Reversion To The Mean

Posted by Sanjeev Pandiya On Thursday, February 02, 2012 4 comments


The Theory Around Beta

Beta Maps:
This time we will discuss an important principle of trading called Beta (migration). The theory around Beta Maps goes like this. 'The Market forgets, and the Market gets obsessed....'. In any Index, there is always one part that is 'under-performing', i.e. it is being 'forgotten'. And there is another stock at the other end, which amplifies the underlying theme (i.e. bullish/ bearish) in the Market. 
The key skill in tracking Betas, is the manner in which you define it, and the construction of the average/ Index around which the Beta is measured. The Index is supposed to aggregate a correlation of assets or asset classes, some of which are logically obvious and even available off-the-shelf (like the Nifty). The Nifty, very sensibly, aggregates the leading stocks in the market, which account for the major part of the Market Cap (58-60% currently), Free Float (>70%) and trading volume (45% currently). This makes the Index a good surrogate for the entire market; over time, if enough people think so, it becomes so.
And since the Nifty is known to all, it would be a good idea to explain the Beta with reference to the Nifty. However, the real benefit of this kind of ‘beta tracking’ will accrue if you structure your own ‘indices’ from the ground upwards. For example, how about a composite Index that includes a particular weightage of Nifty, Gold, Silver and Dollar. You will get a certain ‘beta pattern’, which will bring home to you a mean-reverting pattern, which is unique to your understanding of the market. Trading the outliers, playing ‘contrarian’ to a pattern which shows one instrument going out of whack, will mean that you are betting on mean-reverting movements in your ‘Index’. This is not by itself a complete investment/ trading strategy, but it is a very good confirming indicator for the rest of your stock picking.
I use it even to generate leads on which stocks to focus on, based on the underlying belief that all the other (fundamental) factors remaining the same, a particular stock will follow the ‘moods of the market’, i.e. there will be liquidity and sentimental factors that push and pull on the stock. In a big company, things don’t change so much overnight, although they do (change) dramatically over the longer-term. A short-term (trading) strategy that bets on a ‘return to the mean’, will produce profits more often than not. However, prepare to be surprised by large movements as market expectations drive fundamentals (for example, RCom has been deserted by the market, and this alone will drive its fundamentals in a manner not clearly understood by us). Still, if used carefully, it can be a successful trading strategy over the short-term.
For example, the period July- Sep, 2011 saw huge (shocking) bearishness, which was amplified in Tata Steel (Beta 8, i.e. for a 5% drop in the market, Tata Steel dropped 40%). That is because the European crisis was the key theme during this period, and Tata Steel exemplified this theme. Tata Steel did not drop because the market dropped, BUT the Market dropped because of Tata Steel.

There are many different ways of calculating a Beta, and this word is not to be confused with the Beta (relative daily volatility) that you normally hear in the media. I use this word because it comes closest to a concept that is widely understood. As we go deeper into this, it is very important to remember this. For example, how we choose dates will decide what Beta figures we get, and what 'migration pattern' we see. If we choose the wrong dates to denote the various 'themes' of the market, we will get junk information that will positively mislead.

The first period, 12th Nov, 2010- 12th July, 2011 saw a 'classical bear market' developing. During this period, Bharti and DLF were the underperformers. Bharti was downright profitable, because the Beta finally 'migrated' (upwards) as the market fell. During this period, the market fell 18% from 6336 to 5196. After 12th Jan, 2012, you can see the Betas 'diverging' again. Tata Steel has accelerated and so has DLF. Reliance and Bharti look like 'migrating' downward, i.e. they will underperform a bullish market.

When there is a correction, the low Beta stocks will drop more, while the high Beta stocks will be volatile, but will outperform the market. At the next correction, the Beta 'divergence' will emerge and we will see the Beta lines diverge. The 'train is not leaving us', but the next train is coming in. The last train carried Tata Steel with it.


A stock that takes off, also creates a large potential downside, because it gets populated with 'weak hands', who panic easily. Conversely, the absence of 'weak hands' creates a limited downside on the stock. You do very well when you have limited downside. There is no Bull or Bear Market; you just have to keep your downside limited to 20% and you will do well. An early bull market reduces the downside; but a late bull market (like 14th Nov, 2011) creates a lot of downside risk. Since  profits are a function of volatility (which is almost constant), your only cost is the Value at Risk (VaR) coming from the downside.

In the coming 2 years building up to the bull market, you will have to choose many low Beta punts and trade aggressively. The end of the Bull market does not necessarily mean the end of profits; you can short high Beta and buy low Beta, something I would not recommend just now. Defining the end of the bull market is going to be key; like in case of Aug, 2011, if you are shocked by a reversal, you will be in trouble. Meanwhile, we should map every Beta 'migration' or 'divergence' and trade down aggressively. An early Bull market has limited downside as 'all boats rise with the tide', so we should pick up the first 'divergence' and trade. However, we should not be surprised when the 'divergence' accelerates and the stock tanks to bear market lows in the middle of a bull market (like in Bharti, which went down below 2008 lows during the 2010 bull market). This happens when 'weak hands leave a non-moving train and get onto the fast-moving train', thus weakening the rally and increasing the Risk in the high Beta stocks.

All through this, the Beta Map is a safe, steady measure to reduce Risk through Bull and Bear markets. In the short run, it does not make the most money, but in the long run, it definitely takes the least Risk.  
Please find enclosed below the Beta Map.

P.S. To understand this well, you should superimpose the Nifty chart on the above dates, to understand the significance of the choice of dates, in which to classify the ‘moods of the market’.

4 comments:

Though the idea seems interesting, it requires a fair amount of explaining. Perhaps you could simplify the concept first and then lead to examples.

I am sure you are aware that reversion to mean is a fallacy, as the mean itself keeps changing with the change in progressive values.

However, your concept pre supposes that outliers will eventually turns into the normal range, which is a fair assumption.

I have tried to decipher this article:

“Beta”: The percentage change in the price of a stock relative to one unit of percentage change in an index. For instance, if two consecutive values of an Index are 5,972 and 5,969 (change of -0.05%) and those of a particular stock are 422 and 421 (change of -0.43%) then the Beta value will be -0.43/-0.05 = 8.93.

“Beta” Maps: Charting the percentage change in a stock/s relative to one unit of percentage change in an Index. To create such a chart, the percentage change in the index will have the constant value of 1 and the “Beta” of the stock will move up and down as time passes.

Migration: When the “Beta” of a stock diverges significantly from its average value.

Migration Pattern: Whether the Index and stock’s price are moving in the same or opposite direction.

Reversion to Mean: When the “Beta” goes into relatively extreme categories, the probability is high that the “Beta” will fall or rise back to normal levels.

Trading on the basis of “Beta” & Price: If the “Beta” is “out-of-whack” then it implies that the stock has risen or fallen more than it normally does relative to the Index. Consequently, the expectation would be that the stock would give up some of these changes.

For example, if the average “Beta” of a stock is 2 then at a “Beta” level of +8, the expectation would be that the stock would give up some of its “shooting” gains.

Quote: The end of the Bull market does not necessarily mean the end of profits; you can short high Beta and buy low Beta. Unquote.

This means that if the expectation is that the market is likely to be bearish, then the trading strategy should be to short high beta stocks (to maximize profits) that will fall more or buy low beta stocks that will fall less (to minimize losses).

Quote: We should map every Beta ‘migration’ or ‘divergence’ and trade down aggressively. Unquote.

Every time the “Beta” deviates significantly from its long term average, the expectation will be that the stock will give up some of its gains or losses.

If, relative to the normal behavior of the stock vis-a-vis the index, a stock suddenly shoots up significantly higher, then the expectation will be that it will give up some of its gains. The trading call will be to short the stock.

If, relative to the normal behavior of the stock vis-a-vis the index, a stock suddenly falls significantly lower, then the expectation will be that it will recover some of its losses. The trading call will be to go long on the stock.

Quote: When there is a correction, the low Beta stocks will drop more, while the high Beta stocks will be volatile, but will outperform the market. At the next correction, the Beta ‘divergence’ will emerge and we will see the Beta lines diverge. The ‘train is not leaving us’, but the next train is coming in. The last train carried Tata Steel with it. Unquote.

I am unable to understand this paragraph.

Is my understanding of the other matters in this article correct?

My email address is upadhya.atul@gmail.com

There is nothing like "Beta Maps" on the internet so it is something that you have designed. Fair enough. But if it is a part of an article that is meant for the public, then you might like to clarify how such a Beta Map gets created. Otherwise, nobody will be able to draw conclusions from what you have written so much about.

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