Thread: who has series of random generated price data?

Originally Posted by ;

Please notify me.

Most asset price models derive from log-prices being a random walk. And, in reality, statistical evaluations on real data reveal that stock indices (for example) are close to being log-normal, i.e. the the logarithm of price is roughly equal to a sum of regular factors, with the amount indexed by time.

This kind model of is also developed into a continuous-time model of the markets. By way of example, the Nobel Prize winning option pricing formula is based on such a model.

Getting back to the spreadsheet, the advantage modelled pliers or doubles its price in every time-step, i.e. the log_2 of the price shift is Bernoulli or the flip of a fair coin.

Thus , a balanced portfolio will increase its value by 50 percent if price goes up and it'll lose 25% if price goes down.

Originally Posted by ;

Most asset price models are predicated on log-prices being a random walk. And, in reality, 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 number of regular variables, with the sum indexed by time.

This type model of can also be developed into a continuous-time model of those markets. By way of instance, the Nobel Prize winning option pricing formula is based on a model.

Getting back to the spreadsheet, the advantage modelled doubles or halves its price...

Log return is utilized in random walk model but it does not mean that the price will double or halve in each timestep. Log return is employed in modelling because it will have equivalent percentage of return in every timestep in regardless of its price level.

The main reason that your balanced portfolio is profitable in your original spreadsheet because your successful bet size has reduced to maximum kelly bet size. So this is a mathematic trick to show to newbie that a cash management technique may turn a losing platform into profitable.

Originally Posted by ;

Log return is used in random walk version but it does not signify that the price will double or halve in each timestep. Log return is used in modelling since it will have equal percentage of return in every timestep in no matter its price level.

The main reason that your balanced portfolio is more profitable in your original spreadsheet because your successful bet size has reduced to maximum kelly bet dimensions. So this is just a tip to show to newbie that a creative money management technique can turn a platform into profitable.

Max Kelly does not flip a losing egy into a winning one - on the opposite. The egy is profitable. If you are worth your FF name you should have the ability to compute its expected return that is logarithmic in a few minutes with paper and pen.

Admittedly, the version in the spreadsheet is extreme, but only to show the point. The type of egy and model retains in a realistic situation. Why not try the same calculation with data that is actual that is detrended?

Originally Posted by ;

Max Kelly does not turn a losing egy to a winning one - to the opposite. The egy is profitable. You ought to have the ability to calculate its logarithmic return with paper and pencil in a couple of minutes if you're worth your FF name.

Admittedly, the model from the spreadsheet is intense, but just to show the point. The kind of egy and design holds in a scenario. Why not try the exact same calculation with information that is real that is detrended?

That I want to perform it on real data but also bad I dont understand where to locate a real price information that its ordinary gain is twice of its average loss. If you have one please tell me.

Originally Posted by ;

I want to do it on actual data but also bad I dont understand where to find a real price information that its average gain is double of its average loss. If you got one please inform me.

Just take any stock index over a few years and de-trend the information. The percent daily changes will likely be approximately normal

here, I encourage madici.
We certainly can earn money in random walk market!

Assume:
measure 0: the current stock price is 100, you have $10000 on your stock account.
Measure 1: the stock price change to 150. You've got $15000 on your stock account.
Step two: the stock price change to 100(the first price). You have $10000 on your stock account.
So, after step two, the return is 0 if you just hold the stock from step 0 to step two. You still have $10000 on your account.


But if you use volatility draining,
suppose you rebalance your portifolio using 50% stock and 50% cash in every step.
Measure 0: the current stock price is 100, you have $5000 on your stock account and $5000 in cash.

Measure 1: the stock price change to 150. You've got $7500 on your stock account and $5000 in cash. You want rebalance them you sell $1250 stock and get $1250. Then you have $6250 in you stock account and $6250 in cash.

Step two: the stcok price change to 100(the first price).you have $4166.667 on your stock account and $6250 in cash. The total portfolio is: 4166.667 6250=10416.667.

Here, following step 2, you get (10416.667-10000)=416.667. The price doesn't change after step two volatility here. We just earned money from this volatility

it's possible to alter step 1 to: the stock price change to 120, or 80. In any case, it's still true that you can earn money.
It doesn't have anything to do with the management of their volatility, and the percent changed in every measure. We need the volatility.

In madici's spreadsheet, he assumed: the stock price change from 100 to 200 has exactly the exact same chance as the stock price change from 100 to 50.
This premise may look weird.
We only assumpt: the stock price change from 100 to 120 has exactly the exact same chance as the stock price change from 100 to 80. That's pure random walk. We can earn money.
Look at my spread sheet in the attachment. Simply check it, if the stock price in different rows will be same, no matter how many steps between them, thePortfolio(volatility draining ) increases.

In a long run, the random walk has anticipated return of 0, which means following a lengthy run, the stock price won't change, the Portfolio of volatility draining increases. We can earn money from this random walk market!
https://forexintuitive.com/attachmen...2036328982.xls

95205

Originally Posted by ;

No argument from me on this.

However, would you describe how this formulation (this is, e.g., H11):

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

versions discreet binomial, asymptotic log-Gaussian, behaviour as you describe above?

The logarithm of it is a sum of Bernoulli variables with outcomes log(1.5) and log(0.75).

95352

Originally Posted by ;

The logarithm of it's a number of Bernoulli variables with results log(1.5) and log(0.75).

But is not the sum of ln(3/2) ln(2/3) = 0, which could induce the stray impartial log-Bernoulli coin reverse?

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

So there is an implied drift of half that difference (about 6%, I think) baked in to your spreadsheet's analysis.

95352

Originally Posted by ;

But isn't the sum of ln(3/2) ln(2/3) = 0, which could induce the ramble neutral log-Bernoulli coin reverse?

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

So there is an implied drift of half that difference (roughly 6%, I think) baked into a spreadsheet's analysis.

The formulation you initially asked about models that the development of the portfolio given this egy, not the asset which is modelled by a impartial coin flip with variables two and 1/2.

And 6% is about right for the growth rate of the portfolio.

95352

Originally Posted by ;

The formulation you originally asked about models the development of the portfolio given this egy, not the asset that's modelled by a impartial coin flip with variables two and 1/2.

And 6% is about right for the growth rate of their portfolio.

Alright, now I know what's going on here: the word volatility pumping probably refers to the fact that the anticipation of a log normal is the underlying drift (here, 0, in each flip and so asymptotically) and _sigma^2/2. The 1.5 and .75 weights have been selected to give the portfolio the energetic matching the underlying procedure' variance.

First time I ever saw this type of convexity play introduced was about'87, IIRC. A child (PhD candidate) from MIT came and gave a paper based on his dissertation, where he was performing exactly the same type of thing, only in the fixed income market, in which the log normality of bonds is analytic, if the market rate changes are normal. Because (mean reverting) normal rate change models are what was (and mostly still are) employed the swaption and callable-bond markets, it was a natural.