Calculation of indices

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

Day 1
Day 25

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 *

Also refer http://www.nseindia.com/products/content/equities/indices/total_returns_index.htm

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

Day 1
Day 25

Base composition

Company	Shares outstanding (a)	IWF (b)	Price (c)	Full Mcap (d) (a * c)	FF Mcap * (abc) (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 * (abc) (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 *

Also refer http://www.nseindia.com/products/content/equities/indices/invest_w_fac.htm

Equal weighted

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

Day 1
Day 25

Base composition

Company	Shares outstanding (a)	IWF (b)	Price (c)	FF Mcap* (abc) (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* (abc) (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

Day 1
Day 25

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

Day 1
Day 25

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

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.

Day 25
TR Index Cal

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

Also refer http://www.nseindia.com/products/content/equities/indices/total_returns_index.htm

Price weighted

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.