Let's see if /biz/ is good at basic math.
Say we have an asset that's 100 dollars on day 1. Now, every day, the price can either go up with 30%, or down with 25%, and both price movements have the same probability. What's the return after 4000 days?
It depends, anything between 0 and 59348429003252308012834107202943920995257834690948195302156515900662637463168195
96632372919311696898354989794024626401712625896567585218346637688404219389802400
12479766368170756278731995105816861733049592429788853386702024392783945262681472
63983630206546955261697123386215747025011852513255712970874721929085187613702834
04917002657872134725197214970767027400738832483718437245392551891447407827118917
28493694787664017746930975541845856473663472265145982596563147315023225340971807
32398642429911996383922112507100967950111696400348805222163343358133290412008075
75051735993536409699595787715273699720910894780883669041179871059308419290131006
58277997669987336521977748550859446277085027190956590583065047520779562582989400
42162755506157655068441844747181750318059183134394041564271476901426898626717928
46384860863593957636990756956222057130203171121125770501864193850532554284062888
73542161870749600404582923541829782593606950052371949624569932190690832372061896
80638338772542621312720765663875198696621881828315452342636768954945522390174162
12702159217304615341780471236906484630781964556529589632130604414573568399642526
05053352327717366620856745554553599277771034848622053942630506257040448455542415
66397488130924046976419473497706740683087315839907708420949872205420811755834222
13532571368272732688193733956236809804796710968997887734962740685069671612229759
09390149137712779802174841911778096932750209417090204782679734013976177623582185
(cont)
>>1349024
...85437453864408344294966658319369459669284499972484844617146154390121369665223193
20935335476638997181435935999970623903597256923678669320719856394731957756876404
48158545250116893582764324109234720605997279233305549386315176436308958683857776
45920851353904477614503869516133557638975542294333657367069064685535978427096573
43716426267269633304878720853274177158971761296487389762552363873763268759185469
83221634357076891483203637567252184911952029838903307488191204511949792044297495
94117310279181529774426332669018754782459448030949526494365506756691913448301454
10637724171950424576489546604410176469211860249791539803381851522316250573897313
88986408283048679343836578568960997100360852840565690633867108805126587404899447
10627672419472671716800436557455871420076102832885714742836514447271407710228226
58024326984726732374566022872399681115895635176694179841203158034944448853532573
62898819219185817904906137559127387769115674399560733039548307298444917953287325
30776817869439763859706855280477848689935472193722841065811851693617364647297105
55553861621915344133691328384582345289793519812617492415503931350943176655121716
86895416231665536529795992065769046563088993200297924440525248733075817826224083
71055965843310530362417888206284523446850317237659628876444528373669586026611213
92041553399642928607629641330555264430927806616940564673452477851787094677939316
82874683717506461318315376562252142011535816880677092390388103232902045842365742
93455347556195766401026429358489012498838991777250683972019440392802458964940872
67494978726487061487712419986750571369653611027138537184117918211465813657439599
73265277755838360415479087756388784377720958942435705565423272696991876510450458
43726174792284389684554584628044590856083349352884441788477311336887409777690091
24075886036114819168126571949866344595845057120566413080094754117769321326769054
600990805163695515717928515595265457895
(cont)
>>1349025
...51554569938883461100919660863945552173188
78090291734159216483545139654975492067205840193183565478891062015562640623672219
24182543107083778649306657298479704712747893328172965336745987471220507417184694
75299157382417605423273146766857716921399609175152124587597328406568240774970933
47396571306465815993135604516705003136663287420025076562603403862401677424576450
04397966386621059443585595690054858017901475376266137946516889613526151759745514
95737052531864078757718235762799858157097096898719140239643874010584716061051609
03712736884862241283462899461258844719600046158196379827217278325219624473016804
00495582876300809860397810228557401954046933302675307583106065230675366115633272
69939940654386780511880094124673513808553398330354861730753078680824549884002868
38192319984844495767432959870819569917708659736554240503599865076227453283125304
74691176365557315145917385092653812745574002512855646785271869043373422337748478
16425344899434948199470908267577249430084077564090241298639350453985275587480158
27165210490750324140193591255678852990414296349091108433556200871348452654635482
82653954705199023449656708722075933258217768258943760001 * 10^4052
>>1349028
>You can't calculate the return because in some scenarios your asset will go to negative value, which is counter-factual.
U are a realy stupid idiot.
>>1349012 (OP)
>What's the return after 4000 days?
You can't calculate the return because in some scenarios your asset will go to zero and stay there, which is counter-factual. The best that can be done is to calculate an expected rate of rate based on a series of test cases, something akin to a Monte Carlo analysis.
But, I'm not doing your summer school homework for you, so do the math yourself.
>>1349031
>which is counter-factual.
But it isn't. Pay good attention to the price of Trumpcoin in the following months if you want an example.
>>1349032
Shut up coinfag.
>>1349012
Anywhere between 0 and 100(1.3)^4000
Also, if for some reason the up down movement happened same amount of times
100((1.3)(0.75))^{2000)
Which basically ends up at 0 anyway
>>1349031
I just did this simulation of 50 prices, and they all go to zero in the long run.
>>1349042
As I said, that's expected for many cases, since adding 30% to zero in any case when you get to zero leaves you at zero. However, if it's happening for every case, you either have a too small sample size or your model is setup incorrectly.
>>1349042
Which softrware did you used?
>>1349012
Just thinking about it logically, you're going to most likely end up at 0 well before 4000 days.
>>1349449
>Thinking logically, it always goes to zero after thousands of days.
Thinking logically, there are scenarios where the positive days predominate and the result must necessarily be greater than zero.
>>1349012
You mean, the
>expected
Return. Also anyone that wants to learn stochastic calculus for financial shit here's a textbook.
Brownian Motion Calculus - Ubbo Wiersema
>>1349537
>hurr durr anything can happen
>>1349540
Here's the deal if I ask for the "expected" return, and exactly what's bugging the shit out of me. We'll have the following:
X0 is our start price on day 0, and Xn is our price on day n. The price movement on day n is a random variable N_n.
For day i we have: Xi = X0 * N_1 * N_2 * N_3 *.... * N_{i-1}.
So the expectation for Xi would be:
E(Xi) = E( X0 * N_1 * ... N_{i-1} )
With independence follows:
E(Xi) = E(X0) E(N_1)^{i-1} = X0 * 1.025^{i-1}
So when the i goes to infinity, the expected value goes to infinity.
However, the price is most likely to be somewhere around 0.
Also thanks a lot for that book recommendation, I appreciate it.
>>1349575
>hurr durr anything can happen
That's what Monte Carlo simulations are about, dumbass. Anything can happen, and you're trying to figure out the likelihood.
Fucking retard.
bayes says $5.7173698e+86
your model is not realistic.
>>1349012
this is a GS interview question.....just sayin....on inteview 10.
>>1349012
Statistically: 270 dollars, inflation included.
>>1349610
Actually, using the central limit theorem I just found that the probability of the price being 600 dollars is just 0.0013.
Also here it is with 500 trials.
Funny how so many /biz/nessmen seem to have trouble with elementary problems.
>>1349657
That's where I got it from, the right answer is 0 indeed.