You are reading the 2026 curriculum (exams up to November 2026). Sitting in February 2027 or later? Go to the 2027 Equities guide.

Learning Module 2 of Equity Investments 11–14% of the exam

Security Market Indexes

5 lessons. About 30 minutes in cram mode, 140 minutes in full.

Start with lesson 1 Learn with Sensei Read the module summary

Lessons

1
Index value, price return and total return
calculate 6 min cram, 24 min full
2
Price-weighted and equal-weighted indexes
calculate 8 min cram, 32 min full
3
Market-cap, float-adjusted and fundamental weighting
calculate 8 min cram, 32 min full
4
Rebalancing, reconstitution and what indexes are used for
describe 4 min cram, 24 min full
5
Types of equity, bond and alternative investment indexes
describe 4 min cram, 28 min full

What the exam expects you to do

Describe a security market index.Index value, price return and total return
Calculate and interpret the value, price return, and total return of an index.Index value, price return and total return
Describe the choices and issues in index construction and management.Price-weighted and equal-weighted indexes
Compare the different weighting methods used in index construction.Price-weighted and equal-weighted indexes
Calculate and analyze the value and return of an index given its weighting method.Price-weighted and equal-weighted indexes
Describe rebalancing and reconstitution of an index.Rebalancing, reconstitution and what indexes are used for
Describe uses of security market indexes.Rebalancing, reconstitution and what indexes are used for
Describe types of equity indexes.Types of equity, bond and alternative investment indexes
Compare types of security market indexes.Types of equity, bond and alternative investment indexes
Describe types of fixed-income indexes.Types of equity, bond and alternative investment indexes
Describe indexes representing alternative investments.Types of equity, bond and alternative investment indexes

Module summary

The whole module on one sheet, organised by lesson: what to memorize, how the ideas fit together, the formulas and the key terms. No paragraphs, just what you need to revise.

Hide what I know

How deeply to learn each part

Know the idea: Understand it in general. It frames other topics, but you will not calculate with it.
Use it: Understand it well enough to solve a question with it. Recognize when it applies.
Memorize: Learn it by heart. The exam will not give it to you.

Index value, price return and total return

Known

MemorizeIndex return measures

Measure	Counts	Formula
Price return	price changes only	$(V_1 - V_0) \div V_0$
Total return	price changes + income	$(V_1 - V_0 + I) \div V_0$
Several periods	chained growth factors	$V_0 \prod (1 + R_t)$

Memory hook Total = price + income, always over the START level. Several periods multiply; they never add.

Know it cold Divide by the starting value. Total return is at least the price return whenever income is paid.

Key terms

security market index Use it
constituent securities Know the idea
price return Memorize
price return index Use it
price index Know the idea
total return Memorize
total return index Use it

Two returns from the same constituents

Return on an indexone set of securities, two published versions

Price return Memorize price changes only, shown by the price return index
- Also called price index
Total return Memorize price changes plus income, shown by the total return index
- Price return change in level ÷ start level
- Income return dividends and interest ÷ start level

Formulas

Index price return Memorize

PR = \frac{V_1 - V_0}{V_0}

Quick example

A price return index moves from 2,000 to 2,060. (2,060 − 2,000) ÷ 2,000 = 3.00%.

On your calculator

2060−2000=÷2000= 0.03

2060ENTER2000−2000÷ 0.03

ENTER enter (on the HP, puts the number on the stack)

Index total return Memorize

TR = \frac{V_1 - V_0 + I}{V_0}

Quick example

Index 2,000 to 2,060 with 24 points of income. (2,060 − 2,000 + 24) ÷ 2,000 = 4.20%.

On your calculator

2060−2000+24=÷2000= 0.042

2060ENTER2000−24+2000÷ 0.042

ENTER enter (on the HP, puts the number on the stack)

Index return from constituent returns Use it

R_{index} = \sum_i w_i R_i

Quick example

Weights 40%, 40%, 20% and returns 5%, 1%, −3%. 0.40 × 5 + 0.40 × 1 + 0.20 × (−3) = 1.80%.

On your calculator

(0.4×5)+(0.4×1)−(0.2×3)= 1.8

0.4ENTER5×0.4ENTER1×+0.2ENTER3×− 1.8

ENTER enter (on the HP, puts the number on the stack)

Multi-period index value Memorize

V_T = V_0 \,(1 + R_1)(1 + R_2)\cdots(1 + R_T)

Quick example

An index at 500 returns 6%, −8% and 4%. 500 × 1.06 × 0.92 × 1.04 = 507.10, not 500 × 1.02 = 510.

On your calculator

500×1.06×0.92×1.04= 507.104

500ENTER1.06×0.92×1.04× 507.104

ENTER enter (on the HP, puts the number on the stack)

Price-weighted and equal-weighted indexes

Known

MemorizePrice weighting versus equal weighting

	Price-weighted	Equal-weighted
Weight of i	$P_i \div \sum P$	$1 \div N$
Index value	$\sum P \div$ divisor	average of constituent values
Return	change in $\sum P$ ÷ start $\sum P$	simple average of returns
Bias	high-priced shares; splits shift weights	small companies overweighted
Upkeep	new divisor after a split	frequent rebalancing

Memory hook Price: one share of each, so the dearest share leads. Equal: the same money in each, so a small firm counts like a giant.

Know it cold After a split, new divisor = new sum of prices ÷ old index value, so the index does not move.

Key terms

target market Know the idea
security selection Know the idea
price weighting Memorize
divisor Memorize
equal weighting Memorize

The choices an index provider makes

Building an indexsimilar to building a portfolio

Target market Know the idea which market, segment or asset class it represents
Security selection Know the idea nearly all of the market, or a representative sample
Weighting Memorize how much of each security
- Price weighting weight follows share price
- Equal weighting each constituent gets 1 ÷ N
- Market-cap and fundamental weighting next lesson
Rebalancing Know the idea when weights are reset
Reconstitution Know the idea when the member list is re-examined

Formulas

Price-weighted index value Memorize

V = \frac{\sum_i P_i}{D}

Quick example

Prices 30, 60 and 90 with divisor 3. (30 + 60 + 90) ÷ 3 = 60.

On your calculator

30+60+90=÷3= 60

30ENTER60+90+3÷ 60

ENTER enter (on the HP, puts the number on the stack)

Price weight and price-weighted return Memorize

w_i = \frac{P_i}{\sum_j P_j}, \qquad R = \frac{\sum P_1 - \sum P_0}{\sum P_0}

Quick example

Prices go from 30, 60, 90 to 33, 57, 99. The sum rises from 180 to 189, so the return is 9 ÷ 180 = 5.00%. The 90 share carries 90 ÷ 180 = 50% of the weight.

On your calculator

189÷180−1= 0.05

189ENTER180÷1− 0.05

ENTER enter (on the HP, puts the number on the stack)

Divisor after a split Memorize

D_{new} = \frac{\sum P_{after}}{V_{before}}

Quick example

Prices 40, 60, 100 with divisor 3 give an index of 66.67. The 100 share splits 2-for-1, so the sum falls to 150. New divisor = 150 ÷ 66.67 = 2.25.

On your calculator

150÷(200÷3)= 2.25

150ENTER200ENTER3÷÷ 2.25

ENTER enter (on the HP, puts the number on the stack)

Equal weight and equal-weighted return Memorize

w_i = \frac{1}{N}, \qquad R = \frac{1}{N}\sum_i R_i

Quick example

Four shares return 8%, −2%, 5% and 1%. (8 − 2 + 5 + 1) ÷ 4 = 3.00%.

On your calculator

8+2+|-+5+1=÷4= 3

+|- change sign

8ENTER2CHS+5+1+4÷ 3

ENTER enter (on the HP, puts the number on the stack) · CHS change sign

Market-cap, float-adjusted and fundamental weighting

Known

MemorizeWeighting methods: weight driver, bias, upkeep

Method	Weight driven by	Tilt	Rebalancing
Price	share price	high-priced shares	divisor after splits
Equal	$1 \div N$	small caps	high
Market cap (float-adjusted)	market value of the float	large caps, momentum, maybe overvalued	low (self-rebalancing)
Fundamental	earnings, sales, book value…	value, contrarian	periodic

Memory hook Cap weighting buys more of what has risen. Fundamental weighting buys more of what has become cheap.

Know it cold Cap-weighted return = change in the TOTAL market value, not an average of returns.

MemorizeOne table, five answers (our three-stock table)

Method	Price return
Price-weighted	10.67%
Equal-weighted	8.67%
Cap-weighted	5.19%
Float-adjusted (Y float 60%)	7.27%
Fundamental (earnings)	4.25%

Memory hook The bigger the weight on Y (the one that fell), the lower the return.

Know it cold Exam options are the other methods' answers. Compute the one asked for, then match.

Key terms

market-capitalization weighting Memorize
market float Use it
float-adjusted market-capitalization weighting Memorize
fundamental weighting Memorize

Weighting methods and what each favors

Index weighting methodsthe same shares, a different rule

Price weighting Memorize weight follows share price
- Favors high-priced shares; splits shift weights
Equal weighting Memorize weight 1 ÷ N
- Favors small companies; needs frequent rebalancing
Market-cap weighting Memorize weight follows market value
- Float-adjusted version counts only shares the public can buy
- Favors large, recently risen shares (momentum)
Fundamental weighting Memorize weight follows earnings, sales, book value, cash flow, dividends
- Favors value; contrarian when rebalanced

Formulas

Market-cap weight Memorize

w_i = \frac{P_i N_i}{\sum_j P_j N_j}

Quick example

Share A: 10 million shares at 46. Share B: 30 million shares at 19. Values 460 and 570, total 1,030. A carries 460 ÷ 1,030 = 44.7%.

On your calculator

(10×46)+(30×19)= 1030
460÷1030= 0.4466

10ENTER46×30ENTER19×+ 1030
460ENTER1030÷ 0.4466

ENTER enter (on the HP, puts the number on the stack)

Market-cap-weighted index return Memorize

R = \frac{\sum P_1 N + Div}{\sum P_0 N} - 1

Quick example

Total market value of the constituents goes from 1,000 to 1,030, with 12 of dividends. (1,030 + 12) ÷ 1,000 − 1 = 4.20%. Without dividends the price return is 3.00%.

On your calculator

1030+12=÷1000−1= 0.042

1030ENTER12+1000÷1− 0.042

ENTER enter (on the HP, puts the number on the stack)

Float-adjusted market-cap weight Memorize

w_i = \frac{f_i P_i N_i}{\sum_j f_j P_j N_j}

Quick example

A holder owns 40% of a company with 100 million shares at 30. With float 60%, the index counts 0.60 × 100 × 30 = 1,800 of the 3,000 market value.

On your calculator

0.6×100×30= 1800

0.6ENTER100×30× 1800

ENTER enter (on the HP, puts the number on the stack)

Fundamental weight Memorize

w_i = \frac{F_i}{\sum_j F_j}

Quick example

Earnings of 60, 30 and 10 give weights of 60%, 30% and 10%, whatever the share prices are.

Rebalancing, reconstitution and what indexes are used for

Known

MemorizeRebalancing versus reconstitution

	Rebalancing	Reconstitution
Changes	weights	membership
Trigger	weights drift away from the rule	securities no longer meet the criteria, or new ones qualify
Frequency	usually quarterly	on set review dates (some indexes yearly)
Needs it most	equal-weighted, fundamental	every index

Memory hook Rebalancing = same list, new weights. Reconstitution = new list.

Know it cold Cap-weighted indexes rebalance themselves for price moves. Equal weighting trades back to 1 ÷ N each time.

MemorizeFive uses of an index

Use	Example
Gauge of market sentiment	"the market fell 2% today"
Proxy for returns, systematic risk (beta), risk-adjusted performance	beta against a broad index
Proxy for an asset class	a global bond index stands for "bonds"
Benchmark for active managers	small-cap manager vs small-cap index
Model portfolio for products	index funds and ETFs

Memory hook Sentiment, Proxy, Proxy, Benchmark, Model: how the market feels, what it earns and risks, the asset class, the yardstick, the fund.

Know it cold The benchmark must match the manager's style and universe.

Key terms

rebalancing Memorize
reconstitution Memorize
systematic risk proxy Know the idea
benchmark Use it
model portfolio Use it

Keeping an index up to date

Index managementboth create turnover

Rebalancing Memorize reset the weights of the existing constituents
- Equal-weighted and fundamental rebalance often, usually quarterly
- Market-cap-weighted largely rebalances itself
- Price-weighted weights are the prices; not rebalanced
Reconstitution Memorize change which securities are in the index
- Add new securities that meet the rules
- Remove securities that no longer qualify, merge or delist

Five uses of a security market index

What indexes are used for

Gauge of market sentiment Use it how the market did today
Proxy for returns, systematic risk and risk-adjusted performance Use it beta and alpha need a market index
Proxy for an asset class Use it inputs to asset allocation models
Benchmark for active managers Memorize must match the manager style and universe
Model portfolio for investment products Use it index funds and exchange-traded funds (ETFs) replicate it

Formulas

Alpha against a same-beta passive portfolio Use it

\alpha = R_p - \left[\beta R_m + (1 - \beta) R_f\right]

Quick example

Beta 0.90, index return 10%, cash 3%, active portfolio 11.5%. Passive = 0.90 × 10 + 0.10 × 3 = 9.3%. Alpha = 11.5 − 9.3 = 2.20%.

On your calculator

11.5−((0.9×10)+((1−0.9)×3))= 2.2

0.9ENTER10×1ENTER0.9−3×+ 9.3
11.5−CHS 2.2

ENTER enter (on the HP, puts the number on the stack) · CHS change sign

Types of equity, bond and alternative investment indexes

Known

MemorizeWhich index has which construction problem

Index	The catch
Equity style	shares migrate between styles at reconstitution, so turnover is high
Fixed income	huge universe, bonds mature, dealer prices, costly to replicate
Commodity	futures: roll yield and interest; weighting drives results
Real estate (appraisal)	valuations are smoothed
Real estate (repeat sales)	only properties that sell twice
Hedge fund	voluntary reporting: survivorship and backfill bias, returns biased upward

Memory hook Equity: shares move between boxes. Bonds: they mature and hide with dealers. Commodities: futures roll. Real estate: valued, not traded. Hedge funds: only the winners report.

Know it cold Hedge fund index returns are biased UPWARD. The constituents determine the index, not the provider.

MemorizeThe six basic style boxes

	Value	Growth
Large cap	large-cap value	large-cap growth
Mid cap	mid-cap value	mid-cap growth
Small cap	small-cap value	small-cap growth

Memory hook Three sizes times two styles.

Know it cold Providers define size and value differently, so a "small-cap value" index from two providers can hold different shares.

Key terms

broad market index Use it
multi-market indexes Use it
sector indexes Use it
style indexes Use it
fixed-income index Use it
commodity index Use it
REIT index Know the idea
hedge fund index Use it
survivorship bias Memorize
backfill bias Memorize

Types of equity index

Equity indexes

Broad market Memorize most of one market, usually over 90% of its value
Multi-market Memorize several countries or regions, up to the whole world
- By development developed, emerging, frontier
- By region Americas, Europe and Africa, Asia and Pacific
Sector Memorize one economic sector, national, regional or global
Style Memorize size, value or growth, or a mix
- Size large, mid, small
- Value or growth by valuation ratios
- Six basic styles three sizes by value or growth

How fixed-income indexes are cut

Fixed-income indexesaggregate, market sector, style, economic sector, specialized

Issuer type government, agency, corporate
Financing type general obligation, collateralized
Currency of the payments
Maturity short, medium, long
Credit quality investment grade, high yield
Inflation protection present or absent

Alternative investment indexes and their catch

Alternative investment indexes

Commodity Use it futures contracts, not physical goods
- Return interest rate + futures price changes + roll yield
- Weighting each provider picks its own method
Real estate Use it a thinly traded market
- Appraisal valuations, so returns are smoothed
- Repeat sales price change of properties that sold more than once
- REIT listed shares, priced continuously
Hedge fund Memorize built from returns that funds choose to report
- Survivorship bias failed funds stop reporting
- Backfill bias a fund joins after a good run and brings its history
- Little overlap providers differ widely

Cheat sheet · PDF · 4 A4 pages

Security Market Indexes on 4 pages

What to memorize, the concept maps, every formula with a worked example and keystrokes for the TI BA II Plus and HP 12C, how each idea is asked, and the traps. Print it, or keep it on your phone.

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