My trend following strategy and experience

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305pelusa
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Re: My trend following strategy and experience

Post by 305pelusa » Mon Jan 13, 2020 5:57 pm

willthrill81 wrote:
Mon Jan 13, 2020 4:47 pm

That being said, MC simulations produce much fatter tails than what statistical analysis says they should.
I’m not sure why you keep saying this but it’s wrong. MC simulators produce the exact, correct fat tail size that statistical analysis says they should based on the St Dev provided. You can argue the stock market has thinner tails than what a normal distribution or MC simulator might predict. I know it sounds pedantic, but it’s an important difference.
willthrill81 wrote:
Mon Jan 13, 2020 4:47 pm
This makes sense because most MC simulations assume that annual returns are not in any way correlated with future returns (i.e. a truly random walk), which most finance experts no longer believe to be true. The lag between current returns and future returns may be long and quite variable, but it's certainly been there nonetheless. I don't know that any of us expects to have a period in the stock market as good as 1995-1999 followed immediately by 2010-2017 followed immediately by 1982-1989, but MC simulations can and do produce precisely these kinds of scenarios.
No, the reason why MC simulator displays more extremes than history is for the statistical fundamental law I said before (and Kitces acknowledges). Standard error is always smaller than standard deviation.

That said, the market HAS displayed reversion to the mean. That adds to that. But were there no such reversion, we’d still see the MC simulator show more extreme results.
willthrill81 wrote:
Mon Jan 13, 2020 4:47 pm

Is it useful to investors for a simulation to model a scenario like the Great Depression followed immediately by 2008-2009 followed immediately by 1970s' stagflation? Such a sequence would wipe out virtually any conventional buy-and-hold strategy at least.
This is a matter of opinion. You only think it’s not worth simulating because you think it’s impossible to occur. But you only think I it’s impossible to occur because it has never happened in the past. This is precisely what causes Black Swan events by the way.

The way I handle it is by aiming for a reasonable % of success in my MC simulator. So I acknowledge their possibility and then decide whether the opportunity cost of preparing for it is worth it.

In this context (testing Trend following), I might test a strategy against simulation and simply toss out the really extreme results, acknowledging that they’re so unlikely, in willing to take the risk. This is superior, IMO, than not simulating at all and just testing on past data.

Just my 2 cents.

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willthrill81
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Re: My trend following strategy and experience

Post by willthrill81 » Mon Jan 13, 2020 6:10 pm

305pelusa wrote:
Mon Jan 13, 2020 5:57 pm
willthrill81 wrote:
Mon Jan 13, 2020 4:47 pm

That being said, MC simulations produce much fatter tails than what statistical analysis says they should.
I’m not sure why you keep saying this but it’s wrong. MC simulators produce the exact, correct fat tail size that statistical analysis says they should based on the St Dev provided. You can argue the stock market has thinner tails than what a normal distribution or MC simulator might predict. I know it sounds pedantic, but it’s an important difference.
No, I know precisely what I'm talking about. There is a statistically significant difference (i.e. more than what we would expect due to random chance) between historic returns and MC simulated returns. So you can either believe that (1) historical returns have been statistically anomalous in that they have been better than what a model says they should or (2) the model is wrong. So when I'm saying "should," I mean it in the statistical sense.

When a model doesn't fit the data, the model is most likely flawed.
305pelusa wrote:
Mon Jan 13, 2020 5:57 pm
willthrill81 wrote:
Mon Jan 13, 2020 4:47 pm
This makes sense because most MC simulations assume that annual returns are not in any way correlated with future returns (i.e. a truly random walk), which most finance experts no longer believe to be true. The lag between current returns and future returns may be long and quite variable, but it's certainly been there nonetheless. I don't know that any of us expects to have a period in the stock market as good as 1995-1999 followed immediately by 2010-2017 followed immediately by 1982-1989, but MC simulations can and do produce precisely these kinds of scenarios.
No, the reason why MC simulator displays more extremes than history is for the statistical fundamental law I said before (and Kitces acknowledges). Standard error is always smaller than standard deviation.

That said, the market HAS displayed reversion to the mean. That adds to that. But were there no such reversion, we’d still see the MC simulator show more extreme results.
willthrill81 wrote:
Mon Jan 13, 2020 4:47 pm

Is it useful to investors for a simulation to model a scenario like the Great Depression followed immediately by 2008-2009 followed immediately by 1970s' stagflation? Such a sequence would wipe out virtually any conventional buy-and-hold strategy at least.
This is a matter of opinion. You only think it’s not worth simulating because you think it’s impossible to occur. But you only think I it’s impossible to occur because it has never happened in the past. This is precisely what causes Black Swan events by the way.

The way I handle it is by aiming for a reasonable % of success in my MC simulator. So I acknowledge their possibility and then decide whether the opportunity cost of preparing for it is worth it.

In this context (testing Trend following), I might test a strategy against simulation and simply toss out the really extreme results, acknowledging that they’re so unlikely, in willing to take the risk. This is superior, IMO, than not simulating at all and just testing on past data.

Just my 2 cents.
I never said that "it's impossible" for the markets to have extremely poor returns. Here's what I actually said.
But we've already seen governments default on their bond obligations, stock markets permanently go to zero or go nowhere for decades, etc.
If you're going to misquote me, I will cease responding to you altogether.

I fully acknowledge that the markets can go to zero. But I don't believe that you can sufficiently prepare for such events through Boglehead-approved means. If you do, again, go for it.
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

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305pelusa
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Re: My trend following strategy and experience

Post by 305pelusa » Mon Jan 13, 2020 6:35 pm

willthrill81 wrote:
Mon Jan 13, 2020 6:10 pm

No, I know precisely what I'm talking about. There is a statistically significant difference (i.e. more than what we would expect due to random chance) between historic returns and MC simulated returns.
The MC model comes from the parameters of the historic returns. So I find it very hard to believe that there’s a statistically significant difference between historic returns and the simulations generates by looking at the parameters of such returns. In fact, I don’t even know how you’d measure that.

You claim there is so post your evidence?
willthrill81 wrote:
Mon Jan 13, 2020 6:10 pm

When a model doesn't fit the data, the model is most likely flawed.
Well the model comes from the data so I’m having a hard time envisioning how it wouldn’t do at least a reasonable job fitting it.

Care to provide evidence?

willthrill81 wrote:
Mon Jan 13, 2020 6:10 pm

I never said that "it's impossible" for the markets to have extremely poor returns. Here's what I actually said.
But we've already seen governments default on their bond obligations, stock markets permanently go to zero or go nowhere for decades, etc.
If you're going to misquote me, I will cease responding to you altogether.
First of all, chillax Will. I’m not misquoting you, I might be misinterpreting you. No reason to get angry, we’re all friends here. :happy You wrote:
willthrill81 wrote:
Mon Jan 13, 2020 4:47 pm
I don't know that any of us expects to have a period in the stock market as good as 1995-1999 followed immediately by 2010-2017 followed immediately by 1982-1989, but MC simulations can and do produce precisely these kinds of scenarios.
Clearly, I took your “I don’t expect X to happen” with “I don’t believe X will happen”. For all practical purposes, these are the same since you are making the same decisiones someone who truly believes it’s impossible is taking.

My bigger point that you seem to miss is that you can have your cake and eat it too. Use MC simulations to test your strategy and just toss out the tails that you believe are not worth preparing.

But you seem to just prefer not using simulations at all and only relying on backtest. Oh well.

UberGrub
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Re: My trend following strategy and experience

Post by UberGrub » Mon Jan 13, 2020 6:43 pm

willthrill81 wrote:
Mon Jan 13, 2020 4:47 pm

Is it useful to investors for a simulation to model a scenario like the Great Depression followed immediately by 2008-2009 followed immediately by 1970s' stagflation? Such a sequence would wipe out virtually any conventional buy-and-hold strategy at least.
Well if you only use historical data, then you’re assuming a year like 2008 is definitely going to be followed by a year like 2009. So while the simulation might be unrealistic in that it might place 2008, then 1929, then 1970s, historical simulations are also making a similar problem.

The advantage of a MC simulator is that it might present 2008, and then 1950. Or 1967. Or 1935. Etc. These aren’t drastic extremes and are reasonable expectations. This allows you to really test your strategy.

As 305 said, MC might come with some overly crazy, unrealistic extremes but then you could always toss those out (ex: as long as your strategy offers superior results measured in a certain way, say, 85% of the time, then it’s good enough). I think that’swhat 305 is saying.

marcopolo
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Re: My trend following strategy and experience

Post by marcopolo » Mon Jan 13, 2020 6:45 pm

305pelusa wrote:
Mon Jan 13, 2020 6:35 pm


The MC model comes from the parameters of the historic returns. So I find it very hard to believe that there’s a statistically significant difference between historic returns and the simulations generates by looking at the parameters of such returns. In fact, I don’t even know how you’d measure that.


Well the model comes from the data so I’m having a hard time envisioning how it wouldn’t do at least a reasonable job fitting it.
Perhaps I am missing something, but why would you find it hard to believe that MC simulations based on parameters from the historical data would produce results that don't fit all that well?

The simulation would only fit the data well if the simulation also got the underlying distribution correct. Most MC simulations assume a Guassian distribution. The market returns are not necessarily Gaussian, and they may not really follow any parametric distribution. So, yes you can extract the mean and Std Dev out of historical data, but that does not mean a MC simulation based on those parameters will fit the data all that well in the past, let alone going forward. Even the central limit theorem probably does not help much as the sample size is not that big.
Once in a while you get shown the light, in the strangest of places if you look at it right.

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305pelusa
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Re: My trend following strategy and experience

Post by 305pelusa » Mon Jan 13, 2020 6:46 pm

UberGrub wrote:
Mon Jan 13, 2020 6:43 pm
willthrill81 wrote:
Mon Jan 13, 2020 4:47 pm

Is it useful to investors for a simulation to model a scenario like the Great Depression followed immediately by 2008-2009 followed immediately by 1970s' stagflation? Such a sequence would wipe out virtually any conventional buy-and-hold strategy at least.
Well if you only use historical data, then you’re assuming a year like 2008 is definitely going to be followed by a year like 2009. So while the simulation might be unrealistic in that it might place 2008, then 1929, then 1970s, historical simulations are also making a similar problem.

The advantage of a MC simulator is that it might present 2008, and then 1950. Or 1967. Or 1935. Etc. These aren’t drastic extremes and are reasonable expectations. This allows you to really test your strategy.

As 305 said, MC might come with some overly crazy, unrealistic extremes but then you could always toss those out (ex: as long as your strategy offers superior results measured in a certain way, say, 85% of the time, then it’s good enough). I think that’swhat 305 is saying.
I couldn’t have said that better myself.

Either way, I don’t think Will is going to use an MC simulator. So this conversation is pretty moot.

At the very least, I was hoping to show him the huge advantage of using one and testing his strategy to see how robust it is. And if the extremes are just unreasonable, they can be ignored. Again, have your cake and eat it too.

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305pelusa
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Re: My trend following strategy and experience

Post by 305pelusa » Mon Jan 13, 2020 6:53 pm

marcopolo wrote:
Mon Jan 13, 2020 6:45 pm
305pelusa wrote:
Mon Jan 13, 2020 6:35 pm


The MC model comes from the parameters of the historic returns. So I find it very hard to believe that there’s a statistically significant difference between historic returns and the simulations generates by looking at the parameters of such returns. In fact, I don’t even know how you’d measure that.


Well the model comes from the data so I’m having a hard time envisioning how it wouldn’t do at least a reasonable job fitting it.
Perhaps I am missing something, but why would you find it hard to believe that MC simulations based on parameters from the historical data would produce results that don't fit all that well?

The simulation would only fit the data well if the simulation also got the underlying distribution correct. Most MC simulations assume a Guassian distribution. The market returns are not necessarily Gaussian, and they may not really follow any parametric distribution. So, yes you can extract the mean and Std Dev out of historical data, but that does not mean a MC simulation based on those parameters will fit the data all that well in the past, let alone going forward. Even the central limit theorem probably does not help much as the sample size is not that big.
I’m using the intuition of the CLT and the fact that it’s many years of data. The distribution won’t be a perfect Gaussian (which is why I’m saying it should do a reasonable, but not perfect job). But the distribution would have to be fairly skewed before it would be statistically significantly different from the Gaussian that comes from its St Dev. Again, that’s just my initial thought.

I’m not saying I’m right or wrong. I’m just skeptical.

Either way, it’s trivially easy to make a MC simulator that has multiple moments other than St Dev. You can add or subtract kurtosis and skewness as desired.

You can also handle Will’s serial correlation point. That is much tougher to do I think and requires more assumptions

marcopolo
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Re: My trend following strategy and experience

Post by marcopolo » Mon Jan 13, 2020 7:06 pm

305pelusa wrote:
Mon Jan 13, 2020 6:53 pm
marcopolo wrote:
Mon Jan 13, 2020 6:45 pm
305pelusa wrote:
Mon Jan 13, 2020 6:35 pm


The MC model comes from the parameters of the historic returns. So I find it very hard to believe that there’s a statistically significant difference between historic returns and the simulations generates by looking at the parameters of such returns. In fact, I don’t even know how you’d measure that.


Well the model comes from the data so I’m having a hard time envisioning how it wouldn’t do at least a reasonable job fitting it.
Perhaps I am missing something, but why would you find it hard to believe that MC simulations based on parameters from the historical data would produce results that don't fit all that well?

The simulation would only fit the data well if the simulation also got the underlying distribution correct. Most MC simulations assume a Guassian distribution. The market returns are not necessarily Gaussian, and they may not really follow any parametric distribution. So, yes you can extract the mean and Std Dev out of historical data, but that does not mean a MC simulation based on those parameters will fit the data all that well in the past, let alone going forward. Even the central limit theorem probably does not help much as the sample size is not that big.
I’m using the intuition of the CLT and the fact that it’s many years of data. The distribution won’t be a perfect Gaussian (which is why I’m saying it should do a reasonable, but not perfect job). But the distribution would have to be fairly skewed before it would be statistically significantly different from the Gaussian that comes from its St Dev. Again, that’s just my initial thought.

I’m not saying I’m right or wrong. I’m just skeptical.

Either way, it’s trivially easy to make a MC simulator that has multiple moments other than St Dev. You can add or subtract kurtosis and skewness as desired.

You can also handle Will’s serial correlation point. That is much tougher to do I think and requires more assumptions

Yes, you could do some of the things you mention to improve the fit, but most MC simulations do NOT do any of those. So, that is why you end up with heavier tails than you actually see in the real data, even though the parameters came from the data to begin with.
Once in a while you get shown the light, in the strangest of places if you look at it right.

marcopolo
Posts: 2787
Joined: Sat Dec 03, 2016 10:22 am

Re: My trend following strategy and experience

Post by marcopolo » Mon Jan 13, 2020 7:12 pm

305pelusa wrote:
Mon Jan 13, 2020 6:53 pm
marcopolo wrote:
Mon Jan 13, 2020 6:45 pm
305pelusa wrote:
Mon Jan 13, 2020 6:35 pm


The MC model comes from the parameters of the historic returns. So I find it very hard to believe that there’s a statistically significant difference between historic returns and the simulations generates by looking at the parameters of such returns. In fact, I don’t even know how you’d measure that.


Well the model comes from the data so I’m having a hard time envisioning how it wouldn’t do at least a reasonable job fitting it.
Perhaps I am missing something, but why would you find it hard to believe that MC simulations based on parameters from the historical data would produce results that don't fit all that well?

The simulation would only fit the data well if the simulation also got the underlying distribution correct. Most MC simulations assume a Guassian distribution. The market returns are not necessarily Gaussian, and they may not really follow any parametric distribution. So, yes you can extract the mean and Std Dev out of historical data, but that does not mean a MC simulation based on those parameters will fit the data all that well in the past, let alone going forward. Even the central limit theorem probably does not help much as the sample size is not that big.
I’m using the intuition of the CLT and the fact that it’s many years of data. The distribution won’t be a perfect Gaussian (which is why I’m saying it should do a reasonable, but not perfect job). But the distribution would have to be fairly skewed before it would be statistically significantly different from the Gaussian that comes from its St Dev. Again, that’s just my initial thought.

I’m not saying I’m right or wrong. I’m just skeptical.

Either way, it’s trivially easy to make a MC simulator that has multiple moments other than St Dev. You can add or subtract kurtosis and skewness as desired.

You can also handle Will’s serial correlation point. That is much tougher to do I think and requires more assumptions

Here is an article that examines how well (or poorly) the market returns fit a Guassian model, and suggest a Laplace distribution as a better fit. But, I am not aware of any MC simulators that use this, but it would not be that hard to build one.

https://sixfigureinvesting.com/2016/03/ ... of-normal/
Once in a while you get shown the light, in the strangest of places if you look at it right.

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305pelusa
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Re: My trend following strategy and experience

Post by 305pelusa » Mon Jan 13, 2020 8:22 pm

marcopolo wrote:
Mon Jan 13, 2020 7:12 pm
305pelusa wrote:
Mon Jan 13, 2020 6:53 pm
marcopolo wrote:
Mon Jan 13, 2020 6:45 pm
305pelusa wrote:
Mon Jan 13, 2020 6:35 pm


The MC model comes from the parameters of the historic returns. So I find it very hard to believe that there’s a statistically significant difference between historic returns and the simulations generates by looking at the parameters of such returns. In fact, I don’t even know how you’d measure that.


Well the model comes from the data so I’m having a hard time envisioning how it wouldn’t do at least a reasonable job fitting it.
Perhaps I am missing something, but why would you find it hard to believe that MC simulations based on parameters from the historical data would produce results that don't fit all that well?

The simulation would only fit the data well if the simulation also got the underlying distribution correct. Most MC simulations assume a Guassian distribution. The market returns are not necessarily Gaussian, and they may not really follow any parametric distribution. So, yes you can extract the mean and Std Dev out of historical data, but that does not mean a MC simulation based on those parameters will fit the data all that well in the past, let alone going forward. Even the central limit theorem probably does not help much as the sample size is not that big.
I’m using the intuition of the CLT and the fact that it’s many years of data. The distribution won’t be a perfect Gaussian (which is why I’m saying it should do a reasonable, but not perfect job). But the distribution would have to be fairly skewed before it would be statistically significantly different from the Gaussian that comes from its St Dev. Again, that’s just my initial thought.

I’m not saying I’m right or wrong. I’m just skeptical.

Either way, it’s trivially easy to make a MC simulator that has multiple moments other than St Dev. You can add or subtract kurtosis and skewness as desired.

You can also handle Will’s serial correlation point. That is much tougher to do I think and requires more assumptions

Here is an article that examines how well (or poorly) the market returns fit a Guassian model, and suggest a Laplace distribution as a better fit. But, I am not aware of any MC simulators that use this, but it would not be that hard to build one.

https://sixfigureinvesting.com/2016/03/ ... of-normal/
First of all, I'm well aware that daily market returns are not normally distributed. But we're talking about yearly market returns. Thanks to the CLT, summing up enough independently, non-normally distributed variables leads to somewhat normally distributed results.

Here's a post of someone explaining it to me:
viewtopic.php?p=4627322#p4627322

The posts after that are generally relevant too.

By the way, to be clear. You're posting a link that is claiming that daily stock market returns have fatter tails than normal distributions. So a MC simulator using daily data, if anything, would UNDERSTATE large results. The question at hand is that MC simulations OVERSTATE yearly returns. So it's got nothing to do with stock market fat tails; it's got to do with the difference between sample error, standard deviation, and whether the reversion to the mean of the market has been so statistically significant as to make a Gaussian distribution of yearly returns a useless choice.
marcopolo wrote:
Mon Jan 13, 2020 7:06 pm
305pelusa wrote:
Mon Jan 13, 2020 6:53 pm
marcopolo wrote:
Mon Jan 13, 2020 6:45 pm
305pelusa wrote:
Mon Jan 13, 2020 6:35 pm


The MC model comes from the parameters of the historic returns. So I find it very hard to believe that there’s a statistically significant difference between historic returns and the simulations generates by looking at the parameters of such returns. In fact, I don’t even know how you’d measure that.


Well the model comes from the data so I’m having a hard time envisioning how it wouldn’t do at least a reasonable job fitting it.
Perhaps I am missing something, but why would you find it hard to believe that MC simulations based on parameters from the historical data would produce results that don't fit all that well?

The simulation would only fit the data well if the simulation also got the underlying distribution correct. Most MC simulations assume a Guassian distribution. The market returns are not necessarily Gaussian, and they may not really follow any parametric distribution. So, yes you can extract the mean and Std Dev out of historical data, but that does not mean a MC simulation based on those parameters will fit the data all that well in the past, let alone going forward. Even the central limit theorem probably does not help much as the sample size is not that big.
I’m using the intuition of the CLT and the fact that it’s many years of data. The distribution won’t be a perfect Gaussian (which is why I’m saying it should do a reasonable, but not perfect job). But the distribution would have to be fairly skewed before it would be statistically significantly different from the Gaussian that comes from its St Dev. Again, that’s just my initial thought.

I’m not saying I’m right or wrong. I’m just skeptical.

Either way, it’s trivially easy to make a MC simulator that has multiple moments other than St Dev. You can add or subtract kurtosis and skewness as desired.

You can also handle Will’s serial correlation point. That is much tougher to do I think and requires more assumptions

Yes, you could do some of the things you mention to improve the fit, but most MC simulations do NOT do any of those. So, that is why you end up with heavier tails than you actually see in the real data, even though the parameters came from the data to begin with.
I'll repeat the reason why I believe the MC simulator seems to have bigger extremes. By actually running thousands of simulations, you will be able to see the many parallel universes that history did not show. This is a very basic concept of statistics (standard error vs standard deviation). So in my opinion, historic data is the one understating extremes, not the other way around (since there's only limited historical data). And to be clear, Kitces agrees with me. Once again:
"Of course, it shouldn’t be surprising that Monte Carlo comes up with more extreme best and worst-case scenarios, given that it’s based on 10,000 trials (while the historical data has only 114 series of overlapping data points), and a higher volume of random trials should yield results that are more extreme."

You're claiming the reason is that stock market yearly returns have thinner tails than a normal distribution. That's certainly a new argument, different than Will's serial correlation and different than the link you posted. Do you have evidence for this?

marcopolo
Posts: 2787
Joined: Sat Dec 03, 2016 10:22 am

Re: My trend following strategy and experience

Post by marcopolo » Mon Jan 13, 2020 8:43 pm

305pelusa wrote:
Mon Jan 13, 2020 8:22 pm
marcopolo wrote:
Mon Jan 13, 2020 7:12 pm
305pelusa wrote:
Mon Jan 13, 2020 6:53 pm
marcopolo wrote:
Mon Jan 13, 2020 6:45 pm
305pelusa wrote:
Mon Jan 13, 2020 6:35 pm


The MC model comes from the parameters of the historic returns. So I find it very hard to believe that there’s a statistically significant difference between historic returns and the simulations generates by looking at the parameters of such returns. In fact, I don’t even know how you’d measure that.


Well the model comes from the data so I’m having a hard time envisioning how it wouldn’t do at least a reasonable job fitting it.
Perhaps I am missing something, but why would you find it hard to believe that MC simulations based on parameters from the historical data would produce results that don't fit all that well?

The simulation would only fit the data well if the simulation also got the underlying distribution correct. Most MC simulations assume a Guassian distribution. The market returns are not necessarily Gaussian, and they may not really follow any parametric distribution. So, yes you can extract the mean and Std Dev out of historical data, but that does not mean a MC simulation based on those parameters will fit the data all that well in the past, let alone going forward. Even the central limit theorem probably does not help much as the sample size is not that big.
I’m using the intuition of the CLT and the fact that it’s many years of data. The distribution won’t be a perfect Gaussian (which is why I’m saying it should do a reasonable, but not perfect job). But the distribution would have to be fairly skewed before it would be statistically significantly different from the Gaussian that comes from its St Dev. Again, that’s just my initial thought.

I’m not saying I’m right or wrong. I’m just skeptical.

Either way, it’s trivially easy to make a MC simulator that has multiple moments other than St Dev. You can add or subtract kurtosis and skewness as desired.

You can also handle Will’s serial correlation point. That is much tougher to do I think and requires more assumptions

Here is an article that examines how well (or poorly) the market returns fit a Guassian model, and suggest a Laplace distribution as a better fit. But, I am not aware of any MC simulators that use this, but it would not be that hard to build one.

https://sixfigureinvesting.com/2016/03/ ... of-normal/
First of all, I'm well aware that daily market returns are not normally distributed. But we're talking about yearly market returns. Thanks to the CLT, summing up enough independently, non-normally distributed variables leads to somewhat normally distributed results.

Here's a post of someone explaining it to me:
viewtopic.php?p=4627322#p4627322

The posts after that are generally relevant too.

By the way, to be clear. You're posting a link that is claiming that daily stock market returns have fatter tails than normal distributions. So a MC simulator using daily data, if anything, would UNDERSTATE large results. The question at hand is that MC simulations OVERSTATE yearly returns. So it's got nothing to do with stock market fat tails; it's got to do with the difference between sample error, standard deviation, and whether the reversion to the mean of the market has been so statistically significant as to make a Gaussian distribution of yearly returns a useless choice.
marcopolo wrote:
Mon Jan 13, 2020 7:06 pm
305pelusa wrote:
Mon Jan 13, 2020 6:53 pm
marcopolo wrote:
Mon Jan 13, 2020 6:45 pm
305pelusa wrote:
Mon Jan 13, 2020 6:35 pm


The MC model comes from the parameters of the historic returns. So I find it very hard to believe that there’s a statistically significant difference between historic returns and the simulations generates by looking at the parameters of such returns. In fact, I don’t even know how you’d measure that.


Well the model comes from the data so I’m having a hard time envisioning how it wouldn’t do at least a reasonable job fitting it.
Perhaps I am missing something, but why would you find it hard to believe that MC simulations based on parameters from the historical data would produce results that don't fit all that well?

The simulation would only fit the data well if the simulation also got the underlying distribution correct. Most MC simulations assume a Guassian distribution. The market returns are not necessarily Gaussian, and they may not really follow any parametric distribution. So, yes you can extract the mean and Std Dev out of historical data, but that does not mean a MC simulation based on those parameters will fit the data all that well in the past, let alone going forward. Even the central limit theorem probably does not help much as the sample size is not that big.
I’m using the intuition of the CLT and the fact that it’s many years of data. The distribution won’t be a perfect Gaussian (which is why I’m saying it should do a reasonable, but not perfect job). But the distribution would have to be fairly skewed before it would be statistically significantly different from the Gaussian that comes from its St Dev. Again, that’s just my initial thought.

I’m not saying I’m right or wrong. I’m just skeptical.

Either way, it’s trivially easy to make a MC simulator that has multiple moments other than St Dev. You can add or subtract kurtosis and skewness as desired.

You can also handle Will’s serial correlation point. That is much tougher to do I think and requires more assumptions

Yes, you could do some of the things you mention to improve the fit, but most MC simulations do NOT do any of those. So, that is why you end up with heavier tails than you actually see in the real data, even though the parameters came from the data to begin with.
I'll repeat the reason why I believe the MC simulator seems to have bigger extremes. By actually running thousands of simulations, you will be able to see the many parallel universes that history did not show. This is a very basic concept of statistics (standard error vs standard deviation). So in my opinion, historic data is the one understating extremes, not the other way around (since there's only limited historical data). And to be clear, Kitces agrees with me. Once again:
"Of course, it shouldn’t be surprising that Monte Carlo comes up with more extreme best and worst-case scenarios, given that it’s based on 10,000 trials (while the historical data has only 114 series of overlapping data points), and a higher volume of random trials should yield results that are more extreme."

You're claiming the reason is that stock market yearly returns have thinner tails than a normal distribution. That's certainly a new argument, different than Will's serial correlation and different than the link you posted. Do you have evidence for this?
I think I either mis-stated my point, or it was not clear.

I don't really have a strong opinion on whether or not the real underlying distribution of returns is narrower or fatter than a normal distribution with the same parameters. My only point is that it need not match simulations with the same parameters.

I think it is questionable whether the CLT applies to annual returns. A requirement for CLT is that distributions being summed be independent. Are we sure yearly returns are independent? Maybe.

Your point about MC exposing series of returns that just haven't happened yet is a good one. I do think that is correct. I don't know how to distinguish that from the effect due to the underlying distribution being non-gaussian.
Once in a while you get shown the light, in the strangest of places if you look at it right.

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Re: My trend following strategy and experience

Post by 305pelusa » Mon Jan 13, 2020 9:10 pm

marcopolo wrote:
Mon Jan 13, 2020 8:43 pm
305pelusa wrote:
Mon Jan 13, 2020 8:22 pm
marcopolo wrote:
Mon Jan 13, 2020 7:12 pm
305pelusa wrote:
Mon Jan 13, 2020 6:53 pm
marcopolo wrote:
Mon Jan 13, 2020 6:45 pm


Perhaps I am missing something, but why would you find it hard to believe that MC simulations based on parameters from the historical data would produce results that don't fit all that well?

The simulation would only fit the data well if the simulation also got the underlying distribution correct. Most MC simulations assume a Guassian distribution. The market returns are not necessarily Gaussian, and they may not really follow any parametric distribution. So, yes you can extract the mean and Std Dev out of historical data, but that does not mean a MC simulation based on those parameters will fit the data all that well in the past, let alone going forward. Even the central limit theorem probably does not help much as the sample size is not that big.
I’m using the intuition of the CLT and the fact that it’s many years of data. The distribution won’t be a perfect Gaussian (which is why I’m saying it should do a reasonable, but not perfect job). But the distribution would have to be fairly skewed before it would be statistically significantly different from the Gaussian that comes from its St Dev. Again, that’s just my initial thought.

I’m not saying I’m right or wrong. I’m just skeptical.

Either way, it’s trivially easy to make a MC simulator that has multiple moments other than St Dev. You can add or subtract kurtosis and skewness as desired.

You can also handle Will’s serial correlation point. That is much tougher to do I think and requires more assumptions

Here is an article that examines how well (or poorly) the market returns fit a Guassian model, and suggest a Laplace distribution as a better fit. But, I am not aware of any MC simulators that use this, but it would not be that hard to build one.

https://sixfigureinvesting.com/2016/03/ ... of-normal/
First of all, I'm well aware that daily market returns are not normally distributed. But we're talking about yearly market returns. Thanks to the CLT, summing up enough independently, non-normally distributed variables leads to somewhat normally distributed results.

Here's a post of someone explaining it to me:
viewtopic.php?p=4627322#p4627322

The posts after that are generally relevant too.

By the way, to be clear. You're posting a link that is claiming that daily stock market returns have fatter tails than normal distributions. So a MC simulator using daily data, if anything, would UNDERSTATE large results. The question at hand is that MC simulations OVERSTATE yearly returns. So it's got nothing to do with stock market fat tails; it's got to do with the difference between sample error, standard deviation, and whether the reversion to the mean of the market has been so statistically significant as to make a Gaussian distribution of yearly returns a useless choice.
marcopolo wrote:
Mon Jan 13, 2020 7:06 pm
305pelusa wrote:
Mon Jan 13, 2020 6:53 pm
marcopolo wrote:
Mon Jan 13, 2020 6:45 pm


Perhaps I am missing something, but why would you find it hard to believe that MC simulations based on parameters from the historical data would produce results that don't fit all that well?

The simulation would only fit the data well if the simulation also got the underlying distribution correct. Most MC simulations assume a Guassian distribution. The market returns are not necessarily Gaussian, and they may not really follow any parametric distribution. So, yes you can extract the mean and Std Dev out of historical data, but that does not mean a MC simulation based on those parameters will fit the data all that well in the past, let alone going forward. Even the central limit theorem probably does not help much as the sample size is not that big.
I’m using the intuition of the CLT and the fact that it’s many years of data. The distribution won’t be a perfect Gaussian (which is why I’m saying it should do a reasonable, but not perfect job). But the distribution would have to be fairly skewed before it would be statistically significantly different from the Gaussian that comes from its St Dev. Again, that’s just my initial thought.

I’m not saying I’m right or wrong. I’m just skeptical.

Either way, it’s trivially easy to make a MC simulator that has multiple moments other than St Dev. You can add or subtract kurtosis and skewness as desired.

You can also handle Will’s serial correlation point. That is much tougher to do I think and requires more assumptions

Yes, you could do some of the things you mention to improve the fit, but most MC simulations do NOT do any of those. So, that is why you end up with heavier tails than you actually see in the real data, even though the parameters came from the data to begin with.
I'll repeat the reason why I believe the MC simulator seems to have bigger extremes. By actually running thousands of simulations, you will be able to see the many parallel universes that history did not show. This is a very basic concept of statistics (standard error vs standard deviation). So in my opinion, historic data is the one understating extremes, not the other way around (since there's only limited historical data). And to be clear, Kitces agrees with me. Once again:
"Of course, it shouldn’t be surprising that Monte Carlo comes up with more extreme best and worst-case scenarios, given that it’s based on 10,000 trials (while the historical data has only 114 series of overlapping data points), and a higher volume of random trials should yield results that are more extreme."

You're claiming the reason is that stock market yearly returns have thinner tails than a normal distribution. That's certainly a new argument, different than Will's serial correlation and different than the link you posted. Do you have evidence for this?
I think I either mis-stated my point, or it was not clear.

I don't really have a strong opinion on whether or not the real underlying distribution of returns is narrower or fatter than a normal distribution with the same parameters. My only point is that it need not match simulations with the same parameters.

I think it is questionable whether the CLT applies to annual returns. A requirement for CLT is that distributions being summed be independent. Are we sure yearly returns are independent? Maybe.

Your point about MC exposing series of returns that just haven't happened yet is a good one. I do think that is correct. I don't know how to distinguish that from the effect due to the underlying distribution being non-gaussian.
The requirement for CLT is that daily returns are independent so that the yearly returns look more normal. I don’t have evidence for or against but it seems like a reasonable statement. I’ve seen yearly distributions on the S&P and they look reasonably normal (unlike daily distributions of course). I don’t think skewness and kurtosis are really the biggest factor here.

I’m also skeptical of the serial correlation argument. That implies an ANTI time series momentum effect. If anything, we have seen time-series momentum. Yes I’ve heard about regression to the mean so maybe there’s some of that.

The reality is that simulated data will NOT look like the historical data. What are the odds of that! It will either show more or less extremes. Statistical logic tells us that it will show more extremes by pure chance. And we see that. The only question is if the extremes shown are so large (statistically significant) that there’s actually something else at play. That’s the part I’m skeptical of and perhaps Will will have some material for us to read :)

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Re: My trend following strategy and experience

Post by willthrill81 » Mon Jan 13, 2020 9:26 pm

305pelusa wrote:
Mon Jan 13, 2020 6:35 pm
willthrill81 wrote:
Mon Jan 13, 2020 6:10 pm

No, I know precisely what I'm talking about. There is a statistically significant difference (i.e. more than what we would expect due to random chance) between historic returns and MC simulated returns.
The MC model comes from the parameters of the historic returns. So I find it very hard to believe that there’s a statistically significant difference between historic returns and the simulations generates by looking at the parameters of such returns. In fact, I don’t even know how you’d measure that.

You claim there is so post your evidence?
willthrill81 wrote:
Mon Jan 13, 2020 6:10 pm

When a model doesn't fit the data, the model is most likely flawed.
Well the model comes from the data so I’m having a hard time envisioning how it wouldn’t do at least a reasonable job fitting it.

Care to provide evidence?
Derek Tharp already did in the post on Kitces' web site that I linked to above. Here's a pertinent quote.
s you can see in the graphic above, the most common return that would be selected randomly is 5%, while more extreme values would come up less frequently. Specifically, in a normal distribution, 68% of the values occur within 1 standard deviation of the mean (in this case, a return between -5% and +15%), 95% of the results are within 2 standard deviations (e.g., -15% to 25%), and 99.7% of the values fall within 3 standard deviations (which would be returns from -25% to 35%). In other words, given the parameters above, returns greater than 35% or less than -25% (i.e., more extreme than 3 standard deviations), would only be expected to occur about 0.3% of the time.

However, as noted earlier, a leading criticism of Monte Carlo analyses is that “extreme” returns can occur more often than the 0.3% frequency implied by a normal distribution – in other words, the “tails” of the distribution are “fatter” (i.e., more frequent) than what a normal distribution would project, particularly to the downside (i.e., a catastrophic bear market).
emphasis added

MC simulations that are merely based on purely 'synthetic' data are obviously highly problematic because we cannot have much confidence that such data are worthwhile at all (i.e. 'garbage in, garbage out'). Historic data is certainly preferable in this regard, but then you run into the problem of how much of the historic data to include in each iteration of a specific sequence. Should annual returns be used? How about monthly, or daily? What about three-year periods or decades? You get very different results in MC simulations if you use different periods of time as the unit of analysis.
305pelusa wrote:
Mon Jan 13, 2020 6:35 pm
willthrill81 wrote:
Mon Jan 13, 2020 6:10 pm

I never said that "it's impossible" for the markets to have extremely poor returns. Here's what I actually said.
But we've already seen governments default on their bond obligations, stock markets permanently go to zero or go nowhere for decades, etc.
If you're going to misquote me, I will cease responding to you altogether.
First of all, chillax Will. I’m not misquoting you, I might be misinterpreting you. No reason to get angry, we’re all friends here. :happy You wrote:
willthrill81 wrote:
Mon Jan 13, 2020 4:47 pm
I don't know that any of us expects to have a period in the stock market as good as 1995-1999 followed immediately by 2010-2017 followed immediately by 1982-1989, but MC simulations can and do produce precisely these kinds of scenarios.
Clearly, I took your “I don’t expect X to happen” with “I don’t believe X will happen”. For all practical purposes, these are the same since you are making the same decisiones someone who truly believes it’s impossible is taking.
When some says "you believe X" or "you said Y" and it's not true, I take personal offense at that and will not apologize for feeling that way.

I don't need a MC simulation to tell me that markets can go nowhere for a long time and may go to zero. History has shown that those are possibilities.

At any rate, this discussion about MC simulations is off the thread's topic, so I won't discuss it further here.
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

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Re: My trend following strategy and experience

Post by HomerJ » Mon Jan 13, 2020 9:30 pm

305pelusa wrote:
Mon Jan 13, 2020 8:22 pm
I'll repeat the reason why I believe the MC simulator seems to have bigger extremes. By actually running thousands of simulations, you will be able to see the many parallel universes that history did not show. This is a very basic concept of statistics (standard error vs standard deviation). So in my opinion, historic data is the one understating extremes, not the other way around (since there's only limited historical data). And to be clear, Kitces agrees with me. Once again:
"Of course, it shouldn’t be surprising that Monte Carlo comes up with more extreme best and worst-case scenarios, given that it’s based on 10,000 trials (while the historical data has only 114 series of overlapping data points), and a higher volume of random trials should yield results that are more extreme."
You are missing the fact that annual stock market returns are not independent events.

Some MC simulators account for this (as best they can - that's a whole other argument), many do not.
The J stands for Jay

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Re: My trend following strategy and experience

Post by Barsoom » Mon Jan 13, 2020 9:52 pm

I took a stab at figuring out annual growth rates for myself. Please critique my analysis.

I used the Shiller data set, real total return price (which includes dividends and is adjusted for inflation).

Since the Shiller data set is a monthly snapshot of S&P 500 data going back to 1871, I have 1,776 monthly YoY comparisons for calculating YoY percent change. From this data, I removed the extreme outliers (the bottom and top 1%) and used the rest. This took out some extreme numbers in 1933.

With the remaining 1,741 data points, I ran it through Excel's Percentile function to extract the key probabilistic data points. Here is what I found:
  • P01: -32.64%
  • P10: -15.10%
  • P20: -7.00%
  • P30: -1.00%
  • P40: +4.00%
  • P50: +8.20% (median value)
  • P60: +12.20%
  • P70: +17.20%
  • P80: +23.00%
  • P90: +30.60%
  • P99: +48.20%
  • Arithmetic Mean: +8.01%
  • Mode: +7.70% (11 occurrences)
So, half the growth rates are greater than 8.2%, and half are less.

There is a 10‰ chance of decreases lower than - 15.1%, and a 10% chance of growth higher than 30.6%.

-B

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Re: My trend following strategy and experience

Post by 305pelusa » Mon Jan 13, 2020 10:04 pm

willthrill81 wrote:
Mon Jan 13, 2020 9:26 pm
When some says "you believe X" or "you said Y" and it's not true, I take personal offense at that and will not apologize for feeling that way.
Boy you certainly do. Didn't realize this would be such a big deal. Won't happen again chief.
willthrill81 wrote:
Mon Jan 13, 2020 9:26 pm
At any rate, this discussion about MC simulations is off the thread's topic, so I won't discuss it further here.
Ah well all right then. Nothing more to say then.
HomerJ wrote:
Mon Jan 13, 2020 9:30 pm
305pelusa wrote:
Mon Jan 13, 2020 8:22 pm
I'll repeat the reason why I believe the MC simulator seems to have bigger extremes. By actually running thousands of simulations, you will be able to see the many parallel universes that history did not show. This is a very basic concept of statistics (standard error vs standard deviation). So in my opinion, historic data is the one understating extremes, not the other way around (since there's only limited historical data). And to be clear, Kitces agrees with me. Once again:
"Of course, it shouldn’t be surprising that Monte Carlo comes up with more extreme best and worst-case scenarios, given that it’s based on 10,000 trials (while the historical data has only 114 series of overlapping data points), and a higher volume of random trials should yield results that are more extreme."
You are missing the fact that annual stock market returns are not independent events.

Some MC simulators account for this (as best they can - that's a whole other argument), many do not.
Yeah there's some of that as well.

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Re: My trend following strategy and experience

Post by BlueEars » Mon Jan 13, 2020 10:34 pm

I really think the MC discussion was getting overworked here.

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Re: My trend following strategy and experience

Post by klrjaa » Tue Jan 14, 2020 10:33 am

BlueEars wrote:
Mon Jan 13, 2020 10:34 pm
I really think the MC discussion was getting overworked here.
Did you look at the allocate smartly stuff? You had indicated the a mechanism to evaluate was needed which I believe I provided in my response. Again goes to trying to determine what's the singly best approach is a fools errand IMO and better to spread ones bets from the get go. But if Will is good with his system so am I as the discipline to follow any system is the hardest part so good for him

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Re: My trend following strategy and experience

Post by BlueEars » Tue Jan 14, 2020 11:21 am

klrjaa wrote:
Tue Jan 14, 2020 10:33 am
BlueEars wrote:
Mon Jan 13, 2020 10:34 pm
I really think the MC discussion was getting overworked here.
Did you look at the allocate smartly stuff? You had indicated the a mechanism to evaluate was needed which I believe I provided in my response. Again goes to trying to determine what's the singly best approach is a fools errand IMO and better to spread ones bets from the get go. But if Will is good with his system so am I as the discipline to follow any system is the hardest part so good for him
I am not sure what page you are referring to. I did look back several pages. There are so many posts here that get very long because of multiple quoting which I think is kind of getting out of hand. People should sometimes edit the quoted parts down to show what they are really responding to. But that takes some time. My pet peeve. :|

Will is allocating (among asset classes, not stock/bond ratio) via a timing methodology akin to Dual Momentum. That is the sort of thing I have been doing for over 10 years using my own methods.

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Re: My trend following strategy and experience

Post by willthrill81 » Tue Jan 14, 2020 11:42 am

BlueEars wrote:
Tue Jan 14, 2020 11:21 am
Will is allocating (among asset classes, not stock/bond ratio) via a timing methodology akin to Dual Momentum. That is the sort of thing I have been doing for over 10 years using my own methods.
Have you pleased with your strategy's performance to date?
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

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Re: My trend following strategy and experience

Post by BlueEars » Tue Jan 14, 2020 12:43 pm

willthrill81 wrote:
Tue Jan 14, 2020 11:42 am
BlueEars wrote:
Tue Jan 14, 2020 11:21 am
Will is allocating (among asset classes, not stock/bond ratio) via a timing methodology akin to Dual Momentum. That is the sort of thing I have been doing for over 10 years using my own methods.
Have you pleased with your strategy's performance to date?
Yes but with caveats. The in/out timing part (stocks vs bonds) has kept me fully in the market during those years so that is the same outcome so far as buy-hold. The selection between asset classes has worked pretty well with lots of tinkering by me along the way. This is a spreadsheet run approach and if I find a better way to manage rules I go for it. I'm retired so have the time to do this and all this is done in retirement accounts.

I keep a tally with another 2 portfolio designs to benchmark against. My current approach, one based on Wellington fund plus added international stocks, and one that is fixed like Bogleheads. My approach has worked out in backtesting to beat the other portfolios but not by a country mile ... maybe 1.5% better for a 60/40 portfolio (better for just the equities). I think going forward with my latest idea it will do much better in comparison. Even if I just get 2% more out of the asset selection part of the method it will go a long ways to finance our current living standards.

The real test will be how things go when the we enter a recession and stocks tank. The jury is always out. :happy

I allocate 40% of stocks to US/International and 60% to US only. The US/International part has been mostly in US stocks so that has worked out well this last decade. For the US/International I allocate 40% to large caps (VFIAX or VFWAX) and 60% to small/mid caps (VMVAX/VMGMX or VINEX).

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Re: My trend following strategy and experience

Post by klrjaa » Tue Jan 14, 2020 1:27 pm

BlueEars wrote:
Tue Jan 14, 2020 11:21 am
klrjaa wrote:
Tue Jan 14, 2020 10:33 am
BlueEars wrote:
Mon Jan 13, 2020 10:34 pm
I really think the MC discussion was getting overworked here.
Did you look at the allocate smartly stuff? You had indicated the a mechanism to evaluate was needed which I believe I provided in my response. Again goes to trying to determine what's the singly best approach is a fools errand IMO and better to spread ones bets from the get go. But if Will is good with his system so am I as the discipline to follow any system is the hardest part so good for him
I am not sure what page you are referring to. I did look back several pages. There are so many posts here that get very long because of multiple quoting which I think is kind of getting out of hand. People should sometimes edit the quoted parts down to show what they are really responding to. But that takes some time. My pet peeve. :|

Will is allocating (among asset classes, not stock/bond ratio) via a timing methodology akin to Dual Momentum. That is the sort of thing I have been doing for over 10 years using my own methods.
tues jan 7 908 am thanks. Starts with "When AS introduces a new model..."

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Re: My trend following strategy and experience

Post by BlueEars » Tue Jan 14, 2020 1:39 pm

klrjaa wrote:
Tue Jan 14, 2020 1:27 pm
...
tues jan 7 908 am thanks. Starts with "When AS introduces a new model..."
Yes, I did look at this some more and thanks. I should look even more.

What I find is that reading other ideas, even if I reject them, stimulate me to think in somewhat different ways. This at times has led to new ideas along the path that I am following. This is what I like about Bogleheads, but there is a lot of chaff among the wheat. One needs patience.

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Re: My trend following strategy and experience

Post by Hydromod » Tue Jan 14, 2020 2:14 pm

I enjoy allocate smartly too. Lots of info to consider...

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Re: My trend following strategy and experience

Post by klrjaa » Tue Jan 14, 2020 2:42 pm

Hydromod wrote:
Tue Jan 14, 2020 2:14 pm
I enjoy allocate smartly too. Lots of info to consider...
@ hyrdo and blue....Markets way too unpredictable IMO to think any of us have it figured out enuf mathematically (not saying Will here) which is why I go for the blended approach of combining 5-6 strategies @ 10-20% each to formulate the whole. Way better overall risk/return profile than trying to determine "the" optimal approach. I would encourage you to take it for a one month test drive; I think you'll be shockingly overwhelmed with the what if combine strategies, traunching, and other advanced features behind the paywall. No sales pitch, promise.

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Re: My trend following strategy and experience

Post by Uncorrelated » Wed Jan 15, 2020 12:10 pm

klrjaa wrote:
Tue Jan 14, 2020 2:42 pm
Hydromod wrote:
Tue Jan 14, 2020 2:14 pm
I enjoy allocate smartly too. Lots of info to consider...
@ hyrdo and blue....Markets way too unpredictable IMO to think any of us have it figured out enuf mathematically (not saying Will here) which is why I go for the blended approach of combining 5-6 strategies @ 10-20% each to formulate the whole. Way better overall risk/return profile than trying to determine "the" optimal approach. I would encourage you to take it for a one month test drive; I think you'll be shockingly overwhelmed with the what if combine strategies, traunching, and other advanced features behind the paywall. No sales pitch, promise.
Blending different strategies together is precisely an attempt to find the optimal strategy with the tools you have. I think you're making a huge mistake by thinking such an approach has any chance of outperforming the markets on a risk adjusted basis.
willthrill81 wrote:
Mon Jan 13, 2020 4:33 pm
I'm not lamenting over anything. Read the context of the exchange between myself and Uncorrelated. He believes that we can find the 'optimal' trend following strategy for the future. I do not for multiple reasons, not the least of which is because (1) there are an infinite number of trend following strategies, so it is mathematically impossible to even backtest them all and (2) what was optimal in the past is not likely to be optimal in the future. Yes, MC simulations illustrate what might happen, but we don't know that any of the 'possible futures' that they examine will match up with reality.
I think there is a big disconnect between my methodology and your methodology. My methodology generally starts with an idea to exploit market inefficiency, or model of the market. Then I formulate an optimization problem that maximizes the utility under this model. Then I can say that my solution is optimal under this model or with these assumptions. This doesn't mean it's the best possible solution out of all market timing solutions, because both my model and knowledge are imperfect.

Your approach is different. You formulate a strategy and then you backtest it. I have used this approach with success in the past, it has some advantages but also some disadvantages. There is certainly room for personal disagreement on this topic, let's not get into that right now.

Just like you, I don't believe it is possible to find the optimal trend following approach on anything other than toy models. But so far I haven't said a single thing about optimal trend following. I have been talking about picking sensible score functions aligned with your goal, misconceptions about the markets and optimal asset allocation given that you already have a forecasting algorithm. None of those are hard or depend on perfect knowledge. In fact, the mean variance agent depends on fewer assumptions than your current market timing agent.

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Re: My trend following strategy and experience

Post by Barsoom » Wed Jan 15, 2020 12:19 pm

One of the things I'm looking at with MC is pairing it with Excel's Solver to see if it can find an optimum strategy based on the generated future growth scenarios.

Currently, I'm using only the Retiree Portfolio Model's asset allocations between the taxable, two IRAs, and the two Roth IRAs as the changing variables, maximizing the MC expected value of the portfolio at the last year of the model.

If the results appear credible to people here, I might look at porting the technique to other models (or teaching others to do it) .

-B

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Re: My trend following strategy and experience

Post by BlueEars » Wed Jan 15, 2020 12:23 pm

Uncorrelated wrote:
Wed Jan 15, 2020 12:10 pm
...
I think there is a big disconnect between my methodology and your methodology. My methodology generally starts with an idea to exploit market inefficiency, or model of the market. Then I formulate an optimization problem that maximizes the utility under this model. Then I can say that my solution is optimal under this model or with these assumptions. This doesn't mean it's the best possible solution out of all market timing solutions, because both my model and knowledge are imperfect.

Your approach is different. You formulate a strategy and then you backtest it. I have used this approach with success in the past, it has some advantages but also some disadvantages. There is certainly room for personal disagreement on this topic, let's not get into that right now.
...
Just to point out this thread is titled "My trend following strategy and experience".

Uncorrelated, perhaps you could start a thread on how to go about optimizing a model? I would be interested but a full presentation would be inappropriate in this thread.

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Re: My trend following strategy and experience

Post by klrjaa » Wed Jan 15, 2020 5:54 pm

Uncorrelated wrote:
Wed Jan 15, 2020 12:10 pm
klrjaa wrote:
Tue Jan 14, 2020 2:42 pm
Hydromod wrote:
Tue Jan 14, 2020 2:14 pm
I enjoy allocate smartly too. Lots of info to consider...
@ hyrdo and blue....Markets way too unpredictable IMO to think any of us have it figured out enuf mathematically (not saying Will here) which is why I go for the blended approach of combining 5-6 strategies @ 10-20% each to formulate the whole. Way better overall risk/return profile than trying to determine "the" optimal approach. I would encourage you to take it for a one month test drive; I think you'll be shockingly overwhelmed with the what if combine strategies, traunching, and other advanced features behind the paywall. No sales pitch, promise.
Blending different strategies together is precisely an attempt to find the optimal strategy with the tools you have. I think you're making a huge mistake by thinking such an approach has any chance of outperforming the markets on a risk adjusted basis.
[ quote fixed by admin LadyGeek]

Hi Uncorrelated, thanks for responding. Before I offer evidence I'd like to understand what you consider as "the markets on a risk adjusted basis" Sharpe compared to 60 spy/40 ief sharpe? Other? Just want to make sure I respond with something apples to apples in your mind, thanks and sorry I messed up the highllighting

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Re: My trend following strategy and experience

Post by Uncorrelated » Thu Jan 16, 2020 6:29 pm

BlueEars wrote:
Wed Jan 15, 2020 12:23 pm
Uncorrelated wrote:
Wed Jan 15, 2020 12:10 pm
...
I think there is a big disconnect between my methodology and your methodology. My methodology generally starts with an idea to exploit market inefficiency, or model of the market. Then I formulate an optimization problem that maximizes the utility under this model. Then I can say that my solution is optimal under this model or with these assumptions. This doesn't mean it's the best possible solution out of all market timing solutions, because both my model and knowledge are imperfect.

Your approach is different. You formulate a strategy and then you backtest it. I have used this approach with success in the past, it has some advantages but also some disadvantages. There is certainly room for personal disagreement on this topic, let's not get into that right now.
...
Just to point out this thread is titled "My trend following strategy and experience".

Uncorrelated, perhaps you could start a thread on how to go about optimizing a model? I would be interested but a full presentation would be inappropriate in this thread.
I have plans to create a thread about basic utility theory and mean variance optimization, I have been talking about those topics in various threads. But I probably won't go further than that. The marginal benefit of implementing something like trend following is extremely small compared to the effort you need to put in. If you are interested into optimization I recommend picking up knowledge on linear optimization, search algorithms, AI or machine learning. There isn't any specific field or technique that is most useful, modeling and optimization techniques from almost any field can be applied. It might surprise you to hear that economics knowledge is almost entirely useless.
klrjaa wrote:
Wed Jan 15, 2020 5:54 pm
Hi Uncorrelated, thanks for responding. Before I offer evidence I'd like to understand what you consider as "the markets on a risk adjusted basis" Sharpe compared to 60 spy/40 ief sharpe? Other? Just want to make sure I respond with something apples to apples in your mind, thanks and sorry I messed up the highllighting
For complete strategies I prefer using iso-elastic utility, assuming the markets follow a normal distribution this is calculated as arithmetic_mean_return - 0.5 * stddev^2 * risk_aversion. I generally use a risk aversion of 3 which corresponds to an asset allocation of approximately 60/40. A 1/3 split of total stock market, value and small cap value (without total bond market) can be used as a more stringent benchmark.

But the main problem with trend following isn't choosing the right measurement, but overfitting. There is little hope that in-sample backtests translate to anything useful in practice and running true out of sample backtests is a very hard problem that I leave to people with a statistics degree. Ultimately the question isn't whether trend following works or not (that is impossible to answer), but if you are confident enough in the strategy that you are willing to use it. A large part of that confidence comes from proper out of sample backtests, but since there is no way for me to check whether the proper procedures were followed during the development of the strategy, there is no way I can be confident that a strategy works based on numbers alone. I don't want you to waste any time trying to convince because it ultimately comes down to trust. That is why I mentioned earlier that there is room for disagreement on the specific topic of backtesting techniques.


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Re: My trend following strategy and experience

Post by willthrill81 » Thu Jan 23, 2020 9:07 pm

james22 wrote:
Thu Jan 23, 2020 8:19 pm
Time diversification related:

http://squidarth.com/math/2018/11/27/ergodicity.html

https://ergodicityeconomics.com
How do you see the concept of ergodicity being relevant to my strategy?
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

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Re: My trend following strategy and experience

Post by Uncorrelated » Fri Jan 24, 2020 3:23 am

james22 wrote:
Thu Jan 23, 2020 8:19 pm
Time diversification related:

http://squidarth.com/math/2018/11/27/ergodicity.html

https://ergodicityeconomics.com
That is not related to time diversification. Because all games are independently distributed, the optimal strategy is the same regardless of your time horizon.

To have time diversification, you need something like mean reversion to be present in your data set.

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Re: My trend following strategy and experience

Post by james22 » Fri Jan 24, 2020 10:41 am

Firstly, because sequence matters, avoiding ruin is important.

Secondly, a strategy that provides protection against ruin allows for taking advantage of opportunities.

Taleb: Let me explain the foundation of the problem: All of these analysts who look at you and the stock market assume that if you invest in the stock market, you'll replicate the performance of the stock market. The problem is, if you ever have an "uncle point" -- where you have to liquidate -- then your return will not be the stock market's. It will be the returns to your "uncle point" -- which is negative.

In other words: The market can have a positive expected return, and you have a negative expected return.

It's very similar to Russian roulette. Russian roulette is a very simple example. If you play Russian roulette with a positive expected return of 80% -- or, whatever it is, five out of six?

...

So as an investor you need to think about it in these terms: no investor knows what's going to happen to him or her in the future. You don't know -- I mean, the market may deliver whatever people claim it will deliver. But if you have a drop in the market that may force you to liquidate -- particularly a drop in the market that may correlate with your loss of business elsewhere -- then, automatically, your returns will be the returns from today until that drop in the market. It de-correlates from the market.

...

I tend to make money when the market rallies although I'm short. Because -- typically -- you pick your points -- maybe you're only short for 30% of the year, not the whole year -- so you're dynamically hedged. And you pick your points, and you go in and out.

...

Taleb: If you have tail-hedge protection, then your return will be higher than the market. Because ... you can get more aggressive during the times when people sell.


https://www.fool.com/investing/2018/04/ ... taleb.aspx

https://medium.com/incerto/the-logic-of ... 7bf41029d3

https://www.dropbox.com/s/m2nu1ymugzi48 ... s.pdf?dl=0

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