INSTRUCTOR SLIDES EQUITY LECTURE 46 SECURITY MARKET INDICES Security Market Index A security market index consists of individual securities (also called constituent
securities) that represent a given security market, market segment, or asset class.
භ Each security market index may have two versions depending on how returns are
calculated:
o A price return index only reflects the prices of constituent securities.
o A total return index not only reflects prices, but also assumes reinvestment of
all income received since inception.
™ The values of both versions of an index are the same at inception. As time passes
the total return index will be greater in value than the price return index by an
increasing amount.
INSTRUCTOR SLIDES | Security Market Indices 2 Price Return Price return measures only the percentage change in price.
The price return of each constituent security is calculated as:
The price return of the index equals the weighted average price return of the constituent
securities. It is calculated as:
INSTRUCTOR SLIDES | Security Market Indices 3 Total Return Total return measures the percentage change in price plus interest, dividends and
other distributions.
The total return of each constituent security is calculated as:
The total return of the index equals the weighted average total return of the constituent
securities. It is calculated as:
INSTRUCTOR SLIDES | Security Market Indices 4 Calculation of Index Returns over Multiple Time Periods Given a series of price returns for an index, the value of a price return index can be
calculated as:
where:
VPRI0 = Value of the price return index at inception
VPRIT = Value of the price return index at time t
PRIT = Price return (as a decimal number) on the index over the period
Similarly, the value of a total return index may be calculated as:
where:
VTRI0 = Value of the index at inception
VTRIT = Value of the index at time t
TRIT = Total return (as a decimal number) on the index over the period
INSTRUCTOR SLIDES | Security Market Indices 5 Index Returns E xample: Price Return and Total Return Indices
An analyst obtained the following information regarding an equity market index
created at the beginning of 2008:
Given that the index value at inception is 1,000, calculate the values of price return and
total return indices at the end of 2008 and 2009.
INSTRUCTOR SLIDES | Security Market Indices 6 Index Returns Solution
Price return index
Value at the end of 2008 = 1,000 î 1.075 = 1,075
Value at the end of 2009 = 1,000 î 1.075 î 1.083 = 1,164.225
Total return index
Value at the end of 2008 = 1,000 î 1.126 = 1,126
Value at the end of 2009 = 1,000 î 1.126 î 1.134 = 1,276.884
INSTRUCTOR SLIDES | Security Market Indices 7 Index Construction Constructing and managing a security market index involves:
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Target market selection
Security selection
Index weighting
Rebalancing
Reconstitution
INSTRUCTOR SLIDES | Security Market Indices 8 Index Construction Target Market and Security Selection
භ When constructing a security market index, the first decision that must be made
relates to which market, market segment or asset class the index should represent.
The target market may be based on:
o Asset class (e.g. equities, fixed income, or real estate)
o Geographic region (e.g. Japan, South Africa or Europe)
o The exchange on which the securities are traded (e.g. New York, London or
Tokyo)
o Other characteristics (e.g. economic sector, company size and investment style)
භ An index may consist of all the securities in the target market or just a
representative sample of the target market.
INSTRUCTOR SLIDES | Security Market Indices 9 Price Weighting In a price-weighted index the weight of each constituent security is determined by
dividing its price by the sum of the prices of all constituent securities:
භ The advantage of a price-weighted index is its simplicity.
භ O ne of the issues with a price-weighted index is that a stock split or stock dividend
by one of the constituent securities changes the weights of all securities in the
index.
භ Price-weighted indices suffer from a downward bias. Companies that split their
stock are typically those that have witnessed substantial increases in their stock
prices. As their stock prices fall to adjust for the split, their weight in the index also
falls.
INSTRUCTOR SLIDES | Security Market Indices 10 Price Weighting E xample: Price Weighted Index
A price-weighted equity index consists of one share each of 5 securities. The prices of
these securities at the end of 2008 and 2009 are given below:
1. Calculate the value of the index at the beginning of 2009.
2. Calculate the weights of each security at the beginning of 2009.
3. Calculate the price return of the index for 2009.
INSTRUCTOR SLIDES | Security Market Indices 11 Price Weighting Solution
1. Value of the index at the beginning of 2009:
2. Weight
Weight
Weight
Weight
Weight
of security A = 30/185 = 16.22%
of security B = 22/185 = 11.89%
of security C = 35/185 = 18.92%
of security D = 50/185 = 27.03%
of security E = 48/185 = 25.95%
INSTRUCTOR SLIDES | Security Market Indices 12 Price Weighting Solution (Contd.)
3.
Value of the index at the end of 2009:
Price return of the index for 2009 = (38.2 ± 37) / 37 = 3.24%
INSTRUCTOR SLIDES | Security Market Indices 13 Price Weighting E xample: C alculation of Index Divisor A fter a Stock Split
A price-weighted market index includes four stocks: A, B, C and D. Stock B issues a
four-for-one stock split. The table below lists the prices of the stocks before and after
the split.
If the divisor is not adjusted for the stock split, the index will fall from 60 to 45 (180/ 4)
even though there has been no change in prices other than to adjust for the split. To
reflect the fact that stock values really have not changed, the index divisor must be
adjusted. This new divisor, x, is calculated as (40 + 20 + 70 + 50) / 60 = 3.
INSTRUCTOR SLIDES | Security Market Indices 14 Equal Weighting In an equal-weighted index, each constituent security is given an identical weight in
the index at inception.
where:
wi = Fraction of the portfolio that is allocated to security i or weight of security i
N = Number of securities in the index
භ The number of shares of each security included in the index is calculated as the
value allotted to each constituent security divided by the price of the security.
භ The weights in an equal-weighted index are effectively determined by the index
provider (in choosing the particular weighting mechanism).
INSTRUCTOR SLIDES | Security Market Indices 15 Equal Weighting E xample: E qual Weighted Index
An equal-weighted equity index with an initial value of 10,000 consists of 5 securities
whose prices as at the end of 2008 and 2009 are given below:
1. Calculate the number of shares of each security included in the equal-weighted
index.
2. Calculate the index value at the end of 2009.
3. Calculate the price return of the index for 2009.
INSTRUCTOR SLIDES | Security Market Indices 16 Equal Weighting Solution
Since the index consists of 5 securities, each security will be assigned a weight of 20%
in the index. As the total value of the index is 10,000, the value assigned to each
security will be 2,000.
1.
Number
Number
Number
Number
Number
of shares of Stock A = 2,000/30 = 66
of shares of Stock B = 2,000/22 = 90
of shares of Stock C = 2,000/35 = 57
of shares of Stock D = 2,000/50 = 40
of shares of Stock E = 2,000/48 = 41
INSTRUCTOR SLIDES | Security Market Indices 17 Equal Weighting Solution (Contd.)
2. The value of the index position in each security at the end of 2009 is calculated as:
Security A: 66 î 34 = 2,244
Security B: 90 î 28 = 2,520
Security C: 57 î 31 = 1,767
Security D: 40 î 54 = 2,160
Security E: 41 î 44 = 1,804
Therefore, the total value of the index at the end of 2009 is calculated as:
2,244 + 2,520 + 1,767 + 2,160 + 1,804 = 10,495
3. The price return of the index for 2009 = (10,495 / 10,000) ± 1 = 4.95%
INSTRUCTOR SLIDES | Security Market Indices 18 Equal Weighting භ Equal-weighted indices are also preferred because of their simplicity. However,
they have a few disadvantages:
o Assigning an equal weight to all securities under-represents (over-represents)
those securities that constitute a relatively large (small) fraction of the target
market.
o The index does not remain equally weighted once the prices of the constituent
securities change. Frequent adjustments must be made to maintain equal
weighting.
INSTRUCTOR SLIDES | Security Market Indices 19 Market-­‐Capitalization Weighting A market-capitalization weighted (value weighted) index is based on the total market
value of all stocks in the index.
භ The initial market value is assigned a base number (e.g. 100) and a new market
value is computed periodically.
භ The change in the index is measured by comparing the new market value to the
base market value.
INSTRUCTOR SLIDES | Security Market Indices 20 Market-­‐Capitalization Weighting E xample: M arket C apitalization Weighted Index
A market-capitalization weighted equity index consists of 5 securities whose prices and
number of shares outstanding are given below:
1. Calculate the weight of each security in the index at the beginning of 2009.
2. Calculate the value of the divisor that gives an index value of 1,000 at the beginning
of 2009.
3. Calculate the price return of the index for 2009.
INSTRUCTOR SLIDES | Security Market Indices 21 Market-­‐Capitalization Weighting Solution
1. Total market capitalization at the beginning of 2009:
= (30 î 4,000) + (22 î 6,000) + (35 î 2,000) + (50 î 2,500) + (48 î 3,000)
= 591,000
The weights of each of the 5 securities are calculated below:
Security A = (30 î 4,000) / 591,000 = 20.30%
Security B = (22 î 6,000) / 591,000 = 22.34%
Security C = (35 î 2,000) / 591,000 = 11.84%
Security D = (50 î 2,500) / 591,000 = 21.15%
Security E = (48 î 3,000) / 591,000 = 24.37%
INSTRUCTOR SLIDES | Security Market Indices 22 Market-­‐Capitalization Weighting Solution (Contd.)
2. Value of the divisor = 591,000 / 1,000 = 591
3. Total market capitalization at the end of 2009:
= (34 î 4,000) + (28 î 6,000) + (31 î 2,000) + (54 î 2,500) + (44 î 3,000)
= 633,000
Price return of the index for 2009 = (633,000/591) / 1,000 ± 1 = 7.11%
INSTRUCTOR SLIDES | Security Market Indices 23 Market-­‐Capitalization Weighting F loat-A djusted M arket-C apitalization Weighting
භ In a float-adjusted market-capitalization weighted index, the proportion of each
constituent security is determined by adjusting its market capitalization for its
market float.
භ Shares held by controlling shareholders, other corporations are subtracted from the
total number of outstanding shares to determine the market float.
භ The primary advantage of market capitalization weighting (and float-adjusted
market capitalization weighting) is that securities are held in proportion to their
value in the target market.
භ A disadvantage is that stocks with larger market values have a larger impact on the
index.
INSTRUCTOR SLIDES | Security Market Indices 24 Market-­‐Capitalization Weighting E xample: F loat-A djusted M arket C apitalization Weighted Indices
A float-adjusted market-capitalization weighted equity index consists of 5 securities.
Further information is provided in the table below:
1. Calculate the number of shares of each security that will be included in the index.
2. Calculate the total float-adjusted market-capitalization at the beginning of 2009.
3. Calculate the price return of the index for 2009.
INSTRUCTOR SLIDES | Security Market Indices 25 Market-­‐Capitalization Weighting Solution
1. The number of shares of each security to be included in the index is:
Security A = 4,000 î 40% = 1,600
Security B = 6,000 î 70% = 4,200
Security C = 2,000 î 80% = 1,600
Security D = 2,500 î 50% = 1,250
Security E = 3,000 î 60% = 1,800
2. The total float-adjusted market-capitalization at the beginning of 2009 is:
(30 î 1,600) + (22 î 4,200) + (35 î 1,600) + (50 î 1,250) + (48 î 1,800) = 345,300
INSTRUCTOR SLIDES | Security Market Indices 26 Fundamental Weighting A fundamental ZHLJKWHGLQGH[XVHVRWKHUPHDVXUHVRIDFRPSDQ\¶VVL]HWKDWDUH
independent of the stock price) such as book value, cash flow, revenues and earnings
to determine weights of securities in the index.
where:
Fi = A given fundamental size measure of company I
භ Stocks with a higher earnings yield than that of the overall market weighted
portfolio will be more heavily weighted under fundamental weighting compared to
market value weighting.
INSTRUCTOR SLIDES | Security Market Indices 27 Rebalancing ,QRUGHUWRNHHSWKHZHLJKWVRIFRQVWLWXHQWVHFXULWLHVFRQVLVWHQWZLWKWKHLQGH[¶V
weighting method security weights must be adjusted or rebalanced.
භ Rebalancing an equal-weighted index would require reducing the weight of
securities that have outperformed and increasing the weight of securities that have
underperformed.
භ Price-weighted indices do not need to be rebalanced as the weight of each
constituent security is determined by its price.
භ Market-capitalization weighted indices rebalance themselves to reflect changes in
the market-capitalization of constituent securities.
o They only need to be rebalanced to reflect mergers, acquisitions, liquidations,
etc.
INSTRUCTOR SLIDES | Security Market Indices 28 Reconstitution This refers to the process of changing the constituent securities in an index.
භ Index reconstitution is performed in order to:
o Reflect changes in the target market as a result of bankruptcies, de-listings,
mergers, etc.
o Reflect the judgment of the selection committee.
භ Reconstitution creates turnover within the index (especially for market value
weighted indices) as once the revised list of constituent securities is determined, the
weights of all constituent securities must be recalculated.
භ The frequency of reconstitution is a major issue for widely used indices and their
constituent securities.
INSTRUCTOR SLIDES | Security Market Indices 29 Uses of Security Market Indices භ Used to gauge market sentiment.
භ Used as proxies for measuring and modeling returns, systematic risk, and riskadjusted performance.
භ Act as proxies for asset classes in asset allocation models.
භ Used as benchmarks for actively managed portfolios.
භ Serve as the basis for the creation of numerous investment products.
INSTRUCTOR SLIDES | Security Market Indices 30 Types of Equity Indices භ Broad market indices: A broad equity market index contains securities representing
more than 90% of the selected market.
භ Multi-market indices: Multi-market indices consist of security market indices from
different countries and may represent multiple national markets, geographic
regions, economic development groups or even the entire world.
භ Sector indices: Sector indices only include securities representing a particular
economic sector (e.g. finance, health care, technology, etc.) where the economic
sector may be classified on a national, regional or global basis.
භ Style indices: These indices include those based on size (e.g. small-cap versus
large-cap equities) and others based on style (e.g. growth versus value stocks).
INSTRUCTOR SLIDES | Security Market Indices 31 Fixed-­‐Income Indices භ Creating bond-market indices presents the following challenges:
o There is a broader universe of bonds than of stocks.
o The universe of bonds is constantly changing as a result of new issues, calls,
and maturities.
o The price volatility of a bond (as measured by duration) is constantly
changing.
o Current and continuous transaction prices are not available for bonds.
භ Fixed-income indices can be categorized as follows:
o Aggregate or broad market indices.
o Market sector indices.
o Style indices.
o Economic sector indices.
o Specialized indices such as high-yield, inflation-linked, and emerging market
indices.
INSTRUCTOR SLIDES | Security Market Indices 32 Indices Representing Alternative Investments Commodity indices:
භ Commodity indices consist of futures contracts on one or more commodities.
භ They do not have an obvious weighting method so index providers create their own
weighting methods.
භ Different weighting methods lead to different exposures to specific commodities,
which result in very different risk and return profiles of commodity indices.
භ The performance of commodity indices may differ from that of the underlying
commodities because indices consist of futures contracts on commodities rather
than the actual commodities.
Real estate investment trust indices:
භ Real estate indices represent the market for real estate and real estate securities.
භ They can be categorized as:
o Appraisal indices
o Repeat sales indices
o Real estate investment trust (REIT) indices
INSTRUCTOR SLIDES | Security Market Indices 33 Indices Representing Alternative Investments Hedge fund indices:
Hedge fund indices are designed to represent the performance of hedge funds on a very
broad, global level or the strategy level.
භ They rely on voluntary disclosures from funds as it is not mandatory for hedge
funds to disclose performance to any party other than investors.
භ Poorly performing hedge funds may stop reporting their performance to hedge fund
indices or may cease to exist altogether.
ʹ This leads to survivorship bias and an upward bias in hedge fund
performance as represented by these indices.
INSTRUCTOR SLIDES | Security Market Indices 34