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
|
>0Â – 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.