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.

facebookShare on Facebook
TwitterTweet
FollowFollow us
PinterestSave

No related posts.

80 thoughts on “How is the Sensex calculated?”

  1. Hi Manshu
    Great work indeed.

    I love to see and watch all these happenings in D-street.
    I have a doubt, how base capital is calculated?, how have you calculated?
    Another thing what is the deciding factor for a compn=any to come in top 30 for index?

    Reply

  2. Thank u very much to explain the concept of sensex in details. It will be great to know about how to calculate or take into consideration the base market cap of 1978-79 in details of 100 sensex points.

    Reply

  3. http://www.bseindia.com/mktlive/indiceswatch_scripweight.asp?iname=BSE30&sensid=30&type=sens&total=2905259.98&mktcapteck=1443986.58&dateheader=Friday%2C+November+04%2C+2011
    The above link provided by you is not working for me as whenever I am opening the above link, it lands at http://www.bseindia.com/markets/Equity/EQReports/MarketWatch.aspx?expandable=2

    I just wanna know the free float market cap of 30 companies of some past dates but the link provided by u isn’t provided. Pls help asap!

    Your article deserves 10,000 stars cuz it helped me like hell. Just provide me a correct link from where I can take 30 companies free float market cap of any historical 4-5 days .

    Reply

  8. Dear Manshu… Thanks for explaining precisely. I have a clarification, related to this but more like a next step to this… I was looking to calculate the present P/E ratio for sensex… While i would compute ‘P’ – value of sensex as mentioned above, i had problem in computing ‘E’ – the EPS pf sensex… [clarfn 1] shud we take trailing 12 months EPS of all sensex companies or EPS of last completed FY (eg FY 12); [clarfn 2] When i computed EPS of sensex companies for FY 12, it summed up to Rs 1,378 whereas many reports / websites state that the FY 12 EPS is 1,127 or 1,107. Whr am i doing mistake? [clarfn 3] while computing EPS, shud we take standalone EPS or consolidated EPS? [clarfn 4] Similarly, H1 FY 13 sensex EPS worked out to Rs 685, whereas consensus Sensex EPs estimates for FY 13 is only Rs 1,225. y?

    Manshu, Awaiting your revert. Thanks in advance!!

    Reply

    1. 1. It really depends on what you’re trying to do and I’d imagine both methods are acceptable.

      2. IF you send me a link with a report that says the EPS is this or that, I can take a look at that and see what they are doing and how they are calculating it.

      3. You should take consolidated EPS as that reflects the total results a lot better than standalone.

      4. You have taken just the first half, whereas the consensus is for the whole year and is almost twice so that sounds about right.

      Reply

    2. 1. It really depends on what you’re trying to do and I’d imagine both methods are acceptable.

      2. IF you send me a link with a report that says the EPS is this or that, I can take a look at that and see what they are doing and how they are calculating it.

      3. You should take consolidated EPS as that reflects the total results a lot better than standalone.

      4. You have taken just the first half, whereas the consensus is for the whole year and is almost twice so that sounds about right.

      Reply

  9. Thank you!
    I have a question for you..

    how does anyone company calculate the free float value, and how do they find the price of the per share?

    thanks in advance

    Reply

    1. Free float is the number of shares that are not held by promoters, and price per share is simply the price at which the share is trading in the market at that point in time.

      Reply

  10. This is one of the best and the simplest way of understanding the sensex points calculation. I’ve been searching for something like this in a long time. Thanks a ton for your efforts. Please post more such informative articles in the future.

    Reply

  11. You have lucidly explained the fundamentals. Thank you. It will be great if you can also let us know how exactly is the base market capital computed rather than backworking it.

    Thank you.

    Reply

  12. thankss manshu…

    great job yrr….as i am a ca student so thinking of trying in stocks alsoo…u made my work easier by clearing the concepts behind trading of securities..

    thank youuu…!!!!!

    Reply

  13. Hi, dear manshu, you have explained “HOW CALCULATE SENSEX”. -By a fentastic & simple way. At last i have understood about the calculation of sensex. Thank u very much.

    Reply

  14. where is the sensex calculation on
    Nov 4,2011?? Why didn’t u calculate even u’ve all data of that day.i didn’t get it

    Reply

  17. this article is very informative but i have doubt that while calculating index where is the application of wight. do we multiply wight with free float capitalization figure

    Reply

  18. dear manshu ji,
    i got all above things which i couldnt figured out even in my MBA. sincere thanx.
    just one query,u said base market capital is fixed but how it was calculated in first place?
    i tried hard to figure it out every where but failed.
    can u? plzzzzz

    Reply

  20. Thanx for wonderful article.
    Few Points/queries
    1. As base market cap is for the year 1978-79 and companies keeps getting changed.
    So what if a company was not in existence in the base year then how would Base MktCap be calculated?
    2. As weightage is based on free-float MktCap which in turn based on current share price so it basically an outcome of movement and doesn’t have impact on Sensex calculations.Right?

    Reply

    1. Lokesh – 1. Base market capital is fixed, that doesn’t change. What changes is the index value in relation to that and when they include a new company and replace an older one, they take care of that.

      2. It does – it affects the index and in turn the index affects how much it weighs relative to the overall index. So, if a company with a big weight keeps falling then it will drag down, but with each successive fall its weight in the Sensex will reduce and the Sensex won’t fall as much with each successive drop.

      Reply

Leave a Reply

Your email address will not be published. Required fields are marked *