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Jeff,
On Mon, 25 Feb 2002 14:00:14 -0800 (PST), you wrote:
>> "non-tradeability" = max (stadev (price changes; 1 time step);
>> stadev (price changes; 2 time steps))
>> / stadev (price changes; 4 time steps)
>>
>>If this fraction approaches (or even exceeds) 1, the security is
>>untradeable for the information frequency at hand, and the only (*)
>>way out to make this security tradeable is to increase the information
>>frequency. [(*) other measures to be discussed]
>>
>
>Hmmm, suppose a stock increases in EOD value 90% of the time. Suppose it
>is not very volatile, on any time frame, so then your "non-tradeablity"
>parameter is very close to 1. In other words, I think I've constructed
>an example were we could care less about StdDev, as long as we've
>identified a trend. As a recent, concrete example, take a look
>at the price chart for DLX. Very low volatility, identifiable
>uptrend. What does your "non-tradeability" parameter turn
>out to be for this one?
I have not handy the DLX data, so I cannot test your example, but
there is almost always a non-zero stadev in the price changes of any
security, when taken over eg 1000 time steps. Admittedly, I have
applied this "non-tradeability" criterion to time series that
definitely go up and down, like (almost) any stock prices do. But even
in the case of the prices representing a straight line, this parameter
does not go to 1 (like you seemingly suppose above), but it rather
results in an undefined expression, ie 0/0, which can represent any
value. So its not wrong, it just cannot be used.
And as I stated above, using stadev to represent the volume** of the
probability distribution of course is an approximation. If you want to
be more precise but even practicable: insert the mean value of all
price changes (neglecting any minus sign) instead of stadev, and you
can apply this "non-tradeability" criterion to your "straight-line"
prices without any problem. [** to be defined in detail]
But why discuss the 1% (or less) exceptions? Why not concentrate on
the 99% of price time series, that can be rated sufficiently in terms
of "non-tradeability" (NT) by the criterion given above?
My favorite securities (dax options) eg show NT values of about 0.7
(calculated using stadev), which is a motivation for me to look at
other securities, which might be more easy to trade. Alternatively it
might be helpful to increase the information frequency.
What about the NT of your favorites?
mfg rudolf stricker
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