Let's see if Veeky Forums 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?
0?
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)
...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)
...51554569938883461100919660863945552173188
78090291734159216483545139654975492067205840193183565478891062015562640623672219
24182543107083778649306657298479704712747893328172965336745987471220507417184694
75299157382417605423273146766857716921399609175152124587597328406568240774970933
47396571306465815993135604516705003136663287420025076562603403862401677424576450
04397966386621059443585595690054858017901475376266137946516889613526151759745514
95737052531864078757718235762799858157097096898719140239643874010584716061051609
03712736884862241283462899461258844719600046158196379827217278325219624473016804
00495582876300809860397810228557401954046933302675307583106065230675366115633272
69939940654386780511880094124673513808553398330354861730753078680824549884002868
38192319984844495767432959870819569917708659736554240503599865076227453283125304
74691176365557315145917385092653812745574002512855646785271869043373422337748478
16425344899434948199470908267577249430084077564090241298639350453985275587480158
27165210490750324140193591255678852990414296349091108433556200871348452654635482
82653954705199023449656708722075933258217768258943760001 * 10^4052
>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.
(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.
>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.
Shut up coinfag.
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
I just did this simulation of 50 prices, and they all go to zero in the long run.
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.
Which softrware did you used?
Just thinking about it logically, you're going to most likely end up at 0 well before 4000 days.
MATLAB.
Thinking logically, it always goes to zero after thousands of days.
>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.
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
>hurr durr anything can happen
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.
>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.
this is a GS interview question.....just sayin....on inteview 10.
Statistically: 270 dollars, inflation included.
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 Veeky Forumsnessmen seem to have trouble with elementary problems.
That's where I got it from, the right answer is 0 indeed.