Instead of arbitrarily removing company A from the index, you can use equal weightages to construct an index. Such an index will be an equally weighted index  instead of a market cap weighted index & will not be affected by the bias of tilt in favour of a single or few large cap weighted companies. Even otherwise, when you remove A from the analysis or index construction, your companies are hardly representative of the market as you have removed the factor carrying 55 % weight.

Secondly choosing 20 stocks randomly & picking 10 from amongst them to create an index is not the correct method, as many companies which are large cap must have escaped being picked up in the 20 stock selection. It is best to take any popular index of say 50 or 100 companies & choose 10 from them on any assigned criteria to construct an index.

Hope it helps.

Hemlata

Hello Hemlata Chelawat, Thank you so much for response. Yes you are right equal weighted index can solve the problem. But i want to create market capitalization based index. so i have to use the market cap. any suggestion with market cap index

If you used change in market capitalisation as the weights, would it serve the purpose?

Arun Vishnu Kumar

Basically i want to backtest a strategy.. so i thnik yes. but the issue is subjectevity 

You could alternatively use a 'price weighted index' which would be objective & will be representative of high market cap companies, atleast partly.  In price weighting, the weight of each security is found by dividing its price by the sum of all the prices of the constituent securities. It will serve your purpose of backtesting an investment strategy well.

You could apply any ‘objective’ weighting' methodology that assigns a weight proportional to the variability of the indicator (low variability will have less weight and high variability will have much more weight).  

Hope you get some direction out of this. 

Best,

Hemlata

True, Muhammad, subjectively removing or adding a stock is not appropriate. 

I have three suggestions.

1. For inclusion of a stock in the Index, you can use the Liquidity of the Stock, as measured by the Market Impact Cost.

2. For the Index to be more representative of the Market, you can use float-adjusted market capitalization.

3. For the Index to be a Diversified Index, try to include stocks from all sectors of the economy.

Please see the methodology used for India's National Stock Exchange (NSE) Nifty50 Index in the link below. 

 Hope this helps.

https://www.nseindia.com/content/indices/Method_Nifty_50.pdf

Thank you so much Arun Vishnu Kumar and Hemlata Chelawat for such a fruitfull discussion. 

Hi Muhammad,

It is funny, because totally different answers should apply depending on what you are looking for. What I mean is...

If you want to backtest a trading strategy, and this strategy has to be weighted by market cap, and due to the algorithm you end up with a huge position in one stock, because it is really, really much bigger than the rest in the selected portfolio, what is going to happen...

Some people would say that 55% of a porfolio in one stock would not be good for the robustness of the results of your trading strategy... (it is like a one off)  Also doubts about proper diversification, ... could arise. If that is the case, please dont hesitate to just discard that company... your portfolio would be better served if you do it (That is would I would particularly do). 

Then the question is... subjectivity? Not at all, your algorithm for portfolio or index selection should include a diversification rule which deletes a company or a group of companies if they distort the proper diversification of your portfolio. But write the rules ex ante... Lets say you decide to discard companies that represent more than 15% of the final selected index.

But what if your trading strategy is better if you dont discard the big (or biggest companies)... then is your choice again, but there is going to be a lot of specific risk... Anyway it could be justified but you would need very good reasons.

Good luck!

Carlos

Hello Carlos Fernandez-Herraiz,

Thank you so much for such a nice reply. And I fee lucky atleast you got my point hundred percent right. This is what I was looking for. Exactly.... The issue is diversification make sense. The ax ante constrain will also help.thank you so much for understanding and taking out time for such a detail and concrete reply. 

I think the answer is both Yes and No. As it depends on the topic of the research, if you are trying to find out the profitability in context to some segment then you can not remove the market leader ( the company with maximum weight ) from the index . But in case if you are just trying to backtest to find out the feasibility of your backtested model, then you can remove it.

I will suggest you to use already available indices like Dow Jones, S&P 500, Nifty, CAC, DAX, etc for your study as it will make your study more interesting and wider audience can benefit from the study.