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Pavel314 science forum addict
Joined: 29 Apr 2005
Posts: 78

Posted: Sun Apr 30, 2006 2:01 pm Post subject:
Cumulative Changes Probability



This problem came up during a discussion of trading on the stock market but
the solution probably has wider application. As a disclaimer, I realize that
the past performance of a stock is no indication of future performance
because of many factors in the economy as a whole, and that I am not looking
for a system to beat the market, just a formula to compute probability.
GIVENS: For a particular stock, we have the closing values at the end of
each trading day for a year. From this, we compute the daily changes and
find they have a normal distribution with a mean of m and a standard
deviation of s.
PROBLEM 1: What is the probability that the stock will have increased in
value at least 10% at the end of the next three weeks, i.e., 15 trading
days? The probability should be given as a function of P, m, s, and 15,
the number of days in the observation period. Where P is the current stock
price and c_i is the change in value for trading day i, I would state the
problem as:
P + c_1 + c_2 + c_3 + ... + c_15 >= 1.1 * P
I've thought about expressing the c_i in terms of confidence intervals but I
get into problems with the summation.
PROBLEM 2: What is the probability that the stock will have increased in
value at least 10% at any time before the end of the next three weeks, i.e.,
15 trading days?
P + c_1 >= 1.1 * P OR
P + c_1 + c_2 >= 1.1 * P OR
P + c_1 + c_2 + c_3 >= 1.1 * P OR
...
P + c_1 + c_2 + c_3 + ... + c_15 >= 1.1 * P
The more general statement of the problem would use n days in the
observation period as opposed to the 15 I've used above. Thanks for any
light you can shed on this.
Paul 

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Pavel314 science forum addict
Joined: 29 Apr 2005
Posts: 78

Posted: Tue May 02, 2006 10:47 am Post subject:
Re: Cumulative Changes Simulation



"Pavel314" <Pavel314@NOSPAM.comcast.net> wrote in message
news:ZLednXWtfoYuXsnZnZ2dnUVZ_sKdnZ2d@comcast.com...
Quote:  This problem came up during a discussion of trading on the stock market
but the solution probably has wider application. As a disclaimer, I
realize that the past performance of a stock is no indication of future
performance because of many factors in the economy as a whole, and that I
am not looking for a system to beat the market, just a formula to compute
probability.
GIVENS: For a particular stock, we have the closing values at the end of
each trading day for a year. From this, we compute the daily changes and
find they have a normal distribution with a mean of m and a standard
deviation of s.
PROBLEM 1: What is the probability that the stock will have increased in
value at least 10% at the end of the next three weeks, i.e., 15 trading
days? The probability should be given as a function of P, m, s, and 15,
the number of days in the observation period. Where P is the current stock
price and c_i is the change in value for trading day i, I would state the
problem as:
P + c_1 + c_2 + c_3 + ... + c_15 >= 1.1 * P
I've thought about expressing the c_i in terms of confidence intervals but
I get into problems with the summation.
PROBLEM 2: What is the probability that the stock will have increased in
value at least 10% at any time before the end of the next three weeks,
i.e., 15 trading days?
P + c_1 >= 1.1 * P OR
P + c_1 + c_2 >= 1.1 * P OR
P + c_1 + c_2 + c_3 >= 1.1 * P OR
...
P + c_1 + c_2 + c_3 + ... + c_15 >= 1.1 * P
The more general statement of the problem would use n days in the
observation period as opposed to the 15 I've used above. Thanks for any
light you can shed on this.

Since I couldn't solve this problem theoretically, I wrote a QBasic program
to simulate the situation under various scenarios. The first parameter is
the value of one standard deviation of the historical daily change as a
percent of the initial stock price. The second works into the two problem
statements above; the first checks to see if the stock has appreciated 10%
at the end of 15 days while the second checks to see if it appreciated 10%
on any day within the 15day trading period. I ran each of the six scenarios
1,000,000 times; the results are shown below:
StdDev/Price +10% at End of Period +10% Within Period
1% 1,238
1,576
2% 66,772 97,892
4% 238,162 379,117
The moral seems to be that you should take your profit while you can because
there's a significant chance that the stock will go back down.
Paul 

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Michael Zedeler science forum beginner
Joined: 29 Nov 2005
Posts: 17

Posted: Sat May 06, 2006 7:23 pm Post subject:
Re: Cumulative Changes Probability



Pavel314 wrote:
Quote:  This problem came up during a discussion of trading on the stock market but
the solution probably has wider application. As a disclaimer, I realize that
the past performance of a stock is no indication of future performance
because of many factors in the economy as a whole, and that I am not looking
for a system to beat the market, just a formula to compute probability.
GIVENS: For a particular stock, we have the closing values at the end of
each trading day for a year. From this, we compute the daily changes and
find they have a normal distribution with a mean of m and a standard
deviation of s.[...]
The more general statement of the problem would use n days in the
observation period as opposed to the 15 I've used above. Thanks for any
light you can shed on this.

Here is a starting point:
http://en.wikipedia.org/wiki/Blackscholes
Regards,
Michael.

Which is more dangerous? TV guided missiles or TV guided families?
Visit my home page at http://michael.zedeler.dk/
Get my vcard at http://michael.zedeler.dk/vcard.vcf 

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Pavel314 science forum addict
Joined: 29 Apr 2005
Posts: 78

Posted: Sun May 07, 2006 1:17 pm Post subject:
Re: Cumulative Changes Probability



"Michael Zedeler" <michael@zedeler.dk> wrote in message
news:oJ67g.162$uS7.137@news.get2net.dk...
Quote:  Pavel314 wrote:
This problem came up during a discussion of trading on the stock market
but the solution probably has wider application. As a disclaimer, I
realize that the past performance of a stock is no indication of future
performance because of many factors in the economy as a whole, and that I
am not looking for a system to beat the market, just a formula to compute
probability.
GIVENS: For a particular stock, we have the closing values at the end of
each trading day for a year. From this, we compute the daily changes and
find they have a normal distribution with a mean of m and a standard
deviation of s.[...]
The more general statement of the problem would use n days in the
observation period as opposed to the 15 I've used above. Thanks for any
light you can shed on this.
Here is a starting point:
http://en.wikipedia.org/wiki/Blackscholes
Regards,
Michael.

Thank you, that's exactly what I was looking for.
Paul 

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