SERVING THE QUANTITATIVE FINANCE COMMUNITY

alpher
Topic Author
Posts: 67
Joined: September 1st, 2012, 4:20 pm

### Stock prices are likely always randomly distributed...

Based on my tests recently: there are very obvious signs that returns are randomly distributed and attempting to predict stocks and their derivatives is useless. Though there are several ways to outperform the market through exploiting mispricings..

Not sure if I'm saying anything new here though , if this was elitetrader.com/chartsaresacred.com or so I'd get banned for even hinting of such things...

bearish
Posts: 3131
Joined: February 3rd, 2011, 2:19 pm

### Re: Stock prices are likely always randomly distributed...

OK - I propose you be banned.

Alan
Posts: 9369
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

### Re: Stock prices are likely always randomly distributed...

Yes --  for the crime of cognitive dissonance.

alpher
Topic Author
Posts: 67
Joined: September 1st, 2012, 4:20 pm

### Re: Stock prices are likely always randomly distributed...

bearish wrote:
OK - I propose you be banned.

but, but...I can prove it.

Alan
Posts: 9369
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

### Re: Stock prices are likely always randomly distributed...

Seriously, while it's true that markets are highly efficient, your statistical statement is kind of muddled and likely easily rejected by simple tests. By "returns are randomly distributed", I will guess you mean returns $x_t$ behave as if drawn independently each period (say day) from some fixed distribution -- so called i.i.d. draws. Then $S_T = \sum_{t=0}^T x_t$ is a classic generic random walk, as studied by Frank Spitzer, for example.

But if that was true, not only would one find that $Corr(x_t,x_{t-1}) \approx 0$  -- which one does -- but  $Corr(|x_t|,|x_{t-1}|) \approx 0$ as well. However, for equity markets (for example) the latter (the autocorrelation of absolute returns), is always found to be significantly positive). Add that to your tests!

The effect is called volatility clustering. Unusually large returns (of any sign) tend to be followed by unusually large returns (perhaps with the sign reversed). The net result is that financial researchers do *not* believe returns are i.i.d.  -- even though most believe that markets are highly efficient.

frolloos
Posts: 1507
Joined: September 27th, 2007, 5:29 pm
Location: Netherlands

### Re: Stock prices are likely always randomly distributed...

alpher wrote:
Based on my tests recently: there are very obvious signs that returns are randomly distributed and attempting to predict stocks and their derivatives is useless. Though there are several ways to outperform the market through exploiting mispricings..

Not sure if I'm saying anything new here though , if this was elitetrader.com/chartsaresacred.com or so I'd get banned for even hinting of such things...

over what horizon? intra-day or intra-light years?

alpher
Topic Author
Posts: 67
Joined: September 1st, 2012, 4:20 pm

### Re: Stock prices are likely always randomly distributed...

^ Daily and monthly.

Would like to reply to Alan too but don't know how to use the math signs here and don't have time now...

MartinGale7
Posts: 121
Joined: April 1st, 2011, 7:42 am

### Re: Stock prices are likely always randomly distributed...

Markets are in no way perfectly efficient. Sadly the yield you can easily generate from these inefficiencies is about the same as the transaction costs. If you step back from the problem, you will realise that it sort of has to be this way, otherwise everyone would do it. Eg CDS on RBS probably has a lot more inefficiency than EUR/USD spot, however the transaction costs on the former are much higher making both a bit pointless (unless you are a market maker... perhaps).

A simple testable example of this is to use ADF (or similar) on minute bars of AUD/CAD. You will find it has very significant mean reversion. While the existence of the inefficiency is undeniable, only about half to a full basis point can easily be extracted (which is about the cost of trading it).

Posts: 34
Joined: February 19th, 2016, 4:26 pm

### Re: Stock prices are likely always randomly distributed...

frolloos wrote:
alpher wrote:
Based on my tests recently: there are very obvious signs that returns are randomly distributed and attempting to predict stocks and their derivatives is useless. Though there are several ways to outperform the market through exploiting mispricings..

Not sure if I'm saying anything new here though , if this was elitetrader.com/chartsaresacred.com or so I'd get banned for even hinting of such things...

over what horizon? intra-day or intra-light years?

One of these is a measure of distance, not time.  =)