November 16, 2009

life in financial markets: (part 1 of 2) why be afraid of volatility?

(this is part 1 of the subject matter of this post... part 2 will follow after a few days...)

I can not but feel amused when people, who are supposed to know better, get excited about volatility in the stock markets and then go on to call them all sorts of names like "mad" and "manic".

Volatility is an intrinsic part of the markets that predominantly affects, both positively and otherwise, day traders and short-term speculators. But it does not, I repeat, does not matter to long-term investors how markets are moving from one day to another. When you are investing a little, once or twice a month, on randomly-selected days, you can never be hurt badly by volatility.

So, what exactly is volatility? One out of a couple of dictionary meanings of 'volatile' is something that is difficult to capture or hold permanently.

The commonly accepted technical measure of volatility for a stock—and an index (which is a combination of stocks)—is the standard deviation (SD) of day-to-day price changes for a period. SD is the square root of the variance and variance, in case of stocks or indices, is the average of the squared deviations of the daily changes during a period from their average. An accepted-and-followed mathematical theorem then says that at least 75 per cent of the values will fall within plus and minus two standard deviations from the mean of a distribution.

Take, for example, 10 day-to-day changes in Nifty during 11 trading days. Find its simple average. Say, it is -0.3%. Calculate, for each day-to-day change, its deviation from the mean. Square each of these 10 deviations. Then, total these 10 squared figures and divide by 10 to get their average. This is the variance. Its square root is the SD.

Say, the SD is 1.6%. Now, applying the theorem it follows that would be at least 7-8 days (75%) on which the daily Nifty change would be between -3.5% [-0.3 - (2*1.6)] and 2.9% [-0.3 + (2*1.6)]. If the SD (volatility) for the next set of 10 days is higher than 1.6% then it follows that this range has widened.

Another measure of volatility in the financial markets is the movement of a Volatility Index (VIX) that takes the implied volatility from actively traded index options trades. The most tracked VIX is that of the Chicago Board of Options Exchange. In India, the National Stock Exchange too has its own VIX based on Nifty options trades.

It is generally believed that when VIX goes above 30 the stock market is likely to experience a correction. See below (click on the image to see it enlarged & clear) to the see the co-relation between S&P 500 (US) and CBOE's VIX, as well as between S&P CNX Nifty (India) and NSE's VIX.

Global equity markets tend to co-relate in the short term but it is interesting to note how their narrow differences widen over time. Below is a graph I made of global indices movements from end of 2005 onwards (click on the image to see it enlarged & clear).

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