Tracking Bond Benchmarks
5.6 C OMPARISON OF I NDEXES OVER T IME
We now look at price movements in the different indexes for monthly intervals.
5.6.1 Correlations between Monthly Equity Price Changes
Exhibit 5.13 contains a listing of the correlation coefficients of the monthly percentage of price changes for a set of U.S. and non-U.S. equity-market indexes with the Dow Jones Total Stock Market Index during the 31-year period from 1980 to 2010. The correlation differences are mainly attributable to the different sample of firms listed on the various stock exchanges. All of the indexes—are market-value-weighted indexes that include a large number of stocks.
Therefore, the computational procedure is generally similar and the sample sizes are large or all-encompassing. Thus, the major difference between the indexes is that the samples of stocks are from different segments of the U.S. stock market or from different countries.
There is a high positive correlation (0.98–0.99) between the Dow Jones Total Stock Market Index and the several comprehensive U.S. equity indexes: the S&P 500, and the Russell 3000 and Russell 1000 large cap index. In contrast, there are lower correlations with various style indexes such as the Russell 2000 Small-Cap index (0.828).
The correlations between the Dow Jones Total Stock Market Index and the several non-U.S.
indexes are clearly lower ranging from 0.462 (Pacific Basin) to 0.726 (Europe). All of these sup- port the case for global investing. These diversification results were confirmed with the compos- ite international series—with the MSCI EAFE (0.645) and the IFC Emerging Market (0.542)
138 Part 1:The Investment Background
respectively. These results confirm the benefits of global diversification because, as will be discussed in Chapter 7, such low correlations would definitely reduce the variance of a pure U.S. stock portfolio.
5.6.2 Correlations between Monthly Bond Index Returns
The correlations with the monthly Barclay Capital (BC) Govt. bond return index in Exhibit 5.13 consider a variety of bond indexes. The correlations with the U.S. investment-grade bond in- dexes ranged from about 0.94 to 0.98, confirming that although the levelof interest rates differ due to the risk premium, the overriding determinate of rates of return for investment-grade bonds over time are Treasury interest rates.
In contrast, the correlations with high-yield bonds indicate a significantly weaker relation- ship (correlations about 0.51) caused by strong equity characteristics of high-yield bonds as shown in Reilly, Wright, and Gentry (2009). Finally, the low and diverse relationships among U.S. investment-grade bonds and all world government bonds (0.57) and world government bonds without the United States (about 0.37) reflect different interest rate movements and ex- change rate effects (these non-U.S. government results are presented in U.S. dollar terms).
Again, these results support the benefits of global diversification of bond portfolios alone or with stock portfolios.
5.6.3 Mean Annual Security Returns and Risk
The use of security indexes to measure returns and risk was demonstrated in Exhibit 3.8 and 3.9, which showed the average annual price change, or rate of return, and risk measure for a large set of asset indexes.
Exhibit 5.13C o r r e l a t i o n C o e f f i c i e n t s B e t w e e n M o n t h l y P e r c e n t a g e P r i c e C h a n g e s i n V a r i o u s S t o c k a n d B o n d I n d e x e s : 1 9 8 0–2 0 1 0
Stock Indexes
Dow Jones Total
Stock Market Bond Indexes
Barclays Capital Govt. Bond
S&P 500 0.990 BC Aggregate Bds 0.981
Russell 3000 0.993 BC Corporate Bds 0.936
Russell 1000 0.997 BC High Yield Bds 0.512
Russell 2000 0.828 ML World Govt Bds 0.574
MSCI EAFE 0.645 ML World Govt Bds w/o U.S. 0.368
MSCI Europe 0.726 Treasury Bill–30 day 0.180
MSCI Pacific Basin 0.462 Treasury Bill–6 months 0.526
IFC Emerging Mkts 0.542 Treasury Note–2 years 0.918
FTSE All World 0.943
Brinson GSMI 0.926
SUMMARY
• Given the several uses of security-market indexes, it is important to know how they are constructed and the differences between them. To determine how the market is doing, you need to be aware of what market you are dealing with so you can select the appropriate index. For example, are you only interested in the NYSE or do you also want to consider NASDAQ? Beyond the U.S. mar- ket, are you interested in Japanese or U.K. stocks, or do you want to examine the total world mar- ket? This choice is discussed in Merjos (1990).
• Indexes are also used as benchmarks to evaluate portfolio performance.8 In this case, you must be sure the index (benchmark) is consistent with your investing universe. If you are investing worldwide,
you should not judge your performance relative to the DJIA, which is limited to 30 U.S. blue-chip stocks. For a bond portfolio, the index should like- wise match your investment philosophy. Finally, if your portfolio contains both stocks and bonds, you must evaluate your performance against an appro- priate combination of indexes.
• Investors need to examine numerous market in- dexes to evaluate the performance of their invest- ments. The selection of the appropriate indexes for information or evaluation will depend on how knowledgeable you are about the various in- dexes. The background from this chapter should help you understand what to look for and how to make the right decision in this area.
SUGGESTED READINGS
Fisher, Lawrence, and James H. Lorie.A Half Century of Returns on Stocks and Bonds.Chicago: University of Chicago Graduate School of Business, 1977.
Morningstar, Ibbotson.Stocks, Bonds, Bills, and Infla- tion.Chicago: Morningstar, annual.
QUESTIONS
1. Discuss briefly several uses of security-market indexes.
2. What major factors must be considered when constructing a market index? Put another way, what characteristics differentiate indexes?
3. Explain how a market index is price weighted. In such a case, would you expect a $100 stock to be more important than a $25 stock? Give an example.
4. Explain how to compute a value-weighted index.
5. Explain how a price-weighted index and a value-weighted index adjust for stock splits.
6. Describe an unweighted price index and describe how you would construct such an in- dex. Assume a 20 percent price change in GM ($40/share; 50 million shares outstanding) and Coors Brewing ($25/share and 15 million shares outstanding). Explain which stock’s change will have the greater impact on this index.
7. If you correlated percentage changes in the Dow Jones Total Stock Market Index with percentage changes in the NYSE composite and the NASDAQ composite index, would you expect a difference in the correlations? Why or why not?
8. There are high correlations between the monthly percentage price changes for the alter- native NYSE indexes. Discuss the reason for this similarity: is it size of sample, source of sample, or method of computation?
9. Assume a correlation of 0.82 between the Nikkei and the TSE Composite Index. Examine the correlation between the MSCI Pacific Basin Index and the DJTSM in Exhibit 5.13.
Explain why these relationships differ.
8Chapter 25 includes an extensive discussion of the purpose and construction of benchmarks and considers the use of benchmarks in the evaluation of portfolio performance.
140 Part 1:The Investment Background
10. You learn that the Dow Jones Total Stock Market market-value-weighted index increased by 16 percent during a specified period, whereas a Dow Jones Total Stock Market equal- weighted index increased by 23 percent during the same period. Discuss what this differ- ence in results implies.
11. Why is it contended that bond-market indexes are more difficult to construct and main- tain than stock-market indexes?
12. Suppose the Dow Jones Total Stock Market market-value-weighted index increased by 5 percent, whereas the Merrill Lynch-Dow Jones Capital Markets Index increased by 15 percent during the same period. What does this difference in results imply?
13. Suppose the Russell 1000 increased by 8 percent during the past year, whereas the Russell 2000 increased by 15 percent. Discuss the implication of these results.
14. Based on what you know about theFinancial Times(FT) World Index, the Morgan Stan- ley Capital International World Index, and the Dow Jones World Stock Index, what level of correlation would you expect between monthly rates of return? Discuss the reasons for your answer based on the factors that affect indexes.
15. How would you explain that the ML High-Yield Bond Index was more highly correlated with the NYSE composite stock index than the ML Aggregate Bond Index?
16. Assuming that the mandate to a portfolio manager was to invest in a broadly diversified portfolio of U.S. stocks, which two or three indexes should be considered as an appropri- ate benchmark? Why?
PROBLEMS
1. You are given the following information regarding prices for a sample of stocks.
P R I C E
S t o c k N u m b e r o f S h a r e s T T+ 1
A 1,000,000 60 80
B 10,000,000 20 35
C 30,000,000 18 25
a. Construct a price-weighted index for these three stocks, and compute the percentage change in the index for the period fromTtoT+ 1.
b. Construct a value-weighted index for these three stocks, and compute the percentage change in the index for the period fromTtoT+ 1.
c. Briefly discuss the difference in the results for the two indexes.
2. a. Given the data in Problem 1, construct an equal-weighted index by assuming $1,000 is invested in each stock. What is the percentage change in wealth for this portfolio?
b. Compute the percentage of price change for each of the stocks in Problem 1. Compute the arithmetic mean of these percentage changes. Discuss how this answer compares to the answer in Part a.
c. Compute the geometric mean of the percentage changes in Part b. Discuss how this re- sult compares to the answer in Part b.
3. For the past five trading days, on the basis of figures inThe Wall Street Journal, compute the daily percentage price changes for the following stock indexes.
a. DJIA b. S&P 500
c. NASDAQ Composite Index d. FT-100 Share Index
e. Nikkei 225 Stock Price Average
f. Discuss the difference in results for Parts a and b, a and c, a and d, a and e, and d and e.
What do these differences imply regarding diversifying within the United States versus diversifying between countries?
4.
P R I C E S H A R E S
C o m p a n y A B C A B C
Day 1 12 23 52 500 350 250
Day 2 10 22 55 500 350 250
Day 3 14 46 52 500 175a 250
Day 4 13 47 25 500 175 500b
Day 5 12 45 26 500 175 500
aSplit at close of day 2.
bSplit at close of day 3.
a. Calculate a Dow Jones Industrial Average for days 1 through 5.
b. What effects have the splits had in determining the next day’s index? (Hint: think of the relative weighting of each stock.)
c. From a copy ofThe Wall Street Journal, find the divisor that is currently being used in calculating the DJIA. (Normally this value can be found on pages C2 and C3.)
5. Utilizing the price and volume data in Problem 4,
a. Calculate a Standard & Poor’s Index for days 1 through 5 using a beginning index value of 10.
b. Identify what effects the splits had in determining the next day’s index. (Hint: think of the relative weighting of each stock.)
6. Based on the following stock price and shares outstanding information, compute the be- ginning and ending values for a price-weighted index and a market-value-weighted index.
D E C E M B E R 3 1 , 2 0 1 1 D E C E M B E R 3 1 , 2 0 1 2
P r i c e
S h a r e s
O u t s t a n d i n g P r i c e
S h a r e s O u t s t a n d i n g
Stock K 20 100,000,000 32 100,000,000
Stock M 80 2,000,000 45 4,000,000a
Stock R 40 25,000,000 42 25,000,000
aStock split two-for-one during the year.
a. Compute the percentage change in the value of each index during the year.
b. Explain the difference in results between the two indexes.
c. Compute the percentage change for an unweighted index and discuss why these results differ from those of the other indexes.
Use the Thomson One—Business School Edition Online Database to answer the following questions.
1. Collect price and number of outstanding share data from the past 10 days on the follow- ing firms: Amazon (AMZN), Family Dollar (FDO), J.C. Penney (JCP), Target (TGT), and Walmart (WMT). Using this data, create a “retail sales stock index” by computing a value-weighted index. What is the overall percent change of the index over the 10 days?
2. Using the market values for each stock on day l, compute the relative weight for each of the five stocks. Which stock has the largest weight and which stock has the smallest weight?
142 Part 1:The Investment Background
3. Using the data from above, compute a price-weighted and unweighted stock index. What is the overall percent change on each index? How do the behaviors of the value-weighted, price-weighted, and unweighted indexes compare over the 10 days?
4. Compare the performance during the 10-day time frame of (1) the price-weighted retail sales stock index with the Dow Jones Industrial Average and (2) the value-weighted re- tail sales stock index with the S&P 500.
A P P E N D I X C H A P T E R 5
Stock-Market Indexes
Exhibit 5A.1S u m m a r y o f S t o c k - M a r k e t I n d e x e s
Name of Index Weighting Number of Stocks Source of Stocks
Dow Jones Industrial Average Price 30 NYSE, NASDAQ
Nikkei-Dow Jones Average Price 225 TSE
S&P 400 Industrial Market value 400 NYSE, NASDAQ
S&P Transportation Market value 20 NYSE, NASDAQ
S&P Utilities Market value 40 NYSE, NASDAQ
S&P Financials Market value 40 NYSE, NASDAQ
S&P 500 Composite Market value 500 NYSE, NASDAQ
NYSE
Industrial Market value 1,601 NYSE
Utility Market value 253 NYSE
Transportation Market value 55 NYSE
Financial Market value 909 NYSE
Composite Market value 2,818 NYSE
NASDAQ
Composite Market value 5,575 NASDAQ
Industrial Market value 3,394 NASDAQ
Banks Market value 375 NASDAQ
Insurance Market value 103 NASDAQ
Other finance Market value 610 NASDAQ
Transportation Market value 104 NASDAQ
Telecommunications Market value 183 NASDAQ
Computer Market value 685 NASDAQ
Biotech Market value 121 NASDAQ
AMEX Market Value Market value 900 AMEX
Dow Jones Total Stock Market Index Market value 5,000 NYSE, AMEX, NASDAQ Russell Indexes
3000 Market value 3,000 largest in U.S. NYSE, AMEX, NASDAQ
1000 Market value 1,000 largest of 3,000 NYSE, AMEX, NASDAQ
2000 Market value 2,000 smallest of 3,000 NYSE, AMEX, NASDAQ
Financial TimesActuaries Index
All Share Market value 700 LSE
FT100 Market value 100 largest LSE
Small-Cap Market value 250 LSE
Mid-cap Market value 250 LSE
Combined Market value 350 LSE
Tokyo Stock Exchange Market value 1,800 TSE
Price Index (TOPIX) Value Line Averages
Industrials Equal (geometric
mean)
1,499 NYSE, AMEX, NASDAQ
Utilities Equal 177 NYSE, AMEX, NASDAQ
Rails Equal 19 NYSE, AMEX, NASDAQ
Composite Equal 1,695 NYSE, AMEX, NASDAQ
Financial TimesOrdinary Equal 30 LSE
Share Index (geometric mean)
FT-Actuaries World Indexes Market value 2,275 24 countries, 3 regions (returns in $, £, ¥, DM, and local currency)
1 4 4
Name of Index Weighting Number of Stocks Source of Stocks
MSCI Indexes Market value 1,375 19 countries, 3 international,
38 international industries (returns in $ and local currency)
Dow Jones World Stock Index Market value 2,200 13 countries, 3 regions, 120 industry groups (returns in $, £, ¥, DM, and local currency)
Euromoney—First Boston Global Stock Index
Market value — 17 countries (returns in $ and local currency)
Salomon-Russell World Equity Index
Market value Russell 1000 and S-R PMI of 600 non-U.S. stocks
22 countries (returns in $ and local currency)
Source:Compiled by authors.
Exhibit 5A.1S u m m a r y o f S t o c k - M a r k e t I n d e x e s ( c o n t i n u e d )
Name of Index Weighting Number of Stocks Source of Stocks
Exhibit 5A.2F o r e i g n S t o c k - M a r k e t I n d e x e s
Name of Index Weighting Number of Stocks History of Index
ATX-index (Vienna) Market value All listed stocks Base year 1967,1991 began including all stocks (Value = 100)
Swiss Market Index Market value 18 Base year 1988, stocks selected
from the Basle, Geneva, and Zurich Exchanges (Value = 1500)
Stockholm General Index Market value All listed stocks Base year 1979, continuously updated (Value = 100) Copenhagen Stock Exchange
Share Price Index
Market value All traded stocks Share price is based on average price of the day
Oslo SE Composite Index (Sweden)
Market value 25 Base year 1972 (Value = 100)
Johannesburg Stock Exchange Actuaries Index
Market value 146 Base year 1959 (Value = 100) Mexican Market Index Market value Variable number, based
on capitalization and liquidity
Base year 1978, high dollar returns in recent years Milan Stock Exchange
MIBMarket
Market value Variable number, based on capitalization and liquidity
Change base at beginning of each year (Value = 1000) Belgium BEL-20 Stock Index Market value 20 Base year 1991 (Value = 1000) Madrid General Stock Index Market value 92 Change base at beginning of
each year
Hang Seng Index (Hong Kong) Market value 33 Started in 1969, accounts for 75 percent of total market FT-Actuaries World Indexes Market value 2,275 Base year 1986
FT-SE 100 Index (London) Market value 100 Base year 1983 (Value = 1000) CAC General Share Index
(French)
Market value 212 Base year 1981 (Value = 100) Singapore Straits Times
Industrial Index
Unweighted 30
(continued)
Name of Index Weighting Number of Stocks History of Index
German Stock Market Index (DAX)
Market value 30 Base year 1987 (Value = 1000) Frankfurter Allgemeine Zeitung
Index (FAZ) (German)
Market value 100 Base year 1958 (Value = 100) Australian Stock Exchange Share
Price Indexes
Market value 250 Introduced in 1979
Dublin ISEQ Index Market value All stocks traded Base year 1988 (Value = 1000) HEX Index (Helsinki) Market value Varies with different
indexes
Base changes every day Jakarta Stock Exchange
(Indonesia)
Market value All listed shares Base year 1982 (Value = 100) Taiwan Stock Exchange Index Market value All listed stocks Base year 1966 (Value = 100) TSE 300 Composite Index
(Toronto)
Market value 300 Base year 1975 (Value = 1000) KOSPI (Korean Composite Stock
Price Index)
Market value (adjusted for cross- holdings)
All listed stocks Base year 1980 (Value = 100)
Source:Compiled by authors.
Exhibit 5A.2F o r e i g n S t o c k - M a r k e t I n d e x e s ( c o n t i n u e d )
Name of Index Weighting Number of Stocks History of Index
146 Part 1:The Investment Background
Developments in Investment Theory
Chapter 6
Efficient Capital Markets
Chapter 7
An Introduction to Portfolio Management
Chapter 8
An Introduction to Asset Pricing Models
Chapter 9
Multifactor Models of Risk and Return
1 4 7
The chapters in Part 1 provided background on why individuals invest their funds and what they expect to derive from this activity. We also argued very strongly for a global investment program, described the major instruments and capital markets in a global investment environ- ment, and showed the relationship among these instruments and markets.
We now are ready to discuss how to analyze and value the various investment instruments available. In turn, valuation requires the estimation of expected returns (cash flows) and a de- termination of the risk involved in the securities. Before we can begin the analysis, we need to understand several major developments in investment theory that have influenced how we specify and measure risk in the valuation process. The purpose of the four chapters in Part 2 is to provide this background on risk and asset valuation.
Chapter 6 describes the concept of efficient capital markets, which hypothesizes that secu- rity prices reflect the effect of all information. This chapter considers why markets should be efficient, discusses how one goes about testing this hypothesis, and describes the results of nu- merous tests that both support the hypotheses and indicate the existence of anomalies that are inconsistent with the hypotheses. There is also a consideration of behavioral finance, which has experienced a growth in reputation because it provides a rationale for some of the results.
We conclude the chapter with an extensive discussion of the implications of the results for those engaged in technical and fundamental analysis as well as portfolio management.
Chapter 7 provides an introduction to portfolio theory, which was developed by Harry Markowitz. This theory provided the first rigorous measure of risk for investors and showed how one selects alternative assets to diversify and reduce the risk of a portfolio. Markowitz also derived a risk measure for individual securities within the context of an efficient portfolio.
Following the development of the Markowitz portfolio model, William Sharpe and several other academicians extended the Markowitz model into a general equilibrium asset pricing model that included an alternative risk measure for all risky assets. Chapter 8 contains a de- tailed description of these developments and an explanation of the relevant risk measure im- plied by this valuation model, referred to as the capital asset pricing model (CAPM). We introduce the CAPM at this early point in the book because the risk measure implied by this model has been used extensively in various valuation models. Although the CAPM has long been the preeminent theoretical explanation in finance for the connection between risk and expected return, the past several decades have seen the rise of several competing models.
Chapter 9 is devoted to exploring several of these alternative asset pricing models, which differ from the CAPM primarily by specifying multiple risk factors in lieu of a single market portfolio-based variable. The chapter begins with an examination of thearbitrage pricing the- ory (APT), which is the conceptual foundation for virtually all of the subsequent multifactor asset pricing models. The APT, which was developed by Steve Ross in response to criticisms of the CAPM, suggests a linear relationship between a stock’s expected return and many sys- tematic risk factors.
One severe challenge for investors attempting to use the APT in practice is that it offers no theoretical guidance as to either the number or the identity of the risk factors. To overcome this problem, researchers have developed several multifactor models, which attempt to link a stock’s realized returns to market data on a collection of prespecified variables that are be- lieved to proxy for the APT risk factors. In specifying these variables, both macroeconomic and microeconomic approaches and risk factors have been adopted. After explaining these var- ious approaches, we demonstrate how they are used by investors to both evaluate individual companies and assess the investment styles of money managers and mutual funds.
148