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Investing In Index Funds

What Is an Index?

An index is a process by which we can observe and record the performance of a group of equity assets or stocks.

They can be designed as a broad-based stock index fund that captures the spirit of an entire stock market, other index funds, exchange traded fund or a sub-sector of a stock market index that’s performance or commercial business activity.

Perhaps the most famous index of all is the U.S. based Dow Jones Industrial Average (DJIA or INDU…short for Industrials). It is an index of 30 of the largest blue-chip stocks in the U.S. stock market.

The 30 stocks that are the components are not static. As companies rise or fall in their value, so the components of the index can change, just as may happen if one component entity acquired or merged with another. Indeed, look back 30-years and almost half of all the companies as DJIA components back then are no longer members and some no longer exist in the stock market.

For instance:

  • Bethlehem Steel was the second largest steel company in the U.S.  It’s sales fell heavily in the 1970’s in the face of cheaper imports. It was removed from the DJIA after 70-years and went bankrupt in 2001.The assets were finally sold in 2003 and are now part of Mittal
  • General Motors (GM) was added to the Dow in 1925, but it was removed in 2009 following its bankruptcy filing and was replaced by Cisco Systems (CSCO)
  • Alcoa (AA) or Aluminium Company of America as it was known until formally changing its name in 1999 was replaced by Nike (NKE) in 2013

A quirk of the DJIA is that it is a “price-weighted index”, as opposed to one that is “market-cap weighted”, such as the S&P 500 (see below). The index is calculated by adding the stock prices of the 30 companies and then dividing by the divisor.

Divisor you say…what’s that?  

The Dow divisor is a numerical value used to calculate the level of the DJIA. It is continuously adjusted for corporate actions, such as dividend payments and stock splits.

Index divisors are commonly used in the case of a price-weighted stock market index, such as the DJIA, to generate a more manageable index value. Responsibility for ensuring that the Dow divisor is adjusted properly to maintain the DJIA’s historical accuracy rests with “The Wall Street Journal”. These are extremely useful for an index fund.

How does it work?

The DJIA divisor is used to maintain the historical continuity of the DJIA index since there have been numerous stock splits, spinoffs, and changes among the Dow constituents since the index was first introduced in 1896.

Given the major changes that have taken place within the market, the value of the DJIA divisor has changed significantly over the years. For example, it was at 16.67 in 1928 and as low as 0.147 in September 2019. As of December 2021, the divisor for DJIA is 0.1517 (4SF).    

Calculating The Divisor, A Simple Example:

Consider the following example to explain why we use a divisor.  Say we make a price-weighted index of two stocks A and B.

On Day 1 their prices are: A = 16 and B = 30   Index = 16 + 30 = 46 /2 = 23.0

On Day 2 their prices are: A = 22 and B = 29  Index = 22 + 29 = 51/2 =  25.5  (Index + 2.5)

A + 6, B -1   Net Change is + 5 and divided by two gives the index gain of +2.5.

It looks simple enough, however, say we now want to have a three stock index by adding C to A and B.

We cannot simply use expense ratios or ratio of the total number of stocks in large cap index funds as the divisor anymore. It will distort or skew the overall full index fund value.

Day 3  A = 24, B = 31 and C = 18   If I say the Index = (24 + 31 + 18)/3 = 73/3 = 24.3  Did the index fall, i.e. -1.2? No, as all we did was add a new stock.

Rather than using the number of stocks as the denominator in the calculation we must create a new divisor.

To do so when we expand the index, one must find the new price summation, which is simply the combined value of all stocks in the most popular index funds: i.e. 73, then divide it by the last reliable index value, which was 25.5.

Thus, the result is…………..73/25.5 = 2.8627

We then use that as my new divisor: So Day 3:  A + B + C = (24 + 31 + 18)/2.8627 = 73/2.8627 = 25.5

That has stabilised the value of the index and we use the very same index and divisor until there is a need to alter it.

Given this we can say that the value of the DJIA is given as:

DJIA Value =  1/dt     x     Σi P(i,t)

t = time period dt  = divisor value at time t

P(i,t) = Price of Dow 30 component at time t

NB:  each Dow Jones index e.g. Transport or Utilities has its own divisor.

Calculating Value For A Market-Cap Weighted Index:

Standard & Poor’s 500 Index or SPX is another world famous index of financial markets. It tracks the price movements of 500 leading U.S. companies, capturing the activity of approximately 80% of the market capitalisation of all U.S. stocks.

The value of the SPX is computed by a free-float market capitalisation-weighted methodology. This is used by most of the world’s leading indexes.

Calculate the free-float market capitalisation (FFMC) of individual stocks of each component in the index. The FFMC is the total value of all shares of a stock that are currently available in the market. This ignores shares allocated with exercise rights to executives and other interested parties.

This calculation takes the number of outstanding shares of each company and multiplies that number by the company’s current share price, or market value.

The market capitalisation for all component stocks of particular index is summed to obtain the total market capitalisation of the S&P 500 and this value is used as the numerator in the index calculation.

For example, Apple reported 16.41 Billion common shares outstanding as of May 27, 2022, and it closed the day at a market price of about USD149 per share.

16.41 Billion x USD 149 = USD 2445.09 Billion or a FFMC of USD2.45 Trillion.

As of May 27, 2022, the SPX total market capitalisation was USD38.29 Trillion.

Apple’s weight in the SPX was therefore calculated as:

USD   2.45 Trillion      x 100   =   0.06398 x 100 = 6.4%

USD 38.29 Trillion

The greater  the market weight of a company in benchmark index, the greater impact a change in its price will have on the underlying index.

SPX Value:

SPX Value =  1/dt     x     Σi = 1 to n Pi  x Qi

t = time period          dt  = divisor value at time t

Pi = Price of SPX component i at time t  and Qi = Free Float Shares of i

What Are “Index Funds”?

An index fund is a collection or portfolio that is constructed to mimic or track the components of a specified financial market index, or other than index funds or mutual funds generally, consider Table 1:

Index funds

How an Index Fund Works

“Indexing” is a form of investing in a passive manner into index funds, mutual funds or fund” management (See Below).

Whereas an “Active Fund Manager” is acting as a stock picker by timing their entry and exit from various positions the “Passive Fund Manager” constructs a portfolio whose components mimic the securities of a specified stock index, mutual fund company or index fund only. Put simply, an actively managed fund often seeks to outperform a market by buying and selling more frequently. You must be careful when choosing your fund, some funds invest in high-yield stocks while others want high-growth stocks, these have different investment risk.

The idea behind these passive funds, and for index mutual funds generally, is that by mimicking the profile of the index—the stock market as a whole, or a broad segment of it, the index mutual or index fund manager will match its performance as well. The initial minimum investment for an index mutual fund varies from fund to fund. Sometimes a index fund will have zero minimum investment, while sometimes the index fund requires higher fees.

There is an index and an index fund for nearly every financial market in existence. In the United States, the most popular index mutual funds track indexes of the S&P 500. But several other indexes and mutual funds are widely used as well, including:

  • Wilshire 5000 Total Market Index, the largest U.S. equities index
  • MSCI EAFE Index, consisting of foreign stocks from Europe, Australasia, and the Far East
  • Nasdaq Composite Index, made up of 3,000 stocks listed on the Nasdaq exchange
  • Dow Jones Industrial Average (DJIA), consisting of 30 large-cap companies

An index fund tracking the DJIA, for example, would invest in the same 30 large and publicly owned companies that comprise that particular index itself.

Changing The Portfolio:

The holdings or invest in index portfolio of an index fund’s performance, will only change when the underlying benchmark of what is index funds on experiences a change, e.g. when Nike replaced Alcoa in the DJIA in 2013.

If the index fund is tracking a weighted index the mutual fund’s managers will on a regular basis alter their portfolio by changing the percentage of different stock that they invest. Index funds hold so as to reflect the weightings within the underlying benchmark.

Passive investing means that at the beginning of constructing the mutual fund, the manager will create allocations according to the underlying index structure.  Moving forward, they do not engage in market timing, or rotation to “beat the market”. The most active they will be is when they rebalance to bring the exposure back in line with market indexes. This is fare from the stratergy of actively managed funds.

Active Versus Passive Investing:

Active Versus Passive Investing

Data collected by Richard Ferri, founder of Portfolio Solutions LLC and author of The Power of Passive Investing…More Wealth With Less Work” shows that since the 1930’s for all markets and asset classes of all the active managers 2/3 actively managed funds generally underperform and 1/3 outperform.

However, this outperformance index mutual funds is not sustained and over time the outperformers slip back to underperform index neutral or index tracking funds.

This point was echoed by Dr Charles Ellis, founder of Greenwich Associates, an international strategy consulting firm.  He found that if one took the rate of return achieved by index funds work with any or a group of active fund managers, that say they can beat the market, once one deducts the fees…very few do actually outperform.

Re fees, Anthony Neuberger, Professor Emeritus of Finance, Bayes Business School said the costs of research, transactions and marketing are loaded by many fund managers onto existing clients and too much research is ex-post not ex-ante.

Perhaps the best reason for choosing an investment fund that is passive come from John C Bogle, the founder of Vanguard Group. He concluded from his analysis that opinions were in plentiful supply, the future is largely unknown and that “…nobody knows anything…”. 

Final Thoughts

In this article we have learnt investing in index funds or a mutual fund offers a practical and steady path to financial growth. Index funds tend to be marked by the simplicity of tracking indices, the fascinating intricacies of the DJIA divisor and the power of investing passively.

In the grand debate between actively managed funds and passive strategies, index funds often emerge as the reliable, enduring choice. They may not promise overnight riches, but index funds provide the steady progress of a marathon runner, outperforming many active strategies over the long haul. Remember the wisdom of John C. Bogle: in a world where financial predictions are as elusive as a mirage, simplicity often triumphs. By choosing index funds, you embrace the wisdom of the tortoise, knowing that consistent and measured steps can lead to substantial financial gains.

In this world of financial complexities, the index fund is your compass, guiding you toward your financial goals. It’s a strategy that allows you to invest wisely and live confidently, knowing that you’re on a path that many have trodden successfully before. So, as you embark on your investment journey, may the index fund be your steadfast ally, helping you navigate the financial landscape with simplicity, wisdom, and the potential for long-term prosperity. Now you know all you need to invest in index funds.

Macroeconomic Strategist

Stephen Pope is the Managing Partner of Spotlight Group. He has worked in the world of finance since 1982 and has performed d... Continued