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who has series of random generated price data?

  • #21
  • Feb 19, 2011 1:48pm Feb 19, 2011 1:48pm
Quoting 7bit
You invaded this thread with the bold claim that one could trade a random walk.

Extraordinary claims like this need extraordinary proof.

Instead you come up with the "volatility pumping" example which has nothing to do with trading random walks at all, it is about trading a portfolio of stocks which are not random walks at all, and a flawed excel sheet which also does not implement a random walk as it has become clear after analyzing it.

All arguments were already given in this thread. Simply scroll back and try to understand them....
I didn't make that claim. It was made by Claude Shannon in the 1960s as I duly pointed out. Sufficient references have been given.

Sorry to have to say this, but you may benefit from hearing it:

Your thinking is at the level of a half-educated person, and your manners are at the level of an uneducated person.

Goodbye.
  • #22
  • Feb 19, 2011 1:50pm Feb 19, 2011 1:50pm
Quoting medici
Goodbye.
Your constant insults (which prove that your manners are non-existent) won't help you prove your point or increase your credibility.

Goodbye
  • #23
  • Feb 19, 2011 2:03pm Feb 19, 2011 2:03pm
Quoting 7bit
Your constant insults (which prove that your manners are non-existent) won't help you prove your point or increase your credibility.

Goodbye
Phew...

I have no interest in proving points or building credibility, but to be of help in friendly circumstances.

Getting invited to battles of egos simply tires me. Not interested.

And it isn't an insult to let you know that your thinking, as expressed in this thread, leaves a lot to be asked for - too much to be pointed out in detail. More importantly it is beside the point of the thread - that of assisting bobwang.
  • #24
  • Feb 19, 2011 2:17pm Feb 19, 2011 2:17pm
Quoting medici
And it isn't an insult to let you know that your thinking, as expressed in this thread, leaves a lot to be asked for
If you cannot follow the abstract levels of my thinking then I can understand this, not many people can follow it, but this does not give you the right to insult me by calling my thinking "half-educated" only because you can't (and don't even want to) understand it.

end of discussion + unsubscribe.
  • #25
  • Feb 19, 2011 2:22pm Feb 19, 2011 2:22pm
Quoting 7bit
If you cannot follow the abstract levels of my thinking then I can understand this, not many people can follow it, but this does not give you the right to insult me by calling my thinking "half-educated" only because you can't (and don't even want to) understand it.

end of discussion + unsubscribe.
Sorry, but understanding abstract thinking is not one of my weaknesses. I don't won't to divulge too much of my personal details, but one example from my days in academia would be my solution to a long open (decades) problem in theoretical quantum mechanics.

And I am quite used to, and tired of, having to put up with ramblings like yours.

So don't insult my intelligence ...as if I cared...
  • #26
  • Feb 19, 2011 3:16pm Feb 19, 2011 3:16pm
medici,your excel is wrong, but the conclusion is correct.
the expected return of a random walk is zero. so, that means there are only volatilities in the process. and the volatility pumping will earn money with volatilities.

so, we can earn money in random walk.
  • #27
  • Feb 19, 2011 3:20pm Feb 19, 2011 3:20pm
Quoting medici
What do you mean? See attached spreadsheet modelling flips of a fair coin where this strategy wins.
I just did a quick check on your spreadsheet and I found a flaw. The excel formula in your asset column indicated that you make 100% if you win and lose 50% if you lose. By nature it is already a profitable system because the profit factor is 2. So this is not a random walk system. The reason that the simulation on asset value is hardly profitable because the bet size (50%) has exceed the max Kelly bet size (25%).

I made a minor modification on your spreadsheet. Now it make 50% only if you win but still lose 50% if you lose. So the portfolio is no longer profitable after the rebalancing.

IMHO volatility pumping is just a kind of money management strategy. The general rule of thumb for money management: It wont turn a system into profitable if the system itself has no edge.
Attached File(s)
File Type: xls Volatility Pumping R1.xls   520 KB | 371 downloads
  • #28
  • Feb 19, 2011 3:20pm Feb 19, 2011 3:20pm
Quoting bobowang
medici,your excel is wrong, but the conclusion is correct.
the expected return of a random walk is zero. so, that means there are only volatilities in the process. and the volatility pumping will earn money with volatilities.

so, we can earn money in random walk.
Be that as it may. By now I am a bit tired of the topic.

What do you think of the method for solving your problem suggested in the paper by Marshall et al?
  • #29
  • Edited 3:58pm Feb 19, 2011 3:31pm | Edited 3:58pm
Quoting ForexQuant
I just did a quick check on your spreadsheet and I found a flaw. The excel formula in your asset column indicated that you make 100% if you win and lose 50% if you lose. By nature it is already a profitable system because the profit factor is 2. So this is not a random walk system. The reason that the simulation on asset value is hardly profitable because the bet size (50%) has exceed the max Kelly bet size (25%).

I made a minor modification on your spreadsheet. Now it make 50% only if you win but still lose 50% if you lose. So the portfolio...
Hello FQ, and thank you for the first intelligent argument here. I see what you are saying but the point is that the random walk modeled is log-Bernoulli, so the original spreadsheet needs no modification.
  • #30
  • Feb 19, 2011 3:42pm Feb 19, 2011 3:42pm
Quoting medici
Hello FQ, I see what you are saying but the point is that the random walk modeled is log-Bernoulli, so the original spreadsheet needs no modification.
Please enlighten me.
  • #31
  • Feb 19, 2011 3:54pm Feb 19, 2011 3:54pm
Quoting ForexQuant
Please enlighten me.
Most asset price models are based on log-prices being a random walk. And, in fact, statistical tests on real data show that stock indices (for example) are close to being log-normal, i.e. the the logarithm of price is approximately equal to a sum of normal variables, with the sum indexed by time.

This type model of can also be developed into a continuous-time model of the markets. For example, the Nobel Prize winning option pricing formula is based on such a model.

Getting back to the spreadsheet, the asset modelled doubles or halves its price in each time-step, i.e. the log_2 of the price change is Bernoulli or the flip of a fair coin.

Therefore, a balanced portfolio will increase its value by 50% if price goes up and it will lose 25% if price goes down.
  • #32
  • Feb 19, 2011 4:25pm Feb 19, 2011 4:25pm
Quoting medici
Most asset price models are based on log-prices being a random walk. And, in fact, statistical tests on real data show that stock indices (for example) are close to being log-normal, i.e. the the logarithm of price is approximately equal to a sum of normal variables, with the sum indexed by time.

This type model of can also be developed into a continuous-time model of the markets. For example, the Nobel Prize winning option pricing formula is based on such a model.

Getting back to the spreadsheet, the asset modelled doubles or halves its price...
Log return is used in random walk model but it does not mean that the price will double or halve in each timestep. Log return is used in modelling because it will have equal percentage of return in each timestep in regardless of its price level.

The reason that your balanced portfolio is profitable in your original spreadsheet because your effective bet size has reduced to max kelly bet size. So this is just a mathematic trick to show to newbie that a creative money management technique can turn a losing system into profitable.
  • #33
  • Feb 19, 2011 4:49pm Feb 19, 2011 4:49pm
Quoting ForexQuant
Log return is used in random walk model but it does not mean that the price will double or halve in each timestep. Log return is used in modelling because it will have equal percentage of return in each timestep in regardless of its price level.

The reason that your balanced portfolio is profitable in your original spreadsheet because your effective bet size has reduced to max kelly bet size. So this is just a mathematic trick to show to newbie that a creative money management technique can turn a losing system into profitable.
Max Kelly doesn't turn a losing strategy into a winning one - on the contrary. The strategy is profitable. If you are worth your FF name you should be able to calculate its expected logarithmic return with pen and paper in a few minutes.

Admittedly, the model in the spreadsheet is extreme, but only to prove the point. The type of model and strategy still holds in a realistic scenario. Why don't you try the exact same calculation with detrended real data?
  • #34
  • Feb 19, 2011 5:04pm Feb 19, 2011 5:04pm
Quoting medici
Max Kelly doesn't turn a losing strategy into a winning one - on the contrary. The strategy is profitable. If you are worth your FF name you should be able to calculate its expected logarithmic return with pen and paper in a few minutes.

Admittedly, the model in the spreadsheet is extreme, but only to prove the point. The type of model and strategy still holds in a realistic scenario. Why don't you try the exact same calculation with detrended real data?
I wish to do it on real data but too bad I dont know where to find a real price data that its average gain is double of its average loss. If you got one please tell me.
  • #35
  • Feb 19, 2011 5:08pm Feb 19, 2011 5:08pm
Quoting ForexQuant
I wish to do it on real data but too bad I dont know where to find a real price data that its average gain is double of its average loss. If you got one please tell me.
Just take any stock index over a couple of years and de-trend the data. The percentage daily changes will be approximately normal
  • #36
  • Edited Feb 20, 2011 12:30am Feb 19, 2011 11:46pm | Edited Feb 20, 2011 12:30am
here, I support madici.
We definitely can earn money in random walk market!

suppose:
step 0: the current stock price is 100, you have $10000 in your stock account.
step 1: the stock price change to 150. you have $15000 in your stock account.
step 2: the stock price change to 100(the initial price). you have $10000 in your stock account.
so, after step 2, the return is 0 if you just hold the stock from step 0 to step 2. you still have $10000 in your account.


but if you use volatility pumping,
suppose you rebalance your portifolio with 50% stock and 50% cash in each step.
step 0: the current stock price is 100, you have $5000 in your stock account and $5000 in cash.

step 1: the stock price change to 150. you have $7500 in your stock account and $5000 in cash. you need rebalance them to 50%:50%, you sell $1250 stock and get $1250 in cash. then now you have $6250 in you stock account and $6250 in cash.

step 2: the stcok price change to 100(the initial price).you have $4166.667 in your stock account and $6250 in cash. the total portfolio is: 4166.667+6250=10416.667.

here, after step 2, you earn (10416.667-10000)=416.667. the price doesn't change after step 2, only volatility here. we just earned money from this volatility

you can change step 1 to: the stock price change to 120, or 80. In any case, you still can earn money.
it has nothing to do with the direction of the volatility, and the percentage changed in each step. we just need the volatility.

in madici's spreadsheet, he supposed: the stock price change from 100 to 200 has the same probability as the stock price change from 100 to 50.
this assumption may look weird.
we just assumpt: the stock price change from 100 to 120 has the same probability as the stock price change from 100 to 80. that's pure random walk. We still can earn money in this case.
look at my spread sheet in the attachment. just check it, if the "stock price" in different rows are same, no matter how many steps between them, the"Portfolio(volatility pumping)" will increase.

In a long run, the random walk has expected return of 0, that means after a long run, the stock price will not change, the Portfolio of volatility pumping will increase. we can earn money from this random walk market!
Attached File(s)
File Type: xls Volatility Pumping bobowang.xls   733 KB | 439 downloads
  • #37
  • Feb 20, 2011 3:38am Feb 20, 2011 3:38am
Quoting OldQuant
No argument from me on that.

But, would you explain how this formula (this is, e.g., H11):

IF(D11=1,1.5*H10,0.75*H10)

models discreet binomial, asymptotic log-Gaussian, behavior as you describe above?
The logarithm of it is a sum of Bernoulli variables with outcomes log(1.5) and log(0.75).
  • #38
  • Feb 20, 2011 10:33am Feb 20, 2011 10:33am
Quoting medici
The logarithm of it is a sum of Bernoulli variables with outcomes log(1.5) and log(0.75).
But isn't the sum of ln(3/2) + ln(2/3) = 0, which would induce the drift neutral log-Bernoulli "coin flip"?

As you have it, the sum of ln(3/2) + ln(3/4) > 0.

So there is an implied drift of half that difference (about 6%, I think) baked into your spreadsheet's analysis.
  • #39
  • Feb 20, 2011 10:42am Feb 20, 2011 10:42am
Quoting OldQuant
But isn't the sum of ln(3/2) + ln(2/3) = 0, which would induce the drift neutral log-Bernoulli "coin flip"?

As you have it, the sum of ln(3/2) + ln(3/4) > 0.

So there is an implied drift of half that difference (about 6%, I think) baked into your spreadsheet's analysis.
The formula you initially asked about models the evolution of the portfolio given this strategy, not the asset which is modelled by a neutral coin flip with factors 2 and 1/2.

And 6% is about right for the growth rate of the portfolio.
  • #40
  • Feb 20, 2011 11:07am Feb 20, 2011 11:07am
Quoting medici
The formula you initially asked about models the evolution of the portfolio given this strategy, not the asset which is modelled by a neutral coin flip with factors 2 and 1/2.

And 6% is about right for the growth rate of the portfolio.
Okay, now I understand what's going on here: the term "volatility pumping" probably refers to the fact that the expectation of a log normal is the underlying drift (here, 0, in each flip and so asymptotically) plus _sigma^2/2. The 1.5 and .75 weights are chosen to give the portfolio the dynamic matching the underlying process' variance.

First time I ever saw this kind of "convexity play" presented was around '87, IIRC. A "kid" (PhD candidate) from MIT came down and gave a paper based on his dissertation, where he was doing the same kind of thing, only in the fixed income market, where the log normality of bonds is analytic, if the market rate changes are normal. Since (mean reverting) normal rate change models are what was (and largely still are) used the swaption and callable-bond markets, it was a natural.
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