How do you calculate the % chance the S&P will close X number of points up/down during a given day?
April 24, 2008 9:06 AM Subscribe
Quantitative finance experts: What methods are available for calculating the odds the S&P will close up or down X number of points during a given day?
This is a special project I am tasked with at work and would like to get a sense of where to start. What inputs are required to make such a calculation, and how would the error interval be calculated?
This is a special project I am tasked with at work and would like to get a sense of where to start. What inputs are required to make such a calculation, and how would the error interval be calculated?
This is a special project I am tasked with at work
Is your project at work about the stock market, or is it about some other system? The method for trying to calculate this for the stock market will most likely be very different than calculating the probability that sell 10 less hamburgers tomorrow than today, for example.
calculating the odds the S&P will close up or down X number of points during a given day
Do you mean exactly X number of points, or at least X number of points?
posted by burnmp3s at 9:35 AM on April 24, 2008
Is your project at work about the stock market, or is it about some other system? The method for trying to calculate this for the stock market will most likely be very different than calculating the probability that sell 10 less hamburgers tomorrow than today, for example.
calculating the odds the S&P will close up or down X number of points during a given day
Do you mean exactly X number of points, or at least X number of points?
posted by burnmp3s at 9:35 AM on April 24, 2008
Implied volatility is probably fine for this. It has some problems, but they aren't going to be that big of a deal to you.
VIX is the simplest way to get implied volatility. It is 19.35% as I type this. That's an annualized figure. Divide by the square root of 365 to get the daily figure, about 1%. That's the daily standard deviation. So if you wanted to calculate the estimated probability of a move below a certain value X*, it would be (in Excel):
=normsdist((X/1390)/1%)
* - the probability that it will be exactly X points is effectively zero.
posted by milkrate at 9:52 AM on April 24, 2008
VIX is the simplest way to get implied volatility. It is 19.35% as I type this. That's an annualized figure. Divide by the square root of 365 to get the daily figure, about 1%. That's the daily standard deviation. So if you wanted to calculate the estimated probability of a move below a certain value X*, it would be (in Excel):
=normsdist((X/1390)/1%)
* - the probability that it will be exactly X points is effectively zero.
posted by milkrate at 9:52 AM on April 24, 2008
It is not appropriate to apply Normal distribution methods to the stock market. The underlying distribution of occurrences that make up the index is not random. People will do it anyway, and you will certainly return a result using a method of this type to your boss, but it will not be statistically valid.
posted by ikkyu2 at 10:14 AM on April 24, 2008
posted by ikkyu2 at 10:14 AM on April 24, 2008
To piggyback on what ikkyu2 said, it's pretty easy to figure out the percentage chance that the S&P has closed X percentage points up or down on any given day in its history. However, the maxim that past performance does not predict future results is pretty apt here.
posted by klangklangston at 10:33 AM on April 24, 2008
posted by klangklangston at 10:33 AM on April 24, 2008
Response by poster: Do you mean exactly X number of points, or at least X number of points?
I appreciate the input, for clarification of terms - Yes, "at least X number of points up/down"
posted by yoyoceramic at 10:35 AM on April 24, 2008
I appreciate the input, for clarification of terms - Yes, "at least X number of points up/down"
posted by yoyoceramic at 10:35 AM on April 24, 2008
Response by poster: It is not appropriate to apply Normal distribution methods to the stock market. What would be a better distribution to use?
posted by yoyoceramic at 10:38 AM on April 24, 2008
posted by yoyoceramic at 10:38 AM on April 24, 2008
It might be useful to quickly compare historical daily movements of the S&P against implied volatility (using the same time period as you'd like your final results to cover) to get a better idea if there is sufficiently strong correlation for the desired time period and if the distribution of events is reasonably close to normal.
posted by ssg at 10:50 AM on April 24, 2008
posted by ssg at 10:50 AM on April 24, 2008
It might be useful to quickly compare historical daily movements of the S&P against implied volatility
Well, one obvious thing that comes to mind is that the stock market tends to go up significantly more than it goes down. One would expect that a normal distribution centered at no change to remain relatively constant over time, whereas the S&P index tends to go up around 8% per year over time. My guess is that the simple 1% up or down calculation above would significantly overestimate the chance of having a down day.
posted by burnmp3s at 11:32 AM on April 24, 2008
Well, one obvious thing that comes to mind is that the stock market tends to go up significantly more than it goes down. One would expect that a normal distribution centered at no change to remain relatively constant over time, whereas the S&P index tends to go up around 8% per year over time. My guess is that the simple 1% up or down calculation above would significantly overestimate the chance of having a down day.
posted by burnmp3s at 11:32 AM on April 24, 2008
It goes without saying that you'd want to let the data guide you to the appropriate centre for whatever distribution you end up using.
posted by ssg at 12:13 PM on April 24, 2008
posted by ssg at 12:13 PM on April 24, 2008
Best answer: The problem is not amenable to statistical analysis, yoyoceramic. You can approach it with the assumption that every trading day is like every other trading day, and that (market movements on any given trading day) are independent events, and that (market movements on any given trading day) are assumed to occur owing to precisely the same sets of causes as (market movements on any other trading day.)
Then you can apply statistical methods to analysis and prediction of the future behavior of (market movements on trading days), based on considering data from a prior set of (market movements on trading days).
The set of assumptions described above, about (X), is part of what allows us to do valid and meaningful statistical analysis on (X).
In this case, however, the assumptions are false and invalid. That means that conclusions from statistical analysis that is based on them will not be valid, and should not be assumed to be reliable.
In other words, applying statistical methods to market movements is like trying to hammer in a nail using a crescent wrench.
posted by ikkyu2 at 2:24 PM on April 24, 2008
Then you can apply statistical methods to analysis and prediction of the future behavior of (market movements on trading days), based on considering data from a prior set of (market movements on trading days).
The set of assumptions described above, about (X), is part of what allows us to do valid and meaningful statistical analysis on (X).
In this case, however, the assumptions are false and invalid. That means that conclusions from statistical analysis that is based on them will not be valid, and should not be assumed to be reliable.
In other words, applying statistical methods to market movements is like trying to hammer in a nail using a crescent wrench.
posted by ikkyu2 at 2:24 PM on April 24, 2008
Look at it this way, yoyoceramic: If the stock market were susceptible to this kind of statistical analysis it would be possible to analyze the market and write a computer program that could easily and simply make boatloads of money by playing the volatility in the market. No such program exists.
posted by Justinian at 2:53 PM on April 24, 2008
posted by Justinian at 2:53 PM on April 24, 2008
In other words, applying statistical methods to market movements is like trying to hammer in a nail using a crescent wrench.
Not that this discourages thousands of day traders and chartists who attempt to do exactly that -- most unsuccessfully.
My opinion is that you simply take the history (as far back as you like) of daily percent change in the market and plot each day on a histogram and you are done. The area to the left or right of the desired percent change represents its probability of occurring. Since up days exceed down days by a few percent, the histogram will be skewed to the right.
If you believe in efficient markets and a random walk, you can do no better. Some academics believe they have identified a slight momentum effect, but not large enough to exploit profitably. The momentum effect means that an up day tends to be followed by another up day.
posted by JackFlash at 3:12 PM on April 24, 2008
Not that this discourages thousands of day traders and chartists who attempt to do exactly that -- most unsuccessfully.
My opinion is that you simply take the history (as far back as you like) of daily percent change in the market and plot each day on a histogram and you are done. The area to the left or right of the desired percent change represents its probability of occurring. Since up days exceed down days by a few percent, the histogram will be skewed to the right.
If you believe in efficient markets and a random walk, you can do no better. Some academics believe they have identified a slight momentum effect, but not large enough to exploit profitably. The momentum effect means that an up day tends to be followed by another up day.
posted by JackFlash at 3:12 PM on April 24, 2008
VIX is the simplest way to get implied volatility. It is 19.35% as I type this. That's an annualized figure. Divide by the square root of 365 to get the daily figure, about 1%.
Shouldn't that be the square root of the number of trading days -- usually around 250 or so?
I'm not touching the validity of the underlying model argument with a 10-foot pole...
posted by Opposite George at 3:29 PM on April 24, 2008
Shouldn't that be the square root of the number of trading days -- usually around 250 or so?
I'm not touching the validity of the underlying model argument with a 10-foot pole...
posted by Opposite George at 3:29 PM on April 24, 2008
It might be useful to quickly compare historical daily movements of the S&P against implied volatility
Since I suggested this, I figured I might as well try it out. Just as an example, I tested a linear fit of percent difference between the open and close of the S&P 500 against VIX from ten trading days previous* over the period of '93-'03. The correlation is pretty weak (R = 0.38).
*VIX is intended to give implied volatility for the next 30 calendar days.
posted by ssg at 4:14 PM on April 24, 2008
Since I suggested this, I figured I might as well try it out. Just as an example, I tested a linear fit of percent difference between the open and close of the S&P 500 against VIX from ten trading days previous* over the period of '93-'03. The correlation is pretty weak (R = 0.38).
*VIX is intended to give implied volatility for the next 30 calendar days.
posted by ssg at 4:14 PM on April 24, 2008
VIX is annualized using a 365 day convention (see here) - but yes, 252 trading days is normal.
Implied volatilities are normally slightly higher than subsequent realized volatilities and there are a number of good and bad explanations offered for this.
posted by milkrate at 7:55 PM on April 24, 2008
Implied volatilities are normally slightly higher than subsequent realized volatilities and there are a number of good and bad explanations offered for this.
posted by milkrate at 7:55 PM on April 24, 2008
VIX is annualized using a 365 day convention (see here) - but yes, 252 trading days is normal.
Cool paper. Nothing like reading it from the source.
The measures we used to use back in the Flintstones days were based on trading days but they were for a different audience and calculated completely differently. 252-day normalization might make more sense for measures meant to represent close-to-close volatility, but the original question seems to be looking for open-to-close movement distribution and in that case the calendar-day method used by VIX seems to be more fitting.
Not that I believe any of this has good predictive power, necessarily, especially when you start getting into implied volatility. Yeah, okay, you got it out of me... These sorts of measures and calculations do have their place in risk management and historical analysis -- and despite the naysayers above it certainly isn't impossible to set some bounds on expected movement, even if not to a degree of precision required to beat the market. But if "during a given day" means "today," and "odds" means "something based on best available information," then yeah, my suspicion is relying solely on VIX probably isn't going to get you there. What will? I dunno.
posted by Opposite George at 12:57 AM on April 25, 2008
Cool paper. Nothing like reading it from the source.
The measures we used to use back in the Flintstones days were based on trading days but they were for a different audience and calculated completely differently. 252-day normalization might make more sense for measures meant to represent close-to-close volatility, but the original question seems to be looking for open-to-close movement distribution and in that case the calendar-day method used by VIX seems to be more fitting.
Not that I believe any of this has good predictive power, necessarily, especially when you start getting into implied volatility. Yeah, okay, you got it out of me... These sorts of measures and calculations do have their place in risk management and historical analysis -- and despite the naysayers above it certainly isn't impossible to set some bounds on expected movement, even if not to a degree of precision required to beat the market. But if "during a given day" means "today," and "odds" means "something based on best available information," then yeah, my suspicion is relying solely on VIX probably isn't going to get you there. What will? I dunno.
posted by Opposite George at 12:57 AM on April 25, 2008
These sorts of measures and calculations do have their place in risk management and historical analysis
No, actually, they don't. It's kind of sad to watch people use them as if they meant something. When you use a statistical method you are implicitly endorsing a set of assumptions. If the assumptions aren't true, the results obtained with the methods aren't reliable. They may produce correct answers after all is said and done, but there is no reason to expect them to do so.
and despite the naysayers above it certainly isn't impossible to set some bounds on expected movement
Not with statistical methods alone. You can try to apply statistics, and they will work just until they stop working.
posted by ikkyu2 at 10:34 AM on April 26, 2008
No, actually, they don't. It's kind of sad to watch people use them as if they meant something. When you use a statistical method you are implicitly endorsing a set of assumptions. If the assumptions aren't true, the results obtained with the methods aren't reliable. They may produce correct answers after all is said and done, but there is no reason to expect them to do so.
and despite the naysayers above it certainly isn't impossible to set some bounds on expected movement
Not with statistical methods alone. You can try to apply statistics, and they will work just until they stop working.
posted by ikkyu2 at 10:34 AM on April 26, 2008
This thread is closed to new comments.
posted by fatllama at 9:11 AM on April 24, 2008