Capitalmind
Capitalmind
Actionable insights on equities, fixed-income, macros and personal finance Start 14-Days Free Trial
Actionable investing insights Get Free Trial
Charts & Analysis

Sensex P/E calculation awry?

Update: This entire article is wrong. The P/E calculation is simple: Weighted Market Cap (791,825.38) divided by weighted earnings (40,570.21) which is 19.52, very close to the BSE reported number. That means I am wrong, and the BSE is correct. I’m terrible at mathematics – have made it more complicated and confused myself all ends up. This article will remain for posterity, though, and for the brickbats. And thanks to Akshay J for pointing out my mistake.

Something seems to be wrong with the Sensex Price to Earnings Ratio calculation. Look at the Sensex Index Reach page and you will notice a value there for P/E – the price to earnings ratio of the Sensex.

The Sensex is an index – the BSE 30 Sensitive Index is what it really is – so there’s no real company called the “Sensex”. So what is the earnings of a non-existent company? How can we calculate even the “number of shares” or any information for what is effectively an amalgamation of other companies, but where the ratios change daily?

The answer lies is the calculation. Since the Sensex is a weighted calculation of the various companies it comprises, the earnings can also be weighted in the same way to get the earnings for the Sensex. Divide that by the weighted number of shares in the index and you have a value called “EPS” or Earnings per share for the Sensex. The P/E then is just the Sensex value divided by the Sensex EPS.

Note that the share prices of each constituent company change daily and therefore, these values will change every day.

But the key here is to take the correct data for “earnings”. It seems like the BSE has taken the last reported YEARLY figures instead of considering the last four quarters.

What’s the big deal, you ask. What’s the difference? On March 29 2007, the last four quarter earnings will include figures for January 2006 to December 2006. But the last reported YEARLY figures is for April 2005 to March 2006! (Most companies offer annualised earnings reports only for April to March financial years).

To validate this, what I did was to manually go through each company and calculate the Sensex P/E myself. Here are the steps I used, as of April 02, 2007:

  1. I read the Sensex “free float” calculation methodology, and the free float factors of each company in the index. [1]
  2. Then I created a list of all sensex companies in an excel sheet, got all values for their earnings (both last 4Q and last annual), prices, market prices etc. All for the date of April 02, 2007.
  3. I then calculated the weighted market cap, weighted earnings and the market divisor. Using that I could get the appropriate number of Sensex shares, which I then used to find the Sensex EPS and Sensex P/E.

I may be horrendously wrong here – but if you find that my calculation is a problem please let me know. It took me a while to figure out how they had calculated the Sensex P/E and I think I now am close to it.

The results are for you to see:

(View the spreadsheet here)

The reported Sensex P/E was 19.39 on the BSE pages. This is close to my own calculation based on the last reported ANNUAL earnings where I get a P/E of 19.92. The difference is perhaps in the figure I took as earnings (last reported P&L statement) whereas they may have considered a slightly different figure.

But if I consider the last four quarters, I get a P/E figure of 16.37. The last four quarter P/E is about 18% lower than the BSE reported P/E.

What does this mean to you? If you are using the P/E to consider whether a market is overvalued or undervalued (comparing against potential future earnings growth) you may want to use the last four quarter earnings instead. For example if you want the P/E to match earnings growth, 20% growth expection based on a P/E of 19.39 looks overvalued, but what if you considered only 16.37%? Is that still overvalued?

Use the right data. Don’t use the Sensex P/E to compare against earnings growth.

Note: The NSE has changed the Nifty P/E calculation since Dec 20, 2004 to reflect last 4Q earnings.

Notes:

[1]
The sensex is based on the market cap of the top companies in the BSE. But some companies have a lot more stock held by non promoters than others – Wipro has just 15% available to non-promoters, which ICICI bank has more than 50% – so stock values can be high only due to high demand and low supply. So the BSE weights the individual company market caps by their “free float” – the number of non-promoter shares – and used the weighted market cap instead.

The market caps, suitably weighted by the free float factor, are added up and divided by a figure called the “market cap divisor”. This is a calculated figure that ensures that the sensex value is always comparable, and takes into account any changes in the constituent company shares, dividends, bonuses, splits etc. You can always find the current market cap divisor by dividing the weighted market cap by the sensex value.

  • Sandeep says:

    >nice topic !!
    requires lot of research;
    PE is the most widely used and most widely abused/misunderstood raio in Security Analysis.

    Feel like kicking some of the analysts in the rear when they talk about/start discounting next two years earnings; talking about PE based on Fy 08 earnings when we were not even in FY 07 (say in Jan 07) is ridiculous. Analysts will go to any extent to justify that markets are cheap.

    btw I was also under the impression that sensex eps for last 4 qtrs (ending dec 06) is around 650-660. If what you have figured out is right, good discovery ! Anyways I never worry about sensex eps or PE that much because they represent only 30 stocks and are of only psychological interest for “aam janta”

    Deepak, I am really not able to find time but you have really started a good topic on timing, btw on your last post their you mentioned their that timing and valuation are the same thing – I disagree as this logic is conceptually flawed. Valuation is part of Fundamental Analysis while timing is part of Technical Analysis. FA tells you what to buy and TA tells you when to buy. Two are entirely different concepts.
    Have summary of another study (probably covering the longest period in India)
    Period of study: January 1980 to December 2006

    Investing at the lowest Sensex value every month – returns 18.64%
    Investing at the highest value every month – 18.25%
    Investing at the Average value every month – 18.44%
    Investing at the beginning of every month – 18.51 %

    Before you start calculating how much difference 13 basis points would make over 27 years, here is the second part of the study – The penalty for bad timing is 47% worse then a simple buy and hold approach. The potential downside in case of poor timing is 1.5 times more than the potential upside of buy and hold.
    Another study shows how in last six years 42 % of Infosys’s total gains came in only 12 % of the six year period. 48% of reliance’s gain came in only 9% of the last six year period. And if we missed out those period because of poor timing judgement we would have missed the bulk of the gains.

    No I am not following any superstitions or falling in trap of marketing gimmicks of the fund managers, media, financial services firm.

    No I am not doing any hero worshipping but came to the conclusion after lot of number crunching in my peak professional days and my original conclusion is that if there ever was a trick of market timing some genius would have figured it by now and with that trick he would have bought the whole world by now, starting with zero money in his pocket.

    If you check out the data for March 31 2007 hardly 10% funds could beat the sensex and hardly 20% beat the BSE500. Now these guys are getting crore plus packages/bonuses and I am sure they are not dumbos/low IQ guys or are purposely trying to underperform the market for any strategic business reasons.

    But anyways fund management is altogether different ball game.

    Sense of timing is important but requires lot of discipline and patience and these characteristics are hardly found in individual investors therefore ” we lay investors can do better job with our money” doesn’t work out : lack of primary information (forget CNBC or Economic times) lack of analytical skills, lack of DISCIPLINE, lack of Patience are the reasons 1% investors make money at the expense of 99% invetors, most of the retail investors I meet in day to day life end up BUYING HIGH and SELLING LOW.

    Anyways, keep working, If you need any help in refining some funda let me know so that at least you won’t end up spending time reinventing the wheel.

    Starting Point Tip: First be very very clear whether one is an INVESTOR or TRADER

    Regds
    Sandeep

  • Deepak Shenoy says:

    >Sandeep: Thanks for that! I think I remember reading somewhere that the Sensex p/e calculation was done on outdated earnings, which recently prompted me to do this research.

    You’re right, using the Sensex P/E as a barometer for the stock market is not a good thing. I would perhaps suggest the NSE 100, which is perhaps a much better indicator (since they’re 93% of the market)

    I see where you are with respect to timing versus valuation – though I think the way I look at it, valuation looks at the future, and timing at the past. You need both to be a good investor, in my opinion.

    Interesting results on the Sensex: Does this take into consideration dividends if you invested in companies? (because you couldn’t have invested in the sensex back then)

    Reliance’s gain cannot be taken in isolation – you have to consider net gain due to mergers and demergers which will yield a lot more.

    Also statistics hold good – but if you create a timing methodology and run it on data going back you muigh see how timing makes a difference. i.e. a model can be to invest when P/E is below a certain level, or below a certain comparison point or below known earnings growth. I believe a simplistic model like that will also identify 80% of the upside points in the last 10 years. Have to research this, though.

    It’s always easy to say that if there was a way someone would have figured it out. As an entrepreneur, I know that is just not true, for any market, or any business. There are opportunities everywhere, and sometimes it hits you across the face. Lastly, the best traders in the world are anonymous.

    Fund managers don’t beat the sensex because they don’t have to. As you said, it’s a different ball game.

    Investing is all about discipline. If you are a smart investor and can define and stay with your rules, you can make a lot of money.

    Thanks for the offer for help – I will definitely need it! Will touch base on email. Thanks for the detailed comment too.

  • Vikram says:

    >Deepak
    How on earth are you collecting this data? You cant be doing it manually!How can you retrieve EPS and no. of shares figures from the websites?Is it by some software?I find it hard to believe that you manually enter the figures in the spreadsheet. Calculations can be done easily but how do you get the raw data?

  • Deepak Shenoy says:

    >Vikram, I’m embarassed to say this but I manually entered the earnings data. No. of shares is given in this BSE page.

    Earnings and figures I obtained from StockHive.

    Raw data wise: It’s a pain in the neck, but I’m trying to set up a server to grab and store allthis data so I can make meaningful queries. Like earnings, dividends, splits, bonuses etc. Hopefully then it won’t be this bad.

  • Akshay J says:

    >Nice article. Very meticulous and analytical.

    How did you get these figures? I used the data in your sheet and came up PEs based on LY at 23.75 and current PE at 19.51.

    Something is wrong. The P/E should simple Price/Earnings (weighted Market Cap/Weighted Earnings).

    What has the Sensex as an index got to do with Market P/E. It will always be linearly related. If Sensex moves up, the Weighted Market cap moves up, with reported earnings unchanged.

  • Deepak Shenoy says:

    >akshay: that is a good point, but then my calculation is wrong. It might be in the fact that I use the number of shares; Have to check this out tomorrow. Using weighted market cap / weighted earnings is probably better – in this case, my calculation is totally off base then!

    I will have to create a new post – if I’m wrong, I’m not just a stupid investor, I’m terrible at arithmetic too.