Attachments: A Simple Mean Reversion Strategy

A Simple Mean Reversion Strategy

#281
Edited 3:38pm Sep 10, 2023 3:13pm | Edited 3:38pm

yoriz
Joined Dec 2016 | Status: Trader | 350 Posts

Quoting Riskcuit

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2. Skew is going to manifest itself in long leads. This doesn’t mean it’s actually real. Think of Brownian motion drawn with coin flips. The results have long leads, meaning it rarely even ends where it started, and will spend most of its time “trending” one way or the other, ending above/below where it started. when you look at the paths in isolation, they all have skew one way or the other, but in aggregation, we know there is no actual skew in the data, and all the observable skew on any one path is cancelled out by the other paths that skewed...

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To test that hypothesis, I changed the script from post #169 to only measure the price drift at each M1 bar if price has changed at least +3% in the previous 24 hours. If skew is not real, you would think averaging over the last 4 years (=1.4M bars) would give symmetric price distribution cones similar to post #169. However, this is what I measure:

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That seems to suggest price is indeed mean reverting! However, price rarely moves +3% in 1 day. It happened only 73 times in the last 4 years, so the above is based on only 1893 M1 bars.

Let's look at the price drift after a -2% change in the previous 24 hours (which happened 625 times in the last 4 years, giving 11696 M1 bars):

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Interesting! Now there doesn't seem to be mean reversion, however, the cones are much wider suggesting after a -2% change the volatility of the markets remains a bit higher than usual...

#282
Sep 10, 2023 3:22pm Sep 10, 2023 3:22pm

Riskcuit
Joined May 2021 | Status: Calculating Probabilities... | 133 Posts

Quoting yoriz

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{quote} To test that hypothesis, I changed the script from post #169 to only measure the price drift at each M1 bar if price has changes at least +3% in the previous 24 hours. If skew is not real, you would think averaging over the last 4 years (=1.4M bars) would give symmetric price distribution cones similar to post #169. However, this is what I measure: {image} That seems to suggest price is indeed mean reverting! However, price rarely moves +3% in 1 day, so the above...

Ignored

very cool graph. With the +3% and -2% graphs, are things changes of + or - 3%, etc? Or only looking at +3% moves (not -3% in last 24hr moves)?

can you draw the graphs with no filtering, so it captures all 1.4m data points?

ri · skuht

#283
Edited 3:53pm Sep 10, 2023 3:31pm | Edited 3:53pm

yoriz
Joined Dec 2016 | Status: Trader | 350 Posts

Quoting Riskcuit

Disliked

With the +3% and -2% graphs, are things changes of + or - 3%, etc? Or only looking at +3% moves (not -3% in last 24hr moves)?

Ignored

The +3% graph picks all M1 bars where price has increased 3% or more during the previous 24 hours. The -2% graph picks all M1 bars where price has decreased 2% or more during the previous 24 hours. Starting from that M1 bar, it looks forward to the next 1, 2, 3, etc. hours and keeps track of the price change. It then selects the 0.135-, 2.275-, 15.865-, 50.000-, 84.135-, 97.725- and 99.865-percentiles from the list of price changes at each hour.

Obviously many of the M1 bars will be "clustered" or adjacent because they all had the same strong move in the previous 24 hours. Assuming there are at least 48 hours between "occurances", then the +3% case had 73 occurances, and the -2% case had 625 occurances.

Quoting Riskcuit

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can you draw the graphs with no filtering, so it captures all 1.4m data points?

Ignored

That is the graph in post #169.

#284
Sep 10, 2023 4:23pm Sep 10, 2023 4:23pm

Riskcuit
Joined May 2021 | Status: Calculating Probabilities... | 133 Posts

Quoting yoriz

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{quote} The +3% graph picks all M1 bars where price has increased 3% or more during the previous 24 hours. The -2% graph picks all M1 bars where price has decreased 2% or more during the previous 24 hours. Starting from that M1 bar, it looks forward to the next 1, 2, 3, etc. hours and keeps track of the price change. It then selects the 0.135-, 2.275-, 15.865-, 50.000-, 84.135-, 97.725- and 99.865-percentiles from the list of price changes at each hour. Obviously many of the M1 bars will be "clustered" or adjacent because they all had the same strong...

Ignored

Thank you! The 3 charts together paint a good picture of what I am trying to describe with skew. If you slice certain parts, it appears like there is some kind of skew. However you are simply slicing down to small sample sizes, where the illusion of skew is only going to grow larger and larger as you slice down to a single path like one PipMeUp has posted where it appears to be obvious that forecasting skew is the way to go.

but once you account for the entire picture, the symmetry or lack of obvious/consistent skew is hard to argue against.

It’s very similar to how a median and mean are different. The median is what you observe in time, where as the mean is what you converge to over time as you increase sample size.

you my never actually observe the mean result in a single sample path, but you inevitably will arrive at it in aggregation.

You may never observe true 0 skew in any sample paths, but you will inevitably arrive to it in aggregation.

ri · skuht

#285
Sep 11, 2023 12:06am Sep 11, 2023 12:06am

clemmo17
Joined Jul 2016 | Status: Trader | 2,534 Posts

Initial thought: This system will work until your counterparty gets tired of you and then it will suddenly claw back everything and then some. Reference: the waste elimination volumes of elephants versus the caloric intake of birds.

Second thought: if you are truly trading small compared to the account size then you are earning the risk free rate at a greater risk than holding bonds. What do you estimate for an annual return on average?

#286
Sep 11, 2023 2:56am Sep 11, 2023 2:56am

PipMeUp
Joined Aug 2011 | Status: Trader | 1,327 Posts

Quoting Riskcuit

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{quote} Thank you! The 3 charts together paint a good picture of what I am trying to describe with skew. If you slice certain parts, it appears like there is some kind of skew. However you are simply slicing down to small sample sizes, where the illusion of skew is only going to grow larger and larger as you slice down to a single path like one PipMeUp has posted where it appears to be obvious that forecasting skew is the way to go. but once you account for the entire picture, the symmetry or lack of obvious/consistent skew is hard to argue against....

Ignored

Unfortunately you have to slice because despite the trend is overall zero it is made of a succession of up, then down, then up trends... You don't trade the average, you average the trades. In math terms the limit of the expectancy is different from the expectancy of the limit.

You are absolutely right when you say that no one can distinguish a real trend from a fluke move. It is even worse. Using excel you can generate normally distributed random walks with a positive expectancy (a controlled environment of which you know the parameters). Hitting F9 you get new ones. In general it goes up but sometimes:

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The sample is so small that the estimated mean is negative instead of the true +0.05. (you need at least 10000 samples to estimate the mean of a normal distribution with 1% tolerence).

I personnally think that even if this a fluke move better be short than right when it happens!

Attached File(s)

RW.xlsx 32 KB | 399 downloads

No greed. No fear. Just maths.

#287
Sep 11, 2023 7:25am Sep 11, 2023 7:25am

alphaomega
Joined Aug 2010 | Status: Stare Into the Lights My Pretties! | 795 Posts

If you are so excited about the success of these simple mean reversion strategies.....then just wait until you (re)discover grid trading! It will blow your mind!
Given enough (infinite?) capital you don't have to worry about statistics, directions and predictions. Why? Because you can exploit the entire price curve.
Now I know some people will jump here to tell me how the numbers don't add up and martingale is hopeless and so on....

And this is the problem here - How to get the right answers if you don't know the right questions?
It's a bit like this new "AI" hype with the language models. It's only as smart as the person asking the questions. If you ask dump questions you will get dump (useless) answers. Not to mention the quality of the database. As the saying goes "garbage in, garbage out".

Ask yourself this:

How the market makers can afford to take the other side of every incoming market order at any price level?
And even more important - Why the "regulators" tried so hard to enforce the FIFO rule on retail FX a few years ago?

#288
Sep 11, 2023 8:00am Sep 11, 2023 8:00am

PipMeUp
Joined Aug 2011 | Status: Trader | 1,327 Posts

Quoting alphaomega

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Given enough (infinite?) capital you don't have to worry about statistics, directions and predictions. Why? Because you can exploit the entire price curve.

Ignored

That's exactly what I mean by "You don't trade the average, you average the trades".

And indeed martingale is not the solution except for people who claim they are so smart they can beat the math until they no longer claim anything when their trade explorer suddenly stops updating...

No greed. No fear. Just maths.

#289
Sep 11, 2023 9:35am Sep 11, 2023 9:35am

Riskcuit
Joined May 2021 | Status: Calculating Probabilities... | 133 Posts

Quoting PipMeUp

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{quote} You don't trade the average, you average the trades.

Ignored

This is exactly what I am saying.

ri · skuht

#290
Sep 11, 2023 10:01am Sep 11, 2023 10:01am

Riskcuit
Joined May 2021 | Status: Calculating Probabilities... | 133 Posts

Quoting alphaomega

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Ask yourself this: How the market makers can afford to take the other side of every incoming market order at any price level? And even more important - Why the "regulators" tried so hard to enforce the FIFO rule on retail FX a few years ago?

Ignored

Thanks for dropping in alphaomega! Big fan of your work!

You guys are really missing the point I am making though. I have explained the exact question quoted in detail multiple times in the thread. Specifically, the information around delta hedging to isolate volatility via gamma accumulation (you don't even need the initial contract either to do it).

This is exactly why they can take the opposite side of any trade and don't give 2 shits about the result of any single path... Please re-read the post. The accumulation of delta hedging in aggregate covers the cost of any and every path the price can take, whether it's up or down, so your PnL is only influenced by volatility.

They do not care about any particular path and therefore the result of a particular contract. They care about the number of occurrences as this is what allows you to "trade the average". CLT through a large number of occurrences is precisely how you "trade the average".

Here are some examples showing how this works for certain price paths, using same inputs:

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You can see how the delta-hedge payoff snaps to the contract's payoff at the end of its life. Whether or not this snaping lands above or below the payoff is the result of the path's volatility relative to the volatility used to price the contract, NOT the direction the path took, or if the option ended OTM, ITM, or ATM. Over time, if the paths consistently have more volatility than what was used in the initial calc, on average, the seller would have spent more buying the contract back than they made selling it. Vice versa if it is lower. So the only thing they are trading is volatility, they do not care about the result of any one path, or where the next path will go (will be bull or bear? Who cares!).

As long as you are concerned about the result of any 1 particular path and trying to predict or forecast it, you have completely missed the point...

ri · skuht

#291
Sep 11, 2023 10:33am Sep 11, 2023 10:33am

d5400
Joined Aug 2015 | Status: Training | 762 Posts

Quoting Riskcuit

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{quote} Thanks for dropping in alphaomega! Big fan of your work! You guys are really missing the point I am making though. I have explained the exact question quoted in detail multiple times in the thread. Specifically, the information around delta hedging to isolate volatility via gamma accumulation (you don't even need the initial contract either to do it). This is exactly why they can take the opposite side of any trade and don't give 2 shits about the result of any single path... Please re-read the post. The accumulation of delta hedging in...

Ignored

I think most of us in the mean reversion camp. For my part I hope to learn more tricks.

1.02^200

#292
Sep 11, 2023 1:17pm Sep 11, 2023 1:17pm

alphaomega
Joined Aug 2010 | Status: Stare Into the Lights My Pretties! | 795 Posts

Quoting Riskcuit

Disliked

{quote} Thanks for dropping in alphaomega! Big fan of your work! You guys are really missing the point I am making though. I have explained the exact question quoted in detail multiple times in the thread. Specifically, the information around delta hedging to isolate volatility via gamma accumulation (you don't even need the initial contract either to do it). This is exactly why they can take the opposite side of any trade and don't give 2 shits about the result of any single path... Please re-read the post. The accumulation of delta hedging in...

Ignored

Do you know the history of LTCM and the end result of their "dynamic hedging" strategy?

#293
Edited 7:31pm Sep 11, 2023 1:29pm | Edited 7:31pm

Riskcuit
Joined May 2021 | Status: Calculating Probabilities... | 133 Posts

Quoting alphaomega

Disliked

{quote} Do you know the history of LTCM and the end result of their "dynamic hedging" strategy?

Ignored

Yes sir! They were “highly leveraged” which caused them to blow up. It’s the same thing that causes anyone who has ever blown up in the past or will blow up in the future. Nothing new or revolutionary about it.

A tale as old as time.

Even with positive EV systems, you will blow up if you don’t stay small.

I am curious though, are you arguing that option market makers don’t dynamically hedge to synthetically sell/buy back the options they trade at mid prices?

Do you think MM firms are forecasting skew to transact across the bid and ask?

ri · skuht