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Saturday, 3 November 2007

Stocks -- fooled by randomness?

I chanced upon an interesting idea/concept while reading a book on risk, titled "Against the gods, the remarkable story on risk", by Peter L. Bernstein.

If the results of an activity is truly random, taking statistical measurements of repeated trials should resemble a normal distribution, i.e. a bell curve. The sum total of two dice repeated sufficient number of times will result in a bell curve with more counts centered about 7 and 8, tapered towards the extreme of 2 and 12.

Does that occur to stocks? With the help of my friend, I got hold of the daily closing value of STI from April 1985 to Oct 2007. I plotted the total counts of daily changes in percentage against the changes and got the following graph.

On first look, the graph fit a bell curve quite nicely. But on closer look, other than the change from 0 to 0.5%, there are more counts for almost all corresponding percentage changes in the positive category compared to the negative ones. e.g. there are more counts of 0.5 to 1% compared to -0.5 to -1% etc.

Daily changes of STI index can be said to be nearly random but skewed towards more positive changes. Hence, over time, STI should appreciate. A check on STI index from 1985 to 2007 verifies this.

In other words, if a typical investor blindly dollar averages STI index (e.g. via index ETF) from 1985 to present, he would have reaped sizable returns while being saved from daily emotional stress, swinging between extremes of anguish and euphoria.

One reason why STI index (or any broad based index of any country with open economy) demonstrates daily randomness is because world events, be it fundamental or sentimental, occurs in random and unpredictable manner. STI is thus affected unpredictably, resulting in short term random behavior. But as the economy of any country with open economy increases over time, so does the index which reflects its economic growth.



Blogger la papillion said...

Hmm, I don't agree with your interpretation of results you get from the statistical plot. It's really not significant that the (say) 1 to 1.5% is more than the -1 to -1.5%. This doesn't conclude that STI is skewed positively because it is measured in %, not in absolute terms.

A 200 point drop from 1000 to 800 is a drop of 20%. But a 200 point increase from 800 back to 1000 is an increase of 25%, even though I still get back 1000. So I can't conclude that STI is skewed positively or not. It simply cannot be derived from the information itself.

I have a suggestion. Why not plot a similar graph but use the absolute change in price instead of % change. That should be more revealing of the nature of STI's skewness

Nevertheless, a very intersting graph to look at :)

26 November 2007 at 20:21  
Blogger Market Uncle said...

No, percentage changes shows more meaning than absolute changes.

Losing 10 cents when you have a dollar feels more pinch than losing 10 cents when you have a hundred.

Take for example, increase of 100 from 1000 to 1100 is 10%. This is big.

But when the index increases 100 from 10,000 to 10,100, the 100 only registers 1%. Its no big deal.

Thats the reason why when DOW drop 50 pts, its no big deal, but STI drop 50 pts is considered very bad.

Anyway, the plot is just an illustration of my view, nothing significant.

3 December 2007 at 10:39  
Blogger la papillion said...

hi market uncle,

I agree with the % thing, but my disagreement is on the part that you said STI is skewed positively because of the graph. We can't get that kind of information from that graph alone.

You might be interested in
volatility-of-sti.html (just join them together)

I did more number crunching from the data you posted on your blog, just for fun :)

4 December 2007 at 09:41  
Blogger Market Uncle said...

Hi la papillion,
Just read your blog. I have to agree with you that the positive skew is not that conclusive. Nevertheless, I'm pretty impressed with your statistical discussion on the problem :)

23 December 2007 at 17:11  

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