| Volatility and the Market |
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It's been said that, when the market is at a top or a bottom, the volatility is large
... or, at least, larger than normal (whatever that means).
You decide: 
>Look at 1987! Yes, and there are a few others like ... >I see them ... so it must be true, eh? But the past is no guarantee of the ... >Yeah, yeah, but look at 1990 and 1998 and ... Let's wait and see, but notice that the higher volatilities seem to be correlated with market LOWS, not market highs. >Let's wait and see. Good idea. In the meantime, keep your eye on the Volatility Index. |
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>Remind me ... how does one measure volatility.
It's the Standard Deviation (SD) of returns, over some time period, and SD2 is the average square of the deviations from their Mean return. As a formula it looks like:
SD2 = (1/N) { (r1 - M)2 + (r2 - M)2 + ... + (rN - M)2 }
where r1, r2, ... rN are the monthly (or annual or daily) returns
and M is their Mean: M = (1/N)(r1 + r2 + ... +rN)
>Why the square of the deviations?
Mathematically, it's nice. For example: SD2 = (1/N)Σr2 - { (1/N)Σr }2 = (the Average Square) - (the Square of the Average).
Of course, if just one of the deviations changes to, say, 2x or 3x or 4x what it was, then that deviation has 4x or 9x or 16x the weight in SD2.
>Why not just the average deviation ... instead of the average of their squares?
Okay, let's consider thirty annual returns. Twenty nine are fixed and have a Mean of 7.4%
and one of them, say the first one, varies from -6% to +22%. If we use the Standard Deviation,
namely the sum of squares, we'd get the red curve, below. If we just averaged the ABSolute value
of the deviations, we'd get the blue curve below.
>The SD is over 21% but the blue curve is ... what? About 16% or so?
Yes. There's a moral here. Know what it is?
>If you want to feel good, use the average |deviation| as your volatility!
