How to Exploit Beta of a stock to trade in arbritrage principle?

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Beta of a stock is often defined as the sensitivity of a stock with respect to the market or Index. In other words the beta of a stock is 1.5 with respect to the market or index means each 1% raise or fall in the index the stock will raise or fall by 1.5 %.
Now the question is whether this beta holds well in real life or in practical market in day to day basis ? Certainly not, since the stocks price is fluctuating or dynamic in nature it will deviate from its beta time and again. However it will tend to balance the deviation due to the portfolio churning by the portfolio managers.
Let us take one very simple and basic examples. Say I have chosen 3 stocks from three different sectors say SBI from public sector banking, ACC from cement and Tata Steel from steel sector. All these stocks are the components of one index Nifty. The yearly beta is 1.75 for SBI ,1.65 for ACC and 1.85 for Tata steel. This says each one percent raise in Nifty will bring 1.75%,1.65% and 1.85% change in the respective counter SBI,ACC and tata steel. Same time 1% fall in the Index Nifty will bring -1.75% ,-1.65%,-1.85% change in the respective counters.
As a portfolio manager after 10% raise in the Index I have observe the change in my stock portfolio. Say I found SBI changed by 14%, ACC changed by 20% and tata steel changed by 16%. This says one of my stock ( ACC )has moved ahead of its beta proportion and other 2 are lacking. This says ACC may fall from now to balance the beta and other 2 will rise. In this scenario I will think of exiting out of ACC fully or partly to take the benefit of the beta decoupling. I may add some more stock from different sectors which have moved less as compared to its beta proportion.
The second case scenario is if the Index has moved 10% but all my stocks being the major components of the index (as per there market capitalization) has moved 5%,7%,11% respectively. As a portfolio manager I will conclude 2 things from this movement may be the Index is getting re-ratted by some other index stocks or may be my basket of stocks are re-rating their beta. In either case thinking this as a temporary behavior I will hedge a portion of my portfolio with index buy the way of selling the Index future.
The third use of beta is I can construct a beta hedge portfolio from the beginning. In this method I will construct a basket by choosing stocks from the same index segment but must be from different sectors.
Let us take my previous example Say I have chosen 3 stocks from three different sectors say SBI from public sector banking, ACC from cement and Tata Steel from steel sector.
Now instead of finding the beta of individual stock with the Index I will take the value of my basket. For simplicity assume my basket contains 1 stock from each company. For more realistic explanation say I have bought SBI at 1850, ACC at 900 and Tata steel at 525 each 1 stock. The net value of my basket is 1850+900+525=3275.
Assume I want to hold this portfolio for 3 months then I will take the past 3 month daily closing price of these 3 stocks and Index and find their beta. say today is 11th September 2009 then I will go way back to 11th June 2009 to record the closing price of these 3 stock and index. And find the value of my basket on those days and their % change with respect to index. After this process I will find the beta.say I got the beta as 1.65 for my basket. This says for each 1% change in Index will invite 1.65% change in my stock basket.
Now to exploit this situation I will buy 1 lakh worth of stocks as per my basket proportion and sell 1 lakh worth of Index.If index goes up by 10% from my level of entry I will loss Rs10000/- on the sell transaction and gain Rs16500/- on my buy transaction and happily make profit of Rs6500/-. In contract if index goes down by 10% from my level of entry then my net loss will be Rs6500/-.
Think in other angle say if you would have constructed the portfolio without beta proportion then your loss would have been Rs16500/- in case of any extreme fall your portfolio would have resulted higher loss. Being hedged you have been protected from the extreme case loss. It is always being the good idea to protect the money stock market. The other benefit is this method does not take the help of options for hedging hence nullifies the risk of time value decay.
NOW THE MOST IMPORTANT PART OF MY STUDY IS HOW TO EXPLOIT IT IN INTRADAY.
I have always observed that the deviation in beta never being a permanent one if there is not external cause to it. Using this principle I have devised this wonderful trading technique for the trades. Beta is also not being attested between the stock or index it used exit between two stock of same industry segment also. Observing these facts I made the simple arithmetical arrangements.
A.I have taken the past 10 days beta of the any 2 stocks.
B. I have identified whether any deviation exists between these 2 stocks in intraday basis as per their beta coefficient.
C. if it found then I will exploit this situation and take a trade on this deviation principle.
D. The moment the deviation will perish my trade will be in profit.
E. I too derive the mathematical formula to calculate the maximum profit and loss in these trades.
All these things you will experience in my newly built Intraday Beta decoupling calculator which is avilable in my company Smart finance web site. Though it will take some time to punch the data in it but it is worth to type if you are getting benefited out of it . due to forum rule i will not be in a position to give you the link to access the calculation however you can find the link from my profile page.
Conclusion : The main idea of authoring this article is to inform you the noble and gentle art of trading and investing. However if you will read a bit about t -series analysis of variance and error analysis then this method will be the best to apply in trading. However I have taken the due care of all these concepts in my calculator.