CFA CFA level 3 volume III applications of economic analysis and asset allocation finquiz curriculum note, study session 9, reading 20

Market Indexes and Benchmarks

1.

INTRODUCTION

A reference point used to evaluate the performance of
a portfolio manager or investment portfolio is referred to
2.

Distinguishing between a Benchmark and a Market Index

A market index represents the performance of a
specified security market, market segment, or asset
class. For example, S&P 500 Index represents the
performance of 500 large-cap US equities; Barclays
Sterling Aggregate Bond Index represents the
performance of fixed-rate, investment-grade sterlingdenominated bonds. A market index may be used as a
benchmark for an investment manager.
Characteristics of a Valid Benchmark: A valid
benchmark should have the following seven properties:
1.

2.

3.

4.

5.

6.

Unambiguous: The identities and weights of
securities or factor exposures constituting the
benchmark are clearly defined.
Investable: The benchmark should represent a
passive investment alternative i.e. an investor can
always opt to forgo active management and
simply hold the benchmark.
Measurable: The benchmark’s return can be
readily calculated on a reasonably frequent
basis.
Appropriate: The benchmark reflects the same
risk as the manager and is consistent with the
manager’s investment style or biases or area of
expertise.
Reflective of current investment opinions: The
manager has current investment knowledge
(positive, negative, or neutral) of the securities or
factor exposures constituting the benchmark can
invest in all securities.
Specified in advance: The benchmark is specified
prior to the start of an evaluation period and is
known to all interested parties.
3.

as Benchmark. The benchmark selection depends on
the objectives and constraints of the investor.

7.

Owned/Accountable: The investment manager
should agree to be evaluated against the chosen
benchmark.

A plan sponsor (i.e. trustee, company, or employer
responsible for a public or private institutional investment
plan) is responsible for determining the plan participation
requirements, investment choices, contributions, and
distributions.
A fund manager is the professional manager of separate
accounts or pooled assets or an external investment
manager to whom management of a part of the
sponsor’s assets is delegated.
Active investment strategies seek to generate return in
excess of market return. The excess return is referred to
as the manager’s active return, and the variability of the
active returns is referred to as active risk.
Policy portfolio is a strategic asset allocation that
determines the broad allocation of assets to stocks,
bonds, and other types of securities within the fund to
individual managers within the asset categories.
Investment Style: A natural grouping of investment
disciplines that has some predictive power in explaining
the future variation of portfolio/fund returns across
portfolios/funds is known as Investment Style.

Benchmark Uses and Types

An ideal or “valid” benchmark can be used to evaluate

active investment management skills of the manager.
Benchmarks can also be used to identify investment
manager’s investment universe and investment
discipline.

3.1

Benchmarks: Investment Uses

Benchmarks:
1) can be used as a reference point for segments of
the sponsor’s portfolio;
2) can be used to convey sponsor’s expectations to
the manager regarding expected risk and return
and the way fund assets should be invested.
3) can be used to convey the manager’s area of

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Reading 20


Reading 20

4)
5)
6)
7)

3.2

Market Indexes and Benchmarks

expertise and his investment style to the board of
directors (or any oversight group) and
consultants;
can be used to identify and evaluate the risk
exposures of the manager;
can be used for performance attribution as well
as for appraisal and selection of managers;
can be used by regulators to determine the
compliance with regulations, laws, or standards.
can be used to market investment products to
potential investors by describing investment
strategy to them.

For example, in one-factor model, the return on a
security, or a portfolio of securities, is regressed on the
return on a broad market index (over a long period e.g.
60 months):
Rp = ap + βpRI + εp
Where,
Rp = periodic return on an account
RI = periodic return on the market index
ap = “zero factor” term. It represents the expected value
of Rp if the factor value was zero.
βp = beta = sensitivity of the returns on the account to
the returns on the market index

εp = residual return due to nonsystematic factors

Types of Benchmarks
6)

1)

2)

3)

4)

5)

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Absolute Return Benchmarks: An absolute return can
be a return objective e.g. actuarial rate-of-return
assumption or a minimum return target that the fund
aims to exceed.
Manager universe (Peer groups): It refers to using the
median manager or fund from a broad universe of
managers or funds as a performance evaluation
benchmark e.g. fund that falls at the median when
funds are ranked in descending order.
Broad market indexes: It refers to using broad
market indexes as benchmarks e.g. S&P 500, Wilshire
5000 for U.S. common stocks; the Lehman
Aggregate and the Citigroup Broad InvestmentGrade (U.S. BIG) Bond Indexes for U.S. investmentgrade debt.

Style indexes: It refers to using specific portions of an
asset category as benchmark e.g. largecapitalization growth, large-capitalization value,
small-capitalization growth, small-capitalization
value, mid-capitalization growth and value common
stock indexes are also available.
Factor-model-based benchmarks: Factor models
are used to analyze the portfolio’s sensitivity to a set
of factors (systematic sources of return e.g. return for
a broad market index, company’s size, company
earnings growth, industry, and financial leverage).
Rp = ap + b1F1 + b2F2+…+ bKFK + εp
Where, F1, F2, . . . FK represent the values of
factors 1 through K, respectively.

The higher the sensitivity (bk), the greater positive
exposure to a specified factor the portfolio has and
consequently, the higher expected return, holding all
else equal.

7)

8)

Returns-based benchmarks (Sharpe style analysis):
These benchmarks are constructed using (1) the
series of a manager’s account returns over specified
periods and (2) the series of returns on several
investment style indexes (e.g. small-cap value, smallcap growth, large-cap value, and large-cap
growth) over the same periods. Using these return
series, an allocation algorithm solves for the optimal

set of allocation weights for investment style indexes
that most closely track the account’s returns. In this
optimization process, portfolio’s sensitivities (similar to
bk in factor-model-based benchmarks) are forced to
be non-negative and sum to 1. These allocation
weights represent the returns-based benchmark.
Custom security-based benchmarks: These
benchmarks are constructed by selecting securities
and weightings consistent with the manager’s
investment process and client restrictions. Since
these benchmarks reflect manager’s investment
strategy, they are also referred to as strategy
benchmarks. The benchmark is rebalanced
periodically to ensure that it stays consistent with the
manager’s investment practice. Such benchmarks
are preferred to use when the manager’s strategy
cannot be closely matched to a broad market
index or style index.
Liability-based benchmarks: These benchmarks are
constructed by selecting securities and weightings
consistent with the duration profile and other key
characteristics of the liabilities. These benchmarks
reflect the return required to meet the future
obligations as well as mimic the volatility of the
liabilities. A liability-based benchmark typically
consists of nominal bonds, real return bonds,
common shares, and other assets.


Reading 20

Market Indexes and Benchmarks

4.

Market Indexes Uses and Construction

Market indexes for equities include CAC 40 (French), FTSE
100 (UK), or Dow Jones Industrial Average (US) etc. Broad
market fixed-income indexes include Barclays, JP
Morgan, Markit, and S&P/Citigroup. These market
indexes are used to assess portfolio managers’
performance.
4.1

Inclusion criteria: Inclusion criteria determine the
number and type of eligible securities to be added
in the index. The greater the number of securities
and the more diversified they are by industry and
size, the better the index will measure broad market
performance. Securities are considered eligible if
they meet liquidity standards, minimum trading
price, available shares (float), etc. An index can
serve as a valid benchmark if its security composition
is similar to that of the portfolio of the manager.
Security weighting: Index construction varies
depending on the methodology used for security
weighting e.g. value-weighting, price-weighting etc.
Weights of securities affect index risk and return and
also influence the validity of the index as a

manager’s benchmark.
Index maintenance: Index maintenance refers to
the adjustment of the index for changes in shares
outstanding resulting from buybacks, secondary
offerings, spinoffs, stock distributions.

1)

Use of Market Indexes

a) Asset allocation proxies: A market index can be
used to measure ex-ante return, risk, and
correlations of an asset class. It can also be used to
determine the incremental expected return and risk
from adding a new asset to a portfolio. In other
words, market indexes allow investors to design an
investment policy suitable for different risk aversion
levels.
b) Investment management mandates: Market index
can be used to convey the investment
management mandate of the plan sponsor to
portfolio manager. For example, a portfolio
manager of a passively managed portfolio may be
required to match the index return; whereas, a
portfolio manager of an actively managed portfolio
may be required to generate returns in excess of an
index return.
c) Performance benchmarks: Indexes can be used as
ex-post performance benchmarks for the manager.
d) Portfolio analysis: Market indexes can be used for

more detailed portfolio analysis. For example,
currency-hedged and unhedged versions of nondomestic indexes can be used to evaluate the
effectiveness of a currency management strategy.
e) Gauge of market sentiment: Market indexes indicate
daily (and even intra-day) market movements.
Hence, they can be used to gauge public or market
sentiments. E.g. the Chicago Board Options
Exchange (CBOE) Market Volatility Index (VIX) is
frequently used to measure market uncertainty.
f) Basis for investment vehicles: Market indexes are
also used as a basis for investments, i.e. index mutual
funds, exchange-traded funds (ETFs), and
derivatives.
4.2

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Index Construction

Index is constructed based on the following three
factors.

2)

3)

Types of Security Weighting: There are several weighting
schemes commonly used:
1)

Capitalization weighting (market value weighting,
market cap weighting, or cap weighting): In
market-value weighting, each stock in the index is
weighted according to its market capitalization. A
market value-weighted index is estimated by
adding the total market value of all the stocks in
the index:

Market Value of stock = Number of Shares Outstanding ×
Current Market Price of stock
The performance of a market value-weighted index
represents the buy/hold return of all the outstanding
shares of each stock in the index. Examples of market
value-weighted index include S&P 500 and Nasdaq
Composite, Russell 3000.
Float-weighted index is a subcategory of market valueweighted index. In float-weighted index, weights are
assigned according to the market capitalization of
publicly-traded (free float) shares only.
Weight of a stock = Market cap weight × Free-float
adjustment factor
Where, Free-float adjustment factor = fraction of shares
that float freely.


Reading 20

Market Indexes and Benchmarks

Its performance represents the buy/hold return of all the
shares of each stock in the index that are available for

trading to the public. Examples include FTSE 100, Russell
1000 & 2000, S&P 500 etc.
2)

Price weighting: In this method, weight of each
stock is assigned according to its absolute share
price. A price-weighted index (PWI) is simply an
arithmetic average of current prices
PWI = (P1+P2+…+Pn) / n
Where,
Pi = price of stock i
n = total number of stocks in the index

The performance of a price-weighted index represents
the buy/hold return of 1 share of each stock (or equal
number of shares invested in each stock) in the index.
Index movements are affected by the change in the
prices of the stocks. It is adjusted for stock splits and
changes in the composition of index over time.
Examples include Dow Jones Industrial Average (DJIA)
and Nikkei Dow Jones Average
3)

Equal weighting: In equal-weighting, each stock in
the index is weighted equally regardless of their
price or market value i.e. a $25 stock is as
important as a $50 stock in the index and the total
market value of the company is not important. The
performance of equal-weighting index represents
the buy/hold return of equal dollar amount

invested in shares of each stock in the index.
Examples include Value Line and the Financial
Times Ordinary Share Index.
Equal-weighted indexes must be rebalanced
periodically (e.g., quarterly) to reestablish the
equal weighting because individual security
returns will vary, causing security weights to
drift from equal weights.

4)

4.3

Fundamental weighting: In fundamental weighting,
each stock in the index is weighted based on
company characteristics other than market values,
i.e. sales, cash flow, book value, and dividends. The
performance of a fundamental-weighted index
represents the performance of a portfolio that
invests according to valuation metrics for security.
Index Construction Tradeoffs

a) Completeness vs. investability:
A benchmark should include every possible security
in order to reflect complete coverage of a market.
But small-capitalization securities are too illiquid and
could not be purchased in amounts relevant to
institutional investors. Similarly, some securities are
not accessible for foreign investors if country’s

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government imposes restrictions. A less broad index
is more investable and accessible but not a
representative of broader, more diversified
performance. Hence, indexes must be designed in a
way so that they are broad and have adequate
investability. Popular indexes have greater liquidity
and thus they involve lower trading costs.
b) Reconstitution and rebalancing frequency vs.
turnover:
Reconstitution is the process of periodically adding
and dropping securities from an index in order to
keep pace with changes in index contents.
Rebalancing involves adjusting weights of existing
securities for changes in the number of shares
outstanding. There is also conflict inherent in
maintaining an index‘s representativeness while at
the same time seeking to maintain its simplicity and
cost-efficiency because both reconstitution and
rebalancing result in turnover which is costly for
investors. Security prices rise when securities are
added to an index and fall when they are deleted
from an index. As a result, index reconstitution
decreases returns of managers tracking the index
because they have to buy securities at higher
prices and sell the deleted securities at lower
prices.
The more frequent the reconstitution, the
better the index‘s representation of the pure

market, but the greater the transaction costs in
tracking the index.
Reconstitution is less frequent for all-inclusive
indexes than for those with a fixed number of
securities where securities are added and
dropped from an index on periodic basis (e.g.,
the S&P 500).
Rebalancing is less frequent for wider bands of
float-adjustment because there is high
probability of issue’s estimated free float to
stay within the band.

c) Objective and transparent rules vs. judgment: Some
broad-cap indexes of the U.S. equity market are
constructed using rules that are reasonably
objective, while others are constructed using
judgment. Transparency and objectivity allow
investors to anticipate changes in index constituents
and to manage the index replication process in an
orderly and efficient manner. Less transparency and
greater use of judgment make the index less
investable and create additional costs for tracking
portfolios but at the same time, judgment-based
indexes are considered to be superior in terms of
stability, accurate representation of the industry
distribution of the economy, and other attributes.


Reading 20

Market Indexes and Benchmarks

5.

5.1

Index Weighting Schemes: Advantages and Disadvantages

Capitalization-Weighted Indexes

Advantages:
•
Market prices and the number of tradable
securities are unambiguous measures of value at
a point in time.
•
If all investors held all the securities in capweighted indexes in proportion to their market
value, then investors will be able to hold all
shares. This property is referred to as macro
consistency.
•
Cap-weighted indexes reflect the concept of
CAPM because all investors in a CAPM world
would hold a proportional investment in the
market portfolio.
•
A capitalization-weighted index requires less
rebalancing than other indexes because stock
splits and other changes in the index
composition are automatically adjusted.

Disadvantages:
A capitalization-weighted index is biased
•
towards the shares of firms with the largest
market caps (mostly large, mature firms and
overvalued/overpriced firms) i.e. companies with
larger market values have higher weights.
Hence, the capitalization-weighted index is
potentially more vulnerable to market bubbles.
A capitalization-weighted index is less diversified
•
as it is highly concentrated in few issues i.e. large
cap firms. Therefore, it may not serve as a valid
benchmark for those professionally-managed
portfolios that are prohibited to invest more than
10% of their value in any one stock in order to
meet professional fiduciary duty regarding
diversification.
A value-weighted index may not be consistent
•
with a manager’s investment style.
Capitalization-weighted indexes overweight
•
overvalued issues and underweight undervalued
issues.

5.2

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Price-Weighted Indexes

Advantages:
•
Price-weighted indexes are simple to construct.
•
Historical stock price data is easily available than
market value data.
Disadvantages:
•
Price-weighted indexes are biased towards highest
price stock (i.e. higher priced stocks receive higher
weights) and do not necessarily reflect the

•
•

5.3

economic importance of issuing companies.
Price-weighted indexes are affected by stock splits,
reverse splits and changes in index composition
and thus require adjustments.
In price-weighted indexes it is assumed that
investor holds one unit of each security in the index
that does not explain how most investors form
portfolios.

Equal-Weighted Indexes

Advantages:
•
Equal-weighted indexes are less concentrated in
large-cap securities and more diversified as they
give smaller weights to large-cap securities (and
larger weights to small-cap securities).
•
Equal-weighted indexes may better represent
“how the market did” because they provide an
average of all index security returns.
Disadvantages:
•
Equal-weighted indexes are biased towards
small cap firms because they contain more small
firms.
•
Equal-weighted indexes require frequent
periodic rebalancing which increases
transaction costs.
•
Equal-weighted indexes contain potentially
illiquid stocks.

5.4

Fundamental-Weighted Indexes

Advantages:
•
Fundamental-weighted indexes do not suffer

from disadvantages of market value-weighted,
price-weighted and equal-weighted indexes
because they use valuation metrics to weight
index constituents.
•
Fundamental-weighted indexes more
appropriately represent an issuer’s importance in
an economy because they weight by
fundamentals, rather than by market prices that
are subject to bubbles.
Disadvantages:
•
Fundamental-weighted indexes are based on
subjective judgment.
•
Fundamental-weighted indexes are less
diversified than capitalization weighted indexes if
the valuation screen is restrictive.
•
Fundamental-weighted indexes cannot be held
by all the investors because they are weighted
by valuation metrics rather than available


Reading 20

•
•

Market Indexes and Benchmarks

liquidity (market capitalization).
Fundamental-weighted indexes may not serve
as valid benchmarks because their composition
and weightings are not fully known to investors.
Fundamental-weighted indexes may not serve
as valid benchmarks for investors preferring
large-cap growth securities because they are
biased towards small-cap value stocks.

Among all the types of indexes, capitalization-weighted,
float-adjusted indexes are considered to be the most
preferred for use as benchmarks because they are most
easy to mimic and involve less tracking risk and cost.
End of Reading Practice Problems:
Practice all the questions given at
the end of Reading.

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