Index value, price return and total return

What is a security market index?

A security market index is a group of securities with a rule for combining them into one number, so that the number stands for the performance of a market. The market can be a country, a sector, an investing style or a whole asset class. The securities in the group are its constituent securities .

Think of an index as a recipe: a list of ingredients and a method for blending them. Change either one and you have a different index, even when both claim to track “the same market”.

An index is a financial indicator: you cannot buy it, but its value is computed from observable prices (or estimated values) of its constituent securities. It is the benchmark that portfolios are measured against, and the blueprint that index funds and exchange-traded funds (ETFs) copy.

Most index providers publish two versions from the same constituents. The price return index , also called a price index , tracks price changes only. The total return index tracks price changes plus the income the constituents pay (dividends for shares, interest for bonds), treated as reinvested. Both start at the same level and drift apart as income accumulates.

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

Exam tip When a question says “index” and gives dividends or interest, check which version it wants. Price return ignores the income. Total return includes it.

Go deeper Where indexes came from

The first index, the Dow Jones Average of 1884, tracked eleven companies, most of them railroads. The Dow Jones Industrial Average followed in 1896 with twelve industrial companies. Thousands of indexes exist today, for markets and asset classes all over the world.

How is an index built?

Know the idea

Building an index takes five index construction steps . Each one changes the number the index shows.

1. Objective. The market or sector the index represents.
2. Selection of constituents. Securities chosen by predefined criteria.
3. Weighting method. How each constituent’s price change moves the index.
4. Calculation. A start date and a start value.
5. Maintenance. Rebalancing, reconstitution, corporate actions and a periodic review of the rules.

Building an indexeach step changes the return

• Objective Know the idea the market or sector it represents
• Selection of constituents Know the idea by predefined criteria
• Weighting method Memorize decides how each price change moves the index
  • Price
  • Equal
  • Market cap (float-adjusted)
  • Fundamental factor
• Calculation Know the idea a start date and a start value
• Maintenance Know the idea rebalancing, reconstitution, corporate actions and periodic review of the rules

Lessons 3 and 4 cover the weighting methods; lesson 5 covers maintenance.

How is an index value calculated?

Use it

Every index divides an aggregate reference value by a divisor . The aggregate depends on the weighting: the sum of one share of each constituent for a price-weighted index, the total market value for a cap-weighted one, and so on. The divisor is arbitrary: the provider picks it so that the index starts at a round number, usually 100 or 1,000, and changes it after events that are not investment results (a stock split, a constituent swap) so the index does not jump.

$$V_t = \frac{\text{aggregate reference value}_t}{D}$$

How do you calculate an index return over one period?

Take the change in the index level, add any income for a total return, and divide by the starting level. The price return uses the price return index level only. The total return adds the income paid by the constituents during the period (capital distributions such as dividends, interest and distributed gains), expressed in index points and written $Inc$.

$$r_{price} = \frac{V_1 - V_0}{V_0}$$

$$r_{total} = \frac{V_1 - V_0 + Inc}{V_0}$$

The exam also turns this around: it gives the return and asks for the ending level or the income.

An index return is also the weighted average of its constituents’ returns. Use each constituent’s weight at the start of the period. With price returns you get the index price return; with total returns, the index total return.

$$r_{index} = \sum_i w_i r_i$$

Which version should you use?

Use it

Match the index to what the portfolio earns.

Version	Best for
Price return index	Shares that pay no dividends, short-term trends and price moves, and strategies that do not reinvest income
Total return index	Dividend-paying shares, long-term growth, mutual funds, dividend reinvestment plans, and whenever reinvested income is a large part of the return

Both versions start at the same value. The total return index usually ends higher, and the gap widens with time.

Go deeper Index values over several periods

An index level after several periods is the start value times each period’s growth factor, the same compounding as in Learning Module 1. An index at 1,000 with returns of +5%, −3% and +8% ends at 1,000 × 1.05 × 0.97 × 1.08 = 1,099.98, not 1,100. Adding returns instead of compounding them is the trap.

Go deeper Why the total return index matters over the long run

Dividends and interest are a large part of what long-term investors earn. A price return index ignores all of it, so over decades it understates what a holder of the constituents actually received. A 2% income yield on top of a 5% price return makes the total return index roughly 7% a year, and after ten years the gap between the two is wide. For comparing a portfolio with an index, use the version that matches the portfolio: a fund that reinvests income should be set against a total return index.

Some providers publish gross and net total return indexes. Gross assumes the full dividend is reinvested. Net deducts the withholding tax a typical foreign investor would pay on it, so a net index sits a little below the gross one.