Author 
Message 
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 

Back to top 


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 

Back to top 


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 

Back to top 


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 

Back to top 


Google


Back to top 



The time now is Fri Jul 20, 2018 4:34 am  All times are GMT

