Volatility

Volatility

A word on Volatility.

A stock is said to be more volatile than others or when compared to its past , it means that its stock price has a tendency to fluctuate over a large range.

Hence, a sector ETF maybe less volatile when compared to a single stock of that same sector. This is because this ETF encompasses a wide variety of stocks. If only a small number of stocks within this ETF make huge price movement, and a great deal of others stay relatively unchanged, then the price of this ETF will not gyrate as much. It's all about statistics.

Volatility is, in fact, everything about mathematical statistics.

To understand Volatility a step further, we must introduce another statistical term, called Standard Deviation. They are a pair of Siamese twins. Speaking of one without referencing to another, is of little meaning.

Let's not talk soldiers on paper, so to speak. Let's use a real life example. Lehman Brothers (LEH)

LEH is current trading at ~$5. It was traded for ~$20 some 6 weeks ago and $65 just 9 months ago. One can consider LEH as a highly volatile stock. LEH price dropped a hefty 92% over a period of just 9 months. But exactly how volatile is this LEH and how do we quantify its volatility.

To exact how volatile a stock is, we must always look into its past price action; ie its historical price movement. Therefore, when we refer to a stock's past volatility over a period, we actually mean its Historical Volatility (HV). There's little for argument on this HV figure. Afterall, its the past and how can we argue that the price actions didn't occur.

The only debatable issue is the period in which this HV is calculated. Should the period used for calculation be 1 month, 6 months, 1 year, 5 years, or more? There's no straight answer. For a pattern trader, the shorter term HV makes more sense than to a long term investor, who might be more interested in a 3 year HV. Different periods used will show different HV, the very same reason why MA50 and MA200 are different. Therefore, one must know the period used when deriving HV.

At $5, LEH now exhibits a volatility of ~300%. This 300% is an annualized figure. What this means is that, ceteris paribus, in a year's time, LEH will have a 68% chance of trading between +300% or -300%. Now, of cos, $0, is the most that LEH can go to. But +300% means that LEH could be at $20 by then, and there's a 2/3 chance of it happening. To paraphrase, and using the Gaussian distribution (aka as Normal distribution), LEH stock price has a 68% chance of making ONE standard deviation movement in price, a 95% chance of a price movement within TWO standard deviations and a 99% chance of a THREE standard deviations movement, all in a year's time.

What if a trader wants to know the volatility other than the annualized 300% volatility? The calculation is as such:

3 month vol = 300% x 1/2 = 150% (square root of 3months /12 months = 1/2)
1 month vol = 300% x 1/3.46 = 87% (square root of 1month / 12months = 1/3.46)
1 week vol = 300% x 1/7.2 = 42% ( "" )
1 day vol = 300% x 1/16 = 18.75% ( "" )


so, with 1 day volatility at 18.75%, LEH could range between $5.93 to $4.06, all this in ONE day...

a quick check on LEH's performance today....5..30 to 3.88....now, that's pretty accurate, so far.