Original research: My "time-travelling algorithm" found the risks of buying BTC on different time frames

Imagine that you could go back in BTC's history and buy 50 $ worth of BTC. Would you do it? I'll be ready to guess yes, but what if I modify the rules a bit? You don't know which day in history you go to (it will be random) and you have to sell after 100 days no matter the price. This surely seems less tempting. Would you still go for it?

You could answer from a gut feeling or you could answer empirically. I build an algorithm and had it going back (imaginarily) to random 1000 days (since April 28th, 2013) wait 100 days and record whether a trade would be profitable or not. To answer the above question this deal would have given you a loss or no profit about 44.5 % of the time.

Why ask these hypothetical questions? Because today IS a random day in BTC's history. No one knows the price 100 days from now so looking at history is the best option to quantify the risk. Therefore, I have asked my algorithm to repeat the process described above and hold for different durations before selling:

From this figure, we can draw several conclusions: It seems to be a roughly linear relationship between how long you wait to sell and the risk of losing. A linear fit describes the relationship as 45 * -0.04 (significantly so, p < 0.001). In other words: If you buy BTC on a random day, you should have about 45 % risk of losing money if you sell it the next day. And each additional day you hold should reduce your probability of losing money by 0.04 per cent points.

With this formula, we can ask how likely it would have been to buy in on the day of BTC's ATH and be in loss 440 days later (today). We can see that with 27.4 % probability, this was not at all unexpected by the model. If you want less than 10 % risk of losing, you should prepare to wait about 875 days (roughly 2 years, 5 months) from the time of buying.

I think that this is a good reminder that we should see investing as a long term game. To paraphrase Warren Buffet investing is "transferring money from the impatient to the patient". As always, don't invest money you expect to need within a few years. On the other hand, don't panic if you invest in something and you see it fall one month later. If you are thinking long-term, remind yourself to expect such fluctuations. Remember also that this is historical data. If a bot observed 100000 poker hands, it would tell you that a straight flush only happened in 0.0015 % of them. That obviously does not make it impossible to see one in the next game (but very unlikely).

Future questions: How robust is this model? What is the range of gains and losses? What about other coins?
If you know your statistics, you will probably recognize that what I did here was a Monte Carlo method. If there is interest, I will follow up with posts investigating how much variance we get from one model to the next. For now, though, I tried to model the data being available at 2017-12-16 so the exact day of the ATH. If you did the same calculation as above, you would reach the conclusion that there is a 27% risk of having lost money in 440 days. That is, the model would have told you that it was a realistic outcome while most people were talking moon. Of course, another expansion of the model can also take into consideration HOW MUCH those wins or losses would be. Finally, we could of course also perform the same investigation on LTC, STEEM or some other coin (or even gold or stocks for that matter).

Good luck to all of you and take care.