,500,000 = \$70,000,000

The weight of each index component is determined using the formula below:

## Other weighting schemes

In an equally-weighted index, all the securities in the basket are, as it sounds, weighted in equal amounts. For example, take our hypothetical example index:

 Stock Price Share Weighting A \$3 2 20% B \$1 6 20% C \$7 0.86 20% D \$9 0.67 20% E \$10 0.60 20%

Equal weighting is a highly diversified scheme, and one that avoids the cap-weighting pitfall of overweighting overpriced stocks and underweighting underpriced stocks. But it’s hard to maintain long-term, as fund managers must constantly rebalance their portfolios due to daily price fluctuations.

What’s more, the need to invest equally all securities can cause problems in more illiquid markets or asset classes, as substantial investment by any one player can sometimes end up moving those markets instead of reflecting them.

Recently, new types of indexes have been introduced that eschew market pricing altogether as a means of weighting, and thus determine the value of their securities via other metrics.

Risk-weighted indexes, for example, assign security weights based on common assessments of risk. In a risk-weighted index, securities are weighted by the inverse of their variance, so that securities with lower historical volatility end up with higher weights in the index.

Fundamentally-weighted indexes instead weight their constituents based on their financial health as measured by accounting figures, such as sales, earnings, book value, cash flow and dividends.

## Stock Index

Ike is a securities analyst for a brokerage firm. He has created a small index for a few local companies called the Ike Index. An index tracks the stock price performance of a group of companies.

So instead of looking up a bunch of different stock prices to see how the local ones are doing, interested investors can just look at the Ike Index to see if the group is doing well or poorly. It’s just like the market averages you hear reported on radio and TV all the time, only smaller.

Ike is getting ready to make some big changes to how he calculates his index numbers. His clients would like to see the index weighted, or how much each individual company has on the index number, to make the larger companies count for more than the smaller ones, since the biggest companies have the most influence on the local job market and economic health.

Many of the most widely followed stock market indices are value-weighted. That includes The NASDAQ Composite Index, and the Wilshire 5000 Total Market Index.

## Stock Prices Change

Let’s see what happens later when the stock prices change. Ike will redo the table to reflect the new stock prices. That will also change the market capitalization for each company along with the total and weights.

Company Stock price Shares outstanding Market capitalization Weight
Company A \$195 500,000 \$97,500,000 42%
Company B \$120 1,000,000 \$120,000,000 52%
Company C \$70 200,000 \$14,000,000 6%

Adding up the market capitalization, we get a total market capitalization of \$231,500,000. Therefore, total market capitalization divided by divisor equals 985.1. Note that Company C’s weight has gone from 4% to 6% since the stock price had a big jump, but when we divide the total market capitalization by the divisor to get the new index value, we get \$231,500,000 / 235,000 = 985.1.

We see that the index value has fallen from 1000 to 985.1 even though the stock prices for the three companies increased by a total of \$10! This appropriately reflects the price declines in the bigger companies.

## The price-weighted index

Price-weighted indexes aren’t particularly common anymore. Still, one of the world’s most widely tracked indexes – the Dow Jones Industrial Average – uses price weighting, so the process is worth understanding.

A price-weighted index is one which includes an equal number of shares for each security in its basket – meaning the higher a security’s price goes, the more it will drive the index’s overall value.

For example, let’s look at a hypothetical five member price-weighted index basket:

 Security Price Share Weighting A \$3 10 10% B \$1 10 3% C \$7 10 23% D \$9 10 30% E \$10 10 33%

At \$10/share, Security E has the highest price and therefore the highest weighting in the index. Security B, on the other hand, costs only \$1/share; its weighting barely makes a blip in the overall basket.

A price-weighted index has many advantages: its weighting scheme is simple to understand and its daily value easy to calculate (it’s simply the sum of all the security prices divided by the total number of constituents).

The problem is, a security’s price alone doesn’t necessarily communicate its true market value. It ignores market forces of supply and demand. To fix this, we need a different weighting scheme.

## Value Weighted Index – A New Approach to Long-Term Investing

Ike knows the solution from what he learned in college. He’ll assign a weight to each company in the index based on the company’s value. This weight will determine how much influence each company will have on the results.

Investors value a company based on its market capitalization, which is the price of its stock times the number of shares outstanding. Bigger companies are more valuable, so they have a higher market capitalization.

Let’s look at a sample index for three of Ike’s companies to see how the process works. The first thing he does is look up the three companies’ stock prices and number of shares outstanding. Then he multiplies them together to get the market capitalization for each. Take a look at the table below to see how that looks:

Company Stock price Shares outstanding Market capitalization
Company A \$200 500,000 \$100,000,000
Company B \$125 1,000,000 \$125,000,000
Company C \$50 200,000 \$10,000,000

Now to get the weights for each company, first add up the market capitalization for each company to get the total. Then take each company’s market capitalization and divide it by the total to get its weight.

Company Stock price Shares outstanding Market capitalization Weight
Company A \$200 500,000 \$100,000,000 43%
Company B \$125 1,000,000 \$125,000,000 53%
Company C \$50 200,000 \$10,000,000 4%

As you can see, total market capitalization = \$235,000,000

Note how small company C has a much lower weight than the bigger companies — 4% compared to the 43% of Company A and the 53% of Company B. That means Company C will have a much smaller impact on the index.

On the other hand, value-weighted indexes seek not only to avoid the losses due to the inefficiencies of market-cap weighting, but to

performance by buying more of stocks when they are available at bargain prices. Value-weighted indexes are continually rebalanced to weight most heavily those stocks that are priced at the largest discount to various measures of value. Over time, these indexes can significantly outperform active managers, market cap-weighted indexes, equally-weighted indexes, and fundamentally-weighted indexes.

Annual return* of Value-Weighted Index over trailing 20 years: 16.1%

An

index

in which the price is determined by the price of individual

stocks

, weighted for total

market value

. For example, if the price of a component stock of the index changes, its effect on the index as a whole is proportionate to share’s price multiplied by the number of

shares

the company has outstanding. This means that changes in price will affect the index more if the component company has greater value. Most non-American market value-weighted indices give further weighting (called float-weighted indexing) to properly account for partial government ownership of many large corporations. This method of index weighting contrasts with a

price-weighted index

, in which all price changes are weighted differently, and a

market share-weighted index

, which weights only by the number of shares outstanding and not by their value. Major examples of a market value-weighted index include the

NASDAQ Composite Index

and the Standard {amp}amp; Poor’s 500. The latter uses float-weighted indexing to match its calculations more closely with foreign counterparts.

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