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.

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80 thoughts on “How is the Sensex calculated?”

  1. Dear Manshu,

    Thanks for your efforts which you have put to explain the hidden calculation to us.
    It is really easily understandable.
    But I am not getting how the Base market capitalization is being calculated?
    I am waiting for your reply.
    And thanks in advance..

    Reply

    1. That was something that was calculated once in the beginning and doesn’t change. They have to decide on a base to see how things change later on and so the base remains static and doesn’t change at all.

      Reply

  3. Hi,
    Sincerely, a very informative & interesting post! Honestly, I was just going through basics of SENSEX for an interview tomorrow, this post just threw light on aspects I previously thought ‘boring’. It is written in a way that even a science student (like me) can understand & appreciate. Kudos ! 🙂

    Reply

  7. Very informative article Manshu. I was trying to know this formula during my MBA, but could not figured out. So great work. thanks.

    Question for you:
    > company stock price is decided based on full market cap / total no of outstanding shares.
    Now say for Reliance, price goes up => full market cap goes up => will this incr/decr free float adj factor? how come?
    Basically I am not able to co-relate reliance weight in Sensex calculation & reliance stock price.

    Thanks in anticipation of your reply.

    Daxesh

    Reply

    1. As I said in the post, the weight changes every second as the price changes and in this case since the stock is going down it will have lesser weightage in the Sensex each passing second, so other things being equal I would expect the fall in the Sensex to be less than the fall in the stock. By how much? That is a guess keeping in mind that something with 10% is the biggest component and will still impact it quite a lot.

      In reality you can’t calculate such a percentage because of the way the the Sensex is constructed.
      To quote a relevant passage from the article:

      “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.”

      Also, I assumed that you were just curious about this but if you had any specific reason for knowing this then we might have to think about that reason and do this differently.

      Reply

  9. Thanks for sharing an extemely informative article. Great work.

    I have a query, guess u could help..if a stock has say 10% weightage in index, price being say 1000rs. Then how much will index fall if the stock plunges say 100rs?

    Thanks in advance..

    Reply

  10. Great work Manshu on providing us with the way to calculate Sensex. Also want to share that Sensex has delivered around 16-17% annualised returns since inception in 1979 and around 14% annualised returns in last one decade

    Reply

  12. Thanks a lot for your informative article.
    I have a question in my mind , please help me to get the answer.
    If an investor wants to get the same return /loss as that of sensex, he/she has to make a portfolio of 30 shares in the proportion of
    (a) no. of shares x free float adj factor
    (b) free float market cap
    (c) weights in index
    (d) equal quantities of 30 scripts

    Thanks in advance.

    Reply

    1. None of these.

      It starts with free float x number of shares but then builds on that. I think you need to re-read the article or go over it a few times to understand the methodology and that’s what an investor has to do to replicate the return.

      However, if you tell me why you want to do this I might be able to suggest something else to you.

      Reply

  14. Hi Manshu, you have explained the concept very well. It also means that when the Sensex falls, it is not doomsday for all the sectors and vice versa. The sectoral indices give a better picture of how the industry is performing. Whereas, the Sensex can be a generic indicator of the economy as a whole, it is the sectoral indices that the investors should be spending more time on before investing.

    Reply
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  16. Pingback: Stock Market Index: The Basics « Be Money Aware Blog

  18. Very nice post. thanks. Now we know that which are the top most companies which have higher weight In index.how do we utilize this insight , does it mean , that senses fall or rise is dependent mostly on these top companies or is it vice versa. These companies share price fall or rise in correlation to sensex index. please clarify . Thanks .

    Reply

    1. Thanks Ruchi.

      You are right in observing that the movement in the Sensex will depend on the movements of the heavyweights in the Sensex and the day to day movement will very likely be dictated by biggies like Reliance, Infy or other stocks.

      However, over a longer time frame, as one stock loses value, and the other gains in value – their relative importance will change and evolve to a point where one stock will no longer be that relevant to the index.

      So, I think in the early 90’s ACC would have been a big Sensex mover, then later on HLL must have been important, at some point during the early 2000’s the IT companies must have had a lot more weight but as time progressed the balance changed.

      To me, that’s the big takeaway, that while in the short run a few companies decide much of the movement, if you take a longer term view then the Sensex constituents show which sectors are performing well and are important to the economy and so on.

      Reply

  19. Hello

    Very basic and very informative. There are some things we just take for granted (when it is beyond us) such as how Sensex is calculated. Thanks for sharing
    Is NSE also calculated the same way?

    Reply

    1. Yeah, Nifty is also a free float market cap based index and is calculated similarly, but instead of a base market cap – they have a divisor which is a number that helps base the current market cap to their base.

      Of all the major indices in the world – I know of only the Dow that is a price weighted index. Rest of them are all free float market cap based indices.

      Reply

      1. An index can be calculated in various ways. Some of the ways are as follows:

        Price Weighted index: Ex: Dow Jones Industrial Average,Nikkei 225
        Market value weighted or capitalization-weighted: NASDAQ Composite, NASDAQ-100,
        Free Float Market Capitalization Weighted: Sensex, Nifty-50, FTSE-100, CAC 40

        SENSEX, first compiled in 1986, was calculated on a Market Capitalization-Weighted methodology of 30 component stocks representing large, well-established and financially sound companies across key sectors.Since September 1, 2003, SENSEX is being calculated on a free-float market capitalization methodology.

        More on stock index can be read at Stock Market Index:The Basics

        Reply

  20. dear manshu
    thanks a lot for this post….finally i have understood the method….what i will say…..kudos to your sincere effort….
    some observation:– ICICI bank have all of his share as free float….it must be highly liquid….
    and i want to add one point regarding weight in sensex….i went to the bse link provided in your article and see the market capitalizations…and make some calculation….and understand that weight simply means ( free float market capitalization of that share)/( total free float MC)….
    as market price change ( or occasionaly free float adjustment factor) , the others values keep on changing….really interesting….
    one more observation: Top 7 companies have weightage of more than 50 % …that means how important these companies are…..
    thanks…it have given me some insight about share market….
    i am waiting for your EPS and PE post…

    Reply

    1. Fantastic!!!

      I loved your comment!

      Too often people suggest a post but don’t follow up with comments which makes me a bit mad because a lot of effort goes into writing this. I loved seeing your response and finding out how engaged you were and also went to the BSE site to look at more info – that’s just great.

      EPS and PE post will come up in a week or two – still not sure what data is present and isn’t.

      Thanks!

      Reply

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