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At 2:01 PM +0100 6/23/00, hm wrote:
>To my surprise, almost exactly 50/50. Given the overall upward movement
>of the market since 1992 I initially assumed I had done something wrong.
>Then I realised that these these figures related to intraday movement only,
>and took no account of opening gaps. Turns out that on average, all the
>upward movement in FTSE future since 1992 can be accounted for by the
>opening gaps.
This is easy to show with simple mathematics.
Assume a market like the S&P500 index over the past few years with a
Annualized Annual Return of 20% and an Annualized Standard Deviation
of returns of 15%. This is about what we have been seeing. Assume the
distribution of prices is exactly "normal".
We then need to find what percentage of the time we have winners and
losers. The "NORMDIST" function in Excel does this quite easily.
With one sample each year only 9.1% of the years will be losers.
But now sample monthly. Then the average return will decrease by a
factor of 12 and the standard deviation will decrease by a factor of
SQRT(12) so the distribution becomes relatively fatter and more of it
"spills under" the zero point so then 36% of the months will be losers.
Now sample daily and 47% of the days will be losers.
Now sample 10 times a day and now 49.1% of the samples will be losers.
Eventually, if you sample every minute just under 50% will be losers.
The relationship is shown on the attached gif chart.
Fibonacci adherents will obviously want to sample this market monthly
to prove that the ratio is the proper number to match their
theories...<g>
Bob Fulks
Attachment Converted: "f:\eudora\attach\Normal.gif"
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