Hi, Elitetraders What are the approaches to measure probability that in the next n-minutes time return of an asset just exceeds some r? Can it depend, for example on rolling std? Any clues or hints are appreciated, including math sophisticated ones. Just need direction where to dig.
What do you mean by just exceeds? The probability that the return will be exactly the same as some precise value is of course zero (ignoring discretization effects in prices). The probability that the return will equal or exceed some r will depend on the distribution of returns, which for short horizons will be zero mean and will depend entirely on the standard deviation (ignoring higher moments). GAT
One of the single most abused terms in the futures trading vernacular is "high probability" in which probability, high or otherwise , has not been measured or determined. "High probability" is used like salt is to cooking; it is added to titles, claims, performance etc. all with a single particle of knowledge or understanding. Virtually no one understands actual probability or what it means; if you were so suddenly up and calculate it for real, it would be swamped out by the hundreds of false claims of the same term.
These are some classic corruptions for "high probability": such as likely to succeed (having measured nothing); or meaning trade set ups that occur infrequently but are profitable when they happen (again, having no measured performance or frequency). It is more of a puffery marketing term. Based on failure of market to distribute equally, I use shadow probability for time-based analyses. Try that - maybe after some years of stats.
Hi, You can calculate High Probability easily and it's not going to make you a profitable trader. We have ~50% the price will be higher or lower than the opening price. If you like to know where price will close with 60% probability, you are going to end up with a range. Let's sat ES is 3600 by the opening of day. If the question is where will it be by the end of the day? The answer can be: ES will close the day between $YYY - $XXX within 60% probabiliy. Now $YYY is lower than 3600 and XXX is higher than 3600. But, if price goes below YYY you can not say "Oh I have 60% probability that ES will close above 3600". It's not going to work. That probability was at right at the beginning of the day.
This is all very true, but off-topic and as such maybe worthy of it's own thread? For example, it was revealed in another thread that when Al Brooks talks about a 60-70 % probability - it's just a number that he's pulling out of thin air or rather his 'memory'. Not everything is easily measured (or rather the data to calculate it is not readily available), but I calculate the probability on a lot of stuff I have at hand and I know that the actual numbers would surprise many. Often, it's the opposite of what classical literature would suggest or very close to a 50/50 proposition.
If we take specific point of time, for 1 Minute Returns, how do we determine the sample to calculate standard deviation and which should remain predictive for some future short-term returns?
Well it depends on your holding period. A good rule of thumb is to use a lookback equal to your holding period. So, for example, I use daily data. and my average holding period is about a month. So I use the last 30 days of returns to forecast standard deviation. Shorter and longer periods tend to be less accurate, as the following shows: https://photos.app.goo.gl/uvEUinfxfX7RuWGK8 The graph is the R squared of regressing ex-post vol over 30 days based on vol for the previous X days, you can see the sweet spot is at around X=30 GAT