Volatility

The second most important parameter to look at when considering an investment is the volatility (the most important one is the Return, see here). Volatility is important because it shows how varied the price is. In other words, how consistent the growth is.

Why the consistency of the growth is important? Take a look at this chart:

Low and High Volatility

All 4 lines starts from 100 and ends on 119. But how they arrive at 119 are very different. The volatility of these 4 lines are green: 8.93, red: 9.65, blue: 1.54, purple: 5.34.

Red is up and down like a yoyo. In Sep 2012 I would have no clue whatsoever whether in the next few months it would be going up or down. It goes from +15 and +17 in Oct 2011 and Apr 2012 to -13 in March 2012. Statistically, because it’s like up & down dramatically like a yoyo, the probability of it’s going up is almost the same as it’s going down. The future is completely unpredictable.

Green is shooting up very high in Oct to Dec 2011, then flat in Jan and Feb and down a lot in March. Then up very high again in April, then stepping down until Sep 2011. It goes from +13.5, +12.5 and +17 in Oct 2011, Dec 2011, Apr 2012 to -13 in Mar 2012. Again, we have no idea of where it’s going. But judging by “the near past is more influential than distant past”, in a few months from Oct 2012 I think the probability of it’s going down is high than going up.

Blue is pretty consistent with the growth. It goes from +4 in Jan 2012 to -1.5 in Mar 2012. It is almost a straight line. It is by far more resembling a straight line than red or green. From May to Sep it has been pretty consistent with growing +1 to +2 each month. It is much more predictable than Red or Green. In a few months from Oct 2012 I am pretty sure it will continue to go up at the same pace.

Purple was pretty much flat for 9 months from Nov 2011 to Aug 2012 then suddenly shoot up to reach 119. It is far better than Red or Green, but it is worse than Blue. It is better than Red or Green because staying flat is better than going up and down like a yoyo. But going up consistently +1.5 each month like Blue is better than staying flat for 9 months then shoot up at the end. Better means more predictable.

Yes you are right, I am assuming that if it has been rain, rain, rain in the past 6 days, then the chances of it going rain tomorrow is bigger than sunshine. And if it has been sunshine for the last 6 days, the changes of it’s going to be sunshine on tomorrow is bigger than raining.

If the growth has always been +2 in the past 6 months, the chances of the growth being +2 next month is a lot higher than if it has been yoyo-ing +2, -2, +2, -2, +2, -2.

These charts represents either a company, or a fund (or commodity, or FX). There are real things behind these charts. Assume we are talking equity. These 4 lines are 4 different companies in the stock market. Company red which is up and down like yoyo, is not trustable at all. There is something fundamentally wrong with this company. Why is the share price goes up and down like yoyo? Why did people rushing to buy (hence the price was up) then the following month people rushing to sell? Why in Feb people were buying, in March people were selling, in April buying, in May selling, in June buying, in July selling? We need to find out what’s going on inside this company. There must be something going on. There is no smoke without fire.

Company blue on the other hand is much more consistently growing compared to Red. It is a much more stable company. And because the company is more stable (based on the share price), it is more predictable.

If I have to choose between these 4 companies to buy, hands down I will choose Blue. It is buy far the most stable, the most predictable growth. Yes all for of them gives the same return (from 100 to 119 in a year = 19% return), but I have to predict the future movement, I say that Blue has the highest change of making good, consistent growth in the future.

There is another reason why I prefer the one most resembling straight line (Blue) than the yoyo ones like Red. If it is straight line, I can exit at any time without problem. If it is yoyo-ing, exiting could be a little problem. For example, March 2012 was a bad time to exit from Red because the price was down 12.

If a company made a big fall in the past it is more likely to make it again in the future. Red and Blue in March are both down 12. Whereas Blue is never down more than 1.5. Compare 12 and 1.5: the 12 are more scary! We know that if we buy Blue, if it goes down, it doesn’t go down much. Whereas if we buy Red or Green, we must be prepared to accept big falls.

The volatility of these 4 lines are green: 8.93, red: 9.65, blue: 1.54, purple: 5.34. Blue has the lowest volatility (“vol” for short). Low vol means “growth is consistent”, like it’s always +1 or +2 every month. Red and Green have the highest volatility. High vol means “up and down violently like a yoyo”, like Jan +10, Feb -13, March +15, … Purple’s vol is in the middle between Red/Green and Blue. It’s not “growing consistently” and it’s not “up and down like yoyo” either. It’s consistently flat then up.

So we prefer investment with low vol. Meaning that its growth is consistent.

Calculating Volatility

Calculating Volatility - Blue

These are the numbers for Blue. The growth is between +4 (Jan) and -1.5 (Mar). The average of growth is 1.58.

Delta means how far is the growth from the average. In Oct 2011, the growth is 3.5, so the Delta is 3.5-1.58 = 1.92. In Nov 2011, the delta is 1.5-1.58 = -0.08. Delta^2 means Delta Squared = Delta2. In Oct 2011 the Delta2 was 1.922 = 3.67. And in Nov 2011 the Delta2 was (-0.08)2 = 0.0069, rounded to 0.01. The reason we square the Delta is to avoid the negatives cancelling the positives.

If we average all the Delta2, we get 2.37. This is called the Variance. Variance is a measure of how far a set of numbers are spread out from the mean.

If we take the square root of the variance, we get Standard Deviation (SD). Its matematical symbol is Greek alphabet sigma: σ. It also shows how spread out the values are from the mean. In investment, the values we are comparing is the growth. Hence it is called volatility, meaning how volatile the price is, how different the growth is from one day to the next.

In the growth is distributed normally, 1 sigma = 68%, 2 sigma = 95%, 3 sigma = 99.7%. In the above case of Blue, the sigma is 1.54. Hence 2 sigma = 3.08 so 1.58 ± 3.08 covers 95% of the population.

Below are the calculations for Red, Green and Purple:

Red:

Calculating Volatility - Red

Green:

Calculating Volatility - Green

Purple:

Calculating Volatility - Purple

Volatility

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