## Wednesday, November 28, 2007

### Volatility of STI

I was haunted by the image of a picture in market uncle's blog. Not it wasn't particularly scary, but the image sort of got stuck in my mind's eye and I seriously need to exorcise it out. Research shows that if one is feeling down or happy, one just have to work on some maths or logical problems - it'll bring the level of serotonin to neutral level so that one does not feel happier nor sad. I've tried it before, it works very well. Try Sudoko next time you're feeling unhappy.

For me, I need to work out some maths as I couldn't quite resist lure of the data tempting me to find out more about them. Market uncle did a pretty good collection of the data which enabled me to compute a little bit more stuff about them. The data collect are the percentage daily closing of STI from April 1985 to October 2007 - pretty nasty bit.

As the data are classed, I need to find the class mark to be able to estimate the sample mean and sample variance. For the daily % change of the extreme ends, "above 20%" and "below -20%", I take the class mark conservatively as 20 and -20 respectively. I do not know the extreme upper and lower limit of the daily % change but I figured that it is immaterial as the frequency of those 2 classes are very small, so it shouldn't skew the mean too much. Here's my table:

I computed the summation of x, summation of x² and total frequency of data collected. Since the sample size is huge (5719, mind you), it's very safe to assume that central limit theorem holds. As such, I would take it that the daily % change of STI follows a normal distribution. Let's find the sample mean and variance, and ultimately the standard deviation for this distribution.

Getting interesting huh? The daily % change of STI follows a normal distribution with mean of 0.039% and with a standard deviation of 1.379%. What does that mean? It means that statistically, STI have a mean volatility of about 0.04%, with an 'spread' of about ± 1.38%. To be more precise, we can find out the confidence interval of finding the mean, given a probability of locating the mean.

I'll give a few confidence interval to illustrate:

1. There is a 99% probability of the mean daily % change of STI lying between -0.01% and 0.09%
2. There is a 90% probability of the mean daily % change of STI lying between 0.01% and 0.07%
3. There is a 80% probability of the mean daily % change of STI lying between 0.02% and 0.06%

This is all well and good until one realise that the spread of ± 1.4% basically means that knowing the mean doesn't mean a thing (haha!) because the standard deviation (measures the spread or uncertainty) is so high.

Perhaps it will be even more interesting to find out if periods of high volatility, as predicted by daily % change, will cluster together. According to autoregressive conditional heteroskedasticity (ARCH for short) model by Engle (1982), the volatility is a function of previous volatility and the mean volatility.

Future volatility = f (past volatility, mean volatility)

This models predicts that volatility tends to occur in clusters and they tend to mean revert. Mean reversion means that the property will go back to the mean value. This coincides with my own market experience. I remember that last year, the volatility of STI is very quite low, if we see a rise or drop of 20 pts it's a big hoo-ha already. This low volatility period lasts for quite a while until this year, where I see big swings of ±1 to 2%. HSI is even more volatile, swinging wildly ± 1000 pts. And boy do these periods of high volatility cluster together.

If you know bollinger band, one of the technical indicators, it basically set up a trading rule based on the transitional moment between clusters of high and low volatility. 'Bollinger squeeze' is where the two bands tighten (volatility drops) around the price range. At the critical point, the price breaks out of the band, resulting in a huge change in price (up or down, we have to look at other indicators for the direction) and subsequently huge increase in volatility. We can also make use of the idea that volatility tends to mean-revert to trade based on bollinger band. If it hits the top band, price tend to mean revert and correct, thus moving down. If it hits the lower band, price will mean-revert and move up - creating an overbought/oversold kind of signal.

Haha, enough crap for now :) I explored a few concepts today :)

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STI was pretty flat; it closed down 3 pts at 3369 with a volume of 1.5 billion. Pretty quiet day, nothing much happened.

Just a news to share:

1. Tiong woon was awarded service contract for shell houdini project to provide project cargoes trucking, heavy haulage, storage and marine transportation services. They didn't state the contract value. This stock is heavily beaten down, so will this provide the catalyst for it to move?

Dow futures up +70.