Trend Following and Financial Maths (Brownian motion, etc.)

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Trading Leech
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Trend Following and Financial Maths (Brownian motion, etc.)

Post by Trading Leech » Wed Jul 13, 2011 7:50 pm

This may be a long shot, but I'll give it a try.

Does trend following have anything at all to do with what people learn in financial mathematics -- things like Brownian motion, the Black-Scholes model, stochastic processes, etc.?

Can the two be linked together in any ways? Have some interesting results been published on this?

I ask because I'm looking for an interesting thesis project for my master's (in financial maths). It would be wonderful if I could somehow mix trend following into it. At least then I would have found something I'm interested in.

UPDATE: One of the most interesting (and important) things about trend following strategies is portfolio and risk management. Could this have something to do, in any way whatsoever, with the traditional "portfolio theory" in the financial literature? It seems far-fetched, since that theory has a lot to do with mathematical constraints and standard deviations and optimization theory, as opposed to what we see in the trend following literature. Correct my if I'm wrong!

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Post by sluggo » Wed Jul 13, 2011 8:27 pm

This is a question for your professor. Ask her.

If she says "ABSOLUTELY NOT!" then it may be unwise or dangerous to submit a thesis that disagrees with your professor's strongly held belief.

If she says "YES, OF COURSE!" then you can probe for canonical examples, well-known analyses, prior authors, and "suggestions for further research" as they say in academia.

If she gives an answer which is neither an emphatic NO! nor a definitive YES! then you need to discuss with her further. You can gauge her enthusiasm about your proposed topic. If she finds it trite or hackneyed or boring, you may want to try something else.

One good place to start might be to learn the particular terminology in use at your specific university. Among YOUR faculty members, what is the academically-approved synonym for Trend Following?

Other pieces of terminology to explore: What do they call a mechanical trading system? What do they call a discretionary trader who doesn't use a system? At your university does someone say "a profitable trading strategy," or perhaps "an Efficient Market Hypothesis Anomaly"? And so forth.

Chris67
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Post by Chris67 » Thu Jul 14, 2011 2:43 am

Trading Leech
Heres what I would tell your professor

All currently held beliefs are utter nonsense about investment theory and portfolio management

OPtion pricing developed by an idiot who went on to cause the biggest hedge fund disaster in history almnost bringing down the Worlds financila system

Modern portfolio theory is the real gem - utter garbage from top to bottom - evidence = all those people who follow it are in trouble and dont make any money - witness teh Worlds pension fund industry on the brink of total disaster and the US mutual fund industry (a good business model - similar to selling crack cocoaine) that has seen 95% of all US mutual funds under perform the SP 500 , none of them have made a bean for their clients in 15 years

Traditional portfolio theory - mixing up stocks and bonds and cash and all that other garbage has failed time and time again

I would also tell your professor to grow a set of balls and get out into the real World

Demon

Post by Demon » Thu Jul 14, 2011 5:22 am

:D Chris! Don't you go holding back now..

Chris67
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Post by Chris67 » Thu Jul 14, 2011 6:05 am

hehe YEAH it was a bit aggressive
Trouble is the truth always hurts !!

Trading Leech
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Post by Trading Leech » Thu Jul 14, 2011 12:00 pm

Chris67 wrote:hehe YEAH it was a bit aggressive
Trouble is the truth always hurts !!
Hehehe, you are completely right. However, for better or worse (probably worse), I chose financial mathematics as my field and I guess I'll just have to go with the flow until I graduate. But yeah, I'm beginning to realize how this theory has absolutely nothing to do with reality.

It's pity... :(

Chris67
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Post by Chris67 » Thu Jul 14, 2011 2:48 pm

Trading Leech - I think your ina good spot for what your doing and if you are making those kinds of observations - about the theories being pretty nonsensical - then that will stand you in good stead going forward - what is fairly inotolerable are those who buy the theory hook line and sinker
So being less aggressive :oops: If I were in your shoes and had a chance to do a thesis I would love to right
" how modern portfolio theory has dismally failed and how long trend following has effectively blown the theory out of the water"

PM me for some research info if you need - I'd love to chat more on this stuff

Trading Leech
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Post by Trading Leech » Sun Jul 17, 2011 10:34 am

Chris67 wrote:Trading Leech - I think your ina good spot for what your doing and if you are making those kinds of observations - about the theories being pretty nonsensical - then that will stand you in good stead going forward - what is fairly inotolerable are those who buy the theory hook line and sinker
So being less aggressive :oops: If I were in your shoes and had a chance to do a thesis I would love to right
" how modern portfolio theory has dismally failed and how long trend following has effectively blown the theory out of the water"

PM me for some research info if you need - I'd love to chat more on this stuff
Did you get my PM? There were some problems with PMs this weekend it seems, so I'm not sure...

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Re: Trend Following and Financial Maths (Brownian motion, et

Post by mojojojo » Thu Jul 28, 2011 3:23 pm

Trading Leech wrote:This may be a long shot, but I'll give it a try.

Does trend following have anything at all to do with what people learn in financial mathematics -- things like Brownian motion, the Black-Scholes model, stochastic processes, etc.?

Can the two be linked together in any ways? Have some interesting results been published on this?

I ask because I'm looking for an interesting thesis project for my master's (in financial maths). It would be wonderful if I could somehow mix trend following into it. At least then I would have found something I'm interested in.

UPDATE: One of the most interesting (and important) things about trend following strategies is portfolio and risk management. Could this have something to do, in any way whatsoever, with the traditional "portfolio theory" in the financial literature? It seems far-fetched, since that theory has a lot to do with mathematical constraints and standard deviations and optimization theory, as opposed to what we see in the trend following literature. Correct my if I'm wrong!
My take ...

Yes. Trend following is about trying to identify a trend and jumping in on it. There is no correct way to identify a trend. If you can find some complex stochastic process or what ever that can do it, then your good.

On a different note, there have been comments by well known trend followers who have stated that simple signals work and that it's about risk management and portfolio construction. You can definitely spend time using your math skills to work on this. Read some stuff by Ralph Vince

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Post by drm7 » Thu Jul 28, 2011 5:10 pm

Trend-following takes advantage of the nature of financial markets to have "fat tails" - you cut losers (which protects you from the downside fat tail) and let winners run (which reaps the rewards of the upside fat tail.) The trades in the middle cancel each other out.

You can look at kurtosis, skewness, volatility smiles, etc. Try to come up with a trend-following "formula" (i.e. long-term profit = fat tail profit - (fat tail loss - stop loss)). You can juggle different timeframes and instruments. I have no idea if such a formula exists, maybe it will get you a degree!

Trading Leech
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Re: Trend Following and Financial Maths (Brownian motion, et

Post by Trading Leech » Sat Jul 30, 2011 9:56 pm

mojojojo wrote: My take ...

Yes. Trend following is about trying to identify a trend and jumping in on it. There is no correct way to identify a trend. If you can find some complex stochastic process or what ever that can do it, then your good.

On a different note, there have been comments by well known trend followers who have stated that simple signals work and that it's about risk management and portfolio construction. You can definitely spend time using your math skills to work on this. Read some stuff by Ralph Vince
I somehow doubt I can find a stochastic process to describe those trends. I mean, we have the Black-Scholes process (which is the simplest of them all, with a fixed mean and volatility, i.e. silly). The more complex ones add some twists, such as jumps and random volatilities. The problem though is that these models assume some silly things such as mean reversion. I guess I could keep searching for something, but I'm not sure how it will go.

As for Ralph Vince: Interesting! Didn't know about him. As I peek into his books on Amazon, it seems that they have at least something to do with trend following, i.e. I see such things as "drawdowns", "risk of ruin", etc. Very interesting indeed. I'm just wondering why he didn't identify himself as a "trend follower". How did you hear of him? Was it in the context of trend following per se, or something else?

Trading Leech
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Post by Trading Leech » Sat Jul 30, 2011 10:11 pm

drm7 wrote:Trend-following takes advantage of the nature of financial markets to have "fat tails" - you cut losers (which protects you from the downside fat tail) and let winners run (which reaps the rewards of the upside fat tail.) The trades in the middle cancel each other out.

You can look at kurtosis, skewness, volatility smiles, etc. Try to come up with a trend-following "formula" (i.e. long-term profit = fat tail profit - (fat tail loss - stop loss)). You can juggle different timeframes and instruments. I have no idea if such a formula exists, maybe it will get you a degree!
Yeah, thanks for these tips. Statistics could indeed form an interesting part of the research!

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Re: Trend Following and Financial Maths (Brownian motion, et

Post by mojojojo » Tue Aug 09, 2011 9:59 am

Trading Leech wrote:
mojojojo wrote: My take ...

Yes. Trend following is about trying to identify a trend and jumping in on it. There is no correct way to identify a trend. If you can find some complex stochastic process or what ever that can do it, then your good.

On a different note, there have been comments by well known trend followers who have stated that simple signals work and that it's about risk management and portfolio construction. You can definitely spend time using your math skills to work on this. Read some stuff by Ralph Vince
I somehow doubt I can find a stochastic process to describe those trends. I mean, we have the Black-Scholes process (which is the simplest of them all, with a fixed mean and volatility, i.e. silly). The more complex ones add some twists, such as jumps and random volatilities. The problem though is that these models assume some silly things such as mean reversion. I guess I could keep searching for something, but I'm not sure how it will go.

As for Ralph Vince: Interesting! Didn't know about him. As I peek into his books on Amazon, it seems that they have at least something to do with trend following, i.e. I see such things as "drawdowns", "risk of ruin", etc. Very interesting indeed. I'm just wondering why he didn't identify himself as a "trend follower". How did you hear of him? Was it in the context of trend following per se, or something else?
I just used stochastic process as an example of something that popped into my head.

As far as Mr Vince, I heard of him through this site a while ago. Mainly when it comes to position sizing.

Click on the search feature and put his name in. You will find his name does come up every so often.

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One thought

Post by PNW_Trader » Mon Aug 15, 2011 10:35 pm

Here's a thought - generate a number of price data sets with a random walk process. Then, feed these into a trend following system and see what happens. Now, do the same process with real price data. Compare the results with statistical inference tests.

Descriptively look at a 2x2 table of random data/real data and make money/lose money. Depending on which quadrant your result resides there would be some interesting interpretation to be made.

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Andrew Lo

Post by Mike S » Tue Sep 13, 2011 9:19 pm

Andrew Lo - MIT finance professor - has done some work on replication of LTTF returns.

His work on hedge funds is great all around and useful to study if you're a quant finance guy interested in making money instead of models.

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