CHAPTER 5: SECURITY-MARKET INDICATOR SERIES
• This chapter is about various market indexes. Again, an interesting but descriptive
• Questions we try to answer are:
o What are indexes and why are they useful?
o What are the differences among alternative indexes?
o What are some well-known stock market indexes?
o What are some well-known bond-market indexes?
• Security-Market Indexes and their uses
(Informal definition) A security market index is a number calculated by aggregating
the prices/values of a class of securities, with the idea that changes in this number can
reliably convey changes in all the securities in that class. e.g. the DJIA, the S&P500
Uses of indexes
1. As a benchmark to judge portfolio performance (be sure to analyze differential
risk). For example an index of growth stocks might be useful to evaluate the
performance of a mutual fund that calls itself “high-growth”.
2. To develop an index portfolio. There are several index funds which seek to
mimic or follow the performance of specific indexes. For example, the
Vanguard 500 index fund, which seeks to closely mimic the S&P 500 index
had the following returns:
1-year 3-year 5-year 10-year
Vanguard 500 index fund -14.85% 3.91% 14.45% 15.00%
S&P 500 -14.83 3.89 14.48 15.10
3. To examine factors that influence aggregate security price movement.
4. For technicians, who believe past stock price changes can be used to predict
future price movement.
5. As a proxy for the “market portfolio” when calculating the systematic risk of
• Indexes differ on three factors:
o The sample:
- Size: e.g. S&P 500 contains 500 components, while the DJIA contains only 30
- Breadth: should be broad enough to be representative of the desired class of
o Weighting sample members
- price-weighted series
- value-weighted series
- unweighted (equally weighted) series
o Computational procedure
- arithmetic average
- geometric average
• Stock Market Indexes
o Price-weighted Indexes
- Simply an arithmetic average of current prices of its components.
- The Dow Jones Industrial Average (DJIA) is the oldest and the most popular
index in the U.S.
History Lesson: When Charles Dow created the Dow Jones Industrial
Average, first published on May 26, 1896, it consisted of a dozen stocks. Only
one of the original 12, General Electric, is in the average today. And even GE
dropped out for a while -- deleted in 1898 but back nine years later as a
replacement for Tennessee Coal & Iron. (Source: http://www.dowjones.com)
- The DJIA is calculated as follows:
where the pits are the prices of the stock on a given day, and Dadj is the
adjusted divisor that day. A recent calculation follows:
The Dow Jones Industrial Average +10% HP +10%
09/07/01 9/10/01 09/??/01 09/??/01
Company Symbol Primary Group Close Close Close Close
Boeing BA Aerospace/Defence 45.18 43.46 43.46 43.46
United Technologies UTX Aerospace/Defence 65.64 66.20 66.20 66.20
Alcoa AA Aluminium 35.45 33.80 33.80 33.80
General Motors GM Auto Manufacturing 51.40 51.58 51.58 51.58
J.P. Morgan Chase JPM Banking 37.00 37.26 37.26 37.26
DuPont DD Chemical/Commodity 38.73 38.39 38.39 38.39
Hewlett-Packard HWP Computers 18.08 17.89 17.89 19.68
IBM IBM Computers 96.59 96.47 106.12 96.47
American Express AXP Diversified Financial 34.60 35.01 35.01 35.01
Citigroup C Diversified Financial 43.42 42.45 42.45 42.45
AT&T T Telecom 17.70 17.65 17.65 17.65
SBC Communications SBC Telecom 41.00 43.43 43.43 43.43
Procter & Gamble PG Non-durable goods 74.35 74.20 74.20 74.20
Caterpillar CAT Heavy machinery 48.86 48.10 48.10 48.10
General Electric GE Industrial-diversified 39.66 39.35 39.35 39.35
Honeywell International HON Industrial-diversified 35.75 35.70 35.70 35.70
3M MMM Industrial-diversified 100.78 102.20 102.20 102.20
Exxon Mobil XOM Oil 40.90 41.24 41.24 41.24
Johnson & Johnson JNJ Pharmaceutical 55.73 55.62 55.62 55.62
Merck MRK Pharmaceutical 64.30 66.10 66.10 66.10
International Paper IP Paper products 38.62 37.84 37.84 37.84
Eastman Kodak EK Recreational products 45.17 43.23 43.23 43.23
Walt Disney DIS Recreational products 24.11 23.58 23.58 23.58
Wal-Mart WMT Retail 46.22 46.23 46.23 46.23
Home Depot HD Home improvement 40.95 40.55 40.55 40.55
McDonald's MCD Restaurants 29.96 28.92 28.92 28.92
Intel INTC Semconductors 25.89 26.07 26.07 26.07
Coca-Cola KO Soft Drinks 49.73 49.95 49.95 49.95
Microsoft MSFT Software 55.40 57.58 57.58 57.58
Philip Morris MO Tobacco 47.08 48.15 48.15 48.15
Sum 1388.25 1388.20 1397.85 1389.99
DJIA Value 9605.85 9605.51 9672.26 9617.89
Change in DJIA value 0.69% 0.13%
- Note that the divisor is a scaling factor, and it keep going down as stocks split
over time. Consider Table 5.1 of your text:
After Three-for One
Before Split Split by Stock A
A 30 10
B 20 20
C 10 10
60 ÷ 3 = 20 40 ÷ X = 20
X = 2 (New Divisor)
- In a price-weighted series, higher-priced shares influence the index more than
the low-priced ones. For instance, in the above table, IBM is the high priced
stock and HP is the low priced stock. Assuming nothing else changes,
consider a 10% change in IBM compared to a 10% change in HP. In the
former case, the DJIA will go up by 0.69%, while in the latter, only by0.13%.
- Criticisms of the DJIA:
a) Sample is limited: 30 non-randomly selected blue-chip stocks are not
representative of the 1800 NYSE listed stocks.
b) Price-weighted series: A stock split results in less weighting for sample
stock. This introduces a downward bias in DJIA by reducing weighting of
fastest growing companies whose stock splits.
o Value-weighted Indexes
- Here, a different formula is applied to calculate the value of the index. First, a
base day is picked, usually the day the index is formed.
- Then, the prices of the components of the index, Pb and total number of shares
outstanding Qb that day are recorded.
- A base value is assigned to the index, usually 100.
- Now, the value of a value-weighted index at any time t is:
Index t = n
× Beginning index value
Table 5.4: Market-Value Weighted Stock
Dec 31, 1999 Dec 31, 2000
No. of Case A Case B
Stock Shares (mn) Price Value ($mn) Price Value Price Value
A 1,000,000 $ 10 10 $ 12 12 $ 10 10
B 6,000,000 $ 15 90 $ 15 90 $ 15 90
C 5,000,000 $ 20 100 $ 20 100 $ 24 120
200 202 220
Index Value 100 101 110
- Notice that the largest market value stocks have the greatest impact on the
value of the index.
- Most indexes are value-weighted, including the AMEX market value index,
the NASDAQ Composite, S&P 500 Composite Index etc.
o Unweighted (Equal-weighted) Index
- Movements in the index are typically based on the arithmetic/geometric
averages of the returns of the stocks making up the index.
- Let us see this with an example:
Table 5.6: Changes in an equal weighted index
Stock T T+1 HPR HPY
X 10 12 1.20 0.20
Y 22 20 0.91 -0.09
Z 44 47 1.07 0.07
Geometric mean = ((1.20)x(0.91)x(1.07))1/3 = 1.0523
Arithmetic mean = (0.20-0.09+0.07)/3 = 0.0591
Index value at time T 100.00
Index value at time T+1 (by geometric mean) 105.23
Index value at time T+1 (by arithmetic mean) 105.91
- Notice that since we use returns, prices and market values do not influence the
changes in the index. In other word, a $10 stock is as valuable as a $100 stock.
- Examples of these kinds of indexes are Financial Times ordinary share index,
and the ValueLine indexes.
o International Stock Indexes
Several organizations calculate and publish international (or world) indexes.
- FT/S&P-Actuaries World Indexes (Table 5.7)
- Morgan Stanley Capital International (MSCI) Indexes (Figure 5.3)
- Dow Jones World Stock Index (Figure 5.4)
Table 5.9 shows that all of these indexes have high correlations. i.e. they carry
pretty much the same information, and using any one is fine.
• Bond Market Indexes
o Relatively new and not widely published
o Growth in fixed-income mutual funds increase need for reliable benchmarks for
o Many managers have not matched aggregate bond market return
- increasing interest in bond index funds
- requires an index to emulate
o Difficulties in Creating and Computing Bond-Market Indexes
- Range of bond quality varies from U.S. Treasury securities to bonds in default
- Bond market changes constantly with new issues, maturities, calls, and
- Bond price volatilities are affected by duration, which is dependent on
maturity, coupon, and market yield.
- Correctly pricing individual bond issues without current and continuous
transaction prices available.
o Investment-Grade Bond Indexes
- Four investment firms maintain indexes for Treasury bonds and other
investment grade (rated BBB or higher) bonds. (See Table 5.10)
- The relationship among the bonds making up these indexes is strong
(correlations average 0.95). Thie means returns for all these bonds are driven
by aggregate interest rates - shifts in the government yield curveHigh-Yield
o Non investment-grade bonds
- Bonds rated BB, B, CCC, CC, C.
- Four investment firms and two academicians created indexes (Table 5.10)
- Relationship among alternative high-yield bond indexes is weaker than among
investment grade indexes.
o Global Government Bond Market Indexes
- Global bond market dominated by government issues, as few non-U.S.
countries have a corporate bond market or a high-yield bond market.
- Several indexes created by major investment firms (Table 5.10)
- Differences in index formation affect long-term risk-return performance.
- Low correlation among several countries is similar to stocks
- Significant exchange rate effect on volatility and correlations
• The text contains some more information on Composite stock-bond indexes, as well
as a comparison of indexes over time. I am not going to cover these in this course. I
think we now know what we need to about the basics of indexes.