Introduction

Calculation of Indices

Full market capitalization

Under this methodology, index is calculated based on the full market capitalization of all the index constituents. Market capitalization (Mcap) describes size of a company. Mcap is calculated taking into account total number of shares issued and listed on the exchange multiplied by the current market price of each share. Companies with higher market capitalization are typically included in benchmark indices such as Nifty index. Under Full Mcap methodology, entire equity of a company is considered for index calculation regardless of company’s shareholding pattern. With the result, it is likely that the companies with a large market capitalization get included in the index despite of low public holding or a free-float available in the market. Normally, we notice large amount of shares are owned by the central government or the President of India holding in case of public sector enterprises (PSEs). In case of indices computed based on full mcap method, it is likely that a small change in the stock price of a closely held company (large promoter holding) makes a significant impact on the index value. In such case, index becomes vulnerable to market manipulation. Example: Equity holding of promoter in ONGC Ltd. till 2003 was approximately 97% and only 3% of the shares were available to the investors. However, for computation of index under full mcap method, entire 100% equity would be considered.

Formula: Summation of mcap of all the constituents / index base mcap * base index value

Where

Mcap = Total shares outstanding * stock price of one company

Index Divisor = Mcap of all constituents as on the base date adjusted for change in the indices

Base index value = Initial value assigned to the index on the base date

Base composition

Company Shares
outstanding
IWF Price Full Mcap* FF Mcap*
ABC LTD. 10000 1.00 200 2000000 2000000
BCD LTD. 20000 0.80 300 6000000 4800000
CDE LTD. 30000 0.75 400 12000000 9000000
DEF LTD. 40000 0.40 500 20000000 8000000
EFG LTD. 50000 0.25 600 30000000 7500000
Total 70000000 31300000
Index Divisor 70000000
Base Index Value 1000.00 *
Company Shares
outstanding
IWF Price Full Mcap* FF Mcap*
ABC LTD. 10000 1.00 250 2500000 2500000
BCD LTD. 20000 0.80 350 7000000 5600000
CDE LTD. 30000 0.75 425 12750000 9562500
DEF LTD. 40000 0.40 450 18000000 7200000
EFG LTD. 50000 0.25 610 30500000 7625000
Total 70750000 31300000
Index Divisor 70000000
Base Index Value 1010.71 *

Free-float market capitalization

Unlike full mcap method, shares that are held by the promoter, group company, shares under lock-in period, shares held by the strategic investors (to the extent identifiable) etc. are considered as non-free-float shares and these shares are not included for index computation. Example: As compared with earlier example in 7(a) above of ONGC Ltd. under full mcap method where 100% of companies mcap was considered for index calculation, only 3% of company’s equity would be considered for free-float mcap index calculation as 97% of the shares are held by the central government in the capacity of promoter. Consideration of equity for index computation is the fundamental differentiator between full mcap and free-float mcap method.

Summation of free-float mcap of all the constituents / index base mcap * base index value

Where

Free-float Mcap total shares outstanding * investable weight factor (IWF) * stock price of one company

Index Divisor = Mcap of all constituents as on the base date adjusted for change in the indices

Base index value = Initial value assigned to the index on the base date

Base composition

Company Shares
outstanding
(a)
IWF (b) Price (c) Full Mcap
(d)
(a * c)
FF Mcap *
(a*b*c)
(e)
Weight (%) *
(f)
ABC LTD. 10000 1.00 200 2000000 2000000 6.39
BCD LTD. 20000 0.80 300 6000000 4800000 15.34
CDE LTD. 30000 0.75 400 12000000 9000000 28.75
DEF LTD. 40000 0.40 500 20000000 8000000 25.56
EFG LTD. 50000 0.25 600 30000000 7500000 23.96
Total 70000000 31300000 100.00
Index Divisor 70000000
Index 1000 *
Company Shares
outstanding
(a)
IWF (b) Price (c) Full Mcap
(d)
(a * c)
FF Mcap *
(a*b*c)
(e)
Weight (%) *
(f)
ABC LTD. 10000 1.00 250 2500000 2500000 7.70
BCD LTD. 20000 0.80 350 7000000 5600000 17.24
CDE LTD. 30000 0.75 425 12750000 9562500 29.43
DEF LTD. 40000 0.40 450 18000000 7200000 22.16
EFG LTD. 50000 0.25 610 30500000 7625000 23.47
Total 70750000 32487500 100.00
Index Divisor 31300000
Index 1037.94 *

Equal weighted

As per this methodology, no distinction is being made between large and the small company. Each company is treated in an equal way regardless of its size. In case of CNX 100 Equal weighted index, each security (there are 100 stocks in CNX 100 Equal weighted index) is assigned a weight of 1%. From this point onwards, weight of a stock may go up or down depending upon the movement of stock price. Weightage of each stock in the index are again realigned to 1% at the time of periodic rebalancing.

Formula: Summation of mcap of all the constituents / index base mcap * base index value

Where

Mcap = Shares in index * stock price of one company

Index Divisor = Mcap of all constituents as on the base date adjusted for change in the indices

Base index value = Initial value assigned to the index on the base date

Base composition

Company Shares
outstanding
(a)
price
(b)
Index *
(a*b)
(e)
Weight *
(%)
(f)
ABC LTD. 10000 200 200000000 20.00
BCD LTD. 666667 300 200000000 20.00
CDE LTD. 500000 400 200000000 20.00
DEF LTD. 400000 500 200000000 20.00
EFG LTD. 333333 600 200000000 20.00
Total 1000000000 100.00
Index Divisor 1000000000
Index 1000.00 *
Company Shares
outstanding
(a)
Price (b) Index *
Mcap (e)
(a * b)
Weight *
(%)
(f)
ABC LTD. 1000000 250 250000000 23.17
BCD LTD. 666667 350 233333333 21.62
CDE LTD. 500000 425 212500000 19.69
DEF LTD. 400000 450 180000000 16.68
EFG LTD. 333333 610 203333333 18.84
Total 1079166667 100.00
Index Divisor 1000000000
Index 1079.17 *

Indices with capping methodology

Weightage is high in case of a company with large full or free-float mcap. Such company tends to have a greater share or concentration in the movement of index. In case of capped indices, maximum weightage to any single index constituent is defined. In other words, no single stock can have a weightage of more than prescribed limit. Example: In case of CPSE index, CNX Consumption index of IISL, no single stock can have a weightage of more than 25%. Similarly, indices can also be capped at a sector level. In such cases, weightage of sector cannot exceed the prescribed limit. Normally, for creation of sectoral and thematic indices, capped methodology is widely followed.

Formula: Summation of mcap of all the constituents / index base mcap * base index value

Where

Mcap = total shares outstanding * IWF * capping factor * stock price of one company

Index Divisor = Mcap of all constituents as on the base date adjusted for change in the indices

Base index value = Initial value assigned to the index on the base date

Base composition

Company Shares
outstanding
(a)
IWF
(b)
Price
(c)
FF Mcap* (a*b*c)
(d)
Uncapped* Weight
% (e)
Capping Factor
(f)
Index Mcap* (d* f)
(g)
Capped Weight (%)
(h)
ABC LTD. 10000 1.00 200 2000000 6.39 1.00 2000000 7.35
BCD LTD. 20000 0.80 300 4800000 15.34 1.00 4800000 17.65
CDE LTD. 30000 0.75 400 9000000 28.75 0.76 6800000 25.00
DEF LTD. 40000 0.40 500 8000000 25.26 0.85 6800000 25.00
EFG LTD. 50000 0.25 600 7500000 23.96 0.91 6800000 25.00
Total 31300000 27200000
Index Divisor 27200000
Index 1000.00 *
Company Shares
outstanding
(a)
IWF
(b)
Price
(c)
FF Mcap* (a*b*c)
(d)
Uncapped Weight
% (e)
Capping Factor
(f)
Index * Mcap
(d* f)
(g)
Capped Weight (%)
(h)
ABC LTD. 10000 1.00 250 2500000 7.99 1.00 2500000 9.19
BCD LTD. 20000 0.80 350 5600000 17.89 1.00 5600000 20.59
CDE LTD. 30000 0.75 425 9562500 30.55 0.76 7225000 26.56
DEF LTD. 40000 0.40 450 7200000 23.00 0.85 6120000 22.50
EFG LTD. 50000 0.25 610 7625000 24.36 0.91 6913333 25.42
Total 32487500 28358333
Index Divisor 27200000
Index 1042.59 *

Modified market capitalization

As the name suggests, the weightage pattern of each stock is modified depending upon a theme of an index. In case of CNX Low Volatility index, company that reported lowest volatility gets the highest weight in the index and vice versa. CNX Alpha, CNX High Beta index are few other examples of indices calculated based on modified market capitalization method.

Formula: Summation of mcap of all the constituents / index base mcap * base index value

Where

Mcap = Shares in index * stock price of one company

Index Divisor =Mcap of all constituents as on the base date adjusted for change in the indices

Base index value = Initial value assigned to the index on the base date

i) Allocation of weight (Alpha/ High Beta index)
Company Alpha/ Beta Weight (%) *
ABC LTD. 3.25 31.71
BCD LTD. 2.50 24.39
CDE LTD. 2.00 19.51
DEF LTD. 1.50 14.63
EFG LTD. 1.00 9.76
Total 10.25
Portfolio Rs. 1,000,000,000

Base composition

Company Shares
outstanding
(a)
Price
(b)
Index Mcap*
(e)
(a * b)
Weight
(%)
(f)
ABC LTD. 1585366 200 317073171 31.71
BCD LTD. 813008 300 243902439 24.39
CDE LTD. 487805 400 195121951 19.51
DEF LTD. 292683 500 146341463 14.63
EFG LTD. 162602 600 97560975.6 9.76
Total 1000000000
Index Divisor 1000000000
Index 1000.00 *
Company Shares
outstanding
(a)
Price
(b)
Index Mcap * (e)
(a * b)
Weight
(%)
(f)
ABC LTD. 1585366 250 396341463 35.42
BCD LTD. 813008 350 284552846 25.43
CDE LTD. 487805 425 207317073 18.53
DEF LTD. 292683 450 131707317 11.77
EFG LTD. 162602 610 99186991.9 8.86
Total 1119105691 100.00
Index Divisor 1000000000
Index 1119.11 *
ii) Allocation of weight (Low Volatility Index):
Company Low Volatility Inverse
of Low
Volatility
Weight
(%)
ABC LTD. 3.25 0.31 10.70
BCD LTD. 2.50 0.40 13.92
CDE LTD. 2.00 0.50 17.40
DEF LTD. 1.50 0.67 23.19
EFG LTD. 1.00 1.00 34.79
Total 10.25 2.87
Portfolio Rs. 1,000,000,000

Base composition

Company Shares
outstanding
(a)
Price (b) Index Mcap* (e)
(a* b)
Weight
(%)
(f)
ABC LTD. 535236 200 107047279 10.70
BCD LTD. 463872 300 139161463 13.92
CDE LTD. 434880 400 173951829 17.40
DEF LTD. 463872 500 231935772 23.19
EFG LTD. 579839 600 347903657 34.79
Total
Company Shares
outstanding
(a)
Price (b) Index Mcap* (e)
(a* b)
Weight (%) *
(f)
ABC LTD. 535236 250 133809099 12.82
BCD LTD. 463872 350 162355040 15.56
CDE LTD. 434880 425 184823818 17.71
DEF LTD. 463872 450 208742194 20.01
EFG LTD. 579839 610 353702052 33.90
Total 1043432203 100.00
Index Divisor 1000000000
Index 1043.43 *

Price weighted

The index is calculated considering price of all the index constituents. While selection of scrips under this methodology may be based upon various factors, the calculation does not take into account any factor other than the stocks prices. Dow Jones Industrial Average (DJIA), Nikkei 225 indices are few examples of price weighted method. DJIA is one of the oldest index representing 30 companies traded at NYSE. The index was launched in 1872 with initial composition of 12 companies in the index.

It was originally computed by adding up the per-share price of the stocks of each company in the index and dividing this sum by the number of companies. That's why it's called an average. Over the years, stock splits, spin-offs and other events have resulted in changes in the divisor, making it a very small number.  

Base composition

Company Shares
outstanding
(a)
IWF
(b)
Price (c) Weight *
(%) (d)
ABC LTD. 10000 1.00 200 10.00
BCD LTD. 2000 0.80 300 15.00
CDE LTD. 3000 0.75 400 20.00
DEF LTD. 40000 0.40 500 25.00
EFG LTD. 50000 0.25 600 30.00
Total 2000 100.00
Index Divisor 5
Index 400.00 *
Company Shares
outstanding
(a)
IWF
(b)
Price (c) Weight *
(%) (d)
ABC LTD. 10000 1.00 250 11.99
BCD LTD. 2000 0.80 350 16.79
CDE LTD. 3000 0.75 425 20.38
DEF LTD. 40000 0.40 450 21.58
EFG LTD. 50000 0.25 610 29.26
Total 2085 100.00
Index Divisor 5
Index 417 *

Total return indices

Dividend paid by the companies to its shareholder is typically not included in the index calculation. When a company trades on ex. dividend basis, stock price of the company normally gets reduced by the amount of dividend per share (presuming that other market factors remains constant and there is no other impact on stock price due to any other market factors). With reduction in the stock price of the index constituent on account of dividend, the index value declines proportionately. However, the asset management company receives dividend from the shares they hold on behalf of its unit holders of the index funds/ ETFs and as such there should not be any loss to the investors of the fund. Total return index therefore takes into consideration the dividend paid by the index constituents. As a theory, the amount of dividend so received from the index constituents is re-invested in the index portfolio and the index value calculated based on such re-investment of dividend represents the total return index value. The total return index value is a true benchmark or an indicator for the fund managers managing the passive index funds/ ETFs.

Formula: Return Index =Previous TR Index * [1+((Today’s PR Index + Indexed Dividend)/ Previous PR index)-1)]

Where

PR Index Returns = (Today’s PR Index – Previous PR Index)/ Previous Index *100

Indexed Dividend =(Shares in index * dividend per share)/ Index Divisor * Base Index value

In the example given below, two index constituents are paying dividend with ex. date on 25th day.

Base composition

Company Dividend
per share
Total
Shares
IWF Dividend
amount
Total
Dividend
ABC LTD. 50 100000 1.00 5000000
BCD LTD. 40 200000 0.80 6400000 * 11400000
Date Price
Index
Daily
Return
Divisor Index
Mcap
Dividend
amount
Indexed
Dividend
Total
Return
Index
Day 1 1000.00 31300000 31300000 1000.00
Day 10 1019.17 0.02 31300000 31900000 1019.17
Day 25 1037.94 * 0.02 31300000 32487500 11400000 0.36422 * 1038.30

Price weighted

The index is calculated considering price of all the index constituents. While selection of scrips under this methodology may be based upon various factors, the calculation does not take into account any factor other than the stocks prices. Dow Jones Industrial Average (DJIA), Nikkei 225 indices are few examples of price weighted method. DJIA is one of the oldest index representing 30 companies traded at NYSE. The index was launched in 1872 with initial composition of 12 companies in the index.

It was originally computed by adding up the per-share price of the stocks of each company in the index and dividing this sum by the number of companies. That's why it's called an average. Over the years, stock splits, spin-offs and other events have resulted in changes in the divisor, making it a very small number.  

Base composition

Company Shares
outstanding
(a)
IWF
(b)
Price (c) Weight *
(%) (d)
ABC LTD. 10000 1.00 200 10.00
BCD LTD. 2000 0.80 300 15.00
CDE LTD. 3000 0.75 400 20.00
DEF LTD. 40000 0.40 500 25.00
EFG LTD. 50000 0.25 600 30.00
Total 2000 100.00
Index Divisor 5
Index 400.00 *
Company Shares
outstanding
(a)
IWF
(b)
Price (c) Weight *
(%) (d)
ABC LTD. 10000 1.00 250 11.99
BCD LTD. 2000 0.80 350 16.79
CDE LTD. 3000 0.75 425 20.38
DEF LTD. 40000 0.40 450 21.58
EFG LTD. 50000 0.25 610 29.26
Total 2085 100.00
Index Divisor 5
Index 417 *

Calculation and dissemination of indices

IISL calculates more than 100 indices on a daily basis; of which as many as 29 indices are computed on-line and rest indices are computed on end-of-day basis. Nifty is calculated on per trade basis disseminated on per second basis along with other indices.