Friday, April 30, 2010

old age and obfuscational dialogue

When I was younger, I got angry confused mildly irritated* when I read statements like:

2/3 of stock returns lie within one standard deviation of the mean
and
stock returns have a normal distribution.

Now, much older and (perhaps) wiser, they don't bother me any more.

However, it's still disturbing to note that financial gurus like to change the meaning of words (or attach misleading meanings).

For example, the word risk which the Common Joe would understand to mean:

risk n The possibility of suffering harm or loss.

In financial circles, this guy was assumed to mean the Standard Deviation of a set of stock returns.

Now, to calculate the Standard Deviation of set of n (historical) returns, Rj, the magic formula is:

Standard Deviation
= SquareRoot[(1/n) { (R1-M)2+(R2-M)2+...+(Rn-M)2} ]


where M is the Mean of the returns.

As anybuddy can plainly see, this animal is a measure of the deviation of returns from their Mean.

So why would anyone call it the risk associated with this stock?
If my returns were 10% larger than yours, we'd have the same risk.
That's because the SD doesn't change when you add a constant to the set of numbers.

If we both invested in a guaranteed returns certificate, but my guaranteed returns were twice yours, my investment would be twice as risky.
That's because the SD doubles when you double all the numbers.


Okay, so many (recognizing that "risk" is perhaps a misnomer), began to call it the uncertainty associated with stock returns.

Huh? Where's the uncertainty here?
(The first set of returns has higher SD.)

Why can't we just call SD the Root-Mean-Squared (RMS) deviation of returns from their Mean? **

Anyway, we now have a plethora of risk measures, like downside risk, value at risk, drawdown risk, omega ... ad nauseam.

*In the last century, there was this discussion on obfuscational dialogue.
** We (perhaps unknowingly) use RMS all the time. For example, the RMS voltage that comes rushing from out electrical outlets is 120 volts RMS. The actual voltage ranges between +/- 170 volts.

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As evidence that I'm gettin' old, I ran across the quiz I have on my web site ... and couldn't answer any of the questions ('cept 5.2)
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Once upon a time I thought I'd like to define the sex appeal of a stock as its Standard Deviation. That way, my investing in very volatile stocks (as I do) would make me feel warm all over.

 

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