Ground Rules

February 2024

Guide to Calculation
Methods for the FTSE
UK Index Series
v5.9

lseg.com/en/ftse-russell

Guide to Calculation Methods for the FTSE UK Index Series, v5.9, February 2024

Contents

Section 1 Purpose of the guide ........................................................................................................................................... 3
Section 2 Price indices ........................................................................................................................................................ 3
Section 3 Index points ....................................................................................................................................................... 10
Section 4 Dividends and earnings statistics ..................................................................................................................... 12
Section 5 Total returns ...................................................................................................................................................... 14
Section 6 Further information ........................................................................................................................................... 17

FTSE Russell

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Guide to Calculation Methods for the FTSE UK Index Series, v5.9, February 2024

Section 1

Purpose of the guide1.

Purpose of the guide

1.1

The aims of the guide are:
A. to describe how the indices are calculated;
B. to make it easier for users to replicate the indices to support their investment and trading activities; andC. to assist users in understanding the component factors that influence the performance of the indices.

1.2

FTSE Russell
FTSE Russell is a trading name of FTSE International Limited, Frank Russell Company, FTSE Global Debt
Capital Markets Limited (and its subsidiaries FTSE Global Debt Capital Markets Inc. and FTSE Fixed
Income Europe Limited), FTSE Fixed Income LLC, FTSE (Beijing) Consulting Limited, Refinitiv Benchmark
Services (UK) Limited, Refinitiv Limited and Beyond Ratings.

FTSE Russell

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Guide to Calculation Methods for the FTSE UK Index Series, v5.9, February 2024

Section 2

Price indices2.

Price indices

2.1

The FTSE UK Index Series is an arithmetic weighted series where the weights are the market capitalisationof each company. The price index is the summation of the free float adjusted market values (or capitalisations)of all companies within the index divided by the divisor (see 2.2). The price movement of a larger company(say, representing 5% of the value of the index) will therefore have a larger effect on the index than asmaller company (say, representing 1% of the value of the index).

2.2

The formula used for calculating the indices is straightforward. However, determining the capitalisation ofeach constituent company and calculating the capitalisation adjustments to the index are more complex. At
the starting date for calculating an index, an arbitrary value (e.g. 1,000) is chosen as the initial value. On
that date a divisor is calculated as the sum of the market capitalisations of the index constituents divided by
the initial index value. The divisor is subsequently adjusted for any capital changes in the index constituents.
To prevent discontinuities in the index in the event of a corporate action or change in constituents, it isnecessary to make an adjustment to the prices used to calculate the index to ensure that the change
in index between two consecutive dates reflects only market movements rather than including change
due to the impact of corporate actions or constituent changes. This ensures that the index values remaincomparable over time and that changes in the index level properly reflect the change in value of a portfolio
of index constituents with weights the same as in the index.
The adjustment used by FTSE Russell is based on the Paasche formula (also known as the currentweighted formula, see 2.3 below) adjusts the divisor for the index for the day before a corporate action
and calculates the change from that adjusted index to the index for the following day in which the corporate
action occurs. The implication of this adjustment for a portfolio manager wishing to track the index is thatthe manager needs to either invest or realise cash at the opening of the market on the day of the corporate
action depending on whether the constituent is realising or raising capital. In practice, the portfolio manager
will sell/invest at the previous close.

2.3

Paasche formula
𝐼𝑡𝑃𝑎𝑎𝑠 =∑𝑛𝑖=1 𝑃𝑖,𝑡 𝑄𝑖,𝑡∑𝑛𝑖=1 𝑃𝑖,0 𝑄𝑖,𝑡

Where:
ItPaas=Paasche index.

Pi,t

=

price at start of day t for constituent i after adjustments for corporate action or event.

Pi,0

=

price of constituent i on the starting day of calculating the index.

Qi,t

=

number of shares included in the index for constituent i at the start of day t.

Chained Paasche index
𝑃𝑎𝑠𝑠
𝐼𝑡𝑃𝑎𝑎𝑠 = 𝐼𝑡−1

FTSE Russell∑𝑛𝑖=1 𝑃𝑖,𝑡 𝑄𝑖,𝑡∑𝑛𝑖=1 𝑃𝑖,𝑡−1 𝑄𝑖,𝑡

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– Denominator uses today’s quantities (post-repayment, ex-price) and yesterday’s price (pre-repayment,
cum-price).
– To prevent discontinuities, need to adjust yesterday’s closing price with a price adjustment factor to
make it comparable to today’s.
– Price adjustment factor (PAFi,t) = ex-price/cum-price = (Pt-1-1)/Pt-1.
Example:Suppose there are two constituents, A and B, and the index starts on day t-1 with a value of 100. the priceof A is 10 and the price of B is five on day t-1. B then has a two-for-one split on day t.
PriceMarket cap

t-1

t

t-1

t

PAF

Pt x Qt

Pt-1 x Qt

A

10

11

10

10

1

110

100

B

5

2

5

10

0.5

20

50

Pass
ItPaas = It−1

2.3.1

Number of shares

Numerator ∑(Pt x Qt)

130

Denominator ∑(PAFi,t x Pt-1 x Qt)

125∑ni=1 Pi,t Q i,t130= 100 𝑥= 104n∑i=1 Pi,t−1 Q i,t PAFi,t125

A simple example of the calculation method between two dates when there have been no capital changes is
as follows. Please note, these calculations are to be used only as examples and where necessary, numbers
have been rounded for simplicity. Actual index calculations are undertaken to sufficient significant figures toeliminate rounding errors. In this example, the free float is 100% of shares in issue for each constituent.
Example one
Step one

Calculate the capitalisation of constituent companies at starting date.

Share
price

Sharesin-issue

(p)

(m)

Free float
factorA

270.0

61,443

1.00

165,896.10

B

605.0

22,5791.00

136,602.95

C

968.0

9,229

1.00

89,336.72

Company

Total market value(£m)

391,835.77

Step twoSet starting value of index (say, 100)

Step three

Calculate index divisor on the starting dateIndex divisor

Marketvalue=

Total market value
Index value=391,835.77
100.0

=

FTSE Russell

3,918.36

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Step four

Calculate the capitalisation of constituent companies on the end date

Share
price

Sharesin-issue

(p)

(m)

Free float
factorA

283.0

61,443

1.00

173,883.69

B

588.0

22,5791.00

132,764.52

C

945.0

9,229

1.00

87,214.05

Company

Total market value

Step fiveMarketvalue(£m)

393,862.26

Calculate index value at end dateIndex value=

Total market value
Index divisor=

393,862.26
3,918.36=

100.5

Index value

2.3.2

‒

Start date

=

100.0

‒

End date=

100.5

Example two: shares in issue increase
When a company increases the number of shares it has in issue, the market capitalisation of that company
increases and the total market capitalisation will rise accordingly. The index divisor is adjusted to maintaina constant index value. The change is explained showing the impact of company A having a 700 million
shares in issue increase.
Step one

Calculate index as at close (immediately before the share increase)

Share
price

Sharesin-issue

(p)

(m)

Free float
factorA

283.0

61,443

1.00

173,883.69

B

588.0

22,5791.00

132,764.52

C

945.0

9,229

1.00

87,214.05

Company

Total market value

FTSE Russell

Marketvalue(£m)

393,862.26

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Index value=

Total market value
Latest index divisor=

393,862.26
3,918.36=

Step two

100.5

Adjust company A shares in issue by 700m
Share
price

Sharesin-issue

(p)

(m)

Free float
factorA

283.0

62,143

1.00

175,864.69

B

588.0

22,5791.00

132,764.52

C

945.0

9,229

1.00

87,214.05

Company

Marketvalue(£m)

395,843.26
Step three

Calculate new divisor

New divisor=

Total market value
Constant index value=395,843.26
100.5

=

2.3.3

3,938.74

Example three: shares in issue decrease (buy-back)
When a company decreases the number of shares it has in issue, the market capitalisation of that company
decreases and the total market capitalisation will fall accordingly. The index divisor is adjusted to maintaina constant index value. The change is explained showing the impact of company A having a 700 million
shares in issue decrease.
Step one

Calculate index as at close (immediately before the share decrease)

Share
price

Sharesin-issue

(p)

(m)

Free float
factorA

283.0

61,443

1.00

173,883.69

B

588.0

22,5791.00

132,764.52

C

945.0

9,229

1.00

87,214.05

Company

Total market value

FTSE Russell

Marketvalue(£m)

393,862.26

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Index value=

Total market value
Latest index divisor=

393,862.26
3,918.36=

Step two

100.5

Adjust company A shares in issue by 700m

Share
price

Sharesin-issue

(p)

(m)

Free float
factorA

283.0

60,743

1.00

171,902.69

B

588.0

22,5791.00

132,764.52

C

945.0

9,229

1.00

87,214.05

Company

Marketvalue(£m)

391,881.26

Step three

Calculate new divisor

New divisor=

Total market value
Constant index value=391,881.26
100.5

=

2.3.4

Example four

3,899.32

Company additions and deletions

When a company is added to or deleted from the index, the market capitalisation of that company is added
to or deleted from the index and the total market capitalisation will rise or fall accordingly. The index divisor
is adjusted to maintain a constant index value. The change can be explained using the previous example.
Step one

Calculate index as at close on day before constituent change

Share
price

Sharesin-issue

(p)

(m)

Free float
factorA

283.0

61,443

1.00

173,883.69

B

588.0

22,5791.00

132,764.52

C

945.0

9,229

1.00

87,214.05

Company

Total market value

FTSE Russell

Marketvalue(£m)

393,862.26

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Index value=

Total market value
Latest index divisor=

393,862.26
3,918.36=

Step 2

100.5

Remove C and insert D

Share
price

Sharesin-issue

(p)

(m)

Free float
factorA

283.0

61,443

1.00

173,883.69

B

588.0

22,5791.00

132,764.52

D2,026.0

3,649

1.00

73,928.74

Company

Marketvalue(£m)

380,576.95

Step 3Calculate new divisor

New divisor=

Total market value
Index value=

380,576.95
100.5

=

FTSE Russell

3,786.84

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Guide to Calculation Methods for the FTSE UK Index Series, v5.9, February 2024

Section 3

Index points

3.

Index points

3.1

It is useful to define the concept of index points, which puts a value on the index. The index level at any time
can be equated to the market capitalisation of the constituents at that time, so that one index point has avalue of the market capitalisation divided by the index level (which is equal to the index divisor). The divisor
can therefore be used to quickly calculate the impact of an event on an index. The effect of a change in theprice of a constituent company expressed in index points is calculated as follows.

The impact of a change in price for a constituent is derived from the following formula:
Constituent shares in issue{[] *Change in share price*free float factor} /100
Index divisor
Note: change in share price expressed in the same units as the divisor.
Using company A as an example and a divisor of 3,918.36:((61,443/3918.36) * (13*1))/100= 15.680795 * 13 = 203.850335= 203.850335/100 = 2.04 (rounded up)
Sharesin-issuePricechange(m)(p)

Free float
factorEffect inindex points

A

61,443

13.0

1.00

2.04

B

22,579

-17.0

1.00

-0.98

C

9,229

-23.0

1.00

-0.54

Company

Total change in index points

FTSE Russell

0.52

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Guide to Calculation Methods for the FTSE UK Index Series, v5.9, February 2024

3.2

Similarly, the market value of a rise or fall in an index can be calculated using the index divisor as follows.
Change in index points x index divisor
Using the same example again, the market value of the gain in the index is:

FTSE Russell=

0.52 x 391,836p=

203,755p

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Guide to Calculation Methods for the FTSE UK Index Series, v5.9, February 2024

Section 4

Dividends and earnings statistics

4.

Dividends and earnings statistics

4.1

Dividend yield

4.1.1

Dividend yield is a widely used measure of the income return on a stock or index. In calculating index
dividend yields, FTSE Russell applies a free float adjustment to the number of shares in issue for eachconstituent. The dividend used to calculate the yield is the dividend declared by the companies.

4.1.2

Dividends for the previous 12 months are included in the dividend yield calculation from the XD date. If thedividend is declared in a currency other than Sterling, the 16:00 WM/Reuters Closing Spot Rate on the day
before the dividend is XD is used to convert the dividend into sterling unless the company announces asterling equivalent, which is used instead.

4.1.3

The formula for the dividend yield in percent is:
𝑁

∑
𝑖=1

𝑔𝑖 × 𝑠𝑖 × 𝑓𝑖
× 100𝑐

Where:
gi=

dividends declared in the previous 12 months of the ith component security.

sI=

the weighting of the ith component security (equal to the number of ordinary shares issued by
the company).

c=total market capitalisation of the index constituents, adjusted for free float.

fi=free float factor for the ith component security.

Dividends declared that are denominated in a currency other than Sterling will be converted using
WM/Reuters Closing Spot Rates one day prior to the ex-dividend date.
4.2

Earnings calculations

4.2.1

Earnings are an important element in valuing a company. The treatment of earnings in the calculationof statistics on the FTSE UK Index Series is based on the companies’ own published data. The headline
earnings formula issued by the CFA Society of the UK (previously named the Institute of Investment
Management & Research (IIMR)) in response to FRS3 is used in the calculation of the earnings statistics
to reflect the trading performance of companies on a standardised basis.

4.2.2

A tax adjusted earnings number is derived from a company’s most recent audited report and accounts by
taking tax liabilities expected to be paid and tax credits expected to be received for the current year fully
into account for the purpose of calculating corporate earnings for that year.
Definition of headline earnings from CFA:
Headline earnings (cfauk.org)

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4.2.3

The earnings statistics for the FTSE UK Index Series are calculated on an ‘as reported’ basis (i.e. theyreflect the last reported year’s earnings and interims when published) and represent the sum of the latest
two half years’ earnings (or the sum of quarterly earnings for those companies that report quarterly). It
should also be noted that losses are included in the earnings calculations on the FTSE UK Index Series.

4.2.4

Where a company discloses the tax consequences of individual items in the report and accounts, these will
form the basis of any tax adjustments made. Where a company makes no specific disclosure, but where an
adjustment is required, the guiding principle will be to apply the average rate of tax on the FRS3 profits toany adjustment made.

4.3

Dividend cover

4.3.1

The dividend cover shows the ability of the company to meet dividend payments from its current earnings.
The conventional method for calculating dividend cover is:
Earnings adjusted for free float
Dividends adjusted for free float
Dividends declared that are denominated in a currency other than Sterling will be converted using
WM/Reuters Closing Spot Rates, one day prior to the ex-dividend date.

4.4

Price-earnings (P/E) ratio

4.4.1

The P/E ratio is a measure of value for a stock or an index. The ratio is calculated using net earnings, as
defined under the CFA Society of the UK (previously the UK Society of Investment Professionals) headline
earnings formula, and is the total market value adjusted by free float factors of all index constituents divided
by the sum of the net earnings, calculated similarly, as shown below for an index.
∑𝑛𝑖=1 𝑝𝑖 × 𝑠𝑖 × 𝑓𝑖𝑛∑𝑖=1𝑒𝑖 × 𝑓𝑖
Where:
N=

the number of securities in the index.

si=

the number of shares in issue used by FTSE for the security, as defined in the ground rules.

pi=

price of the ith component security.

ei=

aggregate earnings of the ith component security.

fi=free float factor for the ith component security.

FTSE Russell

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Guide to Calculation Methods for the FTSE UK Index Series, v5.9, February 2024

Section 5

Total returns

5.

Total returns
Using both the price and total return indices, investors have a reliable guide to both the capital performanceand reinvested income returns.

5.1

Ex-dividend adjustment

5.1.1

The ex-dividend (XD) adjustment represents the value of dividends declared by constituent companies on
the XD date expressed in index points (see formula below). XD adjustments are based on declared dividends.
The algorithm used by FTSE Russell for this adjustment assumes that on the ex-dividend date, the index isadjusted at the start of the day to allow for the number of dividends due on that date and that the full amountof the dividend is reinvested at the adjusted price level. Consequently, when the total return index is
calculated at the end of that day’s trading, it assumes that both the price index and the dividend are
adjusted by the change in the price level from the previous day’s close to the current day’s close.
The value of one index point can be expressed as market value of constituents/index. Also, since index =market value of constituents/divisor, one index point is equal to the divisor. The value of dividends cantherefore be converted to index points by the formula:
𝑁

∑
𝑖=1

𝑔𝑖 × 𝑠𝑖 × 𝑓𝑖 × 𝑤𝑚𝑒𝑖−1/100𝑑Where:

5.1.2

N

=

number of securities in the index.

gi=

dividend per share of the ith component security.

si=

the weighting of ith the component security(equal to the number of ordinary shares issued by the company).

d=divisor.

fi=

free float factor for the ith component security.

wmei-1=

WM exchange rate as of 16:00 London time of the index at i-1(applies only to dividends paid in a different currency to the index).

If a company declares a dividend in a currency other than Sterling, the published Sterling equivalent will be
used, if available. If there is no Sterling equivalent, the dividend will be converted to Sterling using the 16:00
WM/Reuters Closing Spot Rate the day before the stock goes XD.

FTSE Russell

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5.1.3

For example, the following table shows the calculation that would be performed if A and B each declared a
dividend payment with an XD date of today to determine the XD-adjustment for the index.
Company

Free float factor

XD adjustment (index
points)7,717.2

1.00

1.97

3,161.0

1.00

0.81

Dividend

SharesValue of dividends

(p)

(m)

(£m)

A

12.56

61,443B

14.00

22,579Total XD adjustment for index

2.78

Index divisor=

3,918.36 (£m)

5.1.4

The method for calculating the XD adjustment uses the divisor as at the close of business on the preceding
day after implementing any capitalisation changes. Where a company has more than one line of shares
included in the indices, the XD adjustment is calculated separately for each line.

5.2

Calculation of the total returns indices (TRIs)

5.2.1

The TRIs measure the total return on the underlying indices, combining both capital performance andreinvested income. The TRIs are calculated using declared dividends. Although there is a timing delay
between the XD date and the receipt of dividends (payment date), it is considered preferable to assume
all income is reinvested on the XD date rather than incur the complications of allowing a time lag before
reinvestment of the declared dividends. The formula for calculation of the current day’s TRI basedon the previous day’s TRI and the XD adjustment is shown below.
𝑅𝑡 = {𝑅𝑦 × 𝐼𝑦 /(𝐼𝑦 − 𝑋𝐷)} × 𝐼𝑡 ⁄𝐼𝑦= 𝑅𝑦 × 𝐼𝑡 /(𝐼𝑦 − 𝑋𝐷)
Where:

5.2.2

Ry

=

TRI value yesterday.

Rt=

TRI value today.

Iy=

underlying capital index yesterday.

It=

underlying capital index today.

XD=

XD adjustment to underlying capital index.

The TRIs are calculated daily and some are also calculated in real time. The calculation method will vary
according to whether any dividends are declared XD on a given day. The following table and examples
explain how the calculation is performed.
Capital index (CI)XD adjust (XD)TRI

Day one

3,190-

1,000.00*

Day two

3,200-

1,003.13

Day
three

3,220

5

1,010.98*Starting value

FTSE Russell

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Where no XD adjustment occurs:
TRI=

Previous TRI

x

Today’s CI
Previous CI

Day two TRI=

1,000.00 x

3,200
3,190

=

1,003.13

Where an XD adjustment occurs:
TRI=

Previous TRI

x

Today’s CI(Previous CI - XD)

Day
three

TRI

=

1,003.13x

3,220(3,200 - 5)=

FTSE Russell

1,010.98

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Section 6

Further information

Further information
A Glossary of Terms used in FTSE Russell’s ground rules can be found using the following link:
Glossary.pdf
Further information on the FTSE UK Index Series is available from FTSE Russell.
For contact details, please visit the FTSE Russell website or e-mail FTSE Russell client services at
info@ftserussell.com.
Website: www.lseg.com/en/ftse-russell/

FTSE Russell

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Disclaimer© 2024 London Stock Exchange Group plc and its applicable group undertakings (“LSEG”). LSEG includes (1) FTSE International Limited (“FTSE”), (2) Frank Russell Company(“Russell”), (3) FTSE Global Debt Capital Markets Inc. and FTSE Global Debt Capital Markets Limited (together, “FTSE Canada”), (4) FTSE Fixed Income Europe Limited (“FTSE FI
Europe”), (5) FTSE Fixed Income LLC (“FTSE FI”), (6) FTSE (Beijing) Consulting Limited (“WOFE”), (7) Refinitiv Benchmark Services (UK) Limited (“RBSL”), (8) Refinitiv Limited (“RL”)
and (9) Beyond Ratings S.A.S. (“BR”). All rights reserved.
FTSE International Limited is authorised and regulated by the Financial Conduct Authority as a benchmark administrator. Refinitiv Benchmark Services (UK) Limited is authorised andregulated by the Financial Conduct Authority as a benchmark administrator.
FTSE Russell® is a trading name of FTSE, Russell, FTSE Canada, FTSE FI, FTSE FI Europe, WOFE, RBSL, RL and BR. “FTSE®”, “Russell®”, “FTSE Russell®”, “FTSE4Good®”, “ICB®”,“WMR™”, “FR™”, “Beyond Ratings®” and all other trademarks and service marks used herein (whether registered or unregistered) are trade marks and/or service marks owned or
licensed by the applicable member of LSEG or their respective licensors and are owned, or used under licence, by FTSE, Russell, FTSE Canada, FTSE FI, FTSE FI Europe, WOFE,RBSL, RL or BR.
All information is provided for information purposes only. All information and data contained in this publication is obtained by LSEG, from sources believed by it to be accurate andreliable. Because of the possibility of human and mechanical inaccuracy as well as other factors, however, such information and data is provided "as is" without warranty of any kind. No
member of LSEG nor their respective directors, officers, employees, partners or licensors make any claim, prediction, warranty or representation whatsoever, expressly or impliedly,
either as to the accuracy, timeliness, completeness, merchantability of any information or LSEG Products, or of results to be obtained from the use of LSEG products, including but notlimited to indices, rates, data and analytics, or the fitness or suitability of the LSEG products for any particular purpose to which they might be put. The user of the information assumes
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No responsibility or liability can be accepted by any member of LSEG nor their respective directors, officers, employees, partners or licensors for (a) any loss or damage in whole or inpart caused by, resulting from, or relating to any inaccuracy (negligent or otherwise) or other circumstance involved in procuring, collecting, compiling, interpreting, analysing, editing,transcribing, transmitting, communicating or delivering any such information or data or from use of this document or links to this document or (b) any direct, indirect, special, consequential
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No member of LSEG nor their respective directors, officers, employees, partners or licensors provide investment advice and nothing in this document should be taken as constituting
financial or investment advice. No member of LSEG nor their respective directors, officers, employees, partners, or licensors make any representation regarding the advisability ofinvesting in any asset or whether such investment creates any legal or compliance risks for the investor. A decision to invest in any such asset should not be made in reliance on any
information herein. Indices and rates cannot be invested in directly. Inclusion of an asset in an index or rate is not a recommendation to buy, sell or hold that asset nor confirmation thatany particular investor may lawfully buy, sell or hold the asset or an index or rate containing the asset. The general information contained in this publication should not be acted upon
without obtaining specific legal, tax, and investment advice from a licensed professional.

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