1 of 47 March 25, 2017
Indices
© Christopher Ting
2 of 47 March 25, 2017
Motivation
© Christopher Ting
Financial and economic indices have evolved into important multi-purpose tools that help investors
track the investment performance
estimate risk
evaluate the performance of investment managers.
Indices also form the basis for new investment products.
Developing and providing indices can be a viable business
Good starting point to learn portfolio management: construction and rebalancing
3 of 47 March 25, 2017
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)
© Christopher Ting
4 of 47 March 25, 2017
Major Companies in the Indexing Business
© Christopher Ting
S&P Dow Jones
MSCI
FTSE Russell
5 of 47 March 25, 2017
Introduction
© Christopher Ting
Define a security market index and explain how to calculate the price return and total return of an index for a single period and over multiple periods.
Describe how indices are constructed and managed.
Differentiate between price return and total return
Discuss the use of market indices.
Describe various types of indices.
6 of 47 March 25, 2017
What is an Index?
© Christopher Ting
In general, an index is a quantitative gauge that provides an eclectic, single-value summary of all endogenous and exogenous factors affecting and driving the state of a system.
Example: Temperature
Typically involving many constituent sub-systems
Example: Dow Jones Industrial Average
7 of 47 March 25, 2017
Price!
© Christopher Ting
Price is an index!
Reflects the forces of supply and demand through the market mechanism
Efficient Market Hypothesis – Prices already incorporate and reflect all relevant information about a company stock.
8 of 47 March 25, 2017
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?
© Christopher Ting
9 of 47 March 25, 2017
Target Market Selection
Target market
Defined broadly or narrowly?
Based on an asset class?
Based on geographic
region?
Based on an exchange?
Other characteristics
?
© Christopher Ting
10 of 47 March 25, 2017
Different Weighting Methods
Index
Price weighted
Market capitalization
weighted
Equally weighted
Fundamentally weighted
© Christopher Ting
11 of 47 March 25, 2017
An Example of Price-Weighted Index
© Christopher Ting
The first stock index in the world is the Dow Jones Industrial Average, which was unveiled on May 26, 1896
The precursor of DJIA can be traced back to May 4, 1885.
At the start, DJIA had only 12 component stocks.
In 1916, DJIA had 20 stocks.
From 1928, the number of component stocks is fixed at 30.
12 of 47 March 25, 2017 © Christopher Ting
Source: http://www.advisorperspectives.com/dshort/guest/Peter-Williams-120108-Dow-Historical-Perspective.php
Dow Jones Industrial Average in Log Scale
13 of 47 March 25, 2017
Another Example of Price-Weighted Index
Nikkei 225 index is also price weighted, with some nuances to the “par value.”
The Nikkei 225 index began on September 7, 1950.
Retroactively could be back-calculated to May 16, 1949.
© Christopher Ting
14 of 47 March 25, 2017
Examples of Market-Cap Weighted Index
© Christopher Ting
S&P 500 Index
MSCI Singapore Free Index
Hang Seng Index
Most if not all stock market indexes
15 of 47 March 25, 2017
Index Calculation: Price versus Market Cap
© Christopher Ting
Let Pi be the price of a component stock and ni the number of its shares used for index calculation.
D
Pn
I
N
i
ii 1
N is the total number of components.
D is the divisor needed to scale the sum into a value called index I of an appropriate value.
D
P
I
N
i
i 1
16 of 47 March 25, 2017
The number of shares, x, to buy for every stock is found by x ($8 + $12 + $20 + $24) = $40,000.
Hence, x = $40,000/$64 = 625 shares
Index Construction: Price Weighted
© Christopher Ting
To construct a price-weighted index, buy the same number of shares for every component stock.
If you buy 1 share of every stock, at inception or initially, D = N. The resulting I is the average price of Nstocks
Suppose you have $40,000 and you wan to construct a price-weighted portfolio with the following 4 stocks:
Stock Name W X Y ZPrice per Share $8 $12 $20 $24 Shares Issued 200,000 310,000 602,000 110,000
17 of 47 March 25, 2017
Tutorial Question
© Christopher Ting
For the example in the previous slide, if you want the price-weighted index to be equal to $16, what should be the value of the divisor?
18 of 47 March 25, 2017
Index Construction: Price versus Market Cap
© Christopher Ting
To construct a market-cap-weighted index,
compute the market cap of every component stock
sum up N market caps.
for every stock, divide its market cap by the total market-cap to obtain its fraction of contribution.
Then apportion the fund according to the fraction.
Use the apportioned fund to buy the number of shares at the price with which its market cap is computed.
Stock Name W X Y ZPrice per Share $8 $12 $20 $24 Shares Issued 200,000 310,000 602,000 110,000Market Cap $1,600,000 $3,720,000 $12,040,000 $2,640,000Weight 2/25 1/5 3/5 1/8
19 of 47 March 25, 2017
Tutorial Questions
© Christopher Ting
Given $40,000, how many shares are to be bought in order to construct a market-cap-weighted portfolio?
The amount apportioned to Stock W is (2/25) ×$40000 = $3,200. With this money, you can buy 3200/8 = 400 shares.
Do likewise for Stocks, X, Y, and Z.
If you want the market cap to start at 100 at inception, what should the divisor D be?
20 of 47 March 25, 2017
Equal Weight
© Christopher Ting
Give the same weight to every component stock by having the same dollar amount to buy every stock.
With $40,000 and 4 stocks, we allocate $10,000 for each stock
How many shares do you buy for every component stock?
If you want your index to start at 100, what should the divisor be?
21 of 47 March 25, 2017
Factor-Weighted Index
© Christopher Ting
In a way, the ubiquitous market cap weighted index is based on the “size factor”.
One can use earnings, for example, to decide the weight for constructing the index.
Consider two stocks, A and B
Stock A
Earnings = €20
Market cap = €200
Market cap weight = 20%
Fundamental weight = 40%
Stock B
Earnings = €30
Market cap = €800
Market cap weight = 80%
Fundamental weight = 60%
22 of 47 March 25, 2017
Weighting Schemes During Construction
© Christopher Ting
How much fund out of the total is allocated?
N
i
i
ii
P
Pw
1
P
Nwi
1E
N
j
jj
iii
Pn
Pnw
1
M
N
j
j
ii
F
Fw
1
F
Price weighted
Equally weighted
Market capitalization weighted
Factor weighted
ni is the number of shares of shares of constituent security i.
23 of 47 March 25, 2017
Very Important
© Christopher Ting
After the index is constructed, i.e., the number of shares for each component stock has already been fixed, the index calculation is now based on the shares and not on the weights anymore.
For equally weighted index, the weights will become unequal, and the index becomes unequally weighted. Regular rebalancing is needed to make it equally weighted again.
Likewise, the factor based index needs to be rebalance to better reflect changes in the factor.
But for price- and market-cap-weighted indices, you don’t have to, if the component stocks don’t change.
24 of 47 March 25, 2017
Myth of Using Weight for Market Cap Index Calculation
Many people misunderstood that to calculate the market-cap-weighted index even after its inception, you must use the weights of the components.
This is wrong!
The weights are the results, not the starting data for index calculation.
The weight changes as soon as any of the component stock price changes!
© Christopher Ting
25 of 47 March 25, 2017
Advantages and Disadvantages
Price weighted
Simple
High price stocks have
greater impact
Stock splits necessitate a
change in divisor
Equally weighted
Simple
Under- and over-representation
Frequent rebalancing
Market capitalization
weighted
Securities held in
proportion to their market
value
Similar to a momentum
strategy
Fundamentally weighted
Ensures a value or
contrarian tilt
Data intensive
© Christopher Ting
26 of 47 March 25, 2017
Real World Example: Singapore MSCI Index
The MSCI Singapore Free Index is a free-float adjusted market capitalization weighted index that is designed to track the equity market performance of Singapore securities listed on Singapore Stock Exchange.
The MSCI Singapore Free Index is constructed based on the MSCI Global Investable Market Indexes Methodology targeting a free-float market capitalization coverage of 85%. The index has a base date of December 31, 1987.
https://app2.msci.com/eqb/custom_indexes/sg_performance.html
© Christopher Ting
27 of 47 March 25, 2017
Reconstitution
Beginning index
Reconstitution date
Reconstituted index
Change constituent securities?
© Christopher Ting
28 of 47 March 25, 2017
Equity Indices
Equity indices
Broad marketWilshire 5000 Total Market
Index
MultimarketMSCI Emerging
Markets
SectorGSTI
Semiconductor Index
StyleDow Jones U.S.
Small-Cap Value Index
© Christopher Ting
29 of 47 March 25, 2017
Challenges Facing Fixed Income Index Construction
Lack of pricing
data
Number of
securities
Illiquid securities
© Christopher Ting
30 of 47 March 25, 2017
Dimensions of Fixed-Income Indices
Market
Global
Regional
Country or currency zone
Type Corporate
CollateralizedSecuritizedMortgage-
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
© Christopher Ting
31 of 47 March 25, 2017
Indices for Alternative Investments
Commodities
Real estate
Hedge funds
Indices for
alternativeinvestments
© Christopher Ting
32 of 47 March 25, 2017
Commodity Indices
Risk-free interest rate
Changes in futures prices
Roll yield
Commodity index return
© Christopher Ting
33 of 47 March 25, 2017
Real Estate Indices
Appraisal indices
Repeat sales indices
Real estate investment trust (REIT) indices
Ownership of properties
Investment in mortgages
© Christopher Ting
34 of 47 March 25, 2017
The FTSE EPRA/NAREIT Global REIT Index Family
Source: FTSE International, “FTSE EPRA/NAREIT Global & Global Ex US Indices” (Factsheet 2009).
© Christopher Ting
35 of 47 March 25, 2017
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 hedge fund indices are equal weighted.
© Christopher Ting
36 of 47 March 25, 2017 © Christopher Ting
Source: https://www.hedgefundresearch.com/?fuse=indices-str
37 of 47 March 25, 2017
Problems Caused by Voluntary Reporting
© Christopher Ting
Voluntary investment
performance
Survivorship bias
Indices reflect different
performances for the same time
period
38 of 47 March 25, 2017
Description of a Security Market Index
Security market index
Price return index Total return index
Constituent securities
© Christopher Ting
39 of 47 March 25, 2017
Value of a Price Return Index
D
Pn
V 1PR
N
i
ii
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
© Christopher Ting
40 of 47 March 25, 2017
Calculation of Single-Period Price Return
N
i
N
i i
iiiii
I
III
1 1 0
01
0PR
0PR1PR
P
PPwPRw
V
VVPR
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
© Christopher Ting
41 of 47 March 25, 2017 © Christopher Ting
%29.141429.000.105
00.10500.120PR
00.120100
)18400()24100()12200(V
00.105100
)15400()25100()10200(V
1PR
0PR
I
I
I
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
Example of Single-Period Price Return
42 of 47 March 25, 2017
Calculation of Single-Period Total Returns
N
i
N
i i
iiiiiiI
I
IPRIII
1 1 0
01
0PR
01PR
P
Inc PPwTRwTR
V
Inc VVTR
TRI = the total return of the index portfolioIncI = the total income from all securities in the indexTRi = the total return of the constituent security iInci = the total income from security i
© Christopher Ting
43 of 47 March 25, 2017 © Christopher Ting© Christopher Ting
44 of 47 March 25, 2017 © Christopher Ting
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
00.3100)]25.0400()00.1100()50.0200[(Inc I
%14.171714.000.105
00.300.10500.120TR
I
Calculation of Single-Period Total Return
45 of 47 March 25, 2017
Index Values over Multiple Time Periods
T210TRTTR
T210PRTPR
TR1TR1TR1VV
PR1PR1PR1VV
IIIII
IIIII
Calculation of index values over multiple time periods requires geometrically linking the series of index returns.
© Christopher Ting
46 of 47 March 25, 2017
Period Return (%) Calculation Ending Value0 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
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:
Calculation Example
© Christopher Ting
47 of 47 March 25, 2017
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
© Christopher Ting