How is the Sensex calculated?

The Sensex is one of the most widely followed index in India, and in this post we are going to look at how the Sensex is calculated.

The Sensex is constructed using the free float methodology, which simply refers to a company’s share capital that is freely available for trading.

You know that market capitalization is the number of shares that a company has multiplied by the price per share, so when they say that Coal India has become the most valuable company in the country – this is what they refer to.

Free float is that part of the company’s capital that’s not held by promoters, governments or other strategic investors and is available to trade on the stock exchange freely.

Now, the free float market capitalization method simply means that the company with a higher free float will have a higher weight in the index, and a great way to understand is to just take a look at the Sensex constituents for a particular date.

In this table I’ve taken the data as it stands on November 4th 2011.

Scrip Code	Company	Close Price	No.of Shares (normal)	Full Mkt. Cap. (Rs. crore)	Free-Float Adj. Factor	Free-Float Mkt. Cap (Rs. crore)	*Weight in Index (%)*
500325	RELIANCE	879.6	3274230107	288001.28	0.55	158400.7	10.97
500209	INFOSYS LTD	2829.1	574203082	162447.79	0.85	138080.62	9.56
500875	I T C LTD	210.35	7773036720	163505.83	0.7	114454.08	7.93
532174	ICICI BANK L	885.2	1152447612	102014.66	1	102014.66	7.06
500010	HOUSING DEVE	682.9	1469093501	100324.4	0.95	95308.18	6.6
500180	HDFC BANK LT	482.1	2335493765	112594.15	0.8	90075.32	6.24
500510	LARSEN & TOU	1392.85	611161097	85125.57	0.9	76613.02	5.31
532540	TCS LTD.	1099.1	1957220996	215118.16	0.3	64535.45	4.47
500112	STATE BANK O	1964.25	634998991	124729.68	0.45	56128.35	3.89
532454	BHARTI ARTL	397.95	3797530096	151122.71	0.35	52892.95	3.66
500312	ONG CORP LTD	277.65	8555490120	237543.18	0.2	47508.64	3.29
500520	MAHINDRA & M	835.05	613974839	51269.97	0.8	41015.98	2.84
500696	HIND UNI LT	378.85	2160326258	81843.96	0.5	40921.98	2.83
500570	TATA MOTORS	188	2691485485	50599.93	0.7	35419.95	2.45
500470	TATA STL	467.9	959214779	44881.66	0.7	31417.16	2.18
532555	NTPC LTD	179.55	8245464400	148047.31	0.2	29609.46	2.05
500103	BHEL	333.65	2447600000	81664.17	0.35	28582.46	1.98
532977	BAJAJ AUTO	1743.1	289367020	50439.57	0.5	25219.78	1.75
532286	JINDAL STEEL	577.3	934509595	53949.24	0.45	24277.16	1.68
507685	WIPRO LTD.	371.55	2457457840	91306.85	0.25	22826.71	1.58
524715	SUN PHARMACE	511.55	1035550385	52973.58	0.4	21189.43	1.47
500182	HEROMOTOCO	2116.2	199687500	42257.87	0.5	21128.93	1.46
533278	COAL INDIA	326.35	6316364400	206134.55	0.1	20613.46	1.43
500440	HINDALCO IN	139	1918551613	26667.87	0.7	18667.51	1.29
500900	STERLITE IN	123.15	3360700478	41387.03	0.45	18624.16	1.29
500400	TATA POWER	103.3	2373072360	24513.84	0.7	17159.69	1.19
532500	MARUTISUZUK	1123.35	288910060	32454.71	0.5	16227.36	1.12
500087	CIPLA LTD.	293.7	802921357	23581.8	0.65	15328.17	1.06
532868	DLF LIMITED	246.8	1698001797	41906.68	0.25	10476.67	0.73
532532	JAIPRAK ASSO	79.25	2126433182	16851.98	0.55	9268.59	0.64

Notice how there is not much difference between the market capitalization of  Reliance and Coal India relative to their weight in the Sensex. One has a weight of almost 12% while the other has a weight of just 1.43%.

The difference is due to the fact that while most of Coal India is owned by the government, most of Reliance is owned by the general public and has a much higher free float as a result.

You will also see that there is a column called Free Float Adj Factor there which indicates what fraction should the total market capitalization be multiplied with to come up with the free float market capital to be considered in the Sensex calculation.

So, they just don’t say this company has a free float of 42.5% so let me multiply its market cap with .425 but rather they have slabs and decide how much to multiply the total market capitalization based on which slab it falls under.

Here is the table that shows the slab:

% Free-Float	Free-Float Factor	% Free-Float	Free-Float Factor
>0 – 5%	0.05	>50 – 55%	0.55
>5 – 10%	0.1	>55 – 60%	0.6
>10 – 15%	0.15	>60 – 65%	0.65
>15 – 20%	0.2	>65 – 70%	0.7
>20 – 25%	0.25	>70 – 75%	0.75
>25 – 30%	0.3	>75 – 80%	0.8
>30 – 35%	0.35	>80 – 85%	0.85
>35 – 40%	0.4	>85 – 90%	0.9
>40 – 45%	0.45	>90 – 95%	0.95
>45 – 50%	0.5	>95 – 100%	1

The next thing to look at are the weights, and it’s obvious that the way the index has been constructed – the weights change every second because price is an input for how much a stock will influence the Sensex, and that changes every second.

I have been recording the percentages for a few days to write this post, and here is a result from the past few days.

Nov 1 2011		 Nov 2 2011		 Nov 4 2011
 Company	Weight	 Company	 Weight	 Company	 Weight
RELIANCE	10.78	RELIANCE	10.93	RELIANCE	10.97
INFOSYS LTD	9.63	INFOSYS LTD	9.61	INFOSYS LTD	9.56
I T C LTD	7.88	I T C LTD	7.93	I T C LTD	7.93
ICICI BANK L	7.18	ICICI BANK L	7.12	ICICI BANK L	7.06
HOUSING DEVE	6.64	HOUSING DEVE	6.62	HOUSING DEVE	6.6
HDFC BANK LT	6.27	HDFC BANK LT	6.29	HDFC BANK LT	6.24
LARSEN & TOU	5.32	LARSEN & TOU	5.31	LARSEN & TOU	5.31
TCS LTD.	4.52	TCS LTD.	4.52	TCS LTD.	4.47
STATE BANK O	3.78	STATE BANK O	3.8	STATE BANK O	3.89
BHARTI ARTL	3.65	BHARTI ARTL	3.56	BHARTI ARTL	3.66
ONG CORP LTD	3.31	ONG CORP LTD	3.32	ONG CORP LTD	3.29
HIND UNI LT	2.92	HIND UNI LT	2.94	MAHINDRA & M	2.84
MAHINDRA & M	2.85	MAHINDRA & M	2.87	HIND UNI LT	2.83
TATA MOTORS	2.54	TATA MOTORS	2.52	TATA MOTORS	2.45
TATA STL	2.2	TATA STL	2.19	TATA STL	2.18
NTPC LTD	2.04	NTPC LTD	2.02	NTPC LTD	2.05
BHEL	1.9	BHEL	1.89	BHEL	1.98
BAJAJ AUTO	1.73	BAJAJ AUTO	1.73	BAJAJ AUTO	1.75
JINDAL STEEL	1.63	JINDAL STEEL	1.64	JINDAL STEEL	1.68
WIPRO LTD.	1.6	WIPRO LTD.	1.6	WIPRO LTD.	1.58
HEROMOTOCO	1.49	SUN PHARMACE	1.46	SUN PHARMACE	1.47
SUN PHARMACE	1.46	HEROMOTOCO	1.45	HEROMOTOCO	1.46
COAL INDIA	1.45	COAL INDIA	1.44	COAL INDIA	1.43
STERLITE IN	1.3	STERLITE IN	1.3	HINDALCO IN	1.29
HINDALCO IN	1.27	HINDALCO IN	1.27	STERLITE IN	1.29
TATA POWER	1.17	TATA POWER	1.18	TATA POWER	1.19
MARUTISUZUK	1.14	MARUTISUZUK	1.13	MARUTISUZUK	1.12
CIPLA LTD.	1.05	CIPLA LTD.	1.05	CIPLA LTD.	1.06
DLF LIMITED	0.7	DLF LIMITED	0.7	DLF LIMITED	0.73
JAIPRAK ASSO	0.62	JAIPRAK ASSO	0.62	JAIPRAK ASSO	0.64

This is an important point, and is something that most people aren’t able to wrap their heads around in the first time. When you think about weight of a stock in the Sensex you think of it as a static value like Reliance has 12%, ICICI Bank has 7% and so on, but that is not true because the weight changes every second as the price changes. In this table I have highlighted two companies whose relative importance changed from one day to another in the Sensex.

So, the weight shows you much the stock is currently worth to the Sensex but that is not a static value, and will change every second.

With those things out of the way – now think of the utility of the Sensex – why do you need the Sensex at all?

Like any other index – it tells you how the stock market is performing at any given time – a higher Sensex means share prices are higher, and a lower Sensex means share prices are lower and that share price movement is captured in the form of free float market capital in the Sensex.

To maintain continuity and make the number comparable across time – the Sensex had to have a base – and that base was the market capital of the stock market in 1978 – 79 and the base index value of the Sensex was 100. The value that you see today is the sum of the free float market capital of the thirty companies relative to the base market capital.

The base is not a static value but keeps changing because they need to account for special events like rights issue, bonus issues, change of companies in the index so that these special events don’t affect the continuity of the index.

Based on the market data that I have seen for the past few days I have calculated the current base market capitalization as Rs. 8,221.94 crores.

Formula to calculate the Sensex

The formula to calculate the Sensex is as follows:

(Sum of Free Float Market Capital / Base Market Capital ) x 100

You can get the sum of free float market capital very easily from this page, however this changes every day so you need to save it with you if you need to refer to it later.

For this post – I have saved the data in my spreadsheet.

Let’s look at some of the past data:

Nov 1 2011 (1,437,262.79 / 8221.94) x 100 = 17,480.83

Nov 2 2011 (1,435,949.06 / 8221.94) x 100 = 17,464.84

Nov 7 2011 (1,443,986.58 / 8221.94) x 100 = 17,562.60

Nov 8 2011 ( 1,444,556/ 8221.94) x 100 = 17,569.53

Nov 9 2011 (1,427,501.45 / 8221.94) x 100 = 17,362.10

You can quite easily calculate the Sensex any day by just going to the BSE Website, and getting the total market free float and putting it in this simple formula. If it doesn’t come up correct, then that means the base market capital has been changed and you need to back calculate that and test it out on a few days to make sure that you have the right base market capital and then use it to calculate the Sensex in the ensuing days.

Once you understand all the inputs that go into the calculation it becomes fairly simple to calculate the final Sensex value, but probably more important than calculating the value is to understand the mechanics behind it and what it’s trying to show to you.

As always, questions and comments welcome – especially if there were some parts that you thought were not clear enough and need more explaining.

This post is from the Suggest a Topic page.