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CHAPTER 2 
SECURITY MARKET INDICES 
Presenter 
Venue 
Date
DESCRIPTION OF A SECURITY MARKET 
INDEX 
Security market 
index 
Price return index Total return index 
Constituent 
securities
VALUE OF A PRICE RETURN INDEX 
n P 
D 
N 
i 
V 1 
PR 
 
  
i i 
I 
VPRI = the value of the price return index 
ni = the number of units of constituent securities in the 
index 
N = the number of constituent securities in the index 
Pi = the unit price of constituent security i 
D = the value of the divisor
CALCULATION OF SINGLE-PERIOD PRICE 
RETURN 
  
  
 
 
 
 
  
 
 
 
  
V  
V 
 
N 
i 
N 
P P 
i i 
i i i 
1 0 
i i 
I I 
PR 1 PR 0 
I 
I 
1 1 0 
PR 0 
P 
w PR w 
V 
PR 
PRI = the price return of index portfolio I 
PRi = the price return of constituent security i 
wi = the weight of security i 
Pi1= the price of constituent security i at the end of the 
period 
Pi0= the price of constituent security i at the beginning 
of the period
EXAMPLE: CALCULATION OF SINGLE-PERIOD 
PRICE RETURN 
(200 10) (100 25) (400 15) 
(200 12) (100 24) (400 18) 
.1429 14.29% 
120.00 105.00 
105.00 
Security 
I 
PR 0 
PR 
120.00 
100 
V 
105.00 
100 
V 
I 
PR 1 
  
 
 
 
     
 
 
     
 
I 
Beginning 
of Period 
Price (€) 
Ending of 
Period Price 
(€) 
Dividends 
per share 
(€) 
Shares 
Outstanding 
LMN 10.00 12.00 0.50 200 
OPQ 25.00 24.00 1.00 100 
RST 15.00 18.00 0.25 400 
Divisor = 100
CALCULATION OF SINGLE-PERIOD TOTAL 
RETURNS 
V  V  
Inc 
N 
I PRI I 
PR 1 0 
V 
PR 0 
  
  
 
 
 
 
   
 
 
 
 
TR  w TR  
w 
I i i i 
i 
N 
P P Inc 
i i i 
1 0 
P 
i i 
I 
I 
1 1 0 
TR 
TRI = the total return of the index portfolio 
IncI = the total income from all securities in the index 
TRi = the total return of the constituent security i 
Inci = the total income from security i
EXAMPLE: CALCULATION OF SINGLE-PERIOD 
Security 
Beginning 
of Period 
Price (€) 
Ending of 
Period 
Price (€) 
Dividends 
per share 
(€) 
Shares 
Outstanding 
LMN 10.00 12.00 0.50 200 
OPQ 25.00 24.00 1.00 100 
RST 15.00 18.00 0.25 400 
Divisor = 100 
Inc [(200 0.50)  (100 1.00)  (400 0.25)] 100  3.00 I 
  
TR   
.1714 17.14% 
120.00 105.00 3.00 
105.00 
 I 
TOTAL RETURN
CALCULATION OF INDEX VALUES OVER 
MULTIPLE TIME PERIODS 
The calculation of index values over multiple time 
periods requires geometrically linking the series of 
index returns. 
    
  
V  V 1  PR 1  PR 1  
PR 
I I I I I 
    
PR T PR 0 1 2 T 
V V 1 TR 1 TR 1 TR 
    
  
TR I T TR I 0 I 1 I 2 I 
T
EXAMPLE: CALCULATION OF INDEX VALUES 
OVER MULTIPLE TIME PERIODS 
For an index with an inception value set to 1,000 and 
price returns of 5 percent and 3 percent for Periods 1 
and 2 respectively, the values of the price return index 
would be calculated as follows: 
Period Return (%) Calculation Ending Value 
0 1,000(1.00) 1,000.00 
1 5.00 1,000(1.05) 1,050.00 
2 3.00 1,000(1.05)(1.03) 1,081.50
CHOICES IN INDEX CONSTRUCTION AND 
MANAGEMENT 
Which target market should the index represent? 
Which securities should be selected from that target market? 
How much weight should be allocated to each security in the index? 
When should the index be rebalanced? 
When should the security selection and weighting decision be re-examined?
TARGET MARKET SELECTION 
Defined 
broadly or 
narrowly? 
Target 
market 
Based on an 
asset class? 
Based on 
geographic 
region? 
Other 
characteristics 
? 
Based on an 
exchange?
DIFFERENT WEIGHTING METHODS USED IN 
INDEX CONSTRUCTION 
Index 
weighting 
Price weighted 
Equal 
weighted 
Market 
capitalization 
weighted 
Fundamentally 
weighted
WEIGHTING SCHEMES 
 N 
 
i 
 
i 
i 
i 
1 
P 
P 
P 
w 
1 
wE  
N i 
 N 
Q P 
 
 
j 
i i 
j j 
i 
1 
M 
Q P 
w 
F 
 N 
 
j 
j 
i 
i 
1 
F 
F 
w 
Price weighted: 
Equal weighted: 
Market capitalization weighted: 
Factor weighted:
EXHIBIT 2-1 EXAMPLE OF A PRICE-WEIGHTED 
INDEX 
Security 
Shares 
in 
Index 
BOP 
Price 
Value 
(Shares 
x BOP 
Price) 
BOP 
Weight 
% 
EOP 
Price 
Dividends 
Per Share 
Value 
(Shares 
x EOP 
Price) 
Total 
Dividends 
Price 
Return 
% 
Total 
Return 
% 
BOP 
Weight 
x Price 
Return 
% 
BOP 
Weight 
x Total 
Return 
% 
EOP 
Weight 
% 
A 1 50.00 50.00 49.26 55.00 0.75 55.00 0.75 10.00 11.50 4.93 5.66 52.38 
B 1 25.00 25.00 24.63 22.00 0.10 22.00 0.10 –12.00 –11.60 –2.96 –2.86 20.95 
C 1 12.50 12.50 12.32 8.00 0.00 8.00 0.00 –36.00 –36.00 –4.43 –4.43 7.62 
D 1 10.00 10.00 9.85 14.00 0.05 14.00 0.05 40.00 40.50 3.94 3.99 13.33 
E 1 4.00 4.00 3.94 6.00 0.00 6.00 0.00 50.00 50.00 1.97 1.97 5.72 
Total 101.50 100 105.00 0.90 3.45 4.33 100.00 
Index 
Value 
20.30 21.00 0.18 3.45 4.33 
Divisor = 5 
BOP = Beginning of period 
EOP = End of period 
Type of Index BOP Value Return % EOP Value 
Price Return 20.30 3.45 21.00 
Total Return 20.30 4.33 21.18
EXHIBIT 2-3 EXAMPLE OF AN EQUAL-WEIGHTED 
EQUITY INDEX 
Security 
Shares 
in 
Index 
BOP 
Price 
Value 
(Shares 
x BOP 
Price) 
Weight 
% 
EOP 
Price 
Dividends 
Per Share 
Value 
(Shares 
x EOP 
Price) 
Total 
Dividends 
Price 
Return 
% 
Total 
Return 
% 
Weight 
x Price 
Return 
% 
Weight 
x Total 
Return 
% 
EOP 
Weight 
% 
A 40 50.00 2,000 20.00 55.00 0.75 2,200 30 10.00 11.50 2.00 2.30 19.93 
B 80 25.00 2,000 20.00 22.00 0.10 1,760 8 –12.00 –11.60 –2.40 –2.32 15.94 
C 160 12.50 2,000 20.00 8.00 0.00 1,280 0 –36.00 –36.00 –7.20 –7.20 11.60 
D 200 10.00 2,000 20.00 14.00 0.05 2,800 10 40.00 40.50 8.00 8.10 25.36 
E 500 4.00 2,000 20.00 6.00 0.00 3,000 0 50.00 50.00 10.00 10.00 27.17 
Total 10,000 100.00 11,040 48 10.40 10.88 100.00 
Index 
Value 
1,000 1,104 4.80 10.40 10.88 
Divisor = 10 
BOP = Beginning of period 
EOP = End of period 
Type of Index BOP Value Return % EOP Value 
Price Return 1,000.00 10.40 1,104.00 
Total Return 1,000.00 10.88 1,108.80
EXHIBIT 2-4 EXAMPLE OF A MARKET-CAPITALIZATION- 
WEIGHTED EQUITY INDEX 
Stock 
Shares 
Out-standing 
BOP 
Price 
BOP 
Market 
cap 
BOP 
Weight 
% 
EOP 
Price 
Dividends 
Per Share 
EOP 
Market 
cap 
Total 
Dividends 
Price 
Return 
% 
Total 
Return 
% 
BOP 
Weight 
x Price 
Return 
% 
BOP 
Weight 
x Total 
Return 
% 
EOP 
Weight 
% 
A 3,000 50.00 150,000 26.29 55.00 0.75 165,000 2,250 10.00 11.50 2.63 3.02 28.50 
B 10,000 25.00 250,000 43.82 22.00 0.10 220,000 1,000 –12.00 –11.60 –5.26 –5.08 38.00 
C 5,000 12.50 62,500 10.96 8.00 0.00 40,000 0 –36.00 –36.00 –3.95 –3.95 6.91 
D 8,000 10.00 80,000 14.02 14.00 0.05 112,000 400 40.00 40.50 5.61 5.68 19.34 
E 7,000 4.00 28,000 4.91 6.00 0.00 42,000 0 50.00 50.00 2.46 2.46 7.25 
Total 570,500 100.00 579,000 3,650 1.49 2.13 100.00 
Index 
1,000 1,014.90 6.40 1.49 2.13 
Value 
Divisor = 570.50 
BOP = Beginning of period 
EOP = End of period 
Type of Index BOP Value Return % EOP Value 
Price Return 1,000.00 1.49 1,014.90 
Total Return 1,000.00 2.13 1,021.30
COMPARISON OF FUNDAMENTAL WEIGHTING WITH 
MARKET-CAPITALIZATION WEIGHTING 
Assume a 2-stock Index, consisting of Stock A and 
Stock B: 
Stock A 
Earnings = €20 
Market cap = €200 
Market cap weight = 20% 
Fundamental weight = 50% 
Stock B 
Earnings = €20 
Market cap = €800 
Market cap weight = 80% 
Fundamental weight = 50%
ADVANTAGES AND DISADVANTAGES 
Price 
weighted 
Simple 
High price 
stocks have 
greater impact 
Stock splits 
result in 
arbitrary 
changes 
Equal 
weighted 
Simple 
Under- and 
over-representation 
Frequent 
rebalancing 
Market 
capitalization 
weighted 
Securities 
held in 
proportion to 
their value 
Similar to a 
momentum 
strategy 
Fundamental 
weighted 
Ensures a 
value or 
contrarian tilt 
Data 
intensive
REBALANCING 
May become 
necessary as 
market prices 
change 
Creates 
turnover 
Rebalancing
RECONSTITUTION 
Beginning 
index 
Reconstitution 
date 
Change 
constituent 
securities? 
New index
USES OF MARKET INDICES 
Gauges of market sentiment 
Proxies for measuring and modeling returns, 
systematic risk, and risk-adjusted performance 
Proxies for asset classes in asset allocation models 
Benchmarks for actively managed portfolios 
Model portfolios for such investment products as 
index funds and exchange-traded funds (ETFs)
EQUITY INDICES 
Equity indices 
Broad market 
Wilshire 5000 
Total Market 
Index 
Multimarket 
MSCI Emerging 
Markets 
Sector 
GSTI 
Semiconductor 
Index 
Style 
Dow Jones 
U.S. Small-Cap 
Value Index
CHALLENGES FACING FIXED INCOME INDEX 
CONSTRUCTION 
Lack of 
pricing 
data 
Number 
of 
securities 
Illiquid 
securities
EXHIBIT 2-9 DIMENSIONS OF FIXED-INCOME 
INDICES 
Market 
Global 
Regional 
Country or currency zone 
Type Corporate 
Collateralized 
Securitized 
Mortgage-backed 
Government 
agency 
Government 
Maturity For example, 1–3, 3–5, 5–7, 7–10, 10+ years; 
short-term, medium-term, or long-term 
Credit 
quality 
For example, AAA, AA, A, BBB, etc.; Aaa, Aa, A, 
Baa, etc.; investment grade, high yield
INDICES FOR ALTERNATIVE 
INVESTMENTS 
Commodities 
Real estate 
Hedge funds 
Indices 
for 
alternative 
investments
COMMODITY INDICES 
Risk-free 
interest rate 
Changes in 
futures 
prices 
Roll yield 
Commodity 
index 
return
REAL ESTATE INDICES 
Appraisal 
indices 
Repeat sales 
indices 
Real estate 
investment trust 
(REIT) indices 
Ownership of 
properties 
Investment in 
mortgages
EXHIBIT 2-12 THE FTSE EPRA/NAREIT GLOBAL 
REIT INDEX FAMILY 
Source: FTSE International, “FTSE EPRA/NAREIT Global & Global Ex US Indices” 
(Factsheet 2009).
HEDGE FUND INDICES 
Hedge funds are private investment 
vehicles that typically use leverage and 
long and short investment strategies. 
Research organizations maintain 
databases of hedge fund returns and 
summarize these returns into indices. 
Most indices reflect performance on a 
broad global level or on a strategy level. 
Most indices are equal weighted.
PROBLEMS CAUSED BY VOLUNTARY 
INVESTMENT REPORTING 
Voluntary 
investment 
performance 
Survivorship 
bias 
Indices reflect 
different 
performances 
for the same 
time period
SUMMARY 
• Price return index 
• Total return index 
• Choices in index construction and 
management 
• Advantages and disadvantages of different 
weighting schemes 
• Rebalancing and reconstitution 
• Uses of market indices 
• Equity, fixed income, and alternative 
investment indices

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Investments chapter2

  • 1. CHAPTER 2 SECURITY MARKET INDICES Presenter Venue Date
  • 2. DESCRIPTION OF A SECURITY MARKET INDEX Security market index Price return index Total return index Constituent securities
  • 3. VALUE OF A PRICE RETURN INDEX n P D N i V 1 PR    i i I VPRI = the value of the price return index ni = the number of units of constituent securities in the index N = the number of constituent securities in the index Pi = the unit price of constituent security i D = the value of the divisor
  • 4. CALCULATION OF SINGLE-PERIOD PRICE RETURN                V  V  N i N P P i i i i i 1 0 i i I I PR 1 PR 0 I I 1 1 0 PR 0 P w PR w V PR PRI = the price return of index portfolio I PRi = the price return of constituent security i wi = the weight of security i Pi1= the price of constituent security i at the end of the period Pi0= the price of constituent security i at the beginning of the period
  • 5. EXAMPLE: CALCULATION OF SINGLE-PERIOD PRICE RETURN (200 10) (100 25) (400 15) (200 12) (100 24) (400 18) .1429 14.29% 120.00 105.00 105.00 Security I PR 0 PR 120.00 100 V 105.00 100 V I PR 1                   I Beginning of Period Price (€) Ending of Period Price (€) Dividends per share (€) Shares Outstanding LMN 10.00 12.00 0.50 200 OPQ 25.00 24.00 1.00 100 RST 15.00 18.00 0.25 400 Divisor = 100
  • 6. CALCULATION OF SINGLE-PERIOD TOTAL RETURNS V  V  Inc N I PRI I PR 1 0 V PR 0                TR  w TR  w I i i i i N P P Inc i i i 1 0 P i i I I 1 1 0 TR TRI = the total return of the index portfolio IncI = the total income from all securities in the index TRi = the total return of the constituent security i Inci = the total income from security i
  • 7. EXAMPLE: CALCULATION OF SINGLE-PERIOD Security Beginning of Period Price (€) Ending of Period Price (€) Dividends per share (€) Shares Outstanding LMN 10.00 12.00 0.50 200 OPQ 25.00 24.00 1.00 100 RST 15.00 18.00 0.25 400 Divisor = 100 Inc [(200 0.50)  (100 1.00)  (400 0.25)] 100  3.00 I   TR   .1714 17.14% 120.00 105.00 3.00 105.00  I TOTAL RETURN
  • 8. CALCULATION OF INDEX VALUES OVER MULTIPLE TIME PERIODS The calculation of index values over multiple time periods requires geometrically linking the series of index returns.       V  V 1  PR 1  PR 1  PR I I I I I     PR T PR 0 1 2 T V V 1 TR 1 TR 1 TR       TR I T TR I 0 I 1 I 2 I T
  • 9. EXAMPLE: CALCULATION OF INDEX VALUES OVER MULTIPLE TIME PERIODS For an index with an inception value set to 1,000 and price returns of 5 percent and 3 percent for Periods 1 and 2 respectively, the values of the price return index would be calculated as follows: Period Return (%) Calculation Ending Value 0 1,000(1.00) 1,000.00 1 5.00 1,000(1.05) 1,050.00 2 3.00 1,000(1.05)(1.03) 1,081.50
  • 10. CHOICES IN INDEX CONSTRUCTION AND MANAGEMENT Which target market should the index represent? Which securities should be selected from that target market? How much weight should be allocated to each security in the index? When should the index be rebalanced? When should the security selection and weighting decision be re-examined?
  • 11. TARGET MARKET SELECTION Defined broadly or narrowly? Target market Based on an asset class? Based on geographic region? Other characteristics ? Based on an exchange?
  • 12. DIFFERENT WEIGHTING METHODS USED IN INDEX CONSTRUCTION Index weighting Price weighted Equal weighted Market capitalization weighted Fundamentally weighted
  • 13. WEIGHTING SCHEMES  N  i  i i i 1 P P P w 1 wE  N i  N Q P   j i i j j i 1 M Q P w F  N  j j i i 1 F F w Price weighted: Equal weighted: Market capitalization weighted: Factor weighted:
  • 14. EXHIBIT 2-1 EXAMPLE OF A PRICE-WEIGHTED INDEX Security Shares in Index BOP Price Value (Shares x BOP Price) BOP Weight % EOP Price Dividends Per Share Value (Shares x EOP Price) Total Dividends Price Return % Total Return % BOP Weight x Price Return % BOP Weight x Total Return % EOP Weight % A 1 50.00 50.00 49.26 55.00 0.75 55.00 0.75 10.00 11.50 4.93 5.66 52.38 B 1 25.00 25.00 24.63 22.00 0.10 22.00 0.10 –12.00 –11.60 –2.96 –2.86 20.95 C 1 12.50 12.50 12.32 8.00 0.00 8.00 0.00 –36.00 –36.00 –4.43 –4.43 7.62 D 1 10.00 10.00 9.85 14.00 0.05 14.00 0.05 40.00 40.50 3.94 3.99 13.33 E 1 4.00 4.00 3.94 6.00 0.00 6.00 0.00 50.00 50.00 1.97 1.97 5.72 Total 101.50 100 105.00 0.90 3.45 4.33 100.00 Index Value 20.30 21.00 0.18 3.45 4.33 Divisor = 5 BOP = Beginning of period EOP = End of period Type of Index BOP Value Return % EOP Value Price Return 20.30 3.45 21.00 Total Return 20.30 4.33 21.18
  • 15. EXHIBIT 2-3 EXAMPLE OF AN EQUAL-WEIGHTED EQUITY INDEX Security Shares in Index BOP Price Value (Shares x BOP Price) Weight % EOP Price Dividends Per Share Value (Shares x EOP Price) Total Dividends Price Return % Total Return % Weight x Price Return % Weight x Total Return % EOP Weight % A 40 50.00 2,000 20.00 55.00 0.75 2,200 30 10.00 11.50 2.00 2.30 19.93 B 80 25.00 2,000 20.00 22.00 0.10 1,760 8 –12.00 –11.60 –2.40 –2.32 15.94 C 160 12.50 2,000 20.00 8.00 0.00 1,280 0 –36.00 –36.00 –7.20 –7.20 11.60 D 200 10.00 2,000 20.00 14.00 0.05 2,800 10 40.00 40.50 8.00 8.10 25.36 E 500 4.00 2,000 20.00 6.00 0.00 3,000 0 50.00 50.00 10.00 10.00 27.17 Total 10,000 100.00 11,040 48 10.40 10.88 100.00 Index Value 1,000 1,104 4.80 10.40 10.88 Divisor = 10 BOP = Beginning of period EOP = End of period Type of Index BOP Value Return % EOP Value Price Return 1,000.00 10.40 1,104.00 Total Return 1,000.00 10.88 1,108.80
  • 16. EXHIBIT 2-4 EXAMPLE OF A MARKET-CAPITALIZATION- WEIGHTED EQUITY INDEX Stock Shares Out-standing BOP Price BOP Market cap BOP Weight % EOP Price Dividends Per Share EOP Market cap Total Dividends Price Return % Total Return % BOP Weight x Price Return % BOP Weight x Total Return % EOP Weight % A 3,000 50.00 150,000 26.29 55.00 0.75 165,000 2,250 10.00 11.50 2.63 3.02 28.50 B 10,000 25.00 250,000 43.82 22.00 0.10 220,000 1,000 –12.00 –11.60 –5.26 –5.08 38.00 C 5,000 12.50 62,500 10.96 8.00 0.00 40,000 0 –36.00 –36.00 –3.95 –3.95 6.91 D 8,000 10.00 80,000 14.02 14.00 0.05 112,000 400 40.00 40.50 5.61 5.68 19.34 E 7,000 4.00 28,000 4.91 6.00 0.00 42,000 0 50.00 50.00 2.46 2.46 7.25 Total 570,500 100.00 579,000 3,650 1.49 2.13 100.00 Index 1,000 1,014.90 6.40 1.49 2.13 Value Divisor = 570.50 BOP = Beginning of period EOP = End of period Type of Index BOP Value Return % EOP Value Price Return 1,000.00 1.49 1,014.90 Total Return 1,000.00 2.13 1,021.30
  • 17. COMPARISON OF FUNDAMENTAL WEIGHTING WITH MARKET-CAPITALIZATION WEIGHTING Assume a 2-stock Index, consisting of Stock A and Stock B: Stock A Earnings = €20 Market cap = €200 Market cap weight = 20% Fundamental weight = 50% Stock B Earnings = €20 Market cap = €800 Market cap weight = 80% Fundamental weight = 50%
  • 18. ADVANTAGES AND DISADVANTAGES Price weighted Simple High price stocks have greater impact Stock splits result in arbitrary changes Equal weighted Simple Under- and over-representation Frequent rebalancing Market capitalization weighted Securities held in proportion to their value Similar to a momentum strategy Fundamental weighted Ensures a value or contrarian tilt Data intensive
  • 19. REBALANCING May become necessary as market prices change Creates turnover Rebalancing
  • 20. RECONSTITUTION Beginning index Reconstitution date Change constituent securities? New index
  • 21. USES OF MARKET INDICES Gauges of market sentiment Proxies for measuring and modeling returns, systematic risk, and risk-adjusted performance Proxies for asset classes in asset allocation models Benchmarks for actively managed portfolios Model portfolios for such investment products as index funds and exchange-traded funds (ETFs)
  • 22. EQUITY INDICES Equity indices Broad market Wilshire 5000 Total Market Index Multimarket MSCI Emerging Markets Sector GSTI Semiconductor Index Style Dow Jones U.S. Small-Cap Value Index
  • 23. CHALLENGES FACING FIXED INCOME INDEX CONSTRUCTION Lack of pricing data Number of securities Illiquid securities
  • 24. EXHIBIT 2-9 DIMENSIONS OF FIXED-INCOME INDICES Market Global Regional Country or currency zone Type Corporate Collateralized Securitized Mortgage-backed Government agency Government Maturity For example, 1–3, 3–5, 5–7, 7–10, 10+ years; short-term, medium-term, or long-term Credit quality For example, AAA, AA, A, BBB, etc.; Aaa, Aa, A, Baa, etc.; investment grade, high yield
  • 25. INDICES FOR ALTERNATIVE INVESTMENTS Commodities Real estate Hedge funds Indices for alternative investments
  • 26. COMMODITY INDICES Risk-free interest rate Changes in futures prices Roll yield Commodity index return
  • 27. REAL ESTATE INDICES Appraisal indices Repeat sales indices Real estate investment trust (REIT) indices Ownership of properties Investment in mortgages
  • 28. EXHIBIT 2-12 THE FTSE EPRA/NAREIT GLOBAL REIT INDEX FAMILY Source: FTSE International, “FTSE EPRA/NAREIT Global & Global Ex US Indices” (Factsheet 2009).
  • 29. HEDGE FUND INDICES Hedge funds are private investment vehicles that typically use leverage and long and short investment strategies. Research organizations maintain databases of hedge fund returns and summarize these returns into indices. Most indices reflect performance on a broad global level or on a strategy level. Most indices are equal weighted.
  • 30. PROBLEMS CAUSED BY VOLUNTARY INVESTMENT REPORTING Voluntary investment performance Survivorship bias Indices reflect different performances for the same time period
  • 31. SUMMARY • Price return index • Total return index • Choices in index construction and management • Advantages and disadvantages of different weighting schemes • Rebalancing and reconstitution • Uses of market indices • Equity, fixed income, and alternative investment indices

Editor's Notes

  1. Security market indices have evolved into important multi-purpose tools that help investors track the performance of various security markets, estimate risk, and evaluate the performance of investment managers. They also form the basis for new investment products. This reading is organized as follows. Section 2 defines a security market index and explains how to calculate the price return and total return of an index for a single period and over multiple periods. Section 3 describes how indices are constructed and managed. Section 4 discusses the use of market indices. Sections 5, 6, and 7 discuss various types of indices, and Section 8 concludes and summarizes the reading. Practice problems follow the conclusions and summary. DISCLAIMER: Candidates should understand this presentation is NOT a substitute for a thorough understanding of the CFA Program curriculum. This presentation is NOT necessarily a reflection of all of the knowledge and skills needed for candidates to successfully complete questions regarding this topic area on the CFA exam.
  2. LOS: Describe a security market index. Page 75 A security market index represents a given security market, market segment, or asset class. Most indices are constructed as portfolios of marketable securities. The value of an index is calculated on a regular basis using either the actual or estimated market prices of the individual securities, known as constituent securities, within the index. As the name suggests, a price return index, also known as a price index, reflects only the prices of the constituent securities within the index. A total return index, in contrast, reflects not only the prices of the constituent securities but also the reinvestment of all income received since inception.
  3. LOS: Calculate and interpret the value, price return, and total return of an index. Page 75 The divisor is a number initially chosen at inception. It is frequently chosen so that the price index has a convenient initial value, such as 1,000. The index provider then adjusts the value of the divisor as necessary to avoid changes in the index value that are unrelated to changes in the prices of its constituent securities. For example, when changing index constituents, the index provider may adjust the divisor so that the value of the index with the new constituents equals the value of the index prior to the changes.
  4. LOS: Calculate and interpret the value, price return, and total return of an index. Pages 75-76 Price return can be calculated either as the percentage change in the value of the price return index or the weighted average of price returns of the constituent securities where the weights are based on beginning-of-period values.
  5. LOS: Calculate and interpret the value, price return, and total return of an index. Pages 75-76 This is an example of a single-period price return calculation. It is not a measure of total return as total return measures the change in the value of the price return index plus the effects of income (dividends, interest, and/or other distributions). Note the size of the initial portfolio is (€10 × 200) + (€25 × 100) + (€15 × 400) = €10,500. Thus, the weights of the three securities in the portfolio are: LMN: (€10 × 200) ÷ €10,500 ≈ 0.1905 OPQ: (€25 × 100) ÷ €10,500 ≈ 0.2381 RST: (€15 × 400) ÷ €10,500 ≈ 0.5714 The price return for each security is: LMN: (€12 - €10) ÷ €10 = 20% OPQ: (€24 - €25) ÷ €25 = - 4% RST: (€18 - €15) ÷ €15 = 20% An alternative approach to calculate the single-period price return is: PRI = (0.1905 × 20%) + (0.2381 × -4%) + (0.5714 × 20%) ≈ 14.29%
  6. LOS: Calculate and interpret the value, price return, and total return of an index. Pages 76-77 Price return measures only price appreciation or percentage change in price. Total return measures price appreciation plus interest, dividends, and other distributions.
  7. LOS: Calculate and interpret the value, price return, and total return of an index. Pages 76-77 This is a continuation of the example in slide 5. The total return for the index could also be determined by weighting out the total return for each individual security: LMN: (€12.00 - €10.00 + €0.50) ÷ €10.00 = 25% OPQ: (€24.00 - €25.00 + €1.00) ÷ €25.00 = 0% RST: (€18.00 - €15.00 + €0.25) ÷ €15.00 ≈ 21.67% The weights of the three securities in the portfolio are: LMN: (€10 × 200) ÷ €10,500 ≈ 0.1905 OPQ: (€25 × 100) ÷ €10,500 ≈ 0.2381 RST: (€15 × 400) ÷ €10,500 ≈ 0.5714 Therefore: TRI = (0.1905 × 25%) + (0.2381 × 0%) + (0.5714 × 21.67%) ≈ 17.14% See the notes to slide 5.
  8. LOS: Calculate and interpret the value, price return, and total return of an index. Pages 77-78
  9. LOS: Calculate and interpret the value, price return, and total return of an index.
  10. LOS: Discuss the choices and issues in index construction and management. Pages 78-79
  11. LOS: Discuss the choices and issues in index construction and management. Page 79 Other characteristics that could be considered in the target market selection include the economic sector, company size, investment style, duration, or credit quality. Some equity indices, such as the S&P 500 Index and the FTSE 100, fix the number of constituent securities included in the index and indicate this number in the name of the index. Other indices allow the number of securities to vary to reflect changes in the target market or to maintain a certain percentage of the target market. For example, the Tokyo Stock Price Index (TOPIX) represents and includes all of the largest stocks, known as the First Section, listed on the Tokyo Stock Exchange. To be included in the First Section—and thus the TOPIX—stocks must meet certain criteria, such as the number of shares outstanding, the number of shareholders, and market capitalization. Stocks that no longer meet the criteria are removed from the First Section and also the TOPIX. Objective or mechanical rules determine the constituent securities of most, but not all, indices. The Sensex of Bombay and the S&P 500, for example, use a selection committee and more subjective decision-making rules to determine constituent securities.
  12. LOS: Compare and contrast the different weighting methods used in index construction. Page 79
  13. LOS: Compare and contrast the different weighting methods used in index construction. Pages 79, 81, 82, and 87 In price weighting, the weight on each constituent security is determined by dividing its price by the sum of all the prices of the constituent securities. A property unique to price-weighted indices is that a stock split on one constituent security changes the weights on all the securities in the index. To prevent the stock split and the resulting new weights from changing the value of the index, the index provider must adjust the value of the divisor. Unlike a price-weighted index, where the weights are arbitrarily determined by the market prices, the weights in an equal-weighted index are assigned by the index provider. In market-capitalization weighting, the weight on each constituent security is determined by dividing its market capitalization by the total market capitalization of all the securities in the index. Market-capitalization weighting is sometimes called value weighting. Market capitalization or value is calculated by multiplying the number of shares outstanding by the market price per share. Fundamental weighting uses measures of a company’s size that are independent of its security price to determine weights. These measures include book value, cash flow, revenues, earnings, dividends, and number of employees.
  14. LOS: Calculate and interpret the value and return of an index on the basis of its weighting method. Pages 80-81 Exhibit 2-1 illustrates the values, weights, and single-period returns following inception of a price-weighted equity index with five constituent securities. The value of the price-weighted index is determined by dividing the sum of the security values (101.50) by the divisor, which is typically set at inception to equal the initial number of securities in the index. Thus, in our example, the divisor is 5 and the initial value of the index is calculated as 101.50 ÷ 5 = 20.30. As illustrated in this exhibit, Security A, which has the highest price, also has the highest weighting and thus will have the greatest impact on the return of the index. Note how both the price return and the total return of the index are calculated on the basis of the corresponding returns on the constituent securities.
  15. LOS: Calculate and interpret the value and return of an index on the basis of its weighting method. Pages 82-83 Exhibit 2-3 illustrates the values, weights, and single-period returns following inception of an equal-weighted index with the same constituent securities as those in Exhibit 2-1. This example assumes a beginning index portfolio value of 10,000 (i.e., an investment of 2,000 in each security). To set the initial value of the index to 1,000, the divisor is set to 10 (10,000 ÷ 10 = 1,000). Exhibits 2-1 and 2-3 demonstrate how different weighting methods result in different returns. The 10.4 percent price return of the equal-weighted index shown in Exhibit 2-3 differs significantly from the 3.45 percent price return of the price-weighted index in Exhibit 2-1.
  16. LOS: Calculate and interpret the value and return of an index on the basis of its weighting method. Page 84 Exhibit 2-4 illustrates the values, weights, and single-period returns following inception of a market-capitalization-weighted index for the same five-security market. Security A, with 3,000 shares outstanding and a price of 50 per share, has a market capitalization of 150,000 or 26.29 percent (150,000/570,500) of the entire index portfolio. The resulting index weights in the exhibit reflect the relative value of each security as measured by its market capitalization. As shown in Exhibits 2-1, 2-3, and 2-4, the weighting method affects the index’s returns. The price and total returns of the market-capitalization index in Exhibit 2-4 (1.49 percent and 2.13 percent, respectively) differ significantly from those of the price-weighted (3.45 percent and 4.33 percent, respectively) and equal-weighted (10.40 percent and 10.88 percent respectively) indices. To understand the source and magnitude of the difference, compare the weights and returns of each security under each of the weighting methods. The weight of Security A, for example, ranges from 49.26 percent in the price-weighted index to 20 percent in the equal-weighted index. With a price return of 10 percent, Security A contributes 4.93 percent to the price return of the price-weighted index, 2.00 percent to the price return of the equal-weighted index, and 2.63 percent to the price return of the market-capitalization-weighted index. With a total return of 11.50 percent, Security A contributes 5.66 percent to the total return of the price-weighted index, 2.30 percent to the total return of the equal-weighted index, and 3.02 percent to the total return of the market-capitalization-weighted index.
  17. LOS: Discuss the choices and issues in index construction and management. LOS: Compare and contrast the different weighting methods used in index construction. Page 87 The earnings weight of Stock A is 50 percent (20/40) which is higher than its market-capitalization weight of 20 percent (200/1,000). The earnings weight of Stock B is 50 percent (20/40), which is less than its market-capitalization weight of 80 percent (800/1,000).
  18. LOS: Compare and contrast the different weighting methods used in index construction. Pages 81, 83, 87-88 The primary advantage of price weighting is its simplicity. Its primary disadvantage is the stocks with the highest price have the greatest impact on index return. Stock split results in arbitrary changes in weights. Like price weighting, the primary advantage of equal weighting is its simplicity. Equal weighting, however, has a number of disadvantages. First, securities that constitute the largest fraction of the target market value are underrepresented, and securities that constitute a small fraction of the target market value are overrepresented. Second, after the index is constructed and the prices of constituent securities change, the index is no longer equally weighted. Therefore, maintaining equal weights requires frequent adjustments (rebalancing) to the index. The primary advantage of market-capitalization weighting (including float adjusted) is that constituent securities are held in proportion to their value in the target market. The primary disadvantage is that constituent securities whose prices have risen the most (or fallen the most) have a greater (or lower) weight in the index (i.e., as a security’s price rises relative to other securities in the index, its weight increases; and as its price decreases in value relative to other securities in the index, its weight decreases). This weighting method leads to overweighting stocks that have risen in price (and may be overvalued) and underweighting stocks that have declined in price (and may be undervalued). The effect of this weighting method is similar to a momentum investment strategy in that over time, the securities that have risen in price the most will have the largest weights in the index. The most important property of fundamental weighting is that it leads to indices that have a “value” tilt. That is, a fundamentally weighted index has ratios of book value, earnings, dividends, etc. to market value that are higher than its market-capitalization-weighted counterpart. Also, in contrast to the momentum “effect” of market-capitalization-weighted indices, fundamentally weighted indices generally will have a contrarian “effect” in that the portfolio weights will shift away from securities that have increased in relative value and toward securities that have fallen in relative value whenever the portfolio is rebalanced.
  19. LOS: Discuss rebalancing and reconstitution. Page 88 Rebalancing may become necessary as market prices change as that will change the weights of the constituent securities in the index. Price-weighted indices are not rebalanced because the weight of each constituent security is determined by its price. For market-capitalization-weighted indices, rebalancing is less of a concern because the indices largely rebalance themselves. Market-capitalization weights are only adjusted to reflect mergers, acquisitions, liquidations, and other corporate actions between rebalancing dates.
  20. LOS: Discuss rebalancing and reconstitution. Page 88 Reconstitution is the process of changing the constituent securities in an index. Initial criteria for index inclusion is applied on the reconstitution date to determine which securities to retain, remove, or add. Indices are reconstituted to reflect changes in the target market (bankruptcies, de-listings, mergers, acquisitions, etc.) and/or to reflect the judgment of the selection committee. Reconstitution creates turnover in a number of different ways, particularly for market-capitalization-weighted indices. When one security is removed and another is added, the index provider has to change the weights of the other securities in order to maintain the market-capitalization weighting of the index. The frequency of reconstitution is a major issue for widely used indices and their constituent securities. The Russell 2000 Index, for example, reconstitutes annually. It is used as a benchmark by numerous investment funds, and each year, prior to the index’s reconstitution, the managers of these funds buy stocks they think will be added to the index—driving those stocks’ prices up—and sell stocks they think will be deleted from the index—driving those stocks’ prices down.
  21. LOS: Discuss uses of security market indices. Pages 90-91 The original purpose of stock market indices was to provide a gauge of investor confidence or market sentiment. The Dow Jones Industrial Average has a long history, is frequently quoted in the media, and remains a popular gauge of market sentiment. The capital asset pricing model (CAPM) defines beta as the systematic risk of a security with respect to the entire market. To represent the performance of the market portfolio, investors frequently use a broad index such as the Tokyo Price Index (TOPIX) and the S&P 500. Alpha, the difference between the return of a actively managed portfolio and the return of a market portfolio, is a measure of risk-adjusted return or investment performance. Because indices exhibit the risk and return profiles of select groups of securities, they play a critical role as proxies for asset classes in asset allocation models. They often provide the historical data used to model the risks and returns of different asset classes. Investors often use indices as benchmarks to evaluate the performance of active portfolio managers. The index selected as the benchmark should reflect the investment strategy used by the manager. Indices also serve as the basis for the development of new investment products. The first ETFs were based on existing indices. As the popularity of ETFs increased, index providers created new indices for the specific purpose of forming ETFs, leading to the creation of numerous narrowly defined indices with corresponding ETFs. The Market Vectors Vietnam ETF, for example, allows investors to invest in the equity market of Vietnam.
  22. LOS: Discuss types of equity indices. Pages 91-94 Broad market equity indices typically include securities representing more than 90 percent of the selected market. The Shanghai Stock Exchange Composite Index (SSE) is a market-capitalization-weighted index of all shares that trade on the Shanghai Stock Exchange. In the United States, the Wilshire 5000 Total Market Index is a market-capitalization-weighted index that includes more than 6,000 equity securities and is designed to represent the entire U.S. equity market. The Russell 3000, consisting of the largest 3,000 stocks by market capitalization, represents 99 percent of the U.S. equity market. Multimarket equity indices usually comprise indices from different countries and are designed to represent multiple security markets. MSCI Barra offers a number of multi-market indices. Countries are classified along two dimensions: level of economic development and geographic region. Developmental groups, which MSCI Barra refers to as market classifications, include developed markets, emerging markets, and frontier markets. The geographic regions are largely divided by longitudinal lines of the globe: the Americas, Europe with Africa, and Asia with the Pacific. MSCI Barra provides country-specific indices for each of the developed and emerging market countries within its multi-market indices. MSCI Barra periodically reviews the market classifications of countries in its indices for movement from frontier markets to emerging markets and from emerging markets to developed markets and reconstitutes the indices accordingly. Usually comprise indices from different countries and are designed to represent multiple security markets. Sector indices represent and track different economic sectors—such as consumer goods, energy, finance, health care, and technology—on either a national, regional, or global basis. Sector indices are organized as families; each index within the family represents an economic sector. Typically, the aggregation of a sector index family is equivalent to a broad market index. Style indices represent groups of securities classified according to market capitalization, value, growth, or a combination of these characteristics. They are intended to reflect the investing styles of certain investors, such as the growth investor, value investor, and small-cap investor.
  23. LOS: Discuss types of fixed-income indices. Pages 94-95 The number of fixed-income securities is many times larger than the number of equity securities. Fixed –income universe includes securities issued by governments, government agencies, and corporations. Each entity may issue a variety of securities with different characteristics. Fixed income markets are primarily dealer markets who buy and sell securities from their inventory. Many securities do not trade frequently and index providers must contact dealers to obtain current prices on constituent securities to update the index or they must estimate the prices of constituent securities using the prices of traded fixed-income securities with similar characteristics.
  24. LOS: Discuss types of fixed-income indices. Pages 95-96 Exhibit 2-9 illustrates how the major types of fixed-income indices can be organized on the basis of various dimensions. The first fixed-income index created, the Barclays Capital U.S. Aggregate Bond Index (formerly the Lehman Brothers Aggregate Bond Index), is an example of a single-country aggregate index. Designed to represent the broad market of U.S. fixed-income securities, it comprises more than 9,200 securities, including U.S. Treasury, government-related, corporate, mortgage-backed, asset-backed, and commercial mortgage-backed securities. Aggregate indices can be subdivided by market sector (government, government agency, collateralized, corporate); style (maturity, credit quality); economic sector, or some other characteristic to create more narrowly defined indices. A common distinction reflected in indices is between investment grade (e.g., those with a Standard & Poor’s credit rating of BBB– or better) and high-yield securities. Investment-grade indices are typically further subdivided by maturity (i.e., short, intermediate, or long) and by credit rating (e.g., AAA, BBB, etc.). The wide variety of fixed-income indices reflects the partitioning of fixed-income securities on the basis of a variety of dimensions. The dimensions fixed-income securities can be classified along include: Coupon type Embedded options Issuer’s economic sector Issuer’s geographic region Economic development of the issuer’s geographic region Type of issuer Type of financing Currency of payments Maturity Credit quality Absence or presence of inflation protection
  25. LOS: Discuss indices representing alternative investments. Page 96 Many investors seek to lower the risk or enhance the performance of their portfolios by investing in assets classes other than equities and fixed income. Interest in alternative assets and investment strategies has led to the creation of indices designed to represent broad classes of alternative investments.
  26. LOS: Discuss indices representing alternative investments. Page 98 Because commodity indices do not have an obvious weighting mechanism, such as market capitalization, commodity index providers create their own weighting methods. Some indices, such as the Commodity Research Bureau (CRB) Index, contain a fixed number of commodities that are weighted equally. The S&P GSCI uses a combination of liquidity measures and world production values in its weighting scheme and allocates more weight to commodities that have risen in price. Other indices have fixed weights that are determined by a committee. Index returns are affected by factors other than changes in the prices of the underlying commodities because futures contracts must be continually “rolled over” (i.e., replacing a contract nearing expiration with a new contract).
  27. LOS: Discuss indices representing alternative investments. Page 98 REITs are public or private corporations organized specifically to invest in real estate: ownership of properties investment in mortgages REIT indices are based on publicly traded REITs with continuous market pricing so their value is calculated continuously.
  28. LOS: Discuss indices representing alternative investments. Page 99 The FTSE EPRA/NAREIT global family of REIT indices shown in Exhibit 2-12 seeks to represent trends in real estate stocks worldwide and includes representation from the European Real Estate Association (EPRA) and the National Association of Real Estate Investment Trusts (NAREIT).
  29. LOS: Discuss indices representing alternative investments. Pages 98-99
  30. LOS: Discuss indices representing alternative investments. Page 99 Most research organizations rely on the voluntary cooperation of hedge funds to compile performance data. As unregulated entities, however, hedge funds are not required to report their performance to any party other than their investors. Therefore, each hedge fund decides to which database(s) it will report its performance. As a result, rather than index providers determining the constituents, the constituents determine the index. Frequently, a hedge fund reports its performance to only one database. The result is little overlap of funds covered by the different indices. With little overlap between their constituents, different global hedge fund indices may reflect very different performance for the hedge fund industry over the same period of time. Another consequence of the voluntary performance reporting is the potential for survivorship bias and, therefore, inaccurate performance representation. This means that hedge funds with poor performance may be less likely to report their performance to the database or may stop reporting to the database, so their returns may be excluded when measuring the return of the index. As a result, the index may not accurately reflect actual hedge fund performance so much as the performance of hedge funds that are performing well.